1-Proportional-resonant controllers and filters for grid-connected voltage-source converters

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Proportional & Integral Controllers

Proportional & Integral Controllers

1. Set TD = 0 & TI = ∞ 2. Increase KP until the system just starts to oscillate (KP = KPO). The frequency of oscillation here is ωc and the period is TO=2π/ωc. Set controller gains as:
NB: this transfer function is non-proper and is therefore difficult to realise in practice. Proper T.F.: Strictly proper T.F.: Order N(s) ≤ Order D(s) Order N(s) < Order D(s)
Error {e(t)} t
The PID regulator is given by: Here:
KI = KP TI
1 de(t ) u (t ) = K P e(t ) + ∫ e(t )dt + TD TI dt
K D = K P TD
KI K D s 2 + K P s + K I N ( s)U (s) = KP + + KDs = = E (s) s s D( s)
Proportional & Integral Controllers Proportional + Integral (PI) controllers were developed because of the desirable property that systems with open loop transfer functions of type 1 or above have zero steady state error with respect to a step input. The PI regulator is:

LCL型并网变换器PR控制研究

LCL型并网变换器PR控制研究
LCL 型并网变换器 PR 控制研究
Research on Proportional-resonant Controller for Grid-connected Converter with LCL-filter
学科专业:电气工程 研究生: 石立光 指导教师:万健如 教授
天津大学电气与自动化工程学院 二零一二年十二月
关键词: 关键词:并网变换器 LCL 滤波器 SVPWM 调制 二倍频分量 PR 控制器
解耦控制 正负序分解 不对称电网
ABSTRACT
With the overusing of the coal, nature gas and other fossil fuel, the human had to search for more durable, more environmental new energy to meet the increasing needs of people. It has been being widely studied that how to make full use of the generation power of solar energy, wind energy, tidal energy and other new energy power, so the grid-connected converter plays an important role in the transformation of electrical energy. The transformed power is either transmitted to electricity grid, or used to drive different loads independently. In this paper, the control policies of grid-connected converter under the symmetric grid and asymmetric grid are studied. First of all, the mathematical model of the grid-connected converter with LCL-filter is analyzed, after which the article builds respectively mathematical models of the static coordinate system and the rotating coordinate system under the symmetric and asymmetric power grid. At the same time, the positive sequence and negative sequence decomposition problem of each electric is considered under the asymmetric power grid, which adopts a modified instantaneous symmetrical component method to make an effective positive sequence and negative sequence decomposition of the grid voltage and current. The results are verified by the theoretical analysis and the simulation. Secondly, the LCL-filter parameters, including converter side inductance, power grid side inductance and the filter capacity, are designed in detail. Secondly, based on the control strategy research of grid-connected converter, this paper firstly analyzes and researches the traditional grid voltage oriented vector control strategy. Under the symmetric grid, this control strategy can be very good to meet grid standards, the access current becomes sine wave, the harmonic distortion rate is very small, as well as the grid power factor is closed to 1. Under the asymmetric grid, because there are the positive and negative sequence components in power grid voltage and access current, the dc side voltage, the active and reactive power and the dq axis component of the access current contain second harmonic frequency component during steady state operation, which seriously affects the quality of grid. Based on this, a kind of commonly used control method is double dq-PI current control strategy based on the positive and negative sequence

A Unified Control Strategy for Three-Phase Inverter

A Unified Control Strategy for Three-Phase Inverter

A Unified Control Strategy for Three-Phase Inverterin Distributed GenerationZeng Liu,Student Member,IEEE,Jinjun Liu,Senior Member,IEEE,and Yalin ZhaoAbstract—This paper presents a unified control strategy that en-ables both islanded and grid-tied operations of three-phase inverter in distributed generation,with no need for switching between two corresponding controllers or critical islanding detection.The pro-posed control strategy composes of an inner inductor current loop, and a novel voltage loop in the synchronous reference frame.The inverter is regulated as a current source just by the inner induc-tor current loop in grid-tied operation,and the voltage controller is automatically activated to regulate the load voltage upon the occurrence of islanding.Furthermore,the waveforms of the grid current in the grid-tied mode and the load voltage in the islanding mode are distorted under nonlinear local load with the conven-tional strategy.And this issue is addressed by proposing a unified load current feedforward in this paper.Additionally,this paper presents the detailed analysis and the parameter design of the control strategy.Finally,the effectiveness of the proposed control strategy is validated by the simulation and experimental results.Index Terms—Distributed generation(DG),islanding,load cur-rent,seamless transfer,three-phase inverter,unified control.I.I NTRODUCTIOND ISTRIBUTED generation(DG)is emerging as a viablealternative when renewable or nonconventional energy resources are available,such as wind turbines,photovoltaic ar-rays,fuel cells,microturbines[1],[3].Most of these resources are connected to the utility through power electronic interfacing converters,i.e.,three-phase inverter.Moreover,DG is a suitable form to offer high reliable electrical power supply,as it is able to operate either in the grid-tied mode or in the islanded mode[2]. In the grid-tied operation,DG deliveries power to the utility and the local critical load.Upon the occurrence of utility outage, the islanding is formed.Under this circumstance,the DG must be tripped and cease to energize the portion of utility as soon as possible according to IEEE Standard929-2000[4].However, in order to improve the power reliability of some local criticalManuscript received December15,2012;revised March4,2013;accepted April21,2013.Date of current version September18,2013.This work was supported in part by the National Basic Research Program(973Program)of China under Project2009CB219705,and by the State Key Laboratory of Elec-trical Insulation and Power Equipment under Project EIPE09109.This paper was presented in part at the26th IEEE Applied Power Electronics Conference and Exposition,Fort Worth,TX,USA,March6–11,2011.Recommended for publication by Associate Editor D.Xu.The authors are with the State Key Lab of Electrical Insulation and Power Equipment,School of Electrical Engineering,Xi’an Jiaotong Univer-sity,Xi’an710049,China(e-mail:zeng.liu@;jjliu@; yobdc54@).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TPEL.2013.2262078load,the DG should disconnect to the utility and continue to feed the local critical load[5].The load voltage is key issue of these two operation modes,because it isfixed by the utility in the grid-tied operation,and formed by the DG in the islanded mode,respectively.Therefore,upon the happening of islanding, DG must take over the load voltage as soon as possible,in order to reduce the transient in the load voltage.And this issue brings a challenge for the operation of DG.Droop-based control is used widely for the power sharing of parallel inverters[11],[12],which is called as voltage mode control in this paper,and it can also be applied to DG to real-ize the power sharing between DG and utility in the grid-tied mode[13]–[16],[53].In this situation,the inverter is always regulated as a voltage source by the voltage loop,and the qual-ity of the load voltage can be guaranteed during the transition of operation modes.However,the limitation of this approach is that the dynamic performance is poor,because the bandwidth of the external power loop,realizing droop control,is much lower than the voltage loop.Moreover,the grid current is not controlled directly,and the issue of the inrush grid current dur-ing the transition from the islanded mode to the grid-tied mode always exists,even though phase-locked loop(PLL)and the virtual inductance are adopted[15].The hybrid voltage and current mode control is a popular alternative for DG,in which two distinct sets of controllers are employed[17]–[40].The inverter is controlled as a current source by one sets of a controller in the grid-tied mode,while as a voltage source by the other sets of controller in the islanded mode.As the voltage loop or current loop is just utilized in this approach,a nice dynamic performance can be achieved. Besides,the output current is directly controlled in the grid-tied mode,and the inrush grid current is almost eliminated.In the hybrid voltage and current mode control,there is a need to switch the controller when the operation mode of DG is changed.During the interval from the occurrence of utility outage and switching the controller to voltage mode,the load voltage is neitherfixed by the utility,nor regulated by the DG, and the length of the time interval is determined by the islanding detection process.Therefore,the main issue in this approach is that it makes the quality of the load voltage heavily reliant on the speed and accuracy of the islanding detection method[6]–[10]. Another issue associated with the aforementioned approaches is the waveform quality of the grid current and the load voltage under nonlinear local load.In the grid-tied mode,the output current of DG is generally desired to be pure sinusoidal[18]. When the nonlinear local load is fed,the harmonic component of the load current will fullyflow into the utility.A single-phase DG,which injects harmonic current into the utility for mitigating0885-8993©2013IEEEFig.1.Schematic diagram of the DG based on the proposed control strategy.the harmonic component of the grid current,is presented in[41]. The voltage mode control is enhanced by controlling the DG to emulate a resistance at the harmonic frequency,and then the harmonic currentflowing into utility can be mitigated[42]. In the islanded mode,the nonlinear load may distort the load voltage[43],and many control schemes have been proposed to improve the quality of the load voltage,including a multiloop control method[43]–[46],resonant controllers[48],[49],sliding mode control[47].However,existing control strategies,dealing with the nonlinear local load in DG,mainly focus on either the quality of the grid current in the grid-tied mode or the one of the load voltage in the islanded mode,and improving both of them by a unified control strategy is seldom.This paper proposes a unified control strategy that avoids the aforementioned shortcomings.First,the traditional induc-tor current loop is employed to control the three-phase inverter in DG to act as a current source with a given reference in the synchronous reference frame(SRF).Second,a novel voltage controller is presented to supply reference for the inner induc-tor current loop,where a proportional-plus-integral(PI)com-pensator and a proportional(P)compensator are employed in D-axis and Q-axis,respectively.In the grid-tied operation,the load voltage is dominated by the utility,and the voltage com-pensator in D-axis is saturated,while the output of the voltage compensator in Q-axis is forced to be zero by the PLL.There-fore,the reference of the inner current loop cannot regulated by the voltage loop,and the DG is controlled as a current source just by the inner current loop.Upon the occurrence of the grid outage,the load voltage is no more determined by the utility, and the voltage controller is automatically activated to regulate the load voltage.These happen naturally,and,thus the proposed control strategy does not need a forced switching between two distinct sets of controllers.Further,there is no need to detect the islanding quickly and accurately,and the islanding detec-tion method is no more critical in this approach.Moreover, the proposed control strategy,benefiting from just utilizing the current and voltage feedback control,endows a better dynamic performance,compared to the voltage mode control.Third,the proposed control strategy is enhanced by introduc-ing a unified load current feedforward,in order to deal with the issue caused by the nonlinear local load,and this scheme is implemented by adding the load current into the reference of the inner current loop.In the grid-tied mode,the DG injects harmonic current into the grid for compensating the harmonic component of the grid current,and thus,the harmonic compo-nent of the grid current will be mitigated.Moreover,the benefit of the proposed load current feedforward can be extended into the islanded operation mode,due to the improved quality of the load voltage.The rest of this paper is arranged as follows.Section II de-scribes the proposed unified control strategy for three-phase inverter in DG,including the power stage of DG,the basic idea, and the control diagram.The detailed operation principle of DG with the proposed control strategy is illustrated in Section III. The parameter design and small signal analysis of the proposed control system are given in Section IV.Section V investigates the proposed control strategy by simulation and experimental results.Finally,the concluding remarks are given in Section VI.II.P ROPOSED C ONTROL S TRATEGYA.Power StageThis paper presents a unified control strategy for a three-phase inverter in DG to operate in both islanded and grid-tied modes.The schematic diagram of the DG based on the proposed control strategy is shown by Fig.1.The DG is equipped with a three-phase interface inverter terminated with a LCfilter.The primary energy is converted to the electrical energy,which is then converted to dc by the front-end power converter,and the output dc voltage is regulated by it.Therefore,they can be represented by the dc voltage source V dc in Fig.1.In the ac side of inverter,the local critical load is connected directly.It should be noted that there are two switches,denoted by S u and S i,respectively,in Fig.1,and their functions are different. The inverter transfer switch S i is controlled by the DG,and the utility protection switch S u is governed by the utility.When the utility is normal,both switches S i and S u are ON,and the DG in the grid-tied mode injects power to the utility.When the utility is in fault,the switch S u is tripped by the utility instantly,and then the islanding is formed.After the islanding has been confirmed by the DG with the islanding detection scheme[6]–[10],the switch S i is disconnected,and the DG is transferred from the grid-tied mode to the islanded mode.When the utility is restored, the DG should be resynchronized with the utilityfirst,and then the switch S i is turned ON to connect the DG with the grid.Fig.2.Overall block diagram of the proposed unified control strategy.B.Basic IdeaWith the hybrid voltage and current mode control[17]–[40], the inverter is controlled as a current source to generate the reference power P DG+j Q DG in the grid-tied mode.And its output power P DG+j Q DG should be the sum of the power injected to the grid P g+j Q g and the load demand P load+ j Q load,which can be expressed as follows by assuming that the load is represented as a parallel RLC circuit:P load=32·V2mR(1)Q load=32·V2m·1ωL−ωC.(2)In(1)and(2),V m andωrepresent the amplitude and fre-quency of the load voltage,respectively.When the nonlinear local load is fed,it can still be equivalent to the parallel RLC circuit by just taking account of the fundamental component. During the time interval from the instant of islanding happen-ing to the moment of switching the control system to voltage mode control,the load voltage is neitherfixed by the utility nor regulated by the inverter,so the load voltage may drift from the normal range[6].And this phenomenon can be explained as below by the power relationship.During this time interval, the inverter is still controlled as a current source,and its output power is kept almost unchanged.However,the power injected to utility decreases to zero rapidly,and then the power consumed by the load will be imposed to the output power of DG.If both active power P g and reactive power Q g injected into the grid are positive in the grid-tied mode,then P load and Q load will increase after the islanding happens,and the amplitude and frequency of the load voltage will rise and drop,respectively,according to (1)and(2).With the previous analysis,if the output power of inverter P DG+j Q DG could be regulated to match the load demand by changing the current reference before the islanding is confirmed, the load voltage excursion will be mitigated.And this basic idea is utilized in this paper.In the proposed control strategy,the output power of the inverter is always controlled by regulating the three-phase inductor current i Labc,while the magnitude and frequency of the load voltage v C abc are monitored.When the islanding happens,the magnitude and frequency of the load volt-age may drift from the normal range,and then they are controlled to recover to the normal range automatically by regulating the output power of the inverter.C.Control SchemeFig.2describes the overall block diagram for the proposed unified control strategy,where the inductor current i Labc,the utility voltage v gabc,the load voltage v C abc,and the load current i LLabc are sensed.And the three-phase inverter is controlled in the SRF,in which,three phase variable will be represented by dc quantity.The control diagram is mainly composed by the inductor current loop,the PLL,and the current reference generation module.In the inductor current loop,the PI compensator is employed in both D-and Q-axes,and a decoupling of the cross coupling denoted byω0L f/k PW M is implemented in order to mitigate the couplings due to the inductor.The output of the inner current loop d dq ,together with the decoupling of the capacitor voltage denoted by1/k PW M,sets the reference for the standard space vector modulation that controls the switches of the three-phase inverter.It should be noted that k PW M denotes the voltage gain of the inverter,which equals to half of the dc voltage in this paper.Fig.3.Block diagram of the current reference generation module.The PLL in the proposed control strategy is based on the SRF PLL[50],[51],which is widely used in the three-phase power converter to estimate the utility frequency and phase. Furthermore,a limiter is inserted between the PI compensator G PLL and the integrator,in order to hold the frequency of the load voltage within the normal range in the islanded operation. In Fig.2,it can be found that the inductor current is regulated to follow the current reference i Lref dq,and the phase of the current is synchronized to the grid voltage v gabc.If the current reference is constant,the inverter is just controlled to be a current source,which is the same with the traditional grid-tied inverter. The new part in this paper is the current reference generation module shown in Fig.2,which regulates the current reference to guarantee the power match between the DG and the local load and enables the DG to operate in the islanded mode.Moreover, the unified load current feedforward,to deal with the nonlinear local load,is also implemented in this module.The block diagram of the proposed current reference gen-eration module is shown in Fig.3,which provides the current reference for the inner current loop in both grid-tied and islanded modes.In this module,it can be found that an unsymmetrical structure is used in D-and Q-axes.The PI compensator is adopted in D-axes,while the P compensator is employed in Q-axis.Besides,an extra limiter is added in the D-axis.More-over,the load current feedforward is implemented by adding the load current i LLdq to thefinal inductor current reference i Lref dq. The benefit brought by the unique structure in Fig.3can be rep-resented by two parts:1)seamless transfer capability without critical islanding detection;and2)power quality improvement in both grid-tied and islanded operations.The current referencei Lredq composes of four parts in D-and Q-axes respectively:1)the output of voltage controller i ref dq;2)the grid current reference I gref dq;3)the load current i LLdq;and4)the current flowing through thefilter capacitor C f.In the grid-tied mode,the load voltage v C dq is clamped by the utility.The current reference is irrelevant to the load voltage,due to the saturation of the PI compensator in D-axis,and the output of the P compensator being zero in Q-axis,and thus,the inverter operates as a current source.Upon occurrence of islanding,the voltage controller takes over automatically to control the load voltage by regulating the current reference,and the inverter acts as a voltage source to supply stable voltage to the local load; this relieves the need for switching between different control architectures.Another distinguished function of the current reference gen-eration module is the load current feedforward.The sensed load current is added as a part of the inductor current refer-ence i Lref dq to compensate the harmonic component in the grid current under nonlinear local load.In the islanded mode,the load current feedforward operates still,and the disturbance from the load current,caused by the nonlinear load,can be suppressed by the fast inner inductor current loop,and thus,the quality of the load voltage is improved.The inductor current control in Fig.2was proposed in pre-vious publications for grid-tied operation of DG[18],and the motivation of this paper is to propose a unified control strategy for DG in both grid-tied and islanded modes,which is repre-sented by the current reference generation module in Fig.3. The contribution of this module can be summarized in two as-pects.First,by introducing PI compensator and P compensator in D-axis and Q-axis respectively,the voltage controller is inac-tivated in the grid-tied mode and can be automatically activated upon occurrence of islanding.Therefore,there is no need for switching different controllers or critical islanding detection, and the quality of the load voltage during the transition from the grid-tied mode to the islanded mode can be improved.The second contribution of this module is to present the load current feedforward to deal with the issue caused by the nonlinear local load,with which,not only the waveform of the grid current in grid-tied is improved,but also the quality of the load voltage in the islanded mode is enhanced.Besides,it should be noted that a three-phase unbalanced local load cannot be fed by the DG with the proposed control strategy,because there is noflow path for the zero sequence current of the unbalanced load,and the regulation of the zero sequence current is beyond the scope of the proposed control strategy.III.O PERATION P RINCIPLE OF DGThe operation principle of DG with the proposed unified control strategy will be illustrated in detail in this section,and there are in total four states for the DG,including the grid-tied mode,transition from the grid-tied mode to the islanded mode, the islanded mode,and transition from the islanded mode to the grid-tied mode.A.Grid-Tied ModeWhen the utility is normal,the DG is controlled as a current source to supply given active and reactive power by the inductor current loop,and the active and reactive power can be given by the current reference of D-and Q-axis independently.First, the phase angle of the utility voltage is obtained by the PLL, which consists of a Park transformation expressed by(3),a PIcompensator,a limiter,and an integratorx d x q=23⎛⎜⎜⎜⎝cosθcosθ−23πcosθ+23π−sinθ−sinθ−23π−sinθ+23π⎞⎟⎟⎟⎠×⎛⎝x ax bx c⎞⎠.(3)Second,thefilter inductor current,which has been trans-formed into SRF by the Park transformation,is fed back and compared with the inductor current reference i Lref dq,and the inductor current is regulated to track the reference i Lref dq by the PI compensator G I.The reference of the inductor current loop i Lref dq seems complex and it is explained as below.It is assumed that the utility is stiff,and the three-phase utility voltage can be expressed as⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩v ga=V g cosθ∗v gb=V g cosθ∗−2π3v gc=V g cosθ∗+2π3(4)where V g is the magnitude of the grid voltage,andθ∗is the actual phase angle.By the Park transformation,the utility voltage is transformed into the SRF,which is shown asv gd=V g cos(θ∗−θ)v gq=V g sin(θ∗−θ).(5) v gq is regulated to zero by the PLL,so v gd equals the mag-nitude of the utility voltage V g.As thefilter capacitor voltage equals the utility voltage in the gird-tied mode,v C d equals the magnitude of the utility voltage V g,and v C q equals zero,too. In the D-axis,the inductor current reference i Lref d can be expressed by(6)according to Fig.3i Lref d=I gref d+i LLd−ω0C f·v C q.(6) Thefirst part is the output of the limiter.It is assumed that the given voltage reference V max is larger than the magnitude of the utility voltage v C d in steady state,so the PI compensator, denoted by G V D in the following part,will saturate,and the limiter outputs its upper value I gref d.The second part is the load current of D-axis i LLd,which is determined by the charac-teristic of the local load.The third part is the proportional part −ω0C f·v C q,whereω0is the rated angle frequency,and C f is the capacitance of thefilter capacitor.It isfixed as v C q de-pends on the utility voltage.Consequently,the current reference i Lref d is imposed by the given reference I gref d and the load current i LLd,and is independent of the load voltage.In the Q-axis,the inductor current reference i Lref q consists of four parts asi Lref q=v C q·k Gv q+I gref q+i LLq+ω0C f·v C d(7) where k Gv q is the parameter of the P compensator,denoted by G V Q in the following part.Thefirst part is the output of G V Q,Fig.4.Simplified block diagram of the unified control strategy when DG operates in the grid-tied mode.which is zero as the v C q has been regulated to zero by the PLL.The second part is the given current reference I gref q,and thethird part represents the load current in Q-axis.Thefinal partis the proportional part−ω0C f·v C d,which isfixed since v C d depends on the utility voltage.Therefore,the current referencei Lref q cannot be influenced by the external voltage loop and isdetermined by the given reference I gref q and the load currenti LLq.With the previous analysis,the control diagram of the invertercan be simplified as Fig.4in the grid-tied mode,and the inverteris controlled as a current source by the inductor current loopwith the inductor current reference being determined by thecurrent reference I gref dq and the load current i LLdq.In otherwords,the inductor current tracks the current reference and theload current.If the steady state error is zero,I gref dq representsthe grid current actually,and this will be analyzed in the nextsection.B.Transition From the Grid-Tied Mode to the Islanded Mode When the utility switch S u opens,the islanding happens,and the amplitude and frequency of the load voltage will drift due to the active and reactive power mismatch between the DG and the load demand.The transition,shown in Fig.5,can be divided into two time interval.Thefirst time intervals is from the instant of turning off S u to the instant of turning off S i when islanding is confirmed.The second time interval begins from the instant of turning off inverter switch S i.During thefirst time interval,the utility voltage v gabc is stillthe same with the load voltage v C abc as the switch S i is in ONstate.As the dynamic of the inductor current loop and the voltageloop is much faster than the PLL[52],while the load voltageand current are varying dramatically,the angle frequency of theFig.5.Operation sequence during the transition from the grid-tied mode to the islandedmode.Fig.6.Transient process of the voltage and current when the islanding happens.load voltage can be considered to be not varied.The dynamic process in this time interval can be described by Fig.6,and it is illustrated later.In the grid-tied mode,it is assumed that the DG injects ac-tive and reactive power into the utility,which can be expressed by (8)and (9),and that the local critical load,shown in (10),represented by a series connected RLC circuit with the lagging power factorP g =32·(v C d i gd +v C q i gq )=32v C d i gd (8)Q g =32·(v C q i gd −v C d i gq )=−32v C d i gq(9)Z s load =R s +jωL s +1jωC s=R s +j ωL s −1ωC s=R s +jX s .(10)When islanding happens,i gd will decrease from positive to zero,and i gq will increase from negative to zero.At the same time,the load current will vary in the opposite direction.The load voltage in D -and Q -axes is shown by (11)and (12),and each of them consists of two terms.It can be found that the load voltage in D -axis v C d will increase as both terms increase.However,the trend of the load voltage in Q -axis v C q is uncertain because the first term decreases and the second term increases,and it is not concerned for a whilev C d =i LLd ·R s −i LLq ·X s (11)v C q =i LLq ·R s +i LLd ·X s .(12)With the increase of the load voltage in D -axis v C d ,when it reaches and exceeds V max ,the input of the PI compensator G V D will become negative,so its output will decrease.Then,the output of limiter will not imposed to I gref d any longer,and the current reference i Lref d will drop.With the regulation of the inductor current loop,the load current in D -axis i LLd willdecrease.As a result,the load voltage in D -axis v C d will drop and recover to V max .After i LLd has almost fallen to the normal value,the load voltage in Q -axis v C q will drop according to (12).As v C q is decreased from zero to negative,then the input of the PI compensator G PLL will be negative,and its output will drop.In other words,the angle frequency ωwill be reduced.If it falls to the lower value of the limiter ωmin ,then the angle frequency will be fixed at ωmin .Consequently,at the end of the first time interval,the load voltage in D -axis v C d will be increased to and fixed at V max ,and the angle frequency of the load voltage ωwill drop.If it is higher than the lower value of the limiter ωmin ,the PLL can still operate normally,and the load voltage in Q -axis v C q will be zero.Otherwise,if it is fixed at ωmin ,the load voltage in Q -axis v C q will be negative.As the absolute values of v C d and v C q ,at least the one of v C d ,are raised,the magnitude of the load voltage will increase finally.The variation of the amplitude and frequency in the load volt-age can also be explained by the power relationship mentioned before.When the islanding happens,the local load must ab-sorb the extra power injected to the grid,as the output power of inverter is not changed instantaneously.According to (1),the magnitude of the load voltage V m will rise with the increase of P load .At the same time,the angle frequency ωshould drop,in order to consume more reactive power with (2).Therefore,the result through the power relationship coincides with the previ-ous analysis.The second time interval of the transition begins from the instant when the switch S i is open after the islanding has been confirmed by the islanding detection method.If the switch S i opens,the load voltage v C abc is independent with the grid volt-age v gabc .At the same time,v gabc will reduce to zero theo-retically as the switch S u has opened.Then,the input of the compensator G PLL becomes zero and the angle frequency is invariable and fixed to the value at the end of the first interval.Under this circumstance,v C dq is regulated by the voltage loop,and the inverter is controlled to be a voltage source.With the previous analysis,it can be concluded that the drift of the amplitude and frequency in the load voltage is restricted in the given range when islanding happens.And the inverter is transferred from the current source operation mode to the voltage source operation mode autonomously.In the hybrid voltage and current mode control [17]–[40],the time delay of islanding detection is critical to the drift of the frequency and magnitude in the load voltage,because the drift is worse with the increase of the delay time.However,this phenomenon is avoided in the proposed control strategy.C.Islanded ModeIn the islanded mode,switching S i and S u are both in OFF state.The PLL cannot track the utility voltage normally,and the angle frequency is fixed.In this situation,the DG is controlled as a voltage source,because voltage compensator G V D and G V Q can regulate the load voltage v C dq .The voltage references in D -and Q -axis are V max and zero,respectively.And the magnitude of the load voltage equals to V max approximately,which will。

适用于电网三相不平衡的光伏逆变器控制策略设计

适用于电网三相不平衡的光伏逆变器控制策略设计

态遥
因此袁 本文所设计策略能很好地应对电网电压不
对称的情况袁 且系统的电流控制快速性较好袁 充分证
明了本文方案的正确性遥
4 结论
本文针对常规光伏逆变器在不平衡电网情况下的 正常运行受影响问题袁提出了改进的控制策略遥
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quasi-proportional-resonant翻译

quasi-proportional-resonant翻译

quasi-proportional-resonant翻译"Quasi-proportional-resonant"的翻译是"准比例谐振"。

这个术语是用来描述控制系统中一种特殊的控制策略。

在准比例谐振控制中,控制系统的输入信号通过一个准比例谐振滤波器进行滤波处理,以提取出特定频率范围内的信号。

这种控制策略常用于工程中的振动控制、噪声抑制和多频谐振控制等应用领域。

以下是12个使用准比例谐振控制相关词汇和双语例句:1. Quasi-proportional-resonant controller:准比例谐振控制器Example: The quasi-proportional-resonant controller effectively suppresses the vibrations in the system.2. Resonance frequency:谐振频率Example: The resonance frequency of the system can be tuned using a quasi-proportional-resonant filter.3. Control strategy:控制策略Example: The quasi-proportional-resonant control strategy provides better performance compared to traditional control methods.4. Vibration control:振动控制Example: The quasi-proportional-resonant technique is widely used for vibration control in mechanical systems.5. Noise suppression:噪声抑制Example: The quasi-proportional-resonant approach effectively suppresses noise for improved signal quality.6. Multi-frequency resonance control:多频谐振控制Example: The quasi-proportional-resonant method allowsfor simultaneous control of multiple resonance frequencies.7. Filtering:滤波处理Example: The quasi-proportional-resonant filter removes unwanted frequency components from the input signal.8. Frequency range:频率范围Example: The quasi-proportional-resonant technique focuses on a specific frequency range for optimal control.9. System stability:系统稳定性Example: The quasi-proportional-resonant control ensures system stability even under varying operating conditions.10. Harmonic suppression:谐波抑制Example: The quasi-proportional-resonant algorithm effectively suppresses harmonic distortions for improved power quality.11. Adaptive control:自适应控制Example: The quasi-proportional-resonant approach allows for adaptive control based on real-time system conditions.12. Control performance:控制性能Example: The quasi-proportional-resonant technique improves the control performance of the system by reducing unwanted vibrations.。

四桥臂有源滤波器在静止坐标系下的改进PR控制 (1)

四桥臂有源滤波器在静止坐标系下的改进PR控制 (1)

第32卷第6期中国电机工程学报V ol.32 No.6 Feb.25, 20122012年2月25日Proceedings of the CSEE ©2012 Chin.Soc.for Elec.Eng. 113 文章编号:0258-8013 (2012) 06-0113-08 中图分类号:TM 46 文献标志码:A 学科分类号:470⋅40四桥臂有源滤波器在静止坐标系下的改进PR控制周娟,张勇,耿乙文,伍小杰(中国矿业大学信息与电气工程学院,江苏省徐州市 221008)An Improved Proportional Resonant Control Strategy in the StaticCoordinate for Four-leg Active Power FiltersZHOU Juan, ZHANG Yong, GENG Yiwen, WU Xiaojie(School of Information and Electrical Engineering, China University of Mining and Technology,Xuzhou 221008, Jiangsu Province, China)ABSTRACT: The current loop control of active power filters (APF) requires the compensation current to track the given signal without any error,while it is difficult to eliminate steady-state errors by using the traditional PI controller in the synchronous dq frame. In this paper, the proportion resonant (PR) controller was adopted to track the different frequency component, thus to obtain zero steady-state errors. As to the grid frequency fluctuation and the unbalanced problem of three-phase systems, the improved controller in the αβγ coordinate was proposed. On the basis of analyzing the effects of PR controller parameters on the performance index, the paper summarized the debugging methods of the parameters. And the Pre-Warped Tustin Transformation was used to discretize the controllers. The proposed strategy was verified through simulation and experiment results. The total harmonic distortion (THD) values of grid currents after filtering reduced and the root mean square value of the neutral current dropped. In addition, the compensating effects was still satisfying while load and frequency were fluctuating. The results suggest that the proposed improved PR control strategy can effectively restrain harmonics and solve the unbalanced problem of three-phase systems. Moreover, this method has excellent adaptability for the load and frequency fluctuation.KEY WORDS: four-leg active power filter (APF); proportional resonant (PR) control; three-phase four wire system; frequency fluctuation摘要:有源电力滤波器(active power filter,APF)电流环控制要求补偿电流无误差地跟踪给定信号,传统的dq坐标系下P I控制很难消除稳态误差。

Proportional

Proportional

Proportional-Resonant Current Control of Single-Phase Grid-TiedPV Inverter SystemSu Xiu’e, B. Author2, and C. Author3Abstract—In this paper, a proportional resonant (PR) control scheme is proposed for single-phase grid-tied boost-buck PV inverter to achieve high-quality sinusoidal output currents. Simulation results are provided to illustrate the effectiveness of the proposed scheme.Index terms—PR (Proportional-Resonant) Control, Single-phase, PV System.Ⅰ IntroductionCurrent distortion is an important performance index for grid connected PV inverters. Low THD of output current requires accurate current control scheme. Resonant controller which is based on internal model principle is found to be zero steady-state tracking error control scheme for sinusoidal signals [1] -[3].This paper proposes a proportional resonant (PR) control scheme for single-phase grid-tied boost-buck inverter to achieve high-quality sinusoidal output currents. Simulation results are provided to illustrate the effectiveness of the proposed scheme.Ⅱ Boost-Buck PV Inverter and Proposed PR Control SchemeFig.1 shows the total structure of the grid-tied inverter of the PV system discussed in this paper.Fig.1 the total structure of the PV systemFig.1 gives a boost-buck PV inverter system, which contains a DC-DC boost converter and a H-bridge inverter. The function of the DC-DC boost converter is to regulate the output current to track maximum power point (MPP) of the PV panel, while the inverter is used to achieve high quality sinusoidal output current and maintain constant dc link voltage.A. Control Scheme of DC-DC ConverterAs all known that the output power of PV arrays is always changing with weather conditions, i.e., solar irradiation and atmospheric temperature. Therefore, real time MPPT control for extracting maximum power from the PV arrays becomes indispensable in PV generation systems [6][7]. There are many methods, e.g., Perturb and Observe (P&O) [9], Incremental Conductance (INC) [8][9], Constant Voltage (CV) and others [9]. Comparing all the methods we choose the INC to implement the MPPT in our system. And the flowchart of the INC MPPT method is shown in Fig.2.Fig.2 the flowchart of the INC Fig.3 the structure of DC-DC converterThe electrical dynamics of the DC-DC converter is shown in Fig.3[4], assuming continuous conduction mode of operation, the state space averaging model will be given in the following equation,()1Lpv dc di LU D U dt=-- (1) where D is the duty cycle.B. PV Inverter and The PR ControllerThe electrical dynamics of the grid-tied inverter as shown in Fig.1 can be described as follows:acAB ac ac di u Li R u dt=++ (2) We can check the u ac and i ac , respectively, but the object of the inverter is to achieve high-quality sinusoidal output currents, so many literatures adopt the current tracking directly, e.g. DB(deadbeat), PI, RP(repetitive proportion) and so on, but a proportional resonant (PR) control scheme is proposed in this paper.As shown in Fig.1, the grid-tied inverter adopts the double-loop control, voltage loop and current loop. The PI controller is used to control the voltage U dc , while the PR controller is adopted to control the current i ac .The transfer function of the PR is described as follows [1],()2222s r c s c Y K s G s E s s ωωω==++ (4) The rational function in (4) can be rewritten as:()()()()2122i c c Y s K E s Y s Y s s s ωωω⎡⎤=--⎢⎥⎣⎦(6)Equation (6) can be represented by the control block representation shown in Fig.4. From this Figure, it can be deduced that the resonant function can be physically implemented using op-amp integrator and inverting/non-inverting gain amplifiers.Fig.4 Decomposition of resonant block into two interlink integratorsThen we analyze the characters of the PR control in frequency domain. The magnitude-frequency characteristic of the PR is described like that:A = (5) And the A is now infinite, so the PR control could implement zero steady-state errors tracking. Ⅲ Simulation ResultsSampling frequency Switching frequency Grid- frequency Boost inductor Boost capacitor Grid-tied inductor AC voltage (RMS) DC reference voltage10kHz 10kHz 50Hz 1mH3000 F μ10mH 220V 400VTable.1 System parameters Open voltage Short currentMaximum power point voltage Maximum power point current Maximum power225V 8A175V 7.15A1251.25W Atmospheric temperature Solar irradiation 25o C1000W/m 225o C600W/m 2203.5V 4.8A679.107W 158.3V 4.29ASolar output capacitor1000 Fμ1000 FμTable.2 PV arrays parametersKey parameters of the system are listed in Table.1, and table.2 shows the PV arrays parameters. As shown in Fig.5 b.) simulation results demonstrate that the MPPT is achieved within certain accuracy under varying solar irradiation. It costs 0.4s to achieve the MPP at begin, and when the solar irradiation changes from 1000W/m 2 to 600W/m 2 at 1.5s, the MPP is tracked in 0.1s. Fig.5 a.) shows the voltage of DC-link which tracks the reference voltage based on the PI control scheme [2], similar with the MPP, it tracks the reference after 0.6s, and when the solar irradiation changes at 1.5s it takes 0.5s to follow the reference again.time/sU d cI p vU p va.)factor is nearly unity.The grid-tied current is the inductance-current is 2.60% as shown in Fig.6b.).time/sU a c /VUac-Iactime/sI a c /AFrequency (Hz)M a g (% o f F u n d a m e n t a l )a.)b.)Fig.6 Simulation results of the inverter, a.) the grid-voltage and inductance-current, b.) the THD of the inductance-current.With the above-mentioned the solar irradiation changes from 1000W/m 2 to 600W/m 2 at 1.5s, so the MPP is changed, the power falls from 1251.25W to 679.107W, and the inductance-current moves from 8.05A(amplitude) to 4.37A as shown in Fig.5 a.). Ⅳ ConclusionsThis paper presents a proportional resonant (PR) control scheme for single-phase grid-tied inverter to achieve high-quality sinusoidal output currents. The system is simple in structure because there is less relation between the two stages (boost and inverter). And the PR is designed to enhance the converter reference tracking performance and alleviate steady-state errors in single-phase systems.Another advantage associated with the PR controllers is the possibility of implementing selective harmonic compensation without requiring excessive computational resources. The effectiveness of the proposed scheme is illustrated by the simulation results provided in this paper.The proposed method can also be introduced to three-phase applications without coordinate transformation. Based on the similar control theory, PR can also be used in an active power filter.Reference[1]R. Teodorescu, F. Blaabjerg, M. Liserre, P.C. Loh, “Proportional-resonant controllers and filtersfor grid-connected voltage-source converters,” IEE Proceedings on The Institution of Engineering and Technology, pp: 750-762, No.20060008.[2]J. Selvaraj, N.A. Rahim, C. Krismadinata, “Digital PI Current Control for Grid Connected PVInverter,” IEEE Trans. on Power Electronics, pp: 742-746, 2008.[3]G.P. Liua, S. Daleyb, “Optimal-tuning PID control for industrial systems,” Control EngineeringPractice, pp: 1185–1194, 9 (2001).[4]J. Mahdavi, A. Emadi, H.A. Toliyat, “Application of State Space Averaging Method to SlidingMode Control of PWM DC DC Co nverters,” IEEE Industry Applications Society Annual Meeting, pp.820-827, October, 1997.[5]Atsuo KAWAMURA, Tomoki YOKOYAMA, “Comparison of Five Different Approaches forReal Time Digital Feedback Control of PWM Inverters,” IEEE Industry Applications Society Annual Meeting, pp: 1005-1011, Oct, 1990.[6]Trishan Esram, Patrick L. Chapman, “Comparison of Photovoltaic Array Maximum Power PointTracking Techniques,” IEEE Trans. on Energy Conversion, Vol.22, No.2, pp.439-449, June 2007.[7]G.M.S. Azevedo, M.C. Cavalcanti, K.C. Oliveira, “Evaluation of Maximum Power PointTracking Methods for Grid Connected Photovoltaic Systems,” IEEE Power Electronics Specialists Conference, June, 2008, pp: 1456-1462.[8]Fangrui Liu, Shanxu Duan, Fei Liu, Bangyin Liu, “A Variable Step Size IN C MPPT Method forPV Systems,” IEEE Transactions on industrial Electronics, Vol.55, No.7, pp: 3622-3628, July, 2008.[9]Trishan Esram, Patrick L. Chapman, “Comparison of Photovoltaic Array Maximum Power PointTracking Techniques,” IEEE Trans. on Energy Conver sion, Vol.22, No.2, pp.439-449, June 2007.。

基于PR控制的三相并网逆变器研究_刘超厚

基于PR控制的三相并网逆变器研究_刘超厚

(3)
其中,Clark 变换矩阵为:
1 1 1 − − 2 2 2 C32 = 3 3 3 0 − 2 2
续时间为 0.4s,对于积分控制器[0—0.2]s 输入信号为 (4) 单位阶跃信号,[0.2—0.4]s 为零,对于谐振控制器[0 —0.2]s 输入为 sin(100π t ) 正弦信号,[0.2—0.4]s 为 零,由此可以得到积分控制器和谐振控制器的输入输 出特性图分别如图 2 和图 3 所示。
参考文献
图 10 准 PR 控制并网电流频谱 [1] Mateus Active F. And Schonardie Reactive and Power Denizar Control C. Martins. dq0 “Three-Phase Grid-Connected Photovoltaic System With Using Transformation,” PESC 2008 Rhodes, pp.1202-1207. [2] R.Teodorescu, F.Blaabjerg, M.Liserre and P.C.Loh. “Proportional-resonant grid-connected controllers and filters for voltage-source converters,”IEE
1.引言
在三相并网逆变器中,电流控制的传统控制方法 是将控制量转换到旋转坐标系下, 然后分别对 d 、 q轴 分量采用 PI 控制,因为在三相旋转坐标系下 d 、 q 轴 分量表现为直流量,而积分器对直流分量有无穷大的 增益,因此可以实现系统无稳态误差控制。然而在三 相并网逆变器中采用旋转坐标系下的 PI 控制要经过 Clark 和 Park 变换,而且 d 、 q 轴分量存在耦合,为 了达到良好的控制效果需要进行解耦控制[1],在实现 中由于解耦不精确会对控制效果产生一定的影响。本 文介绍了一种谐振控制算法, 不需要繁琐的坐标变换, 并且不需要进行解耦控制,可以达到良好的控制效果 [2] 。

三相四线制有源电力滤波器指定次数谐波控制策略

三相四线制有源电力滤波器指定次数谐波控制策略

三相四线制有源电力滤波器指定次数谐波控制策略李彩林;惠梓舟;蔡儒军;周志林【摘要】针对三相四线制低压配电网不平衡非线性负载的电能质量问题,提出采用矢量谐振控制器对电容分离型有源电力滤波器(Active Power Filter,APF)进行指定次数谐波控制方案.在αβγ坐标系下对电容分离型APF进行建模,省去了在dq坐标系下的电流交叉解耦环节.比例谐振控制器应用在APF闭环控制系统时,存在各次谐振点附近谐振尖峰影响闭环控制系统稳定性和补偿精度的问题,采用矢量谐振控制器实现指定次数谐波跟踪控制,其分子零点与控制对象的极点抵消,实现控制系统降阶,提高了控制性能.仿真结果表明,所提控制方法在针对指定次数谐波补偿方面有着良好效果,其三相不平衡被抑制,直流侧电容电压得到均衡控制,证明了所提方法有效性.%In view of the power quality of unbalanced nonlinear load for the three-phase four wire low voltage distribu-tion network, the control scheme of using vector proportional resonant controller to suppress specific harmonic is pro-posed.The split-capacitor-type active power filter ( APF) mathematical model is established based onαβγcoordinate system, and current cross decoupling link under dq coordinate system is omitted.The proportional resonant controller is applied in the closed-loop control system of APF, and the resonance peak near the resonance point can affect the stability and compensation precision.In this paper, the vector resonance controller is adopted to suppress specific har-monic tracking control, and the zero point of the controller can molecule the pole of control object, thus the three-phase unbalanced order of control system is reduced to improve the control performance, and the DC side capacitorvoltage is also controlled in balance.The simulation results verify the validity of the proposed method.【期刊名称】《电测与仪表》【年(卷),期】2017(054)003【总页数】6页(P83-88)【关键词】电容分离型;有源电力滤波器;不平衡;指定次数谐波控制;矢量谐振控制器【作者】李彩林;惠梓舟;蔡儒军;周志林【作者单位】桂林电子科技大学机电工程学院,广西桂林541004;桂林电子科技大学机电工程学院,广西桂林541004;桂林电子科技大学机电工程学院,广西桂林541004;桂林电子科技大学机电工程学院,广西桂林541004【正文语种】中文【中图分类】TM7140 引言随着电力电子技术的不断发展,大量非线性负载被广泛运用于低压配电网中,不平衡、谐波和无功问题日益突出,同时由于中性线的存在,零序电流的补偿也成了一个研究的热点[1]。

探讨适配器电源设计并结合FAN6921芯片介绍

探讨适配器电源设计并结合FAN6921芯片介绍

设计进行理论计算,确定最大应力值,再根据实际测试的结果来最终选定功率器件的电压和电流等规格的参数。

电气性能调试整个电源第一次装上元件后,可以先按功能块来分别调试,每部分功能都调试好后,再合在一起测试性能.如PFC部分,DC-DC部分,辅助电源,保护电路等。

需要测试的内容有:电源的输出电压调整率,电压纹波,电源保护功能等,检验电感是否饱和,主要开关管的最大应力和温度是否有足够余量。

安全验证接下来,就可进行产品安全方面的测试和验证了,如电磁干扰测试,温升测试(主要开关管,电感,变压器,电容的最大工作温度是否在其规格范围内);产品安全性测试,如雷击测试,绝缘耐压测试,电源老化实验,抗静电测试等,最后还要计算整个电源的平均失效时间等;设计流程步骤-1: 确定系统规格通过以上的介绍后,大家会对电源的设计步骤有了一个简单的了解。

下面用一个120W 的电源设计实例来进一步介绍设计过程,电源需求规格如下表:项目规格输入电压(Vin) 90~264Vac输出功率(Pout) 120W输出电压(Vout) 19V输出电流(Iout) 6.3A电压调整率<5%平均效率>87%功率因数(PF) >0.9谐波<15%安规标准IEC61000保护要求短路,过压,过功率,过温尺寸150x50x30 mm散热方式自然步骤-2: 选择电源结构电源功率范围选择可以选择反激或半桥结构,如果成本压力大的话,用反激式DC/DC 的结构是不错的选择。

步骤-3: 选择PFC和DC/DC 芯片因为有功率因数(简称PF)的要求,所以需要PFC芯片。

120W的电源非常适合采用电感电流临界工作模式,可选用的芯片有很多。

这里我们选用飞兆公司的FAN6961临界模式PFC 芯片。

选择DC/DC控制芯片:考虑到效率和电磁干扰及成本因素,用准谐振结构来完成直流-直流转换,可以选用飞兆的FAN6300准谐振芯片。

最近飞兆针对需要PFC的准谐振应用,推出了集成度更高的芯片FAN6921,它集成了FAN6961和FAN6300的所有功能,并增加了如输入欠压保护和过温保护,高低压输入过功率补偿等功能。

用于逆变器的比例-谐振控制器的抗饱和方案

用于逆变器的比例-谐振控制器的抗饱和方案

1
引言
比例 -谐振( PR)控制器,自从被提出之后,便
[1-2]
的方式。文献 提出了一种抗饱和的方法,也可以 归为跟踪积分的方式,只是文中并未做详细的分 析。总体来看,跟踪积分可以达到 PR 控制器抗饱 和的目的,但是需要设计一个反馈系数。 本文从等效电路的角度出发, 提出一种 PR 控制 器的抗饱和新方案。从结构上看,此种策略结合了 条件积分和跟踪积分,属于混合式结构。这种策略 有物理意义明确,简单,容易实现的优点。仿真和 实验结果验证了本方案的有效性。
(3)
当等效电路中各个元器件的参数分别为:
2
1 s
rP K P , rR Ki , CR
路阻抗为:
2 Kic 1 时,电 , LR 2 Kic 2
图2
另一种 PR 控制器的形式
当控制器输出被限幅电路限制时,控制器中的 积分器就可能出现饱和的现象。而 PR 控制器中包 含了两个积分器,因此饱和现象同样是存在的。
GPR ( s) K p
2 Kic s s 2c s 2
2
(2)
同样,这种 PR 控制器也可以用两个积分器组
成,如图 2 所示。
e
Kp
电路,如图 4 所示。其阻抗的传递函数为:
+ +
Z ( s) rP
2c
+ 1 s
2c K i
rR LR s CR rR LR s 2 LR s rR
2c K i
yr
-
+
2
1 s
PR Controller
1 Kp
图6
本文提出的抗饱和方案
新的控制方案便基于此等效电路,如图 6 所示。 虚线框中为 PR 控制器, 图中 y 表示 PR 控制器的输出, yp、yr 分别表示输出 y 的比例部分和谐振部分。他们之 间的关系满足:

应用于MMC环流抑制的准PR控制器参数设计

应用于MMC环流抑制的准PR控制器参数设计

应用于MMC环流抑制的准PR控制器参数设计赵庆玉;余发山;何国锋;韩耀飞;樊晓虹;申慧方【摘要】Modular Multilevel Converter(MMC)phase-to-phase voltage imbalance results in internal generation of three-phase current.To restrain the circulation,an equivalent model of MMC circulation is firstly established,and the parameters of quasi PR controller are designed in the stationary coordinate system,and the influence of the parameters of quasi PR controller on the restraining characteristics of the MMC circulation is analyzed.In order to verify the proposed strategy,a PSCAD/EMTDC simulation model is built and tested on the 35 kV·A five-level MMC prototype.The results show that the designed quasi PR controller can suppress the internal circulation of MMC effectively.%模块化多电平变流器(Modular Multilevel Converter,MMC)相间电压不平衡会导致其内部产生三相环流.为了抑制环流,文章首先建立MMC环流等效模型,并在静止坐标系下设计准PR 控制器参数,分析准PR控制器参数对MMC环流抑制特性的影响.为了验证提出的MMC环流抑制策略,搭建了PSCAD/EMTDC仿真模型,并在35kV·A五电平MMC 样机上进行实验.结果表明,设计的准PR控制器能够有效地抑制MMC内部环流.【期刊名称】《可再生能源》【年(卷),期】2018(036)001【总页数】6页(P51-56)【关键词】MMC环流模型;准PR控制器;环流抑制【作者】赵庆玉;余发山;何国锋;韩耀飞;樊晓虹;申慧方【作者单位】河南理工大学电气工程与自动化学院, 河南焦作 454000;河南城建学院电气与控制工程学院, 河南平顶山 467036;河南理工大学电气工程与自动化学院, 河南焦作 454000;河南城建学院电气与控制工程学院, 河南平顶山 467036;河南城建学院电气与控制工程学院, 河南平顶山 467036;河南城建学院电气与控制工程学院, 河南平顶山 467036;河南理工大学电气工程与自动化学院, 河南焦作454000;河南城建学院电气与控制工程学院, 河南平顶山 467036【正文语种】中文【中图分类】TK8;TM460 引言我国的风电基地主要分布在“三北”地区。

双馈异步风力发电机并网运行中的几个热点问题

双馈异步风力发电机并网运行中的几个热点问题

双馈异步风力发电机并网运行中的几个热点问题作者:贺益康, 胡家兵, HE Yikang, HU Jiabing作者单位:贺益康,HE Yikang(浙江大学电气工程学院,浙江省杭州市,310027), 胡家兵,HU Jiabing(华中科技大学电气与电子工程学院,湖北省武汉市,430074)刊名:中国电机工程学报英文刊名:Proceedings of the Chinese Society for Electrical Engineering年,卷(期):2012,32(27)1.Hu J;He Y;Wang H Adaptive rotor current control for wind-turbine driven DFIG using resonant controllers in a rotor rotating reference frame 2008(02)2.Kiani M;Lee W Effects of voltage unbalance and system harmonics on the performance of doubly fed induction wind generators 2010(02)icua A;Piasecki S;Bobrowska M Coordinated control for grid connected power electronic converters under the presence of voltage dips and harmonics 20094.Ramos C J;Martins A P;Carvalho A S Rotor current controller with voltage harmonics compensation for a DFIG operating under unbalanced and distorted stator voltage 20075.胡家兵;贺益康;郭晓明不平衡电压下双馈异步风力发电系统的建模与控制 2007(11)6.Wessels C;Gebhardt F;Fuchs F W Dynamic voltage restorer to allow LVRT for a DFIG wind turbine 20107.Zhan C;Barker C D Fault ride-through capability investigation of a doubly-fed induction generator with an additional series-connected voltage source converter 20068.Kelber C;Schumacher W Active damping of flux oscillations in doubly fed AC machines using dynamic variations of the system' s structure 20019.Petersson A Analysis,modeling and control of doubly-fed induction generators for wind turbines 200510.Liao Y;Li H;Yao J Operation and control of a grid-connected DFIG-based wind turbine with series grid-side converter during network unbalance 2011(01)11.Singh B;Emmoji V;Singh S N Performance evaluation of new series connected grid-side converter of doubly-fed induction generator 200812.Flannery P;Venkataramanan G A fault tolerant doubly fed induction generator wind turbine using a parallel grid side rectifier and series grid side converter 2008(03)13.周鹏双馈异步风力发电系统低电压穿越技术研究 201114.向大为;杨顺昌;冉立电网对称故障时双馈感应发电机不脱网运行的励磁控制策略 2006(03)15.Flannery P;Venkataramanan G Evaluation of voltage sag ride-through of a doubly fed induction generator wind turbine with series grid side converter 200716.贺益康;周鹏变速恒频双馈异步风力发电系统低电压穿越技术综述 2009(09)17.Abad G;Rodriguez M A;Iwanski G Direct power control of doubly-fed-induction-generator-based wind turbines under unbalanced grid voltage 2010(02)18.Santos-Martin D;Rodriguez-Amenedo J L;Arnalte S Providing ride-through capability to a doubly fed induction generator under unbalanced voltage dips 2009(07)19.Xiang D;Ran L;Tavner P J Control of a doubly fed induction generator in a wind turbine during grid fault ride-through 2006(03)20.Xu L;Wang Y Dynamic modeling and control of DFIG-based wind turbines under unbalanced network conditions 2007(01)21.Hu Jiabing;He Yikang;Xu Lie Improved control of DFIG systems during network unbalance using PI-R current regulators 2009(02)zero steady-state error for current harmonics of concern under unbalanced and distorted operating conditions 2002(02)23.Zmood D N;Holmes D G Stationary frame current regulation of PWM inverters with zero steady-state error 2003(03)24.Xu Hailiang;Hu Jiabing;He Yikang Operation of wind-turbine-driven DFIG systems under distorted grid voltage conditions:analysisand experimental validations 2012(05)25.Hu Jiabing;Nian Heng;Xu Hailiang Dynamic modeling and improved control of DFIG Under Distorted Grid Voltage Conditions 2011(01)26.Lopez J;Gubia E;Sanchis P Wind turbines based on doubly fed induction generator under asymmetrical voltage dips 2008(01)27.Hu Jiabing;He Yikang Reinforced control and operation of DFIG-based wind generation system under unbalanced grid voltage conditions 2009(04)28.Hu Jiabing;He Yikang;Nian Heng Enhanced control of dfig used back-to-back PWM voltage-source converter under unbalanced grid voltage conditions 2007(08)29.Santos-Martin D;Rodriguez-Amenedo J L;Arnalte S Direct power control applied to doubly fed induction generator under unbalanced grid voltage conditions 2008(05)30.Yan X;Venkataramanan G;Flannery P S Voltage-sag tolerance of DFIG wind turbine with a series grid side passive-impedance network 2010(04)31.Rajda J;Galbraith A W;Schauder C D Device,system,and method for providing a low-voltage fault ride-through for a wind generator farm 200632.胡家兵;孙丹;贺益康电网电压骤降故障下双馈风力发电机建模与控制 2006(08)33.向大为;杨顺昌;冉立电网对称故障时双馈感应发电机不脱网运行的系统仿真研究 2006(10)34.AMEC National Electricity Rules,Version 39 201035.Ted K A Brekken;Mohan N Control of a doubly fed induction generator under unbalanced grid voltage conditions2007(01)36.Xu L Coordinated control of DFIG's rotor and grid side converters during network unbalance 2008(03)37.Teodorescu R;Blaabjerg F;Liserre M Proportional-resonant controllers and filters for gridconnected voltage-source converters 2006(05)38.Hu J;He Y Modeling and enhanced control of DFIG under unbalanced grid voltage conditions 2009(02)39.贺益康;胡家兵;徐烈并网双馈异步风力发电机运行控制 201240.Seman S;Niiranen J;Arkkio A Ride-through analysis of doubly fed induction wind-power generator under unsymmetrical network disturbance 2006(04)41.Zhou P;He Y;Sun D Improved direct power control of a DFIG-based wind turbine during network unbalance 2009(11)42.Hong-Geuk P;Abo-Khalil A G;Dong-Choon L Torque ripple elimination for doubly-fed induction motors under unbalanced source voltage 200743.Kearney J;Conlon M F Performance of a variable speed double-fed induction generator wind turbine during network voltage unbalance conditions 200644.Wangsathitwong S;Sirisumrannukul S;Chatratana S Symmetrical components-based control technique of doubly fed induction generators under unbalanced voltages for reduction of torque and reactive power pulsations 2007本文链接:/Periodical_zgdjgcxb201227001.aspx。

采用MMC-RPC治理牵引供电系统负序和谐波的PIR控制策略

采用MMC-RPC治理牵引供电系统负序和谐波的PIR控制策略

采用MMC-RPC治理牵引供电系统负序和谐波的PIR控制策略宋平岗;林家通;李云丰;吴继珍;文发【摘要】为综合治理铁路牵引变压器的负序、无功、谐波问题,设计了基于模块化多电平换流器的铁路功率调节器(MMC-RPC).首先设计了频率自适应功率分离器,并从功率角度分析了Scott牵引变压器(STT)牵引供电系统综合治理的补偿量;然后在构造虚拟正交分量后建立了单相MMC数学模型,在同步旋转坐标系下分析机车谐波电流的特性,指出单相奇次谐波电流在dq坐标系下都以4的倍数次波动;最后提出了需要更少的谐振控制器数量的比例-积分-谐振控制策略.在Matlab中搭建MMC-RPC仿真模型进行仿真,结果证明了所提控制策略有效性.%In order to govern the problems of negative sequence, reactive power and harmonic in railway traction comprehensively, this paper designs a railway static power conditioner based on modular multilevel converter (MMC-RPC). The frequency adaptive controller of power separation is designed firstly, and then the amount of comprehensive governing to Scott traction transformer power supply system is analyzed from the angle of power. Thereafter, a virtual ac component is constructed and then the mathematical model of single-phase MMC is established. After the analysis of locomotive harmonic current characteristics under the synchronization rotating frame, it is shown that the single phase odd harmonic currents fluctuate by a multiple of 4 in dq frame. The design control strategy is then proposed, which needs less proportional-integral-resonant controllers.Finally, the results of a MMC-RPC simulation model in Matlab have verified the proposed control strategy.【期刊名称】《电工技术学报》【年(卷),期】2017(032)012【总页数】9页(P108-116)【关键词】Scott牵引变压器;铁路功率调节器;模块化多电平换流器;比例-积分-谐振【作者】宋平岗;林家通;李云丰;吴继珍;文发【作者单位】华东交通大学电气与电子工程学院南昌 330013;华东交通大学电气与电子工程学院南昌 330013;国网智能电网研究院北京 102200;华东交通大学电气与电子工程学院南昌 330013;华东交通大学电气与电子工程学院南昌 330013【正文语种】中文【中图分类】TM922.3由于铁路的单相供电方式和不同供电区间的负载不同,三相系统存在较大的负序电流[1,2]。

Adaptive Current Control for Grid-Connected

Adaptive Current Control for Grid-Connected

Adaptive Current Control for Grid-Connected Converters with LCL-filterJorge Rodrigo Massing,M´a rcio Stefanello,Hilton Ab´ılio Gr¨u ndling and Humberto PinheiroGroup of Power Electronics and Control-GEPOCUniversidade Federal de Santa Maria,Santa Maria,RS,Brasiljorgemassing@Abstract—This paper presents a discrete-time adaptive current controller for grid-connected voltage source PWM converters with LCL-filter.The main attribute of the proposed current controller is that,in steady state,the damping of the LCL resonance does not depend on the grid characteristic since the adaptive feedback gains ensure a predefined behavior for the closed-loop current control.Simulation and experimental results are presented to validate the analysis and to demonstrate the good performance of the proposed controller for grid-connected converters subjected to large grid impedance variation and grid voltage disturbances.I.I NTRODUCTIONEnvironmental and economical issues are leading to an increase in electricity demand share covered by renewable energy sources.There is a strong trend to connect these distributed generation sources into the grid using current con-trolled voltage source inverters.The parametric uncertainties and disturbances experienced by grid-connected inverters can make the current control design a challenging problem[1]. It is worth noting that in high power voltage source in-verters,with power rate greater than1MW,the switching frequency is typically a few kHz to keep the switching losses at acceptable levels.Since current harmonics resulted from PWM nature of the inverter output voltages must be kept under the limits stated in the grid codes,passive L-or LCL-filters at the inverter AC terminals are deployed[2].LCL-filters are usually adopted in high power grid con-nected inverters since they result in higher attenuation at the high frequencies without increasing significantly the reactive power consumption at the grid frequency if compared with L-filters[3].If for one side the grid equivalent inductance and resistance at the point of connection can be considered as a part of the LCL-filter,from other side the uncertainty regarding their actual values result in changes in the LCL-filter resonance frequency,that should be considered in the current controller design to ensure the stability and the performance of grid connect voltage sources inverters[4],[5].In addition,the current controllers in this case are often required to reject the low order current distortions resulted from the grid background distortion.This combined with the fact that the current controllers are implemented in microcon-trollers or DSPs make the controller design to be far from a trivial task.The two main alternatives presented in the literature to damp the resonance of grid-connected voltage-source inverters with LCL-filters are:the use of passive damping to attenuate the resonance peak,which is undesired due to the loss of profits,specially in renewable energy applications,and the use of active damping which can be achieved by a number of controller approaches,such as specific controller structures [6],[7],state-feedback[8],[9],grid impedance estimation [10],[11],multiloop control strategies[12],among others[13], [14].However,stability problems and/or poor performance in terms of resonance damping are often found as a result of the combinations of two factors:(i)the LCL-filter inductances may change significantly since the converter-side inductance depends on the magnetic core permeability which in turn is a function of the current magnitude and the total inductance at the grid side depends on the short circuit power at the PCC, and(ii)poor damped complex poles close to the unit circle are included in the loop to achieved harmonic disturbance rejection.In order to guarantee the stability as well as to provide a good disturbance rejection of the grid background distortions, robust control design techniques with partial state feedback have been proposed recently[8],[9].Although this control approach is simple to implement and the converter stability is ensured for a given range of grid inductances,its performance in terms of resonance damping is still dependent on the grid impedance.In summary,the desired features of a current controller for grid-connected voltage source converters with LCL-filters can be stated as:(i)good tracking and disturbance rejection capabilities,(ii)robust stability with respect to parametric variations and(iii)robust performance in terms of resonance damping.To accomplish with such requirements,this paper proposes the use of a discrete-time adaptive state-feedback controller[15]for the current loop of grid-connected VSI. With the proposed controller it is possible to select a reference model such that the closed-loop system behaves like this model in steady state thanks to the online adjustment of the state feedback gains.As a result,the input-output response of the closed-loop system converges to the reference model and the resonance damping becomes independent of the grid impedance.Furthermore,as it will be demonstrated in the paper,reference tracking and disturbance rejection can beFig.1.Grid connected voltage source converter with LCL-filter. easily achieved without the use of thefixed gain resonantcontrollers[16],[17]or proportional-integral controllers in dq-reference frame.This paper is organized as follows.Section II derives themodel of the voltage source converter with LCL-filter.SectionIII presents in details the theory concerning the discrete timemodel reference adaptive control as well as disturbance rejec-tion.Section IV carries out a step-by-step procedure for theimplementation of the proposed discrete time adaptive currentcontrol.Finally,simulation results for a distributed generatingsystem are given in Section V,experimental results are givenin Section VI and in Section VII the main conclusions aredrawn.II.M ODELING OF V OLTAGE S OURCE C ONVERTERSWITH LCL-FILTERIn this Section,a discrete model for grid-connected voltage-source inverters with LCL-filter is derived.Fig.1shows atypical VSI with LCL-filter where the grid is represented byits Thevenin equivalent circuit at the point of connection.Inaddition,some of the power circuit resistances are includedin the model to make it minimum phase,which is one ofthe requirements of the proposed adaptive controller imple-mentation.In order to further simplify the model,theαβtransformation is used to render the coupled three-phase powercircuit into two decoupled single phase counterpart,which canbe controlled independently.For simplicity,let us consideronly the single-phase circuit of Fig.2.The state space modelof the system depicted in Fig.2is⎡⎣˙ic˙v C˙ig⎤⎦=⎡⎣−r cL c−1L c1C0−1C01L g−r gL g⎤⎦⎡⎣i cv Ci g⎤⎦+⎡⎣1L c⎤⎦u+⎡⎣−1L g⎤⎦vd y=100⎡⎣i cv Ci g⎤⎦,(1)where the states,the input,the output and the disturbance are functions oftime.Fig.2.Simplified single-phase circuit.The equivalent augmented discrete-time plant,including the digital implementation delay[8]has the following formx(k+1)=Ax(k)+Bu(k)+B d d u(k)y(k)=Cx(k),k∈{0,1,2,···},(2)where x∈R4,u∈R and y∈R with constant matrices A∈R4×4,B∈R4×1and C∈R1×4.Note that in the model(2)both i c or i g can be chosen as the output variable y[1].However,the relative degree of the transfer function i c(s)/u(s)is one,while the relative degree of i g(s)/u(s)is three.Aiming to obtain a minimal phase discrete system model,which is one requirement for the model reference based control,the output variable has been select as i c.The theoretical background of adaptive state-feedback control for output tracking and disturbance rejection is presented in details in the next section.III.M ODEL R EFERENCE A DAPTIVE S TATE-F EEDBACKC ONTOLFigure3presents the block diagram of the discrete-time adaptive controller for theαandβframes,where the control objectives are:1)To provide the same damping and stability characteris-tics of the grid connected converter independent on the grid impedance.2)To guarantee the disturbance rejection of the grid voltagebackground distortions,as well as sinusoidal reference tracking.Initially,the adaptive control problem is solved without the disturbance v d,which corresponds to the grid voltage,then in the second step a modification to provide disturbance rejection is described.Fig.3.Model reference state-feedback adaptive control structure for the current controller.A.Problem Statement(Case v d=0)In the case of absence of disturbances at the input of plant(2),the input-output model is given byy(z)=G(z)u(z),G(z)=C(zI−A)−1=k p Z(z)P(z)(3)with k p=0constant and P(z)=det(zI−A),Z(z)being monic polynomials of constant coefficients and degrees4and 2,respectively.As a result,the relative degree of the discrete model of the converter with LCL–filter is n∗=2.It is assumed that:1)(A,B)is stabilizable.2)Z(z)is a stable polynomial(i.e.,its zeros are in|z|<1).3)The sign of k p and the upper boundρ0≥|k p/k m|areknown.The objective of a model reference based controller is to track the output of a predefined reference model W m(z).The reference model is chosen asy m(k)=W m(z)r(k),k∈{0,1,2,...},W m(z)=k mP m(z)(4)where P m(z)is a stable and monic polynomial of degree n∗= 2(relative degree of the plant)and r∈R is an external reference.B.Controller StructureThe ideal control law that makes the plant to behave like the reference model i.e.y=y m is of typeu(k)=k1∗T x(k)+k2∗r(k),k1∗∈R n,k2∗∈R(5) If(5)is applied to the system(2)with v d=0,the perfect matching between the closed-loop plant and the reference model(4)is achieved,i.e.CzI−A−Bk∗1T−1Bk∗2=k mP m(z)(6)In this adaptive state feedback control,the aim is to movesome poles of A such that they become equal to the zeros ofZ(z)and the remaining poles of A being equal to the zeros ofP m(z)[15].Following this idea and from(6),the followingmatching conditions are obtaineddetzI−A−Bk∗1T=P m(z)Z(z),k2∗=k mk p(7)with C adjzI−A−Bk1∗TB=Z(z).When the plant parameters are known,(7)can be used tocompute k1∗and k2∗.Otherwise,they must be adaptivelyestimated.As the overall grid–side inductance L g1+L g2isunknown,even time varying,an adaptive scheme may bedeveloped.C.Equations for the Adaptive AlgorithmLet us define the following auxiliary signalsω(k)=x T(k),r(k)T(8)ζ(k)=W m(z)ω(k)(9)ξ(k)=θT(k)ζ(k)−W m(z)θTω(k)(10)θ(k)=k T1(k),k2(k)T(11)By using the tracking error e=y−y m it is possible toobtain the augmented error(k)=e(k)+ρ(k)ξ(k)(12)From the augmented error equation(12)and by using thegradient method,it is possible to demonstrate that with thefollowing adaptive lawsθ(k+1)=θ(k)−sign[ρ∗]Γζ(k) (k)m2(k)(13a)ρ(k+1)=ρ(k)−γξ(k) (k)m(k),ρ∗=|k p/k m|(13b)all closed–loop signals are bounded and the tracking errorconverges to zero in afinite time if,in(13),0<γ<2,0<Γ=ΓT<2/ρ0I5,whereΓ∈R5×5,andρ0≥|k p/k m|and the normalization signal is given bym(k)=1+ζT(k)ζ(k)+ξ2(k)(14)The Gradient algorithm has been chosen due to its simplicity and easy implementation,however other adaptive algorithms such as Least-Squares as well as modifications to improve the stability and robustness could also be considered.D.Disturbance Rejection(Case v d=0)The grid voltage v d in Fig.2corresponds to the disturbance term v d in the model(2).Even though v d is not available for measurement,it can be modeled as a sum of sin and cos terms such asv d=ij=1(αj sinωj t+βj cosωj t)(15)where i indicates the harmonic component of the grid distur-bance voltage v d.For rejection of v d,an extra term k3is added in the control law,leading tou(k)=k T1(k)x(k)+k2(k)r(k)+k3(k),k3∈R(16) withk3(k)=ij=1(k3αj(k)sinωj t+k3βj(k)cosωj t)(17)where k3αj and k3βj are the adaptive estimates of the idealparameters k∗3αj and k∗3βj so that the effect of the disturbancev d is rejected.To implement the adaptive state feedback control with disturbance rejection,the vectorsωandθin(8)and(11)are augmented as[15]ω(k)=[x T(k),r(k),sin(ω1),···,sin(ωi),cos(ω1),···,cos(ωi)]T(18)θ(k)=[k T1(k),k2(k),k3α1(k),···,k3αi(k),k3β1(k),···,k3βi(k)]T(19) In the case of grid frequency variation,thefixed distur-bance rejection controllers(proportional-resonant controller withfixed frequency)experience problems.However,with the compensation presented here,there is only the need to generate the sinusoidal signals(sine and cosine)with identification of the grid frequency,information provided by the synchroniza-tion algorithm used[18],[19].In the presence of the disturbance d u,the control law in the form(16)with k1=k∗1,k2=k∗2,k3=k∗3is applied to the plant(2)leading to[15]y(z)=y m(z)+Δ(z)(20) withΔ(z)=C(zI−A−Bk∗1)−1Bk∗3(z)+C(zI−A−Bk∗1)−1B d d u(z)(21)IV.D ESIGN E XAMPLEIn this section,the performance of the adaptive state-feedback control for the current loop of a grid connected VSIis demonstrated.A design example is given for a500kW windturbine.Table I500K W WT P ARAMETERS IN A BSOLUTE AND P.U.V ALUES[1].500kW WT systemLCL-filterBoost inductance L c0.2mH23%Grid side inductance L g10.03mHFilter capacitor C83µF1% GridimpedanceMaximum grid side value L g20.3Ω(inductive)100%Medium grid side value L g20.03Ω(inductive)10%Minimum grid side value L g20.003Ω(inductive)1% BaseValuesV oltage Base380V rms LineValuesCurrent Base750A rmsBefore starting the closed–loop operation,the control pa-rameters must be initialized.As it is possible to have some ideaabout the grid impedance at the point of common coupling,theinitial gains k1(0)and k2(0)can be found from the matchingcondition(7)by assuming,for instance,the parameter L g2with its medium value as in Table I.The other power circuitparameters are considered to be equal to their nominal values.In addition,from(3)by considering a reasonable parametricvariation,it is possible to define a nominalρ(0)and an upperboundρ0,which are used to initialize the adaptive law(13)and to define the positive defined matrixΓ<2/ρ0I5.Thelarger the matrixΓand the gainγ,the faster is the adaptation.The following steps are execute within a sample period.1)Sample of the state variables:At the beginning of eachsampling period,thefilter current and voltages are sampledand sine and cosine signals at the disturbance frequencies arecomputed[18],[19].2)Current reference computation from the P∗and Q∗setpoints:In grid connected wind turbines,the referencecurrents come from the active power P∗and the reactive powerQ∗loops,from which it is possible to derive the referencecurrents r∗αand r∗β.3)Computation of the reference model output:Computethe reference model output y m(k)=W m(z)r(k),whereW m(z)is stable with relative degree two,there isW m(z)=(1−p1)(1−p2)(z−p1)(z−p2)(22)4)Computation of internal signals:Taking the vectorωasin(18),then compute the auxiliary signalsζ(k),ξ(k)and theaugmented error (k).5)Computation of the control law u(k):6)Gain adaptation:The auxiliar signals are used to com-pute the estimated values ofθandρfor the next sample.In order to demonstrate the good performance of the pro-posed adaptive controller for grid connected voltage sourceconverters,the gains k∗1and k∗2have been computed accordingto(7)for a large range of grid short–circuit power as shown in Fig.4.With these gains the closed loop system behaves as the reference model.This can be seen from the open and closed loop frequency responses of Fig.5.Fig.4.Gains to meet the match condition as a function of the grid short circuit powerFig.5.Bode plot of W m(z)(desired closed-loop system)and of G(z) (open-loop plant)for different short-circuit levels at the point of coupling.To counteract the effect of the grid voltage,sin and cos terms are rated by the gains k3,which in steady state converge to values so that the effect of the disturbance is reject and the tracking of the reference is achieved.V.S IMULATION R ESULTSA500kW wind turbine with the parameters given in Table I connected to a power system as shown in Fig.8has been considered,where the controller parameters have been initialized as described in the previous section.The sampling frequency has been chosen12kHz,while the converter switch-ing frequency6kHz.Figure6shows the current transient response due a step change in the reference.It is possible to see that the output current tracks the output of the reference model once this transient has been applied after the parameters have converged to the real ones.The disturbance rejection on the grid-side converter current is verified in Fig.7.Although there is a high voltage distortion at the point of connection,the adaptive term k3is adjusted such that this effect is vanished and does not appear on the controlled current iαc2.If the compensations of thefifth harmonic is not included,the current become distorted,as shown by the current iαc2in Fig.7.Fig.7.Disturbance rejection.Top:Inverter output current with(iαc2)and without(iαc1)5th harmonic rejection.Bottom:The voltage at PCC with16% of5th harmonic.To analyze a more realistic problem concerning the con-nection of converters to the power system,Fig.9presents the response for a short circuit on the power system and disconnection of the faulted feeder,consequently changing the short-circuit impedance at the PCC.Initially,the controller gains were initialized according to the procedure described in Section IV.At t=0.1and t=0.2seconds,transients due to the current reference phase and amplitude variations show that the gains θhave converged toθ∗since i conv−y m is zero.At t=0.3seconds,a three-phase short circuit occurs on the feeder1,which changes significantly the Thevenin impedance and voltage seen by the converter.As a result,a variation on the parameters is observed in k T1and k2,as well as in the parameters of k3.During the short-circuit,a current reference transient is applied in0.35seconds.Once again,it can beFig.8.Simulation of power system fault and feeder disconnection.Fig.9.Gain adaptation for grid parameter variation.seen that the parameters converged to a new set of values, since i conv−y m is zero.Further on,at t=0.4the fault is cleared with the disconnection of feeder1.It causes a reduction on the short circuit current from100pu to10pu.It characterizes a large parameter variation and,as a result,the state feedback gainsθconverge to a newθ∗.The convergence is perceived because at t=0.5seconds a transient in the reference current is applied and the error is practically zero resulting in a negligible change in the controller parameters.VI.E XPERIMENTAL R ESULTSA.SetupThe performance and stability of the adaptive current con-troller presented here has been experimentally verified.The controller has been implemented in a TMS320F2812fixed point DSP.The setup has the following characteristics: converter side inductance L c=800μH,capacitorfilter C=15μF,minimum grid side inductance L g1=400μH,the sampling frequency is12kHz and the switching frequency is 6kHz.However,the grid side inductance is unknown because the connection transformer impedance and the short circuit current on the point of connection are unknown.B.Transient ResponseFigure10presents the transient response when the distur-bance rejection is introduced.This shows that the current phase between the reference model output and the converter current is eliminated.In Fig.11the transient response for phase variation on reference current is presented.A fast responseis verified even for a drastic phase variation of180◦.Fig.10.Transient response when the disturbance rejection isincluded.Fig.11.Transient response for phase variation on reference current.VII.C ONCLUSIONThis paper presents a discrete–time adaptive current con-troller for grid connected voltage source inverters with LCL-filter.The adaptive algorithm has provided a good performance in reference tracking as well as in disturbance rejection even under large parametric variation and abrupt changes in the reference,as well as in the voltage at the point of common coupling.The results point out the effectiveness of the the design procedure which is a key factor for the successful implementation of the adaptive controller.The simulations and experimental results demonstrate that the proposed adaptive state-feedback controller for grid con-nected voltage source converter has the capability to guarantee a very good transient and steady-state performance even under a large variation on the grid characteristic.In addition,the grid-connected converter with LCL-filter behaves as chosen reference model,independent on the grid impedance at the point of connection.Even with a large variation of the grid impedance,the current controller presented superior transient performance and stability characteristics.A CKNOWLEDGMENTSThe authors would like to thank the Companhia Estadual de Energia El´e trica(CEEE)and CAPES for thefinancial support.R EFERENCES[1]M.Liserre,R.Teodorescu,and F.Blaabjerg,“Stability of photovoltaicand wind turbine grid-connected inverters for a large set of grid impedance values,”IEEE Transactions on Power Electronics,vol.21, no.1,pp.263–272,Jan.2006.[2] E.Twining and D.G.Holmes,“Grid current regulation of a three-phasevoltage source inverter with an LCL inputfilter,”IEEE Transactions on Power Electronics,vol.18,no.3,pp.888–895,May2003.[3]J.Dannehl,F.W.Fuchs,and S.Hansen,“PWM rectifier with LCL-filterusing different current control structures,”in European Conference on Power Electronics and Applications,2007.EPE07,Sept.2007,pp.1–10.[4]M.Liserre,F.Blaabjerg,and S.Hansen,“Design and control of an LCL-filter-based three-phase active rectifier,”IEEE Transactions on Industry Applications,vol.41,no.5,pp.1281–1291,September/October2005.[5] E.J.Bueno,F.Espinosa,F.J.Rodriguez,J.Urefia,and S.Cobreces,“Current control of voltage source converters connected to the grid through an LCL-filter,”in IEEE35th Annual Power Electronics Spe-cialists Conference,2004.PESC04,vol.1,June2004,pp.68–73. [6] E.Wu and P.W.Lehn,“Digital current control of a voltage sourceconverter with active damping of LCL resonance,”IEEE Transactions on Power Electronics,vol.21,no.5,pp.1364–1373,Sept.2006. [7]V.Blasko and V.Kaura,“A novel control to actively damp resonancein input LCfilter of a three-phase voltage source converter,”IEEE Transactions on Industry Applications,vol.33,no.2,pp.542–550, March/April1997.[8]I.J.Gabe,J.R.Massing,V.F.Montagner,and H.Pinheiro,“Sta-bility analysis of grid-connected voltage source inverters with LCL-filters using partial state feedback,”in European Conference on Power Electronics and Applications,2007.EPE07,Sept.2007,pp.1–10. [9]I.J.Gabe and H.Pinheiro,“Multirate state estimator applied to thecurrent control of PWM-VSI connected to the grid,”in IEEE34th Annual Conference of Industrial Electronics,2008.IECON2008,Nov.2008,pp.2189–2194.[10]M.Ciobotaru,R.Teodorescu,P.Rodriguez,A.Timbus,and F.Blaabjerg,“Online grid impedance estimation for single-phase grid-connected systems using PQ variations,”in IEEE38th Annual Power Electronics Specialists Conference,2007.PESC2007,June2007,pp.2306–2312.[11]M.Liserre,F.Blaabjerg,and R.Teodorescu,“Grid impedance estimationvia excitation of LCL-filter resonance,”IEEE Transactions on Industry Applications,vol.43,no.5,pp.1401–1407,September/October2007.[12]P.C.Loh and D.G.Holmes,“Analysis of multiloop control strategies forLC/CL/LCL-filtered voltage-source and current-source inverters,”IEEE Transactions on Industry Applications,vol.41,no.2,pp.644–654, March/April2005.[13]M.P.Kazmierkowski and L.Malesani,“Current control techniques forthree-phase voltage-source PWM converters:a survey,”IEEE Transac-tions on Industrial Electronics,vol.45,no.5,pp.691–703,Oct.1998.[14]G.Shen,D.Xu,L.Cao,and X.Zhu,“An improved control strategyfor grid-connected voltage source inverters with an LCLfilter,”IEEE Transactions on Power Electronics,vol.23,no.4,pp.1899–1906,July 2008.[15]G.Tao,Adaptive Control Design and Analysis.John Wiley&Sons,2003.[16] D.N.Zmood and D.G.Holmes,“Stationary frame current regulationof PWM inverters with zero steady-state error,”IEEE Transactions on Power Electronics,vol.18,no.3,pp.814–822,May2003.[17]R.Teodorescu,F.Blaabjerg,M.Liserre,and P.C.Loh,“Proportional-resonant controllers andfilters for grid-connected voltage-source con-verters,”IEE Proceedings-Electric Power Applications,vol.153,no.5, pp.750–762,September2006.[18]R.Cardoso,R.F.de Camargo,H.Pinheiro,and H.A.Grundling,“Kalmanfilter based synchronisation methods,”IET Generation,Trans-mission e Distribution,vol.2,no.4,pp.542–555,July2008.[19]R.F.de Camargo and H.Pinheiro,“Synchronisation method for three-phase PWM converters under unbalanced and distorted grid.”。

单相PWM整流器比例谐振控制与前馈补偿控制

单相PWM整流器比例谐振控制与前馈补偿控制

单相PWM整流器比例谐振控制与前馈补偿控制李立;赵葵银;徐昕远;朱建林【摘要】提出了单相PWM整流器比例-谐振控制(PR)与无延迟前馈补偿控制的策略.系统由比例-谐振控制器、快速的相角估计器和无延迟前馈补偿器组成.与传统的PI控制器和多频率比例-谐振电流控制器相比,该比例谐振控制器结构简单,能显著减少控制延迟时间.通过理论分析,提出的用电网电压和电流的估计值与单步预测值来实现的无延迟前馈补偿器,可避免因延时引起的不良影响、测量噪音及补偿过程中产生的电网电压谐波分量.仿真分析与实验结果验证了系统具有较好的稳态性能和更好的抗扰性能.【期刊名称】《电力系统保护与控制》【年(卷),期】2010(038)009【总页数】6页(P75-79,95)【关键词】PWM整流器;比例-谐振控制;前馈补偿器;相角估计器;延迟时间【作者】李立;赵葵银;徐昕远;朱建林【作者单位】湖南工程学院电气信息学院,湖南,湘潭,411101;湖南工程学院电气信息学院,湖南,湘潭,411101;湖南省电力公司长沙电业局,湖南,长沙,410015;湘潭大学,湖南,湘潭,411105【正文语种】中文【中图分类】TM770 引言PWM 整流器具有输入电压电流同相位、可实现单位功率因数、可四象限运行等诸多优点,因而具有广泛的应用前景[1-3]。

目前常用的电流控制方法有PI、滞环控制。

PI控制具有算法简单和可靠性高的特点,且常规的PI控制只能消除直流参考信号的稳态误差,对给定值中的交流分量难以进行无差跟踪[4-8]。

滞环控制具有电路简单、动态响应快的特点,但是开关频率、损耗及控制精度受滞环宽度的影响[4]。

对交流信号而言,比例谐振控制在基波频率处增益无穷大,可以实现系统零稳态误差[7,9]。

本文利用比例谐振控制算法能够在静止坐标系下对交流信号进行无静差调节的优势[10],并考虑比例-谐振(Proportional-resonant -PR)控制算法虽然控制精度很高,但实时性却不够[11],提出一种新的单相PWM整流器的PR控制策略。

2010-PE-07---Effects of Discretization Methods on the Performance of Resonant Controllers

2010-PE-07---Effects of Discretization Methods on the Performance of Resonant Controllers

Effects of Discretization Methods on the Performance of Resonant ControllersAlejandro G.Yepes,Student Member,IEEE,Francisco D.Freijedo,Member,IEEE, Jes´u s Doval-Gandoy,Member,IEEE,´Oscar L´o pez,Member,IEEE,Jano Malvar,Student Member,IEEE,and Pablo Fernandez-Comesa˜n a,Student Member,IEEEAbstract—Resonant controllers have gained significant impor-tance in recent years in multiple applications.Because of their high selectivity,their performance is very dependent on the ac-curacy of the resonant frequency.An exhaustive study about dif-ferent discrete-time implementations is contributed in this paper. Some methods,such as the popular ones based on two integrators, cause that the resonant peaks differ from expected.Such inac-curacies result in significant loss of performance,especially for tracking high-frequency signals,since infinite gain at the expected frequency is not achieved,and therefore,zero steady-state error is not assured.Other discretization techniques are demonstrated to be more reliable.The effect on zeros is also analyzed,establishing the influence of each method on the stability.Finally,the study is extended to the discretization of the schemes with delay compensa-tion,which is also proved to be of great importance in relation with their performance.A single-phase active powerfilter laboratory prototype has been implemented and tested.Experimental results provide a real-time comparison among discretization strategies, which validate the theoretical analysis.The optimum discrete-time implementation alternatives are assessed and summarized.Index Terms—Current control,digital control,power condition-ing,pulsewidth-modulated power converters,Z transforms.N OMENCLATUREVariablesC Capacitance.f Frequency in hertz.G(s)Model in the s domain.G(z)Model in the z domain.H(s)Resonant controller in the s domain.H(z)Resonant controller in the z domain.i Current.K Gain of resonant controller.L Inductance value.m Pulsewidth modulation(PWM)duty cycle. N Number of samples to compensate with com-putational delay compensation.n Highest harmonic to be compensated. Manuscript received September17,2009;revised December29,2009.Date of current version June18,2010.This work was supported by the Spanish Min-istry of Education and Science under Project DPI2009-07004.Recommended for publication by Associate Editor P.Mattavelli.The authors are with the Department of Electronic Technology,University of Vigo,Vigo36200,Spain(e-mail:agyepes@uvigo.es;fdfrei@uvigo.es;jdoval@ uvigo.es;olopez@uvigo.es;janomalvar@uvigo.es;pablofercom@uvigo.es). Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TPEL.2010.2041256R Equivalent series resistance value.R(s)Resonant term in the s domain.R(z)Resonant term in the z domain.T Period.θPhase of grid voltage.V V oltage.ωAngular frequency in radians per second.u(s)Input value.y(s)Output value.Subscripts1Fundamental component.a Actual value(f).c Generic current controller(G).d Degree of freedom in the zero-pole matchingdiscretization method(K).dc Relative to the dc link(V).f Relative to the passive inductivefilter(V,i,L,R,and G).I Equivalent to the double of the integral gainof a proportional+integral(PI)controller indq frame(K).k Relative to the k th harmonic(H,R,K P,andK I).L Relative to the load(i).Lh Relative to the harmonics of the load(i).o Resonant frequency of a continuous resonantterm or resonant controller(f andω).P Equivalent to the double of the proportionalgain of a PI controller in dq frame(K). PCC Relative to the point of common coupling(V).PL Relative to the plant(G).rms Root mean square.s Relative to sampling(f and T).src Relative to the voltage source(V,i,and L). sw Relative to switching(f).T Sum of the gains for every value of harmonicorder k(K P).X Resonant term R or resonant controller Hdiscretized with method X,where X∈{zoh,foh,f,b,t,tp,zpm,imp}.X&Y Resonant term R or resonant controller Himplemented with two discrete integrators,with the direct one discretized with method Xand the feedback one with method Y,whereX,Y∈{zoh,foh,f,b,t,tp,zpm,imp}.0885-8993/$26.00©2010IEEEX−Y Resonant controller H VPI(z),in whichR1(s)is discretized with method X andR2(s)with method Y,where X,Y∈{zoh,foh,f,b,t,tp,zpm,imp}. Superscripts∗Reference value.1Resonant term R of the form s/(s2+ω2o). 2Resonant term R of the form s2/(s2+ω2o).d Including delay compensation(H and R). PR Resonant controller H of the PR type.VPI Resonant controller H of the VPI type. Others∆x Difference between x and its target value(i f).ˆx Estimated value of x(θ1andω1).I.I NTRODUCTIONI N recent years,resonant controllers have gained significantimportance in a wide range of different applications due to their overall good performance.They have been applied with satisfactory results to cases such as distributed power generation systems[1],[2],dynamic voltage regulators[3],[4],wind tur-bines[5],[6],photovoltaic systems[7],[8],fuel cells[9],[10], active rectifiers[11],active powerfilters(APFs)[12]–[17], microgrids[18],and permanent magnet synchronous motors [19].Resonant controllers allow to track sinusoidal references of arbitrary frequencies with zero steady-state error for both single-phase and three-phase applications.An important saving of computational burden and complexity is obtained due to their implementation in stationary frame,avoiding the coordinates transformations,and providing perfect tracking of both positive and negative sequences[1],[13],[14],[20]–[22].Resonant con-trollers in synchronous reference frame(SRF)have been also proposed to control pairs of harmonics simultaneously when no unbalance exist[7],[15]–[17],[22],[23].An essential step in the implementation of resonant digital controllers is the discretization.Because of the narrow band and infinite gain of resonant controllers,they are specially sensitive to this process.Actually,a slight displacement of the resonant poles causes a significant loss of performance.In the case of proportional+resonant(PR)controllers[14],[20]–[22],even for small frequency deviations,the effect of resonant terms becomes minimal,and the PR controller behaves just as a proportional one[14].The resonant regulator proposed in[16]is less sensitive to these variations when cross coupling due to the plant appears in the dq frame,but if these deviations in the resonant poles are present,it does not achieve zero steady-state error either. Furthermore,if selectivity is reduced to increase robustness to frequency variations,undesired frequencies and noise may be amplified.Thus,an accurate peak position is preferable to low selectivity.Therefore,it is of paramount importance to study the effectiveness of the different alternatives of discretization for implementing digital resonant controllers,due to the critical characteristics of their frequency response.As proved in this paper,many of the existing discretization techniques cause a displacement of the poles.This fact results in a deviation of the frequency at which the infinite gain occurs with respect to the expected resonant frequency.This error becomes more significant as the sampling time and the desired peak frequency increase.In practice,it can be stated that most of these discretization methods result in suitable implementations when tracking50/60Hz(fundamental)references and even for low-order harmonics.However,as shown in this paper,some of them do not perform so well in applications in which signals of higher frequencies should be tracked,such as APFs and ac motor drives. This error has special relevance in the case of implementations based on two integrators,since it is a widely employed option mainly due to its simplicity for frequency adaptation[8],[13], [15],[23]–[25].Discretization also has an effect on zeros,modifying their distribution with respect to the continuous transfer function. These discrepancies should not be ignored because they have a direct relation with stability.In fact,resonant controllers are often preferred to be based on the Laplace transform of a cosine function instead of that of a sine function because its zero im-proves stability[13],[19].In a similar way,the zeros mapped by each technique will affect the stability in a different man-ner.Consequently,it is also convenient to establish which are the most adequate techniques from the point of view of phase versus frequency response.However,for large values of the resonance frequency,the computational delay affects the system performance and may cause instability.Therefore,a delay compensation scheme should be implemented[14],[15],[17],[23].It can be per-formed in the continuous domain as proposed in[15].However, the discretization of that scheme leads to several different expressions.A possible implementation in the z domain was posed in[14],but there are other possibilities.Consequently,it should be analyzed how each method affects the effectiveness of the computational delay compensation.This aspect has a significant relevance since it will determine the stability at the resonant frequencies.The study of these effects of the discretization on resonant controllers has not been analyzed in the existing literature. Therefore,it is of paramount importance to analyze how each method affects the performance in relation with these aspects.A single-phase APF laboratory prototype has been built to check the theoretical approaches,because it is an application very suitable for proving the controllers performance when tracking different frequencies,and results can be extrapolated to other single-phase and three-phase applications where a perfect tracking/rejection of references/disturbances is sought through resonant controllers.The paper is organized as follows.Section II presents alterna-tive digital implementations of resonant controllers.The reso-nant peak displacement depending on the discretization method, as well as its influence on stability,is analyzed in Section III. Several discrete-time implementations including delay compen-sation,and a comparison among them,are posed in Section IV. Section V summarizes the performance of the digital imple-mentations in each aspect and establishes the most optimum alternatives depending on the existing requirements.Finally, experimental results of Section VII validate the theoreticalanalysis regarding the effects of discretization on the perfor-mance of resonant controllers.II.D IGITAL I MPLEMENTATIONS OF R ESONANT C ONTROLLERS A.Resonant Controllers in the Continuous DomainA PR controller can be expressed in the s domain as[14],[20]–[22]H PR(s)=K P+K Iss2+ω2o=K P+K I R1(s)(1)withωo being the resonant angular frequency.R1(s)is the resonant term,which has infinite gain at the resonant frequency (f o=ωo/2π).This assures perfect tracking for components rotating at f o when implemented in closed-loop[21].R1(s) is preferred to be the Laplace transform of a cosine function instead of that of a sine function,since the former provides better stability[13],[19].H PR(s)in stationary frame is equivalent to a propor-tional+integral(PI)controller in SRF[21].However,if cross coupling due to the plant is present in the dq frame,unde-sired peaks will appear in the frequencies around f o in closed loop[17].This anomalous behavior worsens even more the per-formance when frequency deviates from its expected value.An alternative resonant regulator,known as vector PI(VPI)con-troller,is proposed in[16]:H VPI(s)=K P s2+K I ss2+ω2o.(2)The VPI controller cancels coupling terms produced when the plant has the form1/(sL f+R f)[16],[17],[23],such as in shunt APFs and ac motor drives,with L f and R f being, respectively,the inductance and the equivalent series resistance of an R–Lfilter.Parameters detuning due to estimation errors in the values of L f and R f has been proved in[17]to have small influence on the performance.H VPI(s)can be decomposed as the sum of two resonant terms,R1(s)and R2(s),as follows:H VPI(s)=K Ps2s2+ω2o+K Iss2+ω2o=K P R2(s)+K I R1(s).(3) Equation(3)permits to discretize R1(s)and R2(s)with dif-ferent methods.In this manner,the most optimum alternative for H VPI(z)will be the combination of the most adequate discrete-time implementation for each resonant term.B.Implementations Based on the Continuous Transfer Function DiscretizationTable I shows the most common discretization methods.The Simpson’s rule approximation has not been included because it transforms a second-order function to a fourth-order one,which is undesirable from an implementation viewpoint[26].The techniques reflected in Table I have been applied to R1(s) and R2(s),leading to the discrete mathematical expressions shown in Table II.T s is the controller sampling period and f s=1/T s is the sampling rate.From Table II,it can be seen thatTABLE IR ELATIONS FOR D ISCRETIZING R1(s)AND R2(s)BY D IFFERENT METHODS the effect of each discretization method on the resonant poles displacement will be equal in both R1(s)and R2(s),since each method leads to the same denominator in both resonant terms. It should be noted that zero-pole matching(ZPM)permits a degree of freedom(K d)to maintain the gain for a specific frequency[26].C.Implementations Based on Two Discrete IntegratorsThe transfer function H PR(s)can be discretized by decom-posing R1(s)in two simple integrators,as shown in Fig.1(a) [13].This structure is considered advantageous when imple-menting frequency adaptation,since no explicit trigonometric functions are needed.Whereas other implementations require the online calculation of cos(ωo T s)terms,in Fig.1schemes the parameterωo appears separately as a simple gain,so it can be modified in real time according to the actual value of the frequency to be controlled.Indeed,it is a common practice to implement this scheme due to the simplicity it permits when frequency adaptation is required[13],[15],[24],[25].An analogous reasoning can be applied to H VPI(s),leading to the block diagram shown in Fig.1(b).Instead of developing an equivalent scheme to the total transfer function H VPI(s), it could be obtained as an individual scheme for implementing each resonant term R1(s)and R2(s)could be obtained,but in this case the former is preferable because of the saving of resources.It has been suggested in[8]to discretize the direct integrator of Fig.1(a)scheme using forward Euler method and the feedback one using the backward Euler method.Additional alternatives of discretization for both integrators have been analyzed in[25], and it was also proposed to use Tustin for both integrators,or to discretize both with backward Euler,adding a one-step delay in the feedback line.Nevertheless,using Tustin for both integrators poses implementation problems due to algebraic loops[25].In this paper,these proposals have been also applied to the block diagram shown in Fig.1(b).Table III shows these three discrete-time implementations of the schemes shown in Fig.1.TABLE IIz -D OMAIN T RANSFER F UNCTIONS O BTAINED BY D ISCRETIZING R 1(s )AND R 2(s )BY D IFFERENT METHODSFig.1.Block diagrams of frequency adaptive resonant controllers (a)H P R (s )and (b)H V P I (s )based on two integrators.It should be noted that H jt&t (z )and H j t (z )are equivalent for both j =PR and j =VPI ,since the Tustin transformation is based on a variable substitution.The same is true for the rest of methods that consist in substituting s as a function of z .However,zero-order hold (ZOH),first-order hold (FOH),and impulse invariant methods applied separately to each integratordo not lead to H j zoh,H j foh ,and H jimp ,respectively.Indeed,to dis-cretize an integrator with ZOH or FOH results in the same way as a forward Euler substitution,while to discretize an integrator with the impulse invariant is equivalent to employ backward Euler.III.I NFLUENCE OF D ISCRETIZATION M ETHODSON R OOTS D ISTRIBUTIONA.Resonant Poles DisplacementThe z domain transfer functions obtained in Section II can be grouped in the sets of Table IV,since some of them present an identical denominator,and therefore,coinciding poles.Fig.2represents the pole locus of the transfer functions in Table IV.Damped resonant controllers do not assure perfect tracking [21];poles must be placed in the unit circumference,which corresponds to a zero damping factor (infinite gain).All discretization techniques apart from A and B lead to undamped poles;the former maps the poles outside of the unit circle,whereas the latter moves them toward the origin,causing a damping factor different from zero,so both methods should be avoided.This behavior finds its explanation in the fact that these two techniques do not map the left half-plane in the s domain to the exact area of the unit circle [26].However,there is an additional issue that should be taken into account.Although groups C ,D ,and E achieve infinite gain,it can be appreciated that,for an identical f o ,their poles are located in different positions of the unit circumference.This fact reveals that there exists a difference between the actual resonant frequency (f a )and f o ,depending on the employed implementation,as also observed in Fig.3(d).Consequently,the infinite gain may not match the frequency of the controller references,causing steady-state error.Fig.3(a)–(c)depicts the error f o −f a in hertz as a function of f o and f s for each group.The poles displacement increases with T s and f o ,with the exception of group E .The slope of the error is also greater as these parameters get higher.Actually,the denominator of group D is a second-order Tay-lor series approximation of group E .This fact explains the in-creasing difference between them as the product ωo T s becomes larger.Some important outcomes from this study should be highlighted.1)The Tustin transformation,which is a typical choice in digital control due to its accuracy in most applications,features the most significant deviation in the resonant frequency.2)The error exhibited by the methods based on two dis-cretized integrators becomes significant even for highTABLE IIID ISCRETE T RANSFERF UNCTIONS H P R (s )AND H V P I (s )O BTAINED BY E MPLOYING T WO D ISCRETIZED INTEGRATORSTABLE IVG ROUPS OF E XPRESSIONS W ITH I DENTICAL P OLES IN THE z DOMAINFig.2.Pole locus of the discretized resonant controllers at f s =10kHz (fundamental to the 17th odd harmonics).sampling frequencies and low-order harmonics.For in-stance,at f s =10kHz,group D exhibits an error of +0.7Hz for the seventh harmonic,which causes a consid-erable gain loss [see Fig.3(d)].When dealing with higher harmonic orders (h ),such as 13and 17,it raises to 4.6and 10.4Hz,respectively,which is unacceptable.3)Group E leads to poles that match the original continuous ones,so the resonant peak always fits the design frequency f o .B.Effects on Zeros DistributionOnce assured infinite gain due to a correct position of the poles,another factor to take into account is the displacement of zeros caused by the discretization.Resonant controllers that be-long to group E have been proved to be more suitable for an op-timum implementation in terms of resonant peak displacement.However,the numerators of these discrete transfer functions are not the same,and they depend on the discretization method.This aspect has a direct relation with stability,so it should not be ignored.On the other hand,although group D methods produce a resonant frequency error,they avoid the calculation of explicit cosine functions when frequency adaptation is needed.This fact may imply an important saving of resources.Therefore,it is also of interest to establish which is the best option of that set.The analysis will be carried out by means of the frequency response.The infinite gain at ωo is given by the poles po-sition,whereas zeros only have a visible impact on the gain at other frequencies.Concerning phase,the mapping of zeros provided by the discretization may affect all the spectrum,in-cluding the phase response near the resonant frequency.Due to the high gain around ωo ,the phase introduced by the reso-nant terms at ω≈ωo will have much more impact on the phase response of the whole controllers than at the rest of the spec-trum [14].Therefore,the influence of discretization on the stabil-ity should be studied mainly by analyzing the phase lag caused at ω≈ωo .1)Displacement of R 1(s )Zeros by Group E Discretiza-tions:Fig.4compares the frequency response of a resonant controller R 1(s ),designed for the seventh harmonic,when dis-cretization methods of group E are employed at f s =10kHz.An almost equivalent magnitude behavior is observed,eventhough R 1imp(z )has a lower attenuation in the extremes,and both R 1tp (z )and R 1foh (z )tend to reduce the gain at high fre-quencies.However,the phase versus frequency plot differs more significantly.From Fig.4,it can be appreciated that R 1tp(z )and R 1foh (z )are the most accurate when comparing with R 1(s ).On thecontrary,the phase lag introduced by R 1zoh (z )and R 1zpm (z )is higher than for the continuous model.This fact is particu-larly critical at ω≈ωo ,even though they also cause delay for higher frequencies.As shown in Fig.4,they introduce a phase lag at f o =350Hz of 6.3◦.For higher values of ωo T s ,it be-comes greater.For instance,if tuned at a resonant frequency of f o =1750Hz with f s =10kHz,the delay is 32◦.There-fore,the implementation of R 1zoh (z )and R 1zpm (z )may lead to instability.On the other hand,R 1tp (z ),R 1foh (z ),and R 1imp(z )accurately reproduce the frequency response at the resonance frequency,maintaining the stability of the continuous controllerat ωo .Fig.4also shows that R 1imp(z )can be considered the most advantageous implementation of R 1(s ),since it maintains the stability at ω≈ωo and introduces less phase lag in open-loop for the rest of the spectrum,thereby allowing for a larger phase margin.Fig.3.Deviation of the resonance frequency of the discretized controller f a from the resonance frequency f o of the continuous controller.(a)Group C transfer functions.(b)Group D transfer functions.(c)Group E transfer functions.(d)Discretized seventh harmonic resonant resonant controller at f s= 10kHz.Fig.4.Bode plot of R1(s)discretized with group E methods for a seventh harmonic resonant controller at f s=10kHz.In any case,the influence of the discretization atω=ωo is not as important as its effect on the stability atω≈ωo,since the gain of R1(z)is much lower at those frequencies.Consequently, this aspect can be neglected unless low sample frequencies, high resonant frequencies,and/or large values of K I/K P are employed.In these cases,it can be taken into account in order to avoid unexpected reductions in the phase margin that could affect the stability,or even to increase its value over the phase margin of the continuous system by means of R1imp(z).2)Displacement of R2(s)Zeros by Group E Discretizations: The frequency response of R2(s)discretizations is shown in Fig.5(a).It can be seen that ZOH produces a phase lag near the resonant frequency that could affect stability.Among the rest of possibilities of group E,the impulse invari-ant method is also quite unfavorable:it provides much less gain after the resonant peak than the rest of the discretizations.This fact causes that the zero phase provided by R2(z)forω>ωo has much less impact on the global transfer function H VPI(z), in comparison to the phase delay introduced by R1(z).In this manner,the phase response of H VPI(z)would show a larger phase lag if R2(s)is discretized with impulse invariant instead of other methods,worsening the stability atω>ωo. Actually,as shown in Fig.5(b),if R2imp(z)is used,the delay of H VPI(z)can become close to−45◦for certain frequencies, which is certainly not negligible.This is illustrated,as an exam-ple,in Fig.5(b),in which Bode plot of H VPI(z)is shown when it is implemented as R1imp(z),and R2(s)is discretized with the different methods.Fixed values of K I and K P have been employed to make the comparison possible.K I=K P R f/L f has been chosen,so the cross coupling due to the plant is can-celed[16],[17],and an arbitrary value of1has been assigned to K P as an example.According to the real parameters of the laboratory prototype,L f=5mH and R f=0.5Ω.If the ra-tio K I/K P is changed,the differences will become more or less notable,but essentially,each method will still affect in the same manner.It should be remarked that the phase responseFig.5.Study of group E discretizations effect on R2(s)zeros.(a)Frequency response of R2(s)discretized with group E methods for a seventh harmonic resonant controller at f s=10kHz.(b)Frequency response of H V P I(z)for a third harmonic resonant controller at f s=10kHz,with R1im p(z),when R2(s) is discretized by each method of group E.K P=1and K I=K P R f/L f, with R f=0.5Ωand L f=5mH.of H VPI(z)atω≈ωo is not modified by R1imp(z),but only by the discretization of R2(s).Fig.5(b)also shows that some implementations introduce less phase at low frequencies than H VPI(s),but the influence of this aspect on the performance can be neglected.In conclusion,any of the discretization methods of group E, with the exception of impulse invariant and ZOH,are adequate for the implementation of R2(z).Actually,the influence of these two methods is so negative that they could easily lead to instability continuous resonant controllers with considerable stability margins.3)Displacement of Zeros by Group D Discretizations: Fig.6(a)shows the Bode plot of R1(s)implemented with setD schemes.R1f&b (z)produces a phase lead in comparisontoFig.6.Frequency response of R1(s)and H V P I(s)implemented with groupD methods for a seventh harmonic resonant controller at f s=10kHz.(a)R1(s).(b)H V P I(s),K P=1,and K I=K P R f/L f,with R f=0.5Ωand L f=5mH.R1(s),whereas R1b&b(z)causes a phase lag.This is also trueatω≈ωo,which are the most critical frequencies.Therefore,R1f&b(z)is preferable to R1b&b(z).On the other hand,as can beappreciated in Fig.6(b),the Bode plot of H VPIf&b(z)and H VPIb&b(z)scarcely differ.They both achieve an accurate reproduction ofH VPI(s)frequency response.Actually,atω≈ωo,they provideexactly the same phase.Consequently,they can be indistinctlyemployed with satisfactory results.IV.D ISCRETIZATION I NFLUENCE ON C OMPUTATIONALD ELAY C OMPENSATIONA.Delay Compensation in the Continuous DomainFor large values ofωo,the delay caused by T s affects the sys-tem performance and may cause instability.Therefore,a delaycompensation scheme should be implemented[14],[15],[17], [23],[27].1)Delay Compensation for H PR(s):Concerning resonant controllers based on the form H PR(s),a proposal was posed in[15]for performing the compensation of the computational delay.The resulting transfer function can be expressed in the s domain asH PR d(s)=K P+K I s cos(ωo NT s)−ωo sin(ωo NT s)s2+ω2o=K P+K I R1d(4) with N being the number of sampling periods to be compen-sated.According to the work of Limongi et al.[23],N=2is the most optimum value.2)Delay Compensation for H VPI(s):Because of H VPI(s) superior stability,it only requires computational delay for much greater resonant frequencies than H PR(s)[16],[17],[23]. Delay compensation could be obtained by selecting K P= cos(ωo NT s)and K I=−ωo sin(ωo NT s).However,this ap-proach would not permit to choose the parameters so as to satisfy K I/K P=R f/L f;thus,it would not cancel the cross coupling terms as proposed in[16]and[17].Therefore,an alternative approach is proposed shortly. R1d(s)and R2d(s)are individually implemented with a de-lay compensation of N samples each,so K P and K I can be still adjusted in order to cancel the plant pole:H VPI d(s)=K P s2cos(ωo NT s)−sωo sin(ωo NT s)s2+ω2o+K I s cos(ωo NT s)−ωo sin(ωo NT s)s2+ω2o=K P R2d+K I R1d.(5)3)Delay Compensation for R1d(s)and R2d(s):If the res-onant terms are decomposed by the use of two integrators,it is possible to perform the delay compensation by means of the block diagrams depicted in Fig.7(a)and(b)for R1d(s)and R2d(s),respectively.Fig.8illustrates the effect of the computational delay com-pensation for both R1d(s)and R2d(s),setting f o=350Hz and f s=10kHz as an example.As N increases,the180◦phase shift at f o rises,compensating the phase lag that would be caused by the delay.B.Discrete-Time Implementations of Delay Compensation SchemesAs stated in the previous section,the delay compensation should be implemented for each resonant term separately.For this reason,it is convenient to study how each discretization method affects the effectiveness of the delay compensation for R1d(z)and R2d(z)individually.Effects on groups E and D implementations,due to their superior performance,are ana-lyzed.Tables V and VI reflect the discrete transfer functions obtained by the application of these methods to R1d(s)andR2d(s),respectively.R1df&b (z)and R1db&b(z)result of apply-ing the corresponding discretization transforms to theschemeFig.7.Implementations of(a)R1d(s)and(b)R2d(s)based on twointegrators.Fig.8.Frequency response of(a)R1d(s)and(b)R2d(s)for different valuesof N;f o=350Hz and f s=10kHz.shown in Fig.7(a).On the other hand,R2df&b(z)and R2db&b(z) are obtained by discretizing the integrators shown in Fig.7(b).Substituting N=0in Tables V and VI leads to the expres-sions of Tables II and III,respectively.It can be also noted that。

比例谐振控制器在MMCHVDC控制中的仿真研究_张建坡

比例谐振控制器在MMCHVDC控制中的仿真研究_张建坡
(North China Electric Power University), Baoding 071001, Hebei Province, China;
2. Zhuzhou National Engineering Research Center of Converters Co., Ltd., Zhuzhou 412000, Hunan Province, China)
为了克服传统双 dq-PI 控制带来的不利影响, 本 文 提 出 一 种 基 于 坐 标 系 下 的 比 例 谐 振 (proportion plus resonant,PR)控制策略。此控制策 略采用能够对正弦量实现无静差控制的 PR 电流调 节器,直接在静止坐标系下对正负序电流进行 统一控制,避免了电流在双 dq 同步速旋转坐标系 中的正、负序分量分解过程,从而消除了电流控制 环延时,提高了并网型逆变器在不对称故障下的动 态控制性能。
1 MMC-HVDC 电路模型
图 1 为 MMC-HVDC 中单侧系统的等效电路 图,以 a 相为例,桥臂中的 Ra1、Ra2、La1、La2 分别 代表 a 相上下桥臂器件的等值损耗电阻和桥臂电
ia1 等效交流系统
usa isa RX LX o usb isb
usc isc
ia2
2 MMC-HVDC 数学模型研究
由图 2 单相等值电路,在 abc 三相坐标系下,
文章编号:0258-8013 (2013) 21-0053-10 中图分类号:TM 721 文献标志码:A 学科分类号:470·40
比例谐振控制器在 MMC-HVDC 控制中的仿真研究
张建坡 1,赵成勇 1,敬华兵 2
(1.新能源电力系统国家重点实验室(华北电力大学),河北省 保定市 071001; 2.株洲变流技术国家工程研究中心有限公司,湖南省 株洲市 412000)

proportional-integral-derivative

proportional-integral-derivative

proportional-integral-derivativeA continuous process is one in which the output is a continuous flow. Examples are a chemical process, a refining process for gasoline, or a paper machine with continuous output of paper onto rolls. Process control for these continuous processes cannot be accomplished fast enough by PLC on-off control. Furthermore, analog PLC control is also not effective or fast enough by PLC on-off control. Furthermore, analog PLC control is also not effective or fast enough. The control system most often used in continuous processes is PID (proportional-integral-derivative) control. PID control can be accomplished by mechanical, pneumatic, hydraulic, or electronic control systems as well as by PLCs. Many medium-size PLCs and all large PLCs have PID control functions, which are able to accomplish process control effectively. In this chapter, we discuss the basic principles of PID control. We then explain the effectiveness of PID control by using typical process response curves and show some typical loop control and PID functions. Loop and PID control are designations used interchangeably by different manufacturers. Actually, some loop controls are not strictly the PID type. However, assume they are the same.PID PrinciplesPID (proportional-integral-derivative) is an effective control system for continuous processes that performs two control tasks. First, PID control keeps the output at a set level even though varying process parameters may tend to cause the output to vary from the desired set point. Second, PID promptly and accurately changes the process level from one set point level to another set point level. For background, we briefly discuss the characteristics of each of the PID control components: proportional, integral, and derivative.Proportional control, also known as ratio control, is a control system that corrects the deviation of a process from the set level back toward the set point. The correction is proportional to the amount of error. For example, suppose that we have a set point of 575 cubic feet per minute (CFM) in an airflow system. If the flow rises to 580 CFM, a corrective signal is applied to the controlling air vent damper to reduce the flow back to 575 CFM. If the flow somehow rises to 585 CFM, twice the deviation from set point, a corrective signal of four times the magnitude would be applied for correction. The larger corrective signal theoretically gives a faster return to 575 CFM. In actuality, the fast correction is not precise. You return to a new set point at the end of the correction, for example, 576.5 CFM, not 575 CPM. Proportional control does not usually work effectively by itself, resulting in an offset error.To return the flow to the original set point, integral control, also known as reset control, is added. Note that integral control cannot be used by itself. Remember, with proportional control only, we had an output error from our original set point. We ended up at 576.5 CFM, not 575 CFM. Integral control senses the product of the error, 1.5 CFM, and the time the error has persisted. A signal is developed from this product. Integral control then uses this product signal to return to the original set point. An integral control signal can be used in conjunction with the proportional corrective signal. In the controller, the added integral signal reduces the error signal that caused the output deviation from the set point. Therefore, over a period of time, the process deviation from our original 575 CFM is reduced to minimum. However, this correction takes a relatively long period of time.FIGURE 23-1 Block Diagram of a Typical PID ControllerTo speed up the return to the process control, point, derivative control is added to the proportional-integral system. Derivative control, also known as rate control, produces a corrective signal based on the rate of change of the signal. The faster the change from the set point, the larger the corrective signal. The derivative signal is added to the proportional-integral system. This gives us faster action than the proportional-integral system signal alone.A typical PID control system is shown in block diagram form in figure 23-1. This configuration is the commonly used parallel type. The controller output signal of figure 23-1 is utilized through a control system to return the process variable to the set point.An illustration of a system using PID control is shown in figure 23-2. In this system, we need a precise oil output flow rate. The flow rate is controlled by pump motor speed. The pump motor speed is controlled through a control panel consisting of a variable-speed drive. In turn, the drive's speed control output is controlled by an electronic controller. The electronic controller output to the drive is determined by two factors. The first factor is the set point determined by a dial setting (or equivalent device). Second, a flow sensor feeds back the actual output flow rate to the electronic controller. The controller compares the set point and the actual flow. If they differ for some reason, a corrective signal change is sent to the motor controller. The motor controller changes motor speed accordingly by changing the voltage applied to the motor. For example, if the output oil flow rate goes below the set point, a signal to speed up the motor is sent. The controller then uses PID control to make the correction promptly and accurately to return to the set point flow. If the dial is changed to a new setting, the function of the PID system is to reach the new set point as quickly and accurately as possible.FIGURE 23-2 General Control System Diagram—Hydraulic PumpTypical Continuous Process Control CurvesTo illustrate some of the possible system response curves for process control systems, we will use the electromechanical system shown in figure 23-3. By response curves, in this example, we mean output position versus time. The curves to be shown are for various types of control, including PID. Figure 23-3 shows a control system with a feedback loop, which can be PID. The dial is set to a position in degrees, and the output device is to take the position set on the dial. The output is to follow quickly and accurately any change from one dial setting to another.FIGURE 23-3 Position Indicator with PID ControlFurthermore, the output position should not drift out of position over a period of time. Another factor is that the indicator can have two different weights, depending on the application. These are 5 pounds and 20 pounds. Obviously, the output drive will tend to operate more slowly for 20 pounds than for 5 pounds, unless a proper PID control is set up to compensate for weight differences.For illustration we very quickly turn the dial from 0 degrees to 108 degrees at 3 seconds after time base 0. Ideally, the position indicator should instantaneously reach 108 degrees, as shown in figure 23-4. Obviously, this does not happen in actual practice.Figure 23-5 shows five possible curves for different types of control. A is an idealized movement but takes 4 seconds. B undershoots or overshoots the mark. C shows cyclic response and reaches an angular point near the set position but oscillates for a few seconds before reaching the proper position. D shows damped response and reaches the new position exponentially but takes a long time. E reaches the new position but continually oscillates about the final setting. None of these curves shows an acceptable control characteristic for accurate and prompt operation.By comparison, PID control obtains the most ideal response possible—not perfect, but the best we can do. A curve for this control is shown in figure 23-6.FIGURE 23-4 Ideal Position Control Positioning CurveFIGURE 23-5 Typical Response CurvesFIGURE 23-6 Ideal PID Position ControlPID ModulesPLCs often come equipped with PID modules, used to process data obtained by feedback circuitry. Most such modules contain their own microprocessor. Since the algorithms needed to generate the PID functions are rather complex, the PID microprocessor relieves the CPU of having to carry out these time-consuming operations.To understand the PID module, refer to figure 23-7. The PLC sends a set-point signal to the PID module. The module is made up of three elements: the proportional, integral, and derivative circuits. The proportional circuit creates an output signal proportional to the difference between the measurement taken and the setpoint entered in the PLC. The integral circuit produces an output proportional to the length and amount of time the error signal is present. The derivative circuit creates an output signal proportional to the rate of change of the error signal.FIGURE 23-7 Block diagram of PID ModuleThe input transducer generates an output signal from the process being controlled and feeds the measured value to the PID module. The difference between the set point coming from the PLC and the measured value coming from the input transducer is the error signal. Some sort of correcting device, such as a motor control, valve control, or amplifier, takes the error signal and uses it to control the correction sent to the process being controlled.。

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Proportional-resonant controllers and filters for grid-connected voltage-source convertersR.Teodorescu,F.Blaabjerg,M.Liserre and P.C.LohAbstract:The recently introduced proportional-resonant (PR)controllers and filters,and their suitability for current/voltage control of grid-connected converters,are ing the PR controllers,the converter reference tracking performance can be enhanced and previously known shortcomings associated with conventional PI controllers can be alleviated.These shortcomings include steady-state errors in single-phase systems and the need for synchronous d –q transformation in three-phase systems.Based on similar control theory,PR filters can also be used for generating the harmonic command reference precisely in an active power filter,especially for single-phase systems,where d –q transformation theory is not directly applicable.Another advantage associated with the PR controllers and filters is the possibility of implementing selective harmonic compensation without requiring excessive computational resources.Given these advantages and the belief that PR control will find wide-ranging applications in grid-interfaced converters,PR control theory is revised in detail with a number of practical cases that have been implemented previously,described clearly to give a comprehensive reference on PR control and filtering.1IntroductionOver the years,power converters of various topologies have found wide application in numerous grid-interfaced systems,including distributed power generation with renewable energy sources (RES)like wind,hydro and solar energy,microgrid power conditioners and active power filters.Most of these systems include a grid-connected voltage-source converter whose functionality is to synchro-nise and transfer the variable produced power over to the grid.Another feature of the adopted converter is that it is usually pulse-width modulated (PWM)at a high switching frequency and is either current-or voltage-controlled using a selected linear or nonlinear control algorithm.The deciding criterion when selecting the appropriate control scheme usually involves an optimal tradeoff between cost,complexity and waveform quality needed for meeting (for example)new power quality standards for distributed generation in low-voltage grids,like IEEE-1547in the USA and IEC61727in Europe at a commercially favour-able cost.With the above-mentioned objective in view while evaluating previously reported control schemes,the general conclusion is that most controllers with precise reference tracking are either overburdened by complex computationalrequirements or have high parametric sensitivity (sometimes both).On the other hand,simple linear proportional–integral (PI)controllers are prone to known drawbacks,including the presenceof steady-state error in the stationary frame and the need to decouple phase dependency in three-phase systems although they are relatively easy to imple-ment [1].Exploring the simplicity of PI controllers and toimprove their overall performance,many variations have been proposed in the literature including the addition of a grid voltage feedforward path,multiple-state feedback and increasing the proportional gain.Generally,these variations can expand the PI controller bandwidth but,unfortunately,they also push the systems towards their stability limits.Another disadvantage associated with the modified PIcontrollers is the possibility of distorting the line current caused by background harmonics introduced along the feedforward path if the grid voltage is distorted.This distortion can in turn trigger LC resonance especially when a LCL filter is used at the converter AC output for filtering switching current ripple [2,3].Alternatively,for three-phase systems,synchronous frame PI control with voltage feedforward can be used,but it usually requires multiple frame transformations,and can be difficult to implement using a low-cost fixed-point digital signal processor (DSP).Overcoming the computa-tional burden and still achieving virtually similar frequency response characteristics as a synchronous frame PI [6].With the introducedE-mail:fbl@iet.aau.dkR.Teodorescu and F.Blaabjerg are with the Drives,Institute of Energy Technology,straede 101,9220Aalborg East,DenmarkM.Liserre is with the Department of Engineering,Polytechnic of Bari,70125-Bari,P.C.Loh is with the School of Electrical and Technological University,Nanyang Avenue,r The Institution of Engineering and IEE Proceedings online no.20060008doi:10.1049/ip-epa:20060008Paper first received 10th January and in PI 缺点改进方法丗电压前馈丆多状态反馈丆增大增益。

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