# Adaptive Parameter Estimation for Static Var Generators Based on Wind Speed Fluctuation of Wind Farms

Authors: Yonghui Nie; He Wang; Lei Gao; Chunying Wu; Meng Xi
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

The emergence of flexible AC transmission technology provides a new technical means for ensuring the reliable grid connection and stable operation of wind farms. Among them, the static reactive power generator has a fast response speed, which can accurately compensate for the reactive power of the wind farm and improve the power factor; this is widely used in wind farms. To obtain accurate static var generator (SVG) parameters to meet the reliability requirements of a power system, we propose an adaptive estimation method that considers the wind speed fluctuation of wind farms. First, analyzing the dynamic SVG characteristics allowed us to establish a mathematical model. Then, the corresponding relationship between the sensitivity values of the parameters to be identified and the fluctuating wind speed was established, and low and high wind speed models were constructed. Finally, for accurate estimation considering wind speed fluctuation, the parameter initial values are obtained by combining the low wind speed and high wind speed model identification parameters, and we introduce the multimode hybrid estimation of the SVG parameters, providing a new method for accurately identifying the SVG model parameters. The simulation results of the parameter estimation demonstrate the accuracy and stability of the proposed method.


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## Body

## 1. Introduction

Reactive power compensation is essential in wind farms to achieve regional voltage stability and wind power accommodation. The rapid development of new power transmission technologies based on flexible AC transmission system (FACTS) equipment has provided a new way to ensure reliable grid connection and the stable operation of wind farms [1]. Flexible AC transmission equipment includes static var compensators (SVC), static var generators (SVG), and unified power flow controllers (UPFC). An SVG is also known as a static var compensator (STATCOM), which is a dynamic reactive power compensation device based on a self-commutated power semiconductor bridge converter. Owing to their wide operating range and fast adjustment speed, SVGs are widely used in wind farms to compensate for reactive power and to improve the voltage quality at the grid connection point. The accuracy of the SVG parameters determines the reliability of the power system and affects the dispatching operations of wind farms [2–4]. Therefore, research regarding accurate SVG parameter estimation has important theoretical and practical implications.In parameter identification or model verification, different observables have different observabilities to the system dynamics. Choosing the observables improves parameter identification accuracy. The existing observation selection methods can be roughly divided into [5]: structural observability analysis, practical observability analysis, and observability analysis based on sensitivity. Because the observability analysis method based on sensitivity is simple and has high computational efficiency, it is suitable for excitation systems with complex structures and nonlinear links, such as saturation, and is widely used in the selection strategy of model parameter identification observation quantity. There is a close relationship between the accuracy of parameter identification and parameter sensitivity, but the trajectory sensitivity is closely related to the disturbance. The dynamic excitation may differ depending on the location and intensity of the disturbance. The observability of the parameters varied with the different observed quantities under the same disturbance. Therefore, when identifying the parameters of the static reactive power generator, it is necessary to select the appropriate observation quantity according to the specific disturbance for parameter identification. The literature [6] has made a good attempt in this respect. The wind speed variation disturbance is set in this study, and the active power and reactive power of the wind turbine are taken as observation quantities to study the observability of the controller parameters. However, the strategy for selecting observation quantity under different wind speed disturbances is not presented in this paper. The literature [7] established the corresponding relationship between the observed quantity and sensitivity and made a quantitative comparison to analyze the influence of the variation in disturbance quantity on the model parameter identification accuracy. Based on literature, three aspects need to be considered for wind power grid-connected system SVG modeling [8]: (1) the influence of the random characteristics of wind farms on the sensitivity values of the SVG model parameters, and (2) constructing the change law of the random characteristics of wind farms for the sensitivity values of SVG model parameters, and (3) establishing the mapping relationship between the SVG parameter group and the random characteristics of the wind farm. After considering these, the parameters of the SVG device identified under random wind speed conditions will be close to the real dynamic characteristics while satisfying the project requirements.For nonlinear identification modeling, current parameter identification methods mostly adopt the time-domain and optimization methods. However, the model of a static reactive power generator is nonlinear [9], and parameter identification is generally conducted via an optimization method. Theoretically, the optimization methods can be roughly divided into gradient, random, and simulation evolution methods. The simulated evolution method is an adaptive optimization method obtained by simulating and abstracting the natural evolution process. It has robust global search ability and has been widely used in model parameter identification. There are various methods of simulation evolution and genetic algorithms, particle swarm optimization algorithms, and so on that are often used in system identification [10–14]; however, these exhibit many problems, such as long computation time and inaccurate identification of some parameters. The literature [15] proposed a chicken population optimization algorithm that simulates the hierarchical system and search behavior of chickens. This algorithm has a fast convergence speed and high identification accuracy and has not been applied in the field of parameter identification; therefore, it has significant research value. The chicken swarm algorithm can eliminate the strict requirements of traditional identification algorithms for system linearity and is suitable for the parameter identification of wind farm static reactive power generator models [16, 17].In this regard, this study proposes a multimode hybrid identification algorithm based on the chicken flock algorithm. Accordingly, the first step involves calculating the sensitivity of each parameter according to the different wind speed disturbances and establishing the corresponding relationship between the observation and the parameter sensitivity for different wind speeds. The subsequent steps involve analyzing the observability of the system dynamics on different observations, determining the observation selection strategy for parameter identification, and finally, determining the weighting factor according to the sensitivity. This method can accurately identify model parameters that have a more significant influence on the random behavior of wind farms. The main innovations of this article are as follows:(1)
For the random characteristics of wind farms, this paper proposes an SVG parameter identification method that considers the random characteristics of wind farms. The SVG model was divided into low wind speed, high wind speed, and full wind speed models by analyzing the sensitivity of the parameters at each wind speed.(2)
In each wind speed model, the parameters are classified based on the sensitivity analysis. Strongly correlated observations are selected to identify low and high wind speed models, and the identified optimal parameters are used as the initial parameter values of the multimode hybrid identification algorithm. Simultaneously, the active power and reactive power are observed, and power weighing is performed based on the effect of the related parameters under each observation, which reduces the impact on the accuracy of identification caused by only selecting active or reactive power.(3)
In contrast with the traditional step-by-step identification algorithm, the multimode hybrid identification algorithm effectively addresses the problem of being unable to accurately identify model parameters owing to the highly volatile sensitivity of the SVG model parameters that change suddenly with changes in the wind speed. The proposed method weakens the random fluctuation effect of the wind power on the identification and improves the accuracy of SVG parameter identification.(4)
The chicken colony algorithm, which has a simple principle, high convergence accuracy, and good computational robustness, was selected as the parameter identification algorithm to further improve the parameter identification accuracy of the SVG model.


## 2. Mathematical Model of Wind Farm SVG

The SVG usually adopts a double closed-loop control with an outer voltage control loop and an inner current control loop, as shown in Figure1. The DC voltage control compares the DC voltage Udc with the reference voltage and generates a d-axis reference current idref through an outer loop proportional-integral (PI) DC voltage controller. The grid-connected voltage control compares the grid-connected voltage Us with the reference voltage Usref and generates a q-axis reference current iqref through an outer loop PI grid-connected voltage controller. SVG feedback currents id and iq are compared with reference values idref and iqref, respectively, and the SVG voltage control targets, Udref and Uqref, are generated through the PI controller of the inner current control loop. The voltage control signal Ud is generated after comparing Udref with the voltage generated by the grid-connected voltage d-axis component, Usd, and feedback current iq through line inductance L. Similarly, a control signal Uq is generated. Pulse-width modulation based on Ud and Uq is used to generate insulated-gate bipolar transistor (IGBT) break pulse signals, Sa, Sb, and Sc.Figure 1
Block diagram of SVG (PWM, pulse-width modulation).The PI control model of the outer DC voltage control loop is given by(1)dx1dt=Udc−Udcrefidref=KdpUdc−Udcref+Kdix1,where x1 is the intervening variable and Kdp and Kdi are the proportional and integral control gains, respectively.The PI control model of the outer grid-connected voltage control loop is given by(2)dx2dt=Us−Usrefiqref=KqpUs−Usref+Kqix2,where x2 is the intervening variable and Kdp and Kdi are the proportional and integral control gains, respectively.The PI controller model of the inner current control loop is given by(3)dx3dt=idref−idud=Usd−ωLiq−KPIidref−id−KIIx3,(4)dx4dt=iqref−iquq=Usq+ωLid−KPIiqref−iq−KIIx4,where x3 and x4 are intervening variables and KPI and KII are the proportional and integral control gains, respectively.Overall, the wind farm SVG model parameters for estimation wereKdp, Kdi, Kqp, Kqi, KPI, KII, and L.


## 3. Proposed SVG Model Parameter Estimation Based on Chicken Swarm Optimization

### 3.1. Model Classification according to Sensitivity

Sensitivity reflects the influence of parameter changes on the output of the SVG model and can measure the parameter identifiability. Specifically, parameters with high sensitivity are easier to identify than those with low sensitivity [18]. The parameter sensitivity can be expressed as follows:(5)dk=yk,θi∗+Δθiei−yk,θi∗−Δθiei/2yk,θi∗Δθi/θi∗,where θ∗ is the reference value of the parameter to be identified, ei is a unit vector, the denominator describes the variable degree of the parameter to be identified, and the numerator is the variable degree of the model output caused by the change in the parameter to be identified.For a more intuitive comparison of the parameter sensitivity, we can use the average given by(6)S=1K∑k=1Kdk,where K is the number of samples and a larger value of S represents a higher parameter sensitivity.Fluctuations in parameter sensitivity according to wind speed, as shown in Figure2, can be obtained using (6). When the wind speed was 8–9 m/s, the sensitivity of various parameters changed considerably. Consequently, the parameter estimation in this range adversely affects the estimation performance. Therefore, we divided the SVG model into a low wind speed model (6–8 m/s) and a high wind speed model (9–12 m/s). As the sensitivity variation in these models is small, a robust estimation can be obtained under the specific wind speed range of each model. However, these models mostly neglect the wind speed fluctuation of wind farms, and the estimation results may not reflect real SVG dynamics. Nevertheless, parameter estimation in the full range of wind speeds, from 6 to 12 m/s, may lead to unstable results due to the transition between low and high wind speeds, which abruptly changes the parameter sensitivity and, consequently, reduces estimation accuracy.Figure 2
Parameter sensitivity according to wind speed.


### 3.2. Overview of SVG Parameter Estimation

Considering the influence of wind farm wind speed fluctuation on the parameter estimation accuracy, we propose a multimode hybrid estimation algorithm for SVG parameter estimation. The estimation procedure is shown in Figure3. First, the model was divided into low, high, and full wind speed models. The active power and reactive power of the SVG output were selected for measurement. The deviation between the measured power output and simulated power is the objective function. Based on the sensitivity analysis of each SVG parameter, the optimal estimation strategy for low and high wind speeds was used. Then, the SVG active power and reactive power are simultaneously measured; these power components are weighted to determine the objective function of the multimode hybrid algorithm. The optimal parameter estimation under low and high wind speeds is combined to set the initial parameter values for the chicken swarm optimization, providing parameter estimation for the full wind speed model.Figure 3
Schematic diagram of proposed SVG parameter estimation.


### 3.3. Algorithm for SVG Parameter Estimation

#### 3.3.1. SVG Parameter Estimation at Low Wind Speeds

In the low wind speed SVG model, the values of the parameters to be estimated,Kdp, Kdi, Kqp, Kqi, KPI, KII, and L, are successively increased by 5%, and the average sensitivities per parameter under different observation quantities were obtained, as listed in Table 1. The active power sensitivity for parameters Kqp, Kqi, and KPI and the reactive power sensitivity for parameters Kdp, Kdi, KII, and L are relatively large. Thus, the estimation accuracy can be effectively improved; when the active power is the observed quantity for Kqp, Kqi, and KPI, the reactive power is the observed quantity for Kdp, Kdi, KII, and L.Table 1
Parameter sensitivity when observed quantity is active power (P) or reactive power (Q).
Model parameterObserved quantityPQKdp3.1E − 50.020Kdi2.6E − 40.490Kqp0.0508.5E − 6Kqi0.1206.5E − 6KPI0.6103.9E − 5KII8.6E − 40.490L3.5E − 80.050Using chicken swarm optimization, the SVG parameters for the low wind speed model can be estimated successively according to the suitable observed quantity. First, a random wind speed fluctuation in the range of 6–9 m/s was applied, and the active power was taken as the observed quantity to estimateKqp, Kqi, and KPI, whereas Kdp, Kdi, KII, and L are fixed. Then, Kqp, Kqi, and KPI are fixed to their estimated values, and the reactive power is taken as the observed quantity to estimate Kdp, Kdi, KII, and L.


#### 3.3.2. SVG Parameter Estimation at High Wind Speeds

In the high wind speed SVG model, the values of the parameters to be estimated,Kdp, Kdi, Kqp, Kqi, KPI, KII, and L, are successively increased by 5%, obtaining the average sensitivity values listed in Table 2. The high wind speed SVG model provides observation quantities similar to those of the low wind speed model.Table 2
Parameter sensitivity when observed quantity is active power (P) or reactive power (Q).
Model parameterObserved quantityPQKdp2.3E − 60.011Kdi1.8E − 50.100Kqp0.1306.6E − 4Kqi0.1503.4E − 8KPI0.5901.6E − 4KII1.8E − 80.610L2.9E − 110.290Therefore, the parameters of the high wind speed SVG model were estimated to be those of the low wind speed model for a random wind speed fluctuation of 9–12 m/s. ParametersKqp, Kqi, and KPI are estimated using the active power as the observed quantity at fixed Kdp, Kdi, KII, and L. The estimated, Kqp, Kqi, and KPI are then used in conjunction with the power as the observed quantity to estimate Kdp, Kdi, KII, and L.


#### 3.3.3. Multimode Hybrid SVG Parameter Estimation

For the model that uses the estimated parameters to accurately reflect the dynamic SVG characteristics, we propose a multimode hybrid estimation algorithm that combines the advantages of low and high wind speed parameter estimation. Considering the average sensitivity per parameter, more accurate estimated parameters were selected and combined as the initial parameter values for multimode hybrid estimation. Then, the objective function determined by power weighting is used to iteratively update the parameter values via chicken swarm optimization to further improve estimation accuracy.Figure4 shows the average sensitivity of the estimated parameters in the low and high wind speed models. Parameters Kqp, Kqi, and KPI more accurately reflect the dynamic characteristics of the low wind speed model, whereas parameters Kdp, Kdi, KII, and L suitably characterize the high wind speed model. Therefore, the estimated values of Kqp, Kqi, and KPI are strongly correlated with the low wind speed model, and those of Kdp, Kdi, KII, and L are strongly correlated with the high wind speed model. These values are used as the initial parameters in the multimode hybrid estimation algorithm to initialize the population of individuals.(7)PS1:C=Kdp0,Kdi0,Kqp0,Kqi0,KPI0,KII0,L0,where P is the individual population, S1 is the population size, and C is the number of parameters.Figure 4
Sensitivity of low and high wind speed models per parameter.To mitigate the impact of separately selecting the active or reactive power as the observed quantity on estimation accuracy, we propose a power weighting method that combines these two observation quantities and optimizes their weights according to the sensitivity ratio between the parameters that are more sensitive to each observed quantity.The steps involved in the power weighting method are as follows:(1)
For the full wind speed model, we obtain the sumS1 of the average sensitivity values of Kdp, Kdi, KII, and L with the observed reactive power. Similarly, we obtain the sum S2 of the average sensitivity values of Kqp, Kqi, and KPI with the observed active power.(2)
SetS=S1+S2 as the reference value.(3)
S1/S and S2/S are the weights k1 and k2 for the reactive power and active power in the objective function, respectively.(4)
Substitute weightsk1 and k2 in (8) to obtain the objective function of the multimode hybrid estimation algorithm and estimate the parameters for the full wind speed model.(8)Jx=1N∑i=1Nk1eQiVt,It,x2+k2ePiVt,It,x2.


## 3.1. Model Classification according to Sensitivity

Sensitivity reflects the influence of parameter changes on the output of the SVG model and can measure the parameter identifiability. Specifically, parameters with high sensitivity are easier to identify than those with low sensitivity [18]. The parameter sensitivity can be expressed as follows:(5)dk=yk,θi∗+Δθiei−yk,θi∗−Δθiei/2yk,θi∗Δθi/θi∗,where θ∗ is the reference value of the parameter to be identified, ei is a unit vector, the denominator describes the variable degree of the parameter to be identified, and the numerator is the variable degree of the model output caused by the change in the parameter to be identified.For a more intuitive comparison of the parameter sensitivity, we can use the average given by(6)S=1K∑k=1Kdk,where K is the number of samples and a larger value of S represents a higher parameter sensitivity.Fluctuations in parameter sensitivity according to wind speed, as shown in Figure2, can be obtained using (6). When the wind speed was 8–9 m/s, the sensitivity of various parameters changed considerably. Consequently, the parameter estimation in this range adversely affects the estimation performance. Therefore, we divided the SVG model into a low wind speed model (6–8 m/s) and a high wind speed model (9–12 m/s). As the sensitivity variation in these models is small, a robust estimation can be obtained under the specific wind speed range of each model. However, these models mostly neglect the wind speed fluctuation of wind farms, and the estimation results may not reflect real SVG dynamics. Nevertheless, parameter estimation in the full range of wind speeds, from 6 to 12 m/s, may lead to unstable results due to the transition between low and high wind speeds, which abruptly changes the parameter sensitivity and, consequently, reduces estimation accuracy.Figure 2
Parameter sensitivity according to wind speed.


## 3.2. Overview of SVG Parameter Estimation

Considering the influence of wind farm wind speed fluctuation on the parameter estimation accuracy, we propose a multimode hybrid estimation algorithm for SVG parameter estimation. The estimation procedure is shown in Figure3. First, the model was divided into low, high, and full wind speed models. The active power and reactive power of the SVG output were selected for measurement. The deviation between the measured power output and simulated power is the objective function. Based on the sensitivity analysis of each SVG parameter, the optimal estimation strategy for low and high wind speeds was used. Then, the SVG active power and reactive power are simultaneously measured; these power components are weighted to determine the objective function of the multimode hybrid algorithm. The optimal parameter estimation under low and high wind speeds is combined to set the initial parameter values for the chicken swarm optimization, providing parameter estimation for the full wind speed model.Figure 3
Schematic diagram of proposed SVG parameter estimation.


## 3.3. Algorithm for SVG Parameter Estimation

### 3.3.1. SVG Parameter Estimation at Low Wind Speeds

In the low wind speed SVG model, the values of the parameters to be estimated,Kdp, Kdi, Kqp, Kqi, KPI, KII, and L, are successively increased by 5%, and the average sensitivities per parameter under different observation quantities were obtained, as listed in Table 1. The active power sensitivity for parameters Kqp, Kqi, and KPI and the reactive power sensitivity for parameters Kdp, Kdi, KII, and L are relatively large. Thus, the estimation accuracy can be effectively improved; when the active power is the observed quantity for Kqp, Kqi, and KPI, the reactive power is the observed quantity for Kdp, Kdi, KII, and L.Table 1
Parameter sensitivity when observed quantity is active power (P) or reactive power (Q).
Model parameterObserved quantityPQKdp3.1E − 50.020Kdi2.6E − 40.490Kqp0.0508.5E − 6Kqi0.1206.5E − 6KPI0.6103.9E − 5KII8.6E − 40.490L3.5E − 80.050Using chicken swarm optimization, the SVG parameters for the low wind speed model can be estimated successively according to the suitable observed quantity. First, a random wind speed fluctuation in the range of 6–9 m/s was applied, and the active power was taken as the observed quantity to estimateKqp, Kqi, and KPI, whereas Kdp, Kdi, KII, and L are fixed. Then, Kqp, Kqi, and KPI are fixed to their estimated values, and the reactive power is taken as the observed quantity to estimate Kdp, Kdi, KII, and L.


### 3.3.2. SVG Parameter Estimation at High Wind Speeds

In the high wind speed SVG model, the values of the parameters to be estimated,Kdp, Kdi, Kqp, Kqi, KPI, KII, and L, are successively increased by 5%, obtaining the average sensitivity values listed in Table 2. The high wind speed SVG model provides observation quantities similar to those of the low wind speed model.Table 2
Parameter sensitivity when observed quantity is active power (P) or reactive power (Q).
Model parameterObserved quantityPQKdp2.3E − 60.011Kdi1.8E − 50.100Kqp0.1306.6E − 4Kqi0.1503.4E − 8KPI0.5901.6E − 4KII1.8E − 80.610L2.9E − 110.290Therefore, the parameters of the high wind speed SVG model were estimated to be those of the low wind speed model for a random wind speed fluctuation of 9–12 m/s. ParametersKqp, Kqi, and KPI are estimated using the active power as the observed quantity at fixed Kdp, Kdi, KII, and L. The estimated, Kqp, Kqi, and KPI are then used in conjunction with the power as the observed quantity to estimate Kdp, Kdi, KII, and L.


### 3.3.3. Multimode Hybrid SVG Parameter Estimation

For the model that uses the estimated parameters to accurately reflect the dynamic SVG characteristics, we propose a multimode hybrid estimation algorithm that combines the advantages of low and high wind speed parameter estimation. Considering the average sensitivity per parameter, more accurate estimated parameters were selected and combined as the initial parameter values for multimode hybrid estimation. Then, the objective function determined by power weighting is used to iteratively update the parameter values via chicken swarm optimization to further improve estimation accuracy.Figure4 shows the average sensitivity of the estimated parameters in the low and high wind speed models. Parameters Kqp, Kqi, and KPI more accurately reflect the dynamic characteristics of the low wind speed model, whereas parameters Kdp, Kdi, KII, and L suitably characterize the high wind speed model. Therefore, the estimated values of Kqp, Kqi, and KPI are strongly correlated with the low wind speed model, and those of Kdp, Kdi, KII, and L are strongly correlated with the high wind speed model. These values are used as the initial parameters in the multimode hybrid estimation algorithm to initialize the population of individuals.(7)PS1:C=Kdp0,Kdi0,Kqp0,Kqi0,KPI0,KII0,L0,where P is the individual population, S1 is the population size, and C is the number of parameters.Figure 4
Sensitivity of low and high wind speed models per parameter.To mitigate the impact of separately selecting the active or reactive power as the observed quantity on estimation accuracy, we propose a power weighting method that combines these two observation quantities and optimizes their weights according to the sensitivity ratio between the parameters that are more sensitive to each observed quantity.The steps involved in the power weighting method are as follows:(1)
For the full wind speed model, we obtain the sumS1 of the average sensitivity values of Kdp, Kdi, KII, and L with the observed reactive power. Similarly, we obtain the sum S2 of the average sensitivity values of Kqp, Kqi, and KPI with the observed active power.(2)
SetS=S1+S2 as the reference value.(3)
S1/S and S2/S are the weights k1 and k2 for the reactive power and active power in the objective function, respectively.(4)
Substitute weightsk1 and k2 in (8) to obtain the objective function of the multimode hybrid estimation algorithm and estimate the parameters for the full wind speed model.(8)Jx=1N∑i=1Nk1eQiVt,It,x2+k2ePiVt,It,x2.


## 3.3.1. SVG Parameter Estimation at Low Wind Speeds

In the low wind speed SVG model, the values of the parameters to be estimated,Kdp, Kdi, Kqp, Kqi, KPI, KII, and L, are successively increased by 5%, and the average sensitivities per parameter under different observation quantities were obtained, as listed in Table 1. The active power sensitivity for parameters Kqp, Kqi, and KPI and the reactive power sensitivity for parameters Kdp, Kdi, KII, and L are relatively large. Thus, the estimation accuracy can be effectively improved; when the active power is the observed quantity for Kqp, Kqi, and KPI, the reactive power is the observed quantity for Kdp, Kdi, KII, and L.Table 1
Parameter sensitivity when observed quantity is active power (P) or reactive power (Q).
Model parameterObserved quantityPQKdp3.1E − 50.020Kdi2.6E − 40.490Kqp0.0508.5E − 6Kqi0.1206.5E − 6KPI0.6103.9E − 5KII8.6E − 40.490L3.5E − 80.050Using chicken swarm optimization, the SVG parameters for the low wind speed model can be estimated successively according to the suitable observed quantity. First, a random wind speed fluctuation in the range of 6–9 m/s was applied, and the active power was taken as the observed quantity to estimateKqp, Kqi, and KPI, whereas Kdp, Kdi, KII, and L are fixed. Then, Kqp, Kqi, and KPI are fixed to their estimated values, and the reactive power is taken as the observed quantity to estimate Kdp, Kdi, KII, and L.


## 3.3.2. SVG Parameter Estimation at High Wind Speeds

In the high wind speed SVG model, the values of the parameters to be estimated,Kdp, Kdi, Kqp, Kqi, KPI, KII, and L, are successively increased by 5%, obtaining the average sensitivity values listed in Table 2. The high wind speed SVG model provides observation quantities similar to those of the low wind speed model.Table 2
Parameter sensitivity when observed quantity is active power (P) or reactive power (Q).
Model parameterObserved quantityPQKdp2.3E − 60.011Kdi1.8E − 50.100Kqp0.1306.6E − 4Kqi0.1503.4E − 8KPI0.5901.6E − 4KII1.8E − 80.610L2.9E − 110.290Therefore, the parameters of the high wind speed SVG model were estimated to be those of the low wind speed model for a random wind speed fluctuation of 9–12 m/s. ParametersKqp, Kqi, and KPI are estimated using the active power as the observed quantity at fixed Kdp, Kdi, KII, and L. The estimated, Kqp, Kqi, and KPI are then used in conjunction with the power as the observed quantity to estimate Kdp, Kdi, KII, and L.


## 3.3.3. Multimode Hybrid SVG Parameter Estimation

For the model that uses the estimated parameters to accurately reflect the dynamic SVG characteristics, we propose a multimode hybrid estimation algorithm that combines the advantages of low and high wind speed parameter estimation. Considering the average sensitivity per parameter, more accurate estimated parameters were selected and combined as the initial parameter values for multimode hybrid estimation. Then, the objective function determined by power weighting is used to iteratively update the parameter values via chicken swarm optimization to further improve estimation accuracy.Figure4 shows the average sensitivity of the estimated parameters in the low and high wind speed models. Parameters Kqp, Kqi, and KPI more accurately reflect the dynamic characteristics of the low wind speed model, whereas parameters Kdp, Kdi, KII, and L suitably characterize the high wind speed model. Therefore, the estimated values of Kqp, Kqi, and KPI are strongly correlated with the low wind speed model, and those of Kdp, Kdi, KII, and L are strongly correlated with the high wind speed model. These values are used as the initial parameters in the multimode hybrid estimation algorithm to initialize the population of individuals.(7)PS1:C=Kdp0,Kdi0,Kqp0,Kqi0,KPI0,KII0,L0,where P is the individual population, S1 is the population size, and C is the number of parameters.Figure 4
Sensitivity of low and high wind speed models per parameter.To mitigate the impact of separately selecting the active or reactive power as the observed quantity on estimation accuracy, we propose a power weighting method that combines these two observation quantities and optimizes their weights according to the sensitivity ratio between the parameters that are more sensitive to each observed quantity.The steps involved in the power weighting method are as follows:(1)
For the full wind speed model, we obtain the sumS1 of the average sensitivity values of Kdp, Kdi, KII, and L with the observed reactive power. Similarly, we obtain the sum S2 of the average sensitivity values of Kqp, Kqi, and KPI with the observed active power.(2)
SetS=S1+S2 as the reference value.(3)
S1/S and S2/S are the weights k1 and k2 for the reactive power and active power in the objective function, respectively.(4)
Substitute weightsk1 and k2 in (8) to obtain the objective function of the multimode hybrid estimation algorithm and estimate the parameters for the full wind speed model.(8)Jx=1N∑i=1Nk1eQiVt,It,x2+k2ePiVt,It,x2.


## 4. Case Study

To verify the performance of the proposed estimation method, we considered wind power systems in the wind fields of Xinjiang, China. The system topology is shown in Figure5 and consists of 18 conventional large-scale integrated wind power systems. The main model of each wind generator was a direct-drive wind turbine equipped with an SVG. Wind power is collected at power substation D through the 35/110/220 kV line and transmitted to the main network through a double 220 kV line.Figure 5
Topology of the wind power system in Xinjiang, China.


### 4.1. Effect Verification of Traditional Step-by-Step Identification Algorithm

#### 4.1.1. Traditional Step-by-Step Identification Algorithm under Constant Wind Speed

For low and high wind speed conditions, the parameter values to be identified (Kdp, Kdi, Kqp, Kqi, KPI, KII, and L) are increased by 5% before calculating the sensitivity of the SVG model parameters to determine the high and low sensitivity parameters of the SVG model. Subsequently, the active power P and reactive power output Q are observed, and wind power collection station A is selected as the test system for the simulation to identify the high and low wind speed parameters based on the traditional step-by-step identification method [19, 20]. Finally, the average value of the final result is considered. Table 3 summarizes the results and errors of the traditional step-by-step identification. The error is defined as follows:(9)e=estimation value−real valuereal value×100%,Table 3
Traditional step-by-step identification results under a stable wind speed.
Estimated parameterReal valueObserved quantity,PObserved quantity,QEstimated valueError (%)Estimated valueError (%)Kdp0.1E − 39.71E − 52.9009.82E − 51.800Kdi0.020.02011.0000.019980.200Kqp55.00220.0444.86822.600Kqi1000999.3220.0687989.2311.076KPI0.30.300810.2700.29342.200KII109.65013.49910.0280.280L0.220.218890.5050.21940.273It can be seen from Table3 that for the q-axis current controller parameters (Kdp, Kdi, KII, and L), the reactive power Q has a smaller identification error and higher identification accuracy compared with those of active power P. For the d-axis current controller parameters (Kqp, Kqi, and KPI), the active power P has a smaller identification error and higher identification accuracy compared with those of reactive power Q. This agrees with the parameter sensitivity analysis results in Section 3.3.1. The traditional step-by-step identification algorithm has a smaller identification error under a fixed wind speed. However, further discussion is needed for the random fluctuation of wind speed.


#### 4.1.2. Traditional Step-by-Step Identification Algorithm under Random Wind Speed Fluctuations

To further verify the influence of different observations on the identification accuracy, the wind farm SVG active powerP and reactive output power Q are observed when the wind speed changes randomly. Based on the traditional step-by-step identification method [19, 20], wind power collection station A is used as the test system for the simulation analysis to verify the influence of different observations on the identification results. Table 4 lists the identification results of the SVG model parameters, and Figure 6 illustrates the identification error curves of various parameters at different wind speeds.Table 4
Estimated parameters when the observed quantity is active power (P) or reactive power (Q).
Estimated parameterReal valueObserved quantity,PObserved quantity,QEstimated valueError (%)Estimated valueError (%)Kdp0.1E − 39.68E − 53.2009.74E − 52.600Kdi0.020.02115.5000.019383.100Kqp54.81323.3764.79924.016Kqi1000999.1010.089988.2171.178KPI0.30.301270.4200.29322.260KII109.55214.47910.1491.490L0.220.1978910.050.24139.682Figure 6
Identification error of each parameter under different wind speed.It can be seen from Figures4 and 6 that different wind speed excitations have different effects on the sensitivity and identification error of each parameter. Under low wind speed conditions, the sensitivity values of the parameters Kdp, Kdi, and KPI are higher, which better reflects the dynamic response characteristics of the low wind speed model. Therefore, it is helpful to identify the parameters Kdp, Kdi, and KPI under low wind speed conditions. However, it is not conducive for the identification of Kqp, Kqi, KII, and L. Under high wind speed conditions, the sensitivity values of the parameters Kqp, Kqi, KII, and L are higher, which determine the dynamic characteristics of high wind speed models, which is beneficial for identifying the parameters Kqp, Kqi, KII, and L, but not conducive to identifying Kdp, Kdi, and KPI. It can be seen that when the parameter sensitivity under different wind speed conditions changes, it leads to poor robustness of the parameter identification results under random wind speed excitation. Meanwhile, when comparing the results of Tables 3 and 4, it is evident that in the transition period between low and high wind speeds, the sensitivity values of parameters Kdi, Kqp, and L change suddenly, and the error variation values of the identification results of parameters Kdi, Kqp, and L are far greater than those of other parameters, among which the error of parameter L varies from 0.273% to 9.682%. These results further verify that the parameter sensitivity changes lead to a large error in the identification results. Therefore, the traditional step-by-step identification method that does not consider the influence of the random characteristics of the wind farm and the coupling relationship between some parameters makes it difficult to identify parameters and results in poor identification robustness, even for the optimal observation.


### 4.2. Effect Verification of the Multimode Hybrid Identification Algorithm

To further improve the SVG parameter estimation, we used the proposed multimode hybrid estimation algorithm that considers wind speed fluctuations at wind farms. To quantitatively analyze the influence of wind speed fluctuation on the estimation results, we analyzed the estimation accuracy by considering the estimation convergence according to the iterations of the optimization algorithm. Figure7 shows the convergence characteristic curve of the wind field A model parameter identification value with the number of iterations under the traditional step-by-step identification method with different observations and the multimode hybrid identification method.Figure 7
Convergence of conventional and proposed multimode hybrid estimation algorithms according to iteration number for parameters: (a)Kdp, (b) Kdi, (c) Kqp, (d) Kqi, (e) KPI, (f) KII, and (g) L. (Black curve – real curve, blue curve – P is the observed quantity, yellow curve – Q is the observed quantity, and red curve – multimode hybrid algorithm).
(a)(b)(c)(d)(e)(f)(g)As seen from Figure7: (1) because the multimode hybrid identification method fully considers the influence of the random characteristics of the wind farm on the parameter identification results, decoupling identification of the identified parameters is conducted. The fitting degree between the parameter convergence curve and the real value curve obtained by this method is significantly increased, indicating that the identification accuracy of the parameters has been greatly improved; (2) after adopting the multimode hybrid identification method, the search interval of the initial parameter value is reduced. With an increase in the number of iterations, the convergence stability of the identification parameter was also greatly improved, that is, ideal parameter identification accuracy can be achieved in fewer iterations, thus improving the efficiency of parameter identification.The traditional step-by-step identification method is compared with the proposed method for wind power collection station A. Multiple identifications are performed, and the average values considered as the final results are listed in Table5. It is evident that the proposed method improves the identification accuracy with small errors, and the identification results satisfy the system simulation requirements.Table 5
Parameter estimation results and errors using conventional and proposed hybrid estimation.
Estimated parameterReal valueMultimode hybrid estimateError (%)Conventional estimateError (%)Kdp0.1E − 39.76E − 53.1001.071E − 46.300Kdi0.020.02010.5000.02105.000Kqp54.99860.0284.7664.680Kqi1000998.800.1209782.200KPI0.30.29860.4700.28544.480KII109.9810.19010.181.800L0.220.2171.3000.21303.180The identification results of the multimode hybrid identification method were substituted into the wind power grid-connected system for nonlinear simulation, and the simulated output reactive power curve was compared with the real value curve, as shown in Figure8. Considering the influencing factors of wind power random characteristics and adopting the decoupling identification strategy of model parameters, the identification curve obtained by the multimode hybrid identification method is highly fitted with the real value curve, whereas the traditional identification method is affected by the random fluctuation of wind speed and the obtained trajectory has an obvious error with the real value trajectory.Figure 8
Comparison of the output of two identification methods for wind power collection station A.To further verify the generality of the method proposed in this paper, the same multiway hybrid identification algorithm was used to identify the parameters of the SVG model in wind manifold B, and the identification results are substituted into the original wind power grid-connected system for simulation. The simulation results are shown in Figure9. As shown, the identification curve obtained by the multiway hybrid algorithm has a higher degree of fit with the real value curve, further verifying the feasibility of the method proposed in this paper.Figure 9
Comparison of the output of two identification methods for wind power collection station B.In conclusion, the intelligent model parameter identification method of the static reactive power generator—which accounts for the random characteristics of the wind farm—can identify the parameters of the SVG model in the wind farm more accurately than the traditional identification method.


## 4.1. Effect Verification of Traditional Step-by-Step Identification Algorithm

### 4.1.1. Traditional Step-by-Step Identification Algorithm under Constant Wind Speed

For low and high wind speed conditions, the parameter values to be identified (Kdp, Kdi, Kqp, Kqi, KPI, KII, and L) are increased by 5% before calculating the sensitivity of the SVG model parameters to determine the high and low sensitivity parameters of the SVG model. Subsequently, the active power P and reactive power output Q are observed, and wind power collection station A is selected as the test system for the simulation to identify the high and low wind speed parameters based on the traditional step-by-step identification method [19, 20]. Finally, the average value of the final result is considered. Table 3 summarizes the results and errors of the traditional step-by-step identification. The error is defined as follows:(9)e=estimation value−real valuereal value×100%,Table 3
Traditional step-by-step identification results under a stable wind speed.
Estimated parameterReal valueObserved quantity,PObserved quantity,QEstimated valueError (%)Estimated valueError (%)Kdp0.1E − 39.71E − 52.9009.82E − 51.800Kdi0.020.02011.0000.019980.200Kqp55.00220.0444.86822.600Kqi1000999.3220.0687989.2311.076KPI0.30.300810.2700.29342.200KII109.65013.49910.0280.280L0.220.218890.5050.21940.273It can be seen from Table3 that for the q-axis current controller parameters (Kdp, Kdi, KII, and L), the reactive power Q has a smaller identification error and higher identification accuracy compared with those of active power P. For the d-axis current controller parameters (Kqp, Kqi, and KPI), the active power P has a smaller identification error and higher identification accuracy compared with those of reactive power Q. This agrees with the parameter sensitivity analysis results in Section 3.3.1. The traditional step-by-step identification algorithm has a smaller identification error under a fixed wind speed. However, further discussion is needed for the random fluctuation of wind speed.


### 4.1.2. Traditional Step-by-Step Identification Algorithm under Random Wind Speed Fluctuations

To further verify the influence of different observations on the identification accuracy, the wind farm SVG active powerP and reactive output power Q are observed when the wind speed changes randomly. Based on the traditional step-by-step identification method [19, 20], wind power collection station A is used as the test system for the simulation analysis to verify the influence of different observations on the identification results. Table 4 lists the identification results of the SVG model parameters, and Figure 6 illustrates the identification error curves of various parameters at different wind speeds.Table 4
Estimated parameters when the observed quantity is active power (P) or reactive power (Q).
Estimated parameterReal valueObserved quantity,PObserved quantity,QEstimated valueError (%)Estimated valueError (%)Kdp0.1E − 39.68E − 53.2009.74E − 52.600Kdi0.020.02115.5000.019383.100Kqp54.81323.3764.79924.016Kqi1000999.1010.089988.2171.178KPI0.30.301270.4200.29322.260KII109.55214.47910.1491.490L0.220.1978910.050.24139.682Figure 6
Identification error of each parameter under different wind speed.It can be seen from Figures4 and 6 that different wind speed excitations have different effects on the sensitivity and identification error of each parameter. Under low wind speed conditions, the sensitivity values of the parameters Kdp, Kdi, and KPI are higher, which better reflects the dynamic response characteristics of the low wind speed model. Therefore, it is helpful to identify the parameters Kdp, Kdi, and KPI under low wind speed conditions. However, it is not conducive for the identification of Kqp, Kqi, KII, and L. Under high wind speed conditions, the sensitivity values of the parameters Kqp, Kqi, KII, and L are higher, which determine the dynamic characteristics of high wind speed models, which is beneficial for identifying the parameters Kqp, Kqi, KII, and L, but not conducive to identifying Kdp, Kdi, and KPI. It can be seen that when the parameter sensitivity under different wind speed conditions changes, it leads to poor robustness of the parameter identification results under random wind speed excitation. Meanwhile, when comparing the results of Tables 3 and 4, it is evident that in the transition period between low and high wind speeds, the sensitivity values of parameters Kdi, Kqp, and L change suddenly, and the error variation values of the identification results of parameters Kdi, Kqp, and L are far greater than those of other parameters, among which the error of parameter L varies from 0.273% to 9.682%. These results further verify that the parameter sensitivity changes lead to a large error in the identification results. Therefore, the traditional step-by-step identification method that does not consider the influence of the random characteristics of the wind farm and the coupling relationship between some parameters makes it difficult to identify parameters and results in poor identification robustness, even for the optimal observation.


## 4.1.1. Traditional Step-by-Step Identification Algorithm under Constant Wind Speed

For low and high wind speed conditions, the parameter values to be identified (Kdp, Kdi, Kqp, Kqi, KPI, KII, and L) are increased by 5% before calculating the sensitivity of the SVG model parameters to determine the high and low sensitivity parameters of the SVG model. Subsequently, the active power P and reactive power output Q are observed, and wind power collection station A is selected as the test system for the simulation to identify the high and low wind speed parameters based on the traditional step-by-step identification method [19, 20]. Finally, the average value of the final result is considered. Table 3 summarizes the results and errors of the traditional step-by-step identification. The error is defined as follows:(9)e=estimation value−real valuereal value×100%,Table 3
Traditional step-by-step identification results under a stable wind speed.
Estimated parameterReal valueObserved quantity,PObserved quantity,QEstimated valueError (%)Estimated valueError (%)Kdp0.1E − 39.71E − 52.9009.82E − 51.800Kdi0.020.02011.0000.019980.200Kqp55.00220.0444.86822.600Kqi1000999.3220.0687989.2311.076KPI0.30.300810.2700.29342.200KII109.65013.49910.0280.280L0.220.218890.5050.21940.273It can be seen from Table3 that for the q-axis current controller parameters (Kdp, Kdi, KII, and L), the reactive power Q has a smaller identification error and higher identification accuracy compared with those of active power P. For the d-axis current controller parameters (Kqp, Kqi, and KPI), the active power P has a smaller identification error and higher identification accuracy compared with those of reactive power Q. This agrees with the parameter sensitivity analysis results in Section 3.3.1. The traditional step-by-step identification algorithm has a smaller identification error under a fixed wind speed. However, further discussion is needed for the random fluctuation of wind speed.


## 4.1.2. Traditional Step-by-Step Identification Algorithm under Random Wind Speed Fluctuations

To further verify the influence of different observations on the identification accuracy, the wind farm SVG active powerP and reactive output power Q are observed when the wind speed changes randomly. Based on the traditional step-by-step identification method [19, 20], wind power collection station A is used as the test system for the simulation analysis to verify the influence of different observations on the identification results. Table 4 lists the identification results of the SVG model parameters, and Figure 6 illustrates the identification error curves of various parameters at different wind speeds.Table 4
Estimated parameters when the observed quantity is active power (P) or reactive power (Q).
Estimated parameterReal valueObserved quantity,PObserved quantity,QEstimated valueError (%)Estimated valueError (%)Kdp0.1E − 39.68E − 53.2009.74E − 52.600Kdi0.020.02115.5000.019383.100Kqp54.81323.3764.79924.016Kqi1000999.1010.089988.2171.178KPI0.30.301270.4200.29322.260KII109.55214.47910.1491.490L0.220.1978910.050.24139.682Figure 6
Identification error of each parameter under different wind speed.It can be seen from Figures4 and 6 that different wind speed excitations have different effects on the sensitivity and identification error of each parameter. Under low wind speed conditions, the sensitivity values of the parameters Kdp, Kdi, and KPI are higher, which better reflects the dynamic response characteristics of the low wind speed model. Therefore, it is helpful to identify the parameters Kdp, Kdi, and KPI under low wind speed conditions. However, it is not conducive for the identification of Kqp, Kqi, KII, and L. Under high wind speed conditions, the sensitivity values of the parameters Kqp, Kqi, KII, and L are higher, which determine the dynamic characteristics of high wind speed models, which is beneficial for identifying the parameters Kqp, Kqi, KII, and L, but not conducive to identifying Kdp, Kdi, and KPI. It can be seen that when the parameter sensitivity under different wind speed conditions changes, it leads to poor robustness of the parameter identification results under random wind speed excitation. Meanwhile, when comparing the results of Tables 3 and 4, it is evident that in the transition period between low and high wind speeds, the sensitivity values of parameters Kdi, Kqp, and L change suddenly, and the error variation values of the identification results of parameters Kdi, Kqp, and L are far greater than those of other parameters, among which the error of parameter L varies from 0.273% to 9.682%. These results further verify that the parameter sensitivity changes lead to a large error in the identification results. Therefore, the traditional step-by-step identification method that does not consider the influence of the random characteristics of the wind farm and the coupling relationship between some parameters makes it difficult to identify parameters and results in poor identification robustness, even for the optimal observation.


## 4.2. Effect Verification of the Multimode Hybrid Identification Algorithm

To further improve the SVG parameter estimation, we used the proposed multimode hybrid estimation algorithm that considers wind speed fluctuations at wind farms. To quantitatively analyze the influence of wind speed fluctuation on the estimation results, we analyzed the estimation accuracy by considering the estimation convergence according to the iterations of the optimization algorithm. Figure7 shows the convergence characteristic curve of the wind field A model parameter identification value with the number of iterations under the traditional step-by-step identification method with different observations and the multimode hybrid identification method.Figure 7
Convergence of conventional and proposed multimode hybrid estimation algorithms according to iteration number for parameters: (a)Kdp, (b) Kdi, (c) Kqp, (d) Kqi, (e) KPI, (f) KII, and (g) L. (Black curve – real curve, blue curve – P is the observed quantity, yellow curve – Q is the observed quantity, and red curve – multimode hybrid algorithm).
(a)(b)(c)(d)(e)(f)(g)As seen from Figure7: (1) because the multimode hybrid identification method fully considers the influence of the random characteristics of the wind farm on the parameter identification results, decoupling identification of the identified parameters is conducted. The fitting degree between the parameter convergence curve and the real value curve obtained by this method is significantly increased, indicating that the identification accuracy of the parameters has been greatly improved; (2) after adopting the multimode hybrid identification method, the search interval of the initial parameter value is reduced. With an increase in the number of iterations, the convergence stability of the identification parameter was also greatly improved, that is, ideal parameter identification accuracy can be achieved in fewer iterations, thus improving the efficiency of parameter identification.The traditional step-by-step identification method is compared with the proposed method for wind power collection station A. Multiple identifications are performed, and the average values considered as the final results are listed in Table5. It is evident that the proposed method improves the identification accuracy with small errors, and the identification results satisfy the system simulation requirements.Table 5
Parameter estimation results and errors using conventional and proposed hybrid estimation.
Estimated parameterReal valueMultimode hybrid estimateError (%)Conventional estimateError (%)Kdp0.1E − 39.76E − 53.1001.071E − 46.300Kdi0.020.02010.5000.02105.000Kqp54.99860.0284.7664.680Kqi1000998.800.1209782.200KPI0.30.29860.4700.28544.480KII109.9810.19010.181.800L0.220.2171.3000.21303.180The identification results of the multimode hybrid identification method were substituted into the wind power grid-connected system for nonlinear simulation, and the simulated output reactive power curve was compared with the real value curve, as shown in Figure8. Considering the influencing factors of wind power random characteristics and adopting the decoupling identification strategy of model parameters, the identification curve obtained by the multimode hybrid identification method is highly fitted with the real value curve, whereas the traditional identification method is affected by the random fluctuation of wind speed and the obtained trajectory has an obvious error with the real value trajectory.Figure 8
Comparison of the output of two identification methods for wind power collection station A.To further verify the generality of the method proposed in this paper, the same multiway hybrid identification algorithm was used to identify the parameters of the SVG model in wind manifold B, and the identification results are substituted into the original wind power grid-connected system for simulation. The simulation results are shown in Figure9. As shown, the identification curve obtained by the multiway hybrid algorithm has a higher degree of fit with the real value curve, further verifying the feasibility of the method proposed in this paper.Figure 9
Comparison of the output of two identification methods for wind power collection station B.In conclusion, the intelligent model parameter identification method of the static reactive power generator—which accounts for the random characteristics of the wind farm—can identify the parameters of the SVG model in the wind farm more accurately than the traditional identification method.


## 5. Conclusion

To accurately estimate SVG parameters, we propose an adaptive estimation method that considers the wind speed fluctuation of wind farms. The performance of the proposed method is verified using parameter estimation simulations. From this study, we can draw the following conclusions:We used sensitivity to analyze the influence of wind speed fluctuations of wind farms on SVG parameter estimation. From the analysis, we divided the SVG model into low, high, and full wind speed variants. There are clear differences in parameter estimation accuracy between the low and high wind speed models.Under fixed wind speed conditions, the traditional step-by-step identification algorithm can better identify the wind farm SVG model parameters. However, under random wind speed conditions, the sensitivity of the SVG parameters changes abruptly with the changing wind speed, resulting in inaccuracies in the identification of model parameters. Therefore, the multimode hybrid identification algorithm is proposed in this study. Its initial parameter values combine the high-precision identification results from the low and the high wind speed model to fully consider the influence of the random characteristics of the wind farm on the model parameter identification results. The model addresses the shortcomings of low identification accuracy and poor robust stability of the traditional step-by-step identification methods.Because of the wind farm static reactive power generator model with nonlinear characteristics, the traditional recognition algorithms cannot accurately identify parameters for parameter identification, and this paper proposes a chicken identification parameter recognition algorithm to solve the nonlinear model on the influence of parameter identification precision, obtaining improved parameter identification results.



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*Source: 3877777-2022-03-10.xml*