Power-Flow Control and Stability Enhancement of Four Parallel-Operated Offshore Wind Farms Using a L

1190IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010Power-Flow Control and Stability Enhancement of Four Parallel-Operated Offshore Wind Farms Using a Line-Commutated HVDC LinkLi Wang, Senior Member, IEEE, Kuo-Hua Wang, Wei-Jen Lee, Fellow, IEEE, and Zhe Chen, Senior Member, IEEEAbstract—This paper presents an effective control scheme using a line-commutated high-voltage direct-current (HVDC) link with a designed rectifier current regulator (RCR) to simultaneously perform both power-fluctuation mitigation and damping improvement of four parallel-operated 80-MW offshore wind farms delivering generated power to a large utility grid. The proposed RCR of the HVDC link is designed by using modal control theory to contribute adequate damping to the studied four offshore wind farms under various wind speeds. A systematic analysis using a frequency-domain approach based on eigenvalue analysis and a time-domain scheme based on nonlinear model simulations is performed to demonstrate the effectiveness of the proposed control scheme. It can be concluded from the simulation results that the proposed HVDC link combined with the designed RCR can not only render adequate damping characteristics to the studied offshore wind farms under various wind speeds but also effectively mitigate power fluctuations of the offshore wind farms under wind-speed disturbance conditions. Index Terms—Eigenvalue analysis, high-voltage direct-current (HVDC), induction generator (IG), modal control theory, nonlinear model simulations, offshore wind farms, rectifier current regulator (RCR).P.u. quantities of stiffness and mutual damping. Input p.u. mechanical torque of IG. P.u. electromagnetic torque of IG. P.u. synchronous angular speed. Eigenvalue and wind speed. Firing angle of converter and extinction angle of inverter. Gains of PID controller. Washout time constant of PID controller. Pitch angle, tip speed ratio, and power coefficient of wind turbine. Subscripts - and -axis quantities. Stator- and rotor-winding quantities of IG. Quantities of hub and IG. Quantities of step-up transformer of offshore wind farm and transmission line connected to grid. Quantities of rectifier of HVDC link. Quantities of inverter of HVDC link. Quantities of HVDC line and base. 0, Quantities of the th blade of wind turbine. Quantities of initial operating point and grid. Quantities of maximum and minimum. Quantities of reference.NOMENCLATURE General Differential operator with respect to time . Per unit (p.u.) quantities of ac (dc) voltage and current. P.u. quantities of resistance and reactance. P.u. excitation capacitance bank of wind IG. P.u. quantities of angular speed and rotor angle. P.u. quantities of inertia and self damping.I. INTRODUCTIONManuscript received January 13, 2009; revised April 19, 2009. First published December 11, 2009; current version published March 24, 2010. This work was supported by the National Science Council of Taiwan under Grants NSC 96-2221-E-006-313-MY3 and NSC 97-2918-I-006-010. Paper no. TPWRD-00952-2008. L. Wang and K.-H. Wang are with the Department of Electrical Engineering, National Cheng Kung University, Tainan City 70101, Taiwan, R.O.C. (e-mail: liwang@.tw). W.-J. Lee is with the Energy Systems Research Center (ESRC), The University of Texas at Arlington (UTA), Arlington, TX 76013 USA (e-mail: wlee@uta. edu). Z. Chen is with the Institute of Energy Technology (IET), Aalborg University, Aalborg, Denmark (e-mail: zch@iet.aau.dk). Digital Object Identifier 10.1109/TPWRD.2009.2034915AN offshore wind farm that is located a distance of less than 25 km away from seashore consists of several paralleloperated wind-turbine generators (WTGs). The use of several wind induction generators (IGs) and doubly-fed induction generators (DFIGs) connected directly to a power grid is the simplest way of running an offshore wind farm because wind IGs have the inherent advantages of cost effectiveness, less maintenance, and robustness, etc. However, operation of an offshore wind farm with a group of wind IGs requires large reactive power for magnetization, and the absorbed reactive power of the offshore wind farm can severely affect the voltage magnitude of the bus to which the wind farms are connected under0885-8977/$26.00 © 2010 IEEEWANG et al.: POWER-FLOW CONTROL AND STABILITY ENHANCEMENT OF FOUR PARALLEL-OPERATED OFFSHORE WIND FARM1191random wind-speed variations. This paper proposes an effective control strategy using a line-commutated high-voltage direct-current (HVDC) link joined with a modal-control designed rectifier current regulator (RCR) to perform both reactive-power compensation and stability enhancement of parallel-operated IG-based offshore wind farms and control the generated active power delivered to the onshore substation. The use of an HVDC link for the offshore wind farms has several advantages such as fast active-power modulation, effective reactive-power compensation, and less voltage drop on an onshore substation when comparing with the use of conventional long-distance ac transmission cables that contain higher inductive reactance and cause larger voltage drop. To evaluate the performance of current controllers operated in the control loops of an HVDC link, the characteristics of using different types of current regulator were compared [1]. A novel current controller that was designed based on a linearized ac/dc system model and a pole-placement technique for an HVDC link was presented in [2]. The influence of the control loops of an HVDC link on dynamic stability of an HVDC-HVAC system was discussed in [3]. The design and implementation of an ac-voltage dependent current order limiter at the Pacific HVDC Intertie was presented in [4] to demonstrate the consistent benefit of the proposed control scheme on enhancing stability and dynamic performance of the studied system. The potential of the fast growing offshore and onshore wind farms as well as the quick development of larger-capacity higher-efficiency WTGs in the whole world today can be obviously anticipated when an HVDC link is utilized to effectively control the generated power of the wind farms [5]. A time-domain model of an HVDC link using voltage-source converters (VSCs) for real-time simulations and its application to a wind energy conversion system were presented in [6]. An HVDC link combined with a capacitor commutated converter (CCC) model that was suitable for power flow and transient stability studies was proposed in [7]. The exploitation of an offshore wind farm was addressed in [8], and the proposed multiterminal VSC-HVDC system connected at the ac terminals of the WTGs enabled optimal acquisition and aggregation of wind power. The development of a linear continuous-time state model for analyzing small-signal dynamics of an HVDC transmission system was presented in [9], and a small-signal state-space model of the CIGRE benchmark HVDC transmission system was employed. The modeling and control design of a VSC-based HVDC using 12-pulse threelevel converter topology was proposed in [10], and eigenvalue analysis, controller design and transient simulations were performed. A linear time-invariant small-signal dynamic model for the main circuit of an HVDC link under synchronous rotating d-q reference frame by means of sampled-data modeling approach was proposed in [11], and the linearized model was validated by time-domain simulations. The operation characteristics of a wind farm that was made up of several IG-based WTGs and modeled by an equivalent large IG incorporated VSC-HVDC were analyzed in [12]. Characteristics of a VSC-based HVDC link, an HVAC cable interconnection, and a synchronous generator under a faulted condition were compared, and the analyzed results showed that theVSC-based HVDC link demonstrated the ability to provide fault ride-through capability for the studied wind farm consisting of simple IG-based WTGs [13]. An improved model for the transient energy functions (TEFs) of integrated ac/dc power systems involved the omission of dc control dynamics was presented in [14]. The control requirements of a DFIG-based wind farm connected to a grid through a conventional thyristor-based HVDC link were investigated in [15]. The performance of a large IG-based offshore wind farm connected to a long-distance weak ac grid was studied, and the simulation results showed that the proposed HVDC link was able to supply the variable active power of the offshore wind farm to the weak grid and keep the ac voltage fluctuations at the point of common coupling (PCC) at an acceptable level [16]. A large 200-MW offshore wind farm consisting of 100 individual 2-MW WTGs connected to the grid through a multiterminal HVDC link with 25 VSCs was presented in [17]. A large 200-MW offshore wind farm consisting of 100 individual 2-MW WTGs connected to the grid through a multiterminal HVDC link with 25 current source inverters (CSIs)s was studied in [18]. A detailed technical-economic analysis of three transmission strategies (150-kV ac, 400-kV ac, and VSC-HVDC) on benefits and drawbacks of onshore grid connection of three offshore wind farms (100 MW, 200 MW, and 500 MW) was evaluated and compared in [19]. The control system for a large offshore wind farm with an HVDC link using line-commutated converter (LCC) connection to the main onshore network using an aggregate system under operational and faulted conditions was proposed in [20]. A solution for integration of large DFIG-based offshore wind farms with a common collection bus controlled by a static compensator (STATCOM) into the main onshore grid using linecommutated HVDC link was presented in [21]. The control paradigm using the grid frequency control to regulate the rectifier firing angle or dc-link current to control the power flow of an offshore wind farm connected with line-commutated HVDC link was examined in [22]. A frequency controller in the converter to increase the ride through capability of the VSC-HVDC-supplied industrial system was proposed in [23] to exploit the inertia energy of rotating masses in case of voltage disturbances. Three different frequency controllers and their effects on the voltagedisturbance ride-through capability of a VSC-HVDC-supplied industrial system were proposed in [24]. A new concept applicable to large power converters consisting of two series-connected twelve-pulse groups and a new type of converter control applicable to multilevel HVDC schemes with two or more 12-pulse groups per terminal were shown in [25]. Two types of FACTS devices, STATCOM and VSC-HVDC system, were presented in [26] to offer a realistic alternative to conventional network reinforcement to solve a range of operational problems in power systems. This paper presents damping controller design of rectifier, steady-state eigenvalue analysis and transient time-domain simulations of four parallel-operated IG-based offshore wind farms connected to an onshore substation through an HVDC link. For steady-state analysis, system eigenvalues, eigenvalue sensitivity, and design of rectifier current regulator (RCR) of the HVDC link are performed. For time-domain simulations,1192IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010connected to the common ac bus through an excitation capacitor bank and a step-up transformer with an equivalent impedance . The HVDC link consisting of an ac-to-dc conof verter (or rectifier), a T-equivalent dc line, and a dc-to-ac inverter delivers the generated power of the four offshore wind farms to the onshore power grid through a step-down transformer and an ac transmission line. The equivalent impedance of in Fig. 1 is used to represent the combined impedance of the step-down transformer and the ac transmission line. The employed system parameters are listed in Appendix for conciseness and the mathematical models for the subsystems shown in Fig. 1 are described as below. The equations in the following subsections are expressed in p.u. or MKS quantities except that the time variable is in seconds. A. Wind Speed Model The wind speed is modeled as the algebraic sum of base wind speed, gust wind speed, ramp wind speed, and noise wind speed [27]. The base wind speed can be expressed by (1) where is a constant. It is assumed that is always present in the study of wind turbine systems. The gust wind speed can be described by (2)Fig. 1. Configuration of the studied four parallel-operated offshore wind farms with a line-commutated HVDC link.where (3)transient responses of the studied offshore wind farms with and without the designed RCR subject to different wind-speed disturbances are also carried out. This paper is organized as follows. Section II introduces the configuration and the employed mathematical models for the offshore wind farms with an HVDC link in this paper. Section III demonstrates the design procedure for the RCR of the HVDC link using pole-placement technique. Section IV describes the results of eigenvalue analysis under various wind speeds and eigenvalue sensitivity with respect to the parameters of the designed RCR. Section V compares transient responses of the studied offshore wind farm with and without the designed RCR under wind-speed disturbance conditions. Specific important conclusions of this paper are drawn in Section VI. II. CONFIGURATION OF THE STUDIED SYSTEM Fig. 1 shows the configuration of the studied four 80-MW offshore wind farms connected to an onshore power grid through an HVDC link. The four 80-MW offshore wind farms are rep, , , and ) resented by four equivalent wind IGs ( connected to a common ac bus. Each equivalent 80-MW IG that is driven by an equivalent variable-speed wind turbine through an equivalent gearbox (GB) is obtained by aggregating forty 2-MW IGs together. The output of each equivalent 80-MW IG is, , and are the period, the starting and where time, and the peak of the gust wind speed, respectively. The gust wind is the usual (1-cosine) gust used in wind studies. The ramp wind speed can be depicted by (4) where (5) , , and are the maximum, the and where starting time, and the maximum time of the ramp wind speed, respectively. The noise wind speed can be expressed by (6) where , is a random variable with uniform probability density on the interval (7)WANG et al.: POWER-FLOW CONTROL AND STABILITY ENHANCEMENT OF FOUR PARALLEL-OPERATED OFFSHORE WIND FARM1193is the spectral density function, is the surface drag coefficient, is the turbulence scale, and is the mean speed of wind and at the reference height. Various researchers used –2.0 rad/s to obtain excellent results. According to the above four wind speeds, the employed wind speed model in this paper can be defined as (8) B. Wind Turbine Model The mechanical power produced by a wind turbine is given by (9) where is the mechanical power in W, is the air density , is the blade impact area in , is the wind in is the power coefficient velocity in m/s as depicted in (8), and [28] that can be expressed byFig. 2. Simplified equivalent mass-spring-damper model of a three-blade wind turbine coupled to the shaft of an induction generator.(10) in which (11) (12) and are, respectively, the blade angular velocity in where rad/s and blade radius in m, is the tip speed ratio, is the blade are the constant coefficients pitch angle in degrees, and for power coefficient . C. Mass-Spring-Damper Model Fig. 2 shows the simplified equivalent mass-spring-damper model of a three-blade wind turbine coupled to the rotor of the studied wind IG [29]. The masses of gearbox and IG are combined together. The p.u. mechanical equations of each blade are described byFig. 3. D-q axis equivalent circuit of the studied IG.where is the initial p.u. angular speed of the hub. The p.u. mechanical-torque equations of the IG are determined by(17) (18) where is the initial p.u. angular speed of the IG, and is the p.u. electromagnetic torque of the IG and it can be expressed by [30] (19) D. Induction Generator Model Fig. 3 shows the axis equivalent-circuit of an IG with an excitation capacitor bank under a synchronously rotating reference frame [30]–[32]. The p.u. voltage-current equations of the studied IG can be described by(13) (14) where and are, respectively, the p.u. angular speed and angle is the input p.u. mechanical displacement of each mass, torque from wind, is the p.u. self damping coefficient, is the p.u. mutual damping coefficient, is the p.u. spring constant or is the initial p.u. angular speed of the th blade, stiffness, , 2, and 3 refers to the quantities of blades 1, 2, and 3, and respectively. The p.u. mechanical equations of the hub are given by(20) (21) (15) (16) (22)1194IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010(23) is the p.u. mutual reactance between stator and rotor where and ( and windings, ) are the p.u. self (leakage) reactances of stator and the rotor windings of the studied IG, respectively. E. Excitation Capacitor Bank Model The p.u. voltage-current equations of the excitation capacitor bank shown in Fig. 3 can be expressed by (24) (25) and are, respectively, the p.u. - and -axis exwhere and are the p.u. citation-capacitor currents while and -axis currents flowing through the step-up transformer, respectively. F. Step-Up Transformer, AC Line, and Power Grid Models The p.u. voltage-current equations from the output terminals of the inverter to the power grid through the step-up transformer and the ac transmission line are given by (26) (27) and are respectively the p.u. - and -axis line where and are, respectively, the p.u. - and currents, -axis grid voltages, and and are the p.u. - and -axis output voltages of the inverter, respectively. G. Line-Commutated HVDC Link Model The line-commutated HVDC link model consists of an ac-to-dc converter, a dc line, and a dc-to-ac inverter [33]–[38]. The base values for the ac and dc quantities should be properly selected such that the p.u. values of dc quantities remain unchanged when they are converted to the synchronous reference frame of the ac system [34], [36], [38]. The p.u. output dc voltage and current of the rectifier can be properly converted with reference to the common reference frame of the -axis of the ac system according to the phasor diagram shown in Fig. 4 [36]–[38] (28) (29) (30) (31) where is the angle by which -axis lags the -axis as shown in Fig. 4. Since the reference direction of the -axis with respect to the -axis is arbitrary, the operation of the converter can is properly chosen. Under be easily expressed when this particular selection for the reference frame, we have (32) - and The p.u. expressed byFig. 4. Phasor diagram for transformation of d0 q and d 0 qquantities.(33) (34) (35) -axis components shown in Fig. 4 can be(36) (37) The dc line is represented by a T-equivalent circuit that has two placed on both identical series impedances of sides of a lumped charging capacitor . The p.u. voltage-current equations of the rectifier and inverter can be written as, respectively, [36]–[38] (38) (39) is the delay angle of the converter, is the extincwhere and are respectively the tion angle of the inverter, p.u. commutation choke reactance of the converter and inverter, and are, respectively, the p.u. ac-side voltage of the converter and inverter , and . Figs. 5 and 6 show the block diagrams of the rectifier-current regulator (RCR) of the converter and the inverter-current regulator (ICR) of the inverter [36]–[38], respectively. The p.u. equations for the RCR and the ICR can be expressed by, respectively (40) (41) is generated by the where the p.u. damping control signal PID controller that will be designed in the next section. III. DESIGN OF A PID RCR USING MODAL CONTROL THEORY This section presents a unified approach based on modal control theory to design a PID RCR for the proposed HVDC link. To have a clear observation of the damping effect contributed by the proposed PID RCR, the eigenvalues to be assigned onWANG et al.: POWER-FLOW CONTROL AND STABILITY ENHANCEMENT OF FOUR PARALLEL-OPERATED OFFSHORE WIND FARM1195TABLE I EIGENVALUES (rad/s) OF THE STUDIED SYSTEM UNDER WIND SPEED OF 12 m/sFig. 5. Block diagram of the rectifier-current regulator (RCR) of the converter including the designed PID RCR.denotes exactly assigned eigenvalues Fig. 6. Block diagram of the ICR of the inverter.the complex plane are properly selected. The design procedures and results are given as below [36]–[38]. A. Linearized System The nonlinear system equations developed in the previous section are first linearized around a nominal operating point to obtain a set of linearized dynamic equations of the form:Fig. 7. Block diagram of the studied system with the designed damping controller.(42) where is the state vector, is the output vector, is the exis the disturbance input ternal or compensated input vector, are all constant matrices of apvector while , , , and propriate dimensions. To design a damping controller for the proposed RCR, the variation term and the external input in (42) are properly neglected by letting . The state can be partitioned into four substate vectors as vector , where , , , and are referred to the state vectors of the four wind IGs, the excitation capacitor banks and the transmission line, the mechanical systems of four wind turbines, and the HVDC link, respectively. Since the wind speed of the studied four offshore wind farms seldom reaches the rated wind speed of 15 m/s of the WTGs, of 12 m/s is properly selected as the operating point for the PID RCR design in the next subsection. The eigenvalues of the studied four offshore wind farms with the proposed HVDC link of 12 m/s are listed in the second column of Table I. under , or 4 The eigenvalues listed in Table I with represent the repeated eigenvalues or modes of the studied four offshore wind farms since the studied four offshore wind farms have identical WTG-IG sets and parameters. An examination of these eigenvalues listed in Table I reveals that the damping and can be improved by adding a damping of both controller to the HVDC link. The PID RCR will be designed by using modal control theory in the next subsection. B. Design of a PID RCR Fig. 5 showed the control block diagram of the RCR of the converter including the designed PID RCR. It is seen that the PID damping controller employs as a feedback signal to generate a damping control signal in order that the damping characteristics of the poorly damped modes listed in Table I can was given be improved. The block diagram for determining in Fig. 5, where the reference values for active power of four IGs , , , and ) can be determined from the rotor ( speeds of the four wind IGs. Hence, the output signal in (42) is (43) and (44) is the input vector. The transfer function PID RCR in domain is given by of the proposed(45)1196IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010TABLE II A PART OF THE EIGENVALUES (rad/s) OF THE CLOSED-LOOP SYSTEM WITH THE DESIGNED PID RCR UNDER DIFFERENT WIND SPEEDSdenotes the operating condition at which the PID RCR is designedwhere is the time constant of a washout term, and , , and are gains of the damping controller. The four unknowns for the PID damping controller can be determined by using modal control theory and the first step is to obtain the state equations in domain by taking Laplace transformation from (42) to (44). The second step is to derive an algebraic equation of the feedback system using eigenvalue analysis in domain and the unknown parameters can be solved. The input signal in domain can be expressed by (46) Combining (42), (43), (45), and (46), we have (47) The block diagram the studied system with the designed damping controller is given in Fig. 7. The characteristic equation of the closed-loop system with the designed PID damping controller is given by (48) Since the studied system with the proposed PID RCR constitutes a single-input single-output (SISO) system, (48) is a scalar equation. The parameters of the PID controller can be determined by substituting two pairs of prespecified complex-conjugated eigenvalues corresponding to the assigned poles into (48). Four simultaneous algebraic equations with the four unknowns, , , , and , can then be solved to obtain a unique solution. The design results are presented as follows. Eigenvalues of four offshore wind farms with the HVDC linkIV. STEADY-STATE ANALYSIS This section examines the effectiveness of the proposed HVDC link joined with the designed PID RCR on dynamic-stability enhancement of the studied four offshore wind farms. The variations of the designed PID RCR’s parameters on the closed-loop eigenvalues are also carried out using relative sensitivity coefficients (RSCs). A. Dynamic Stability Under Various Wind Speeds Table II lists the calculated eigenvalues of the studied four offshore wind farms with the designed PID RCR when wind speed increases from 4 m/s (cut-in wind speed) to 24 m/s (cut-off wind speed). The eigenvalue results listed in Table II are analyzed as below according to different wind-speed ranges. The root-loci plots of these eigenvalues when wind speed varies from 4 to 24 m/s are also shown in Fig. 8. , the damping of both and (a) When gets worse when wind speed becomes lower. All system modes are located on the left half of the complex plane. Some mechanical modes are close to the imaginary axis of the complex plane but they are nearly fixed on the complex plane. , the damping of initially drops (b) When of 14 m/s and then increases to a higher value at at of 15 m/s. When , the damping of gets worse as wind speed becomes higher. The damping gets better before reaches 18 m/s. When is of becomes worse. higher than 18 m/s, the damping of Again, all system eigenvalues are positioned on the left half of the complex plane and some mechanical modes are nearly fixed on the complex plane. B. Eigenvalue Sensitivity of PID RCR’s Parameters Whenever there is a small change in one of the system parameter , the system matrix in (48) and the associated system eigenvalues will vary accordingly. The eigenvalue sensitivity can be determined by (49) where is the eigenvector of associated with the -th eigenvalue . Since the parameter in (49) may range from a very small value to very large one, it is more meaningful toPrespecified eigenvaluesParameters of the PID RCR. The system eigenvalues of the studied four offshore wind farms with the designed PID RCR are listed in the third column of Table I. It can be obviously found from Table I that the eigenand have been exactly assigned values of both modes on desired locations of the complex plane.WANG et al.: POWER-FLOW CONTROL AND STABILITY ENHANCEMENT OF FOUR PARALLEL-OPERATED OFFSHORE WIND FARM1197Fig. 8. Root loci of the eigenvalues listed in Table II when the wind speed is varied from 4 m/s to 24 m/s. (a) 3 ; (b) 3 ; (c) 3 ; (d) 3 ; (e) 3 ; (f) 3 ; (g) 3 ; (h) 3 . TABLE III RSC OF THE CLOSED-LOOP EIGENVALUES WITH RESPECT TO THE DESIGNED PID RCR’S FOUR PARAMETERSdenotes the value that is less than 10determine the fractional variation of the parameter. The RSC is defined by [39] (50) Table III lists the RSCs of the closed-loop eigenvalues with , , , and respect to the four PID RCR’s parameters ( ). It is clearly found from the RSC results listed in Table III that only are more sensitive to the varaitions of , , and while all RSCs are very small. Hence, a small variation of four parameters of the designed PID RCR will not cause severe variations on the closed-loop eigenvalues. Theclosed-loop system can maintain stable operation subject to a small variation of the PID RCR’s parameters. C. Summary of the Analyzed Results The major constraints for selecting the assigned eigenvalues in this paper are analyzed as below. (a) The obtained parameters of the PID RCR should be reasonable. For example, the time constant of the washout term must be positive and the gains of the PID RCR should be as small as possible. (b) The eigenvalues of the closed-loop system including the designed PID RCR must be completely located on the。