Optimal Control for Reactive Power Wind Farms Consisting of VSCF DFIG Wind Turbine Generator Systems

An Optimal Control Strategy for Reactive Power in Wind Farms Consisting of VSCF DFIG WindTurbine Generator SystemsJingmei Fang, Gengyin Li, Xuefeng Liang, Ming ZhouState Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources(North China Electric Power University)Beijing 102206, P.R.Chinaclearvic@, ligy@, liangxuefeng@, zhouming@Abstract—Doubly-fed Induction Generator (DFIG) is a kind of variable-speed constant-frequency (VSCF) wind generator (WG) which can output reactive power when not working in the constant power factor mode and be used as a reactive power supply for wind farm. In this paper, an optimal control strategy for reactive power in wind farms consisting of DFIG is proposed by combining the reactive power compensation ability of both DFIG and reactive power compensation device (RPCD). The control target is minimum power loss and optimal power flow (OPF) of wind farm. First, the reactive power characteristic of DFIG is detailed analyzed. Then the control strategy which includes three modules is presented based on the “Fix-place and Quantitative” thought, and the modules of which are Wind Farm Data Process Module (WFDPM), Wind Farm Data Acquisition Module (WFDAM) and Wind Farm Control Module (WFCM). As the core part of the strategy, WFDPM applies Sensitivity Analysis (SA) and improved genetic algorithm (IGA) to optimize the control strategy. At last, a wind farm consisting of twenty DFIGs of 1.5MW is built in DIgSILENT/PowerFactory, and the results data show that the optimal reactive power control strategy proposed in this paper can effectively achieve the minimum power loss and OPF.Keywords-wind farm; DFIG; reactive power optimisation control; sensitivity analysis; improved genetic algorithm; optimal power flowI.I NTRODUCTIONWind power is a kind of intermittent energy source, which makes the output power of wind farm unstable and random. Moreover, the random change of active power in wind farm makes the reactive power consumption of equipments and transmission cables changes as well, so as to affect the voltage stability and power flow distribution of the wind farm and local grid [1]. Therefore, research on the optimal control strategy of reactive power compensation in wind farm which aims to achieve optimal power flow (OPF) has become a research focus at home and abroad [2].As the development of wind power generation technology, variable-speed constant-frequency (VSCF) wind turbine generator system (WTGS) such as doubly-fed induction generator (DFIG) has gradually become the mainstream model type in newly set-up wind farms. Such type of WTGS can achieve active and reactive power decoupling control, absorb or output reactive power according to the requirement of system operation plan and control strategy, so that they can be applied in the voltage control of wind farms [3]. However, the DFIG WTGS in domestic wind farm usually operates with constant power factor, and its fast and flexible reactive power regulation ability has not been fully used. So it is urgent to study how to make this capability of DFIG WTGS combined with all kinds of reactive power compensation device (RPCD) to participate in regulating the reactive power and voltage of grid.While currently, little papers about reactive power control strategy in wind farm consisting of VSCF DFIG WTGS have compositely considered the reactive power compensation ability of both RPCD and wind generator (WG), and most of them focus on how to allocate the reactive power among all the WGs or how to take advantage of RPCD individually to compensate the reactive power in wind farm. According to the reactive power limit of DFIG, [4] proposed a reactive power nearby compensation strategy to the local consumers in wind farm, which mainly discussed the reactive power distribution rules between WGs in wind farm and between the stator-side and grid-side converters of a single WG, but the compensation ability of RPCD is ignored. Reference [5] presented a reactive power compensation method which includes local compensation on the WG terminal and centralized compensation on the substation of wind farm using shunt capacitors, while it didn’t think over the reactive power output capability of WG.In this paper, on the basis of taking full account of all the reactive power regulation measures including both reactive power output ability of DFIG and various RPCD, an optimal control strategy for reactive power in wind farms consisting of VSCF DFIG WTGS with the aim of minimizing the active power loss and achieving OPF is proposed. Issues about optimization belong to the multi-constraint non-linear combinatorial optimization research scope. Simply it is an optimal problem aiming to achieve minimum reactive power loss and making the solution vectors to meet various constraints through the control of wind farm. In recent years,This work was supported in part by National Eleven-Five Scientific and Technical Supporting Program of China (2008BAA14B05), National Natural Science Foundation of China (50877027), and “111” Project (B08013).genetic algorithm (GA) is widely applied for researches about reactive power optimization of power system, for it has extraordinary capability of solving discrete variables and owns good robustness [6]. In this paper, the reactive power characteristic of DFIG is discussed firstly. Then establishing an active power loss/reactive power sensitivity model of a single wind farm and solves the model for identifying the compensation place. Moreover this paper uses an improved GA for calculating the compensation capacities of WGs and RPCDs on the compensation spots. At last, the effectiveness of this optimal control strategy is validated in the 20*1.5MW wind farm model built in DIgSILENT/PowerFactory. The results show that the reactive power optimization control strategy for wind farms consisting of VSCF DFIG WTGS can effectively reduce the active power loss in wind farm, maintain the voltage of each bus within the required range and achieve the OPF.II.R EACTIVE P OWER C HARACTERISTIC OF DFIGA. Wind Generation System Model of DFIG WTGSThe model of DFIG WTGS is composed of wind turbine, doubly-fed induction generator, AC-DC-AC inverter and control system. The detailed structural diagram of windgeneration system is shown in Fig.1.Figure 1. Diagram of the structure of wind generation system of DFIGWTGSThe vector control of rotor-side converter realizes the active power and reactive power decoupling control of the stator of generator. The rotor-side converter provides excitation current component and torque current component to rotor current, which are used for controlling reactive power of stator and achieving the maximum wind capture respectively. While the vector control of grid-side converter plays a role in maintaining the voltage of DC-capacitor in a fixed value and regulating the reactive power which flows to grid through converter. B. The Reactive Power Limit of DFIG WTGS1) The reactive power elements of DFIG WTGSThe power relationship of DFIG wind generation system isshown in Fig.2, where P M is the mechanical power which is produced by wind turbine and transported to generator; P s and Q s are the active power and reactive power from stator; P c and Q c are the active power and reactive power from grid-side converter; P r and Q r are the active power and reactive power from rotor-side converter; P E and Q E are the active power andreactive power transported from generator to grid.Figure 2. The power relationship of DFIGUnder the condition of neglecting the power loss of stator, rotor and transformer, the relationship among P M , P s , P r , P E can be expressed by (1).r s M E P P P P −== (1)And ignoring the rotor winding resistance r r , the following expressions are obtained.⎪⎪⎩⎪⎪⎨⎧−=−=E r E s P s s P P s P 111 (2) The dc-link between two converters makes only activepower exchanges happen to the converters, and reactive power Q c and Q r are decoupled.According to the direction of power flow defined in Fig.1, the reactive power flowing into grid from generator is expressed as (3).c s E Q Q Q −= (3)As a result, discussions about reactive power limits transported from generator to grid can be put into two parts, one is the upper and lower reactive power limits Q s max and Q s min of stator, the other is upper and lower reactive power limits Q c max and Q c min of grid-side converter.2) The reactive power limitsIn this paper, study on the reactive power constraint of stator in DFIG takes three constraints into account, which are stator current constraint, rotor-side converter current constraint and grid-side converter capacity constraint.a) Stator current constraintAccording to the standard positive direction of motor and excluding the zero-axis component, the voltage and flux equations of DFIG based on per-unit system in the stator rotating coordinate system DQ can be established, and ignoring the stator winding transient procedure, (4) and (5) are obtained.⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡ΨΨ⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡r s r s r s I I D C B A U U 11110000 (4) ⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡ΨΨr s r s I I C B B A 2222(5) where[]T qs ds s U U U =, []T qr dr r U U U =, []T qr ds s ΨΨ=Ψ,[]TqrdrrΨΨ=Ψ, []T qs ds s I I I =, []T qr dr r I I I =,and⎥⎦⎤⎢⎣⎡−=01101A , ⎥⎦⎤⎢⎣⎡−=001s s B , ⎥⎦⎤⎢⎣⎡−=s s r r C 001,⎥⎦⎤⎢⎣⎡=r r r r D 001, ⎥⎦⎤⎢⎣⎡−=s s X X A 002, ⎥⎦⎤⎢⎣⎡=m mX X B 002,⎥⎦⎤⎢⎣⎡=r r X XC 002where U ds , U qs , U dr , U qr are the d -axis and q -axis componentsof stator and rotor winding voltage; ψds , ψqs , ψdr and ψqr are the d -axis and q -axis components of stator and rotor synthetic flux; r s and r r are the winding resistance of stator and rotor; X m is the exciting reactance; X sr is the stator leakage reactance; X rr is the rotor leakage reactance value equivalent to the stator-side; s is the slip ratio; p is the differential operator. In addition, X s =X sr +X m , X r =X rr +X m .Set the synchronous rotating reference frame d -axis in the same direction of stator synthetic flux, then ψqs =0. Neglect r r and suppose U s =U ds +j U qs , then (6) is got.⎪⎩⎪⎨⎧==s qsds U U U 0 (6) According to the active and reactive power equations ofstator-side, the following equations are gots s qs s s dsP U I Q U I ⎧=⎪⎨=−⎪⎩ (7) So the first constraint condition is (8).2max222s s s s I U Q P ≤+ (8) b) Rotor-side converter current constraintThe active power and reactive power of stator-side can be expressed by rotor-side current, as shown in (9).ss m qrs s m dr s s s U P X I X U X I Q U X ⎧⎪=⎪⎪⎨⎛⎞−⎪⎜⎟=−⎪⎜⎟⎪⎝⎠⎩(9)Then the second constraint condition is (10).2max 22222r sm s s s s s I X X U X U Q P ≤⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛++ (10) c) The reactive power constraint of grid-side converterGrid-side converter usually operates at the unit power factor state, and the choice of capacity of which is based on the maximum slip active power. In fact, the wind turbine runs at variable speed as the wind speed changes, so the converter cannot always operate at the maximum slip active power status. When the wind turbine is running at low speed and the grid-side converter is in the under-power state, in which the power handling capability is not fully played, if the grid has requirement of reactive power, making the grid-side converter operate in the non-unit power factor mode is admissible.Assume the maximum designed power of grid-side converter is S c max , its ability of outputting or absorbing reactive power can identified as (11).2max 22c c c S Q P ≤+ (11)P c equals P r when ignoring the transformer loss, the upperand lower reactive power constraint condition of grid-side converter is2max 2max 11⎟⎠⎞⎜⎝⎛−−≤≤⎟⎠⎞⎜⎝⎛−−−E c c E c P s s S Q P s s S (12) According to the analysis above, the reactive power limitsof DFIG can be concluded as (13).max min E E E Q Q Q ≤≤ (13)where2min 2max s E s s E s U Q X U Q X ⎧⎪=−⎪⎪⎨⎪⎪=−⎪⎩III. T HE O PTIMAL C ONTROL S TRATEGY OF R EACTIVEP OWER IN W IND F ARM C ONSISTING OF DFIG A. Reactive Power Control Strategy of DFIGDFIG has a certain capability of absorbing or outputting reactive power, as a result of which it can be used as a reactive power supply to stabilize the voltage of point of interconnection (POI) as well as used as an active power supply to afford electrical energy to grid.Currently, the reactive power control strategies of DFIG WTGS include constant power factor control, constant terminal voltage control and optimal compensation control (OCC) [7].1)Constant power factor controlWhen small-scale wind farm is integrated into grid, the output change of wind farm has little influence that can be ignored to grid, and the WTGS usually operates in the constant power factor mode. Actually the power factor is often set to one and no reactive power exchanges between WTGS and grid, the reference reactive power Q ref=0.2)Constant terminal voltage controlWhen the scale of wind farm is large and the wind farm accesses to the weak power grid, the wind farm output changes as the wind speed fluctuates and it may cause the voltage fluctuation of integration point of wind farm, even seriously leads to the voltage limit violation and threatens the continuous operation of grid-connected WTGS. However, constant terminal voltage control takes the voltage of integration point as its control target, maintaining the voltage stability through changing the reactive power output.3)Optimal compensation controlIn order to make full use of reactive power regulation ability of wind farm that connected to the strong power grid, an optimal control mode for dynamic reactive power, which takes account of the reactive power limit of WTGS and the actual operation mode of power system, is proposed with the control target of satisfying the reactive power requirement of load near to the integration point and absorbing excess reactive power of grid.As a result, the reactive power control mode of all the DFIGs in this paper is OCC, in which the reactive power compensation capability of DFIG can be fully used. If the terminal voltage or power factor of WTGS is within the required range, the dispatch center can send any command to WTGS as long as Q iref is smaller than the upper reactive power limit Q i max of WTGS and larger than the lower reactive power limit Q i min of WTGS (Q i max and Q i min are calculated according to the actual operation situation of WTGS), realizing the role of WTGS as a reactive power supply, as well as reducing the operation costs of wind farm. In this paper, every DFIG is viewed as a dynamic RPCD which possesses continuously reactive power regulation ability, participating in the reactive power optimization task together with RPCD.B.The Optimal Control Strategy for Reactive Power in WindFarms Consisting of DFIGAn optimal control strategy called “Fix-place and Quantitative (FQ) Control Strategy” (FQCS) is proposed in this paper. “Fix-place” means the best compensation places are determined ahead, for not all the equipments are needed to supply the reactive power. “Quantitative” means the compensation capacity is identified ahead as well.The control strategy is composed of three modules, which are wind farm data process module (WFDPM), wind farm data acquisition module (WFDAM) and wind farm control module (WFCM). WFDAM is used for recording the correlative data of wind farm, such as parameters and operation mode of each WTGS, wind speed and power flow distribution of wind farm and so on. WFDAM is the data exchange part of the strategy. WFDPM plays the role of allocating the reference reactive power from dispatch center, deciding the place and the capacity of reactive power compensation, aim to achieve minimum loss and OPF. It is the core part of the strategy. WFCM is used for sending command signals to selected WTGS or RPCD. It is the executive part of the strategy. The diagram of control strategy is shown in Fig.3.Process(WFDPM)1+2<0DatabaseWind Farm Monitor CenterReactive Power Compensationneedreactivepower fromwind farm)Signal2RecollectingData...Collecting Data (minute level)Figure 3. Schematic diagram of the optimal control strategy for reactivepower in wind farms consisting of DFIGWFDAM is in charge of collecting related data in wind farm for regular internals (minute level) and recording them in database. When the voltage of POI fluctuates and need the wind farm to supply reactive power, the dispatch center will send a signal to WFDAM, which includes the required reactive power (Q req) and the event emergency value kT0 (i.e. tolerable waiting time, in units of s). The WFDAM decide neither to execute data collection operation nor to provide latest data in database. Assume the data acquisition time of WFDAM is T1, the total time of transfer data back and forth is T2. If T1+T2<kT0, WFDAM will start its data collection task by using its remote monitoring system (the signal is “Signal2” as show in Fig.3); If T1+T2>kT0, WFDAM will transfer the latest minute level data to WFDPM (the signal is “Signal1” as show in Fig.3).After WFDPM has received the current data of wind farm (by “Signal 1”), it begins to calculate the reactive power support ability of entire wind farm and feedback theinformation to dispatch center. Then the dispatch center sends the value of Q ref to WFDPM, and WFDPM starts to operate again. First, choose the best compensation place by using sensitivity analysis (SA), then “fix-place” has been realized; second, calculate the reactive power compensation capacity of every compensation place by improved genetic algorithm (IGA), then “quantitative” is achieved. After the optimal calculation, WFDPM transfers the results (Q iref ) to WFCM, and WFCM starts to send command signals (Q c and Q g ) to the corresponding WTGS or RPCD. The equipments run following the command, finally, the POI acquire the needed reactive power, the power loss of wind farm is least and the power flow distribution is best.IV. A CHIEVEMENT OF O PTIMAL C ONTROL S TRATEGY The core content of optimal control strategy of reactive power in wind farm consisting of DFIG in this paper is the FQ thought, which will be realized through combination of SA and IGA. The first step is to establish the optimal mathematical model of the entire wind farm.A. Mathematical Model of the Reactive Power Optimization of Wind Farm 1) Objective function()21min max11sin cos min ∑∑∑===⎟⎟⎠⎞⎜⎜⎝⎛−Δ++=Ni i i iNj ij ij ij ij j N i i U U U k B G U U F θθ(14) The control target of the optimal control strategy is theminimum power loss. In the target function, U i or U j is the voltage per-unit value of node i or j , G ij and B ij are the conductance and susceptance between node i and j , N is the number of all the nodes and k is the penalty function factor. ΔU i equals 0 when U i min ≤U i ≤U i max (U i min is the minimum value of U i , U i max is the maximum value of U i ), ΔU i equals (U i -U i max ) when U i >U i max and ΔU i equals (U i min -U i ) when U i <U i min . 2) Constraint conditions()()⎪⎪⎩⎪⎪⎨⎧−==−++==−∑∑==N j ij ij ij ij j i i Li Ci GiN j ij ij ij ij j i i Li Gi B G U U Q Q Q Q B G U U P P P 11cos sin sin cos θθθθ(15) max min Ci Ci Ci Q Q Q ≤≤ (16) max min Gi Gi Gi Q Q Q ≤≤ (17)max min i i i U U U ≤≤ (18)In these constraint conditions, P Gi , P Li , Q Gi , Q Ci , Q Li represent active power output of DFIG, active power load, reactive power output of DFIG, reactive power output of RPCD and reactive power load. Q Gi min , Q Gi max , Q Ci min , Q Ci max are the reactive power lower limit of DFIG, upper limit of DFIG, lower limit of RPCD and upper limit of RPCD. U i min and U i max are the lower and upper voltage fluctuation limit of node i .B. Sensitivity AnalysisFirst calculate the sensitivity of system loss to the reactive power of node. Second, choose some of the nodes which have high sensitivity for reactive power compensation. Then the search space of optimization algorithm can be limited to the most effective areas, which can effectively reduce the calculation time and system loss.The active loss of wind farm is()∑∑∑===+==Nj ij ij ij ijjN i iN i iLoss B GU U P P 111sin cos θθ (19)The sensitivity of wind farm loss to the change of active and reactive power of nodes can be obtained according to (15) and (20), as shown in (21).()⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡∂∂∂∂=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡∂∂∂∂⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡⋅∂∂∂∂⋅∂∂∂∂=⎥⎦⎤⎢⎢⎢⎢⎣⎡∂∂∂∂−U U P P J U P P U Q U Q U P U PQ P P P Loss Loss TLoss Loss i i i i i Loss i Loss θθθθ111(20) where J is the Jacobian matrix of power flow equation, and⎪⎪⎩⎪⎪⎨⎧=∂∂−=∂∂∑∑==Nj ij ij j Loss N j ij ij j i LossG U UP G U U P 11cos 2sin 2θθθ (21) Large sensitivity means large power loss control ability,and has much value for the target of minimum power loss of entire system. Adjusting the control variables according to the descending order of the magnitude of sensitivity, not only can effectively reduce the power loss, but has great significance for avoiding the system shock caused by control simultaneously. C. Improved Genetic AlgorithmGA is widely applied in reactive power optimization issues of power system due to it has extraordinary advantages in solving the multivariable, nonlinear, discontinuous and multi-constraint problems [8]. This paper gives certain improvements to the traditional GA.1) Improvement for the selection of initial populationIn order to achieve the global optimal solution, the initial population should be as distributed as possible in the solution space. Standard GA generates the initial solution by predetermination and stochastic method, which may leads to the uneven distribution of initial solution and then affects the performance of the algorithm. In this paper, the “uniform distribution and random selection” principle is used for the generation of the initial solution matrix, as shown in (22).()min min max i i i i X X X r X +−⋅= (22)where r is a random figure which meets the standard normal distribution.2) Improvement of codeBinary code is used in traditional GA, the individual of which will be a very long string of code. So the computation is large and the search performance is bad due to the large search space. However, the application of real-coded gene in GA has much more advantages compared with binary code. For example, the omission of the encoding and decoding process has improved the efficiency; there is no precision loss compared with discrete binary code; it is free to use different genetic operators and so on. Therefore, the real-coded GA is applied in this paper.3) Fitness functionIn the early stages during the running of GA, there may be only a few individuals which have higher fitness than others. Premature convergence may occur in GA if determine the number of genetic individuals by using common method, which will lead to relatively better individuals have high percentage in the population of next generation and a local optimal solution to become the final answer. While in the later stages, the average fitness of all the individuals is close to the fitness of the best individual. In a word, the evolutionary process will be stagnancy due to the few differences between the individuals and it eventually becomes a random selection process, which will result in failure search of certain key areas.In order to solve the issues above, a horizontal-displacement linear transformation of fitness is applied as show in (23).B AF F +=' (23)()()⎪⎪⎩⎪⎪⎨⎧−≤−−>−=max min minmax min max22F F F F F F F F F F F F A aver aver averaver aver aver (24)()()()⎪⎪⎩⎪⎪⎨⎧−≤−⋅−−>−−⋅=max min minmin max min max max 222F F F F F F F F F F F F F F F B aver aver aver aver aver aver aver (25)where F aver , F max and F min are the average value, maximumvalue and minimum value of fitness.4) Self-adaptive crossover and mutation operatorsChanging the value of crossover probability P c and mutation probability P m adaptively according to the specific situation of individual, and dividing the evolutionary process into two different stages: the progressive stage and mutation stage. In the progressive stage, enhance the crossover and weaken the mutation; in the mutation stage, enhance the mutation and weaken the crossover. The two stages can be expressed by the following equations.⎪⎩⎪⎨⎧<≥−−−=aver ij c aver ij c c c c F F P F F F F P P P P max ,max max ,minmax min max max (26) ⎪⎩⎪⎨⎧<≥−−−=aver ij m aver ij m m m m F F P F F F F P P P P max ,max max ,minmax min max max (27) where P c max , P c min , P m max , P m min are the maximum value of P c , minimum value of P c , maximum value of P m and minimum value of P m respectively. And F ij,max is the larger fitness of two individuals i and j , which will crossover.V.T HE E XAMPLES FOR V ERIFYING THE E FFECTIVENESS OFTHE S TRATEGYTo verify the effectiveness of the proposed strategy, in this paper, a small wind farm consisting of twenty DFIGs of 1.5MW is built in DIgSILENT/PowerFactory. This wind farm is composed of twenty DFIG WTGSs, twenty step-up transformers of 1.6MVA (transformation ratio is 20kV/0.69kV) and a main transformer of 80MVA (transformation ratio is 220kV/20kV). The DFIGs are placed in three rows, the voltage of which is stepped up to 20kV by step-up transformers, and then be collected to the main transformer of 220kV though three voltage lines of 20kV. The electric diagram of the windfarm is shown in Fig.4.Figure 4. The electric diagram of the wind farmThe wind farm model in this paper has forty-two nodes. Five of them will be selected to be the compensation place. For all the twenty DFIGs are controlled in OCC mode, they can supply reactive power with RPCD to compensate the needed reactive power of wind farm or POI. First the power loss/reactive power sensitivity model of wind farm is analyzed by programming calculation before the compensation. According to the value of sensitivity, choose node No.6, No.9 and No.16 as the reactive power compensation place by WTGS, and node No.14 and No.20 as the reactive power compensation places by SVC, which is a kind of RPCD that can be adjusted continuously. The voltage range of each node, the reactive power limits of node No.6, No.9 and No.16, andthe reactive power compensation range of node No.14 and No.20 are shown in Table I.TABLE I. T HE L IMITS OF THE V OLTAGE OF E ACH N ODE AND THE REACTIVE P OWER C OMPENSATION L IMITS OF RPCD AND DFIGLimitU i(pu) RPCD (MVar) DFIG (MVar) i=1,3…41 i=2,4…42No.14 No.20 No.6 No.9 No.16Lower limit 0.95 0.97 0 0-1.6-1.6-1.6Upper limit 1.05 1.07 20 201.61.61.6In this paper, the wind speed is represented by active power output of WTGS (%). The voltages, active power and reactive power of part of the nodes before and after the optimization are shown in Table II and Table III when the output is 50% and 100% respectively.TABLE II. T HE P ARAMETER V ALUES O F P ART OF THE N ODES B EFORE A NDA FTER O PTIMIZATION (THE A CTIVE P OWER O UTPUT I S 50%)Node No.Before Optimization After OptimizationU i(pu)P i (MW)Q i(MVar)U i(pu)P i (MW)Q i (MVar)1 1.007 0.750 -0.514 1.001 0.75 -0.632 6 1.009 0.744 -0.478 1.024 0.748 0.419 10 0.998 0.745 -0.399 1.001 0.743 -0.127 14 0.987 0.746 -0.07 1.003 0.744 10.340 16 1.006 0.745 -0.321 1.012 0.742 0.306 19 1.001 0.75 -0.224 0.999 0.749 -0.275 28 0.997 0.746 -0.074 1.002 0.747 -0.001 36 0.999 0.738 -0.476 1.006 0.748 -0.379 38 0.996 0.746 -0.056 1.003 0.748 -0.003 42 0.984 14.525 -6.844 1.000 14.611 -5.772 The power loss of entire wind farm beforethe optimization (MW)0.475The power loss of entire wind farm afterthe optimization (MW)0.389From the data of the Table II, it can be seen that the power loss is reduced by about 18.1% after the optimization when the output is 50%. While the data from the Table III show that the power loss is decreased by 20.2% after the optimization when the output is 100%. The compare between the two situation shows that the power loss is much less than the situation when there is no “Fix-place and Quantitative” reactive power compensation in the wind farm. And the voltage of all the nodes are within their voltage limits, no evident voltage fluctuation happens. In this paper, DFIG WTGS has fully showed its ability of supplying reactive power to wind farm, and all the results show that the optimal reactive power control strategy of wind farm proposed in this paper is effective and useful for achieving the minimum power loss and OPF.VI.CONCLUSIONDFIG can absorb or output reactive power within limits toTABLE III. T HE P ARAMETER V ALUES OF P ART OF THE N ODES B EFORE ANDA FTER O PTIMIZATION (THE A CTIVE P OWER O UTPUT I S 100%)NodeNo.Before Optimization After Optimization U i (pu)P i (MW)Q i (MVar)U i(pu)P i (MW)Q i (MVar)1 1.006 1.500 -0.908 1.001 1.500 -1.002 6 1.017 1.479 -0.892 1.028 1.496 0.119 10 1.02 1.481 -0.730 1.001 1.492 -0.942 14 0.96 1.483 -0.083 1.012 1.489 10.340 16 1.003 1.482 -0.585 1.010 1.491 0.216 19 1.002 1.500 -0.345 0.999 1.498 -0.498 28 0.991 1.483 -0.092 0.998 1.493 -0.002 36 0.999 1.456 -0.791 1.012 1.486 -0.179 38 0.993 1.483 -0.056 0.998 1.495 -0.003 42 0.986 28.546 -12.381 1.002 28.839 -10.124 The power loss of entire wind farm beforethe optimization (MW) 1.454The power loss of entire wind farm after theoptimization (MW) 1.161participate in the voltage and power flow regulation of wind farms. 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