Active optimization scheduling of wind farms based on wind turbine state evaluation

Abstract

In response to the limited power operation mode of wind farms, an active power optimization scheduling method for wind farms is proposed based on the state evaluation of wind turbines. This method achieves optimal operational control of wind farms. The computational complexity is relatively low. Firstly, the indicators in the comprehensive scoring system for wind turbines are defined. Additionally, the fuzzy entropy method is employed to calculate and rank the overall deterioration of power up-regulation/down-regulation. Then, wind turbines are classified according to their operational state, and the power regulation capacity of each class of wind turbines is determined. Subsequently, the active power optimization scheduling of wind farms is implemented based on the classification and ranking of wind turbines. Finally, a simulation test is conducted using historical data from a wind farm. The results demonstrate that the proposed method can achieve higher power command tracking accuracy under different power limitation levels of wind farms. Moreover, power scheduling based on the comprehensive deterioration ranking of the turbines can effectively reduce power fluctuation differences, load fatigue differences, and overall power fluctuations between the turbines. The standard deviation of the power fluctuation coefficient has been reduced to 0.0705, marking a 9.85% decrease compared to the previous scheme.

Introduction

The optimization of wind farm scheduling has become a crucial focus area within the renewable energy sector, driven by the need to address the challenges posed by the variable nature of wind power. In a limited power operation mode, the overall power command is allocated to individual turbines of wind farms through a specific active power scheduling method. Therefore, an active power scheduling method is essential to ensure the accuracy of tracking the wind farm's power commands. Conventional active power scheduling methods for wind farms include the average allocation method and the proportional allocation method. ¹ However, these methods may induce frequent changes in power commands to the turbines due to random fluctuations in the wind speed, thus leading to increased operational frequency and load fatigue on the turbines. ²

The need for system flexibility has led to the classification of individual generators within wind farms as the smallest units, with different types of units treated as distinct virtual power sources. This classification allows for more flexible participation in system dispatch, resulting in new methods enabling for wind power to actively engage in grid operations to optimize production schedules and minimize losses. ³ In microgrids with multiple wind farms, the accurate representation of uncertainties is crucial. To overcome the limitations of data availability in newly commissioned wind farms, a novel transfer learning-based scenario generation method has been proposed, which uses historical information from other data-rich farms to generate wind speed scenarios, thereby improving decision-making reliability. ⁴

Predictive coordination control frameworks have been proposed to improve wind power control performance. In order to maximise self-reserve and minimise control errors, these frameworks integrate wind power forecasting modules, online optimisation and feedback loops. ⁵ Data-driven approaches for assessing wind turbine health have also emerged, using operational condition recognition and machine learning models to predict fatigue loads and ensure the integrity of wind farms. ⁶ As wind generation increases its share in the power mix, the operation and maintenance of wind farms have become more critical. Decision-dependent stochastic strategies are being studied to optimize maintenance schedules, taking into account the influence of wake effects and uncertainties in wind speed and electricity prices. ⁷ Online health assessment of wind turbines is also receiving increased attention, with data-driven methods being proposed for recognizing operational conditions. ⁸

As the grid requirements for power command tracking accuracy of wind farms increase and wind farms place more emphasis on their power generation efficiency, such factors as turbine wind power prediction results, turbine operating state, and wind farm operating costs should be incorporated into active power scheduling. ⁹ This contributes to higher power tracking accuracy and lower operation and maintenance costs for the wind farm. Currently, intelligent optimization algorithms and turbine state evaluation-based methods are adopted in most existing studies on power optimization scheduling for wind farms under limited power.

Extensive research has been conducted on intelligent optimization algorithms to date. Li ¹⁰ proposed a new chaotic quantum Harris hawk optimization named CQMHHO to address the issues of premature convergence; Zhang ¹¹ proposed a new DRO-based model for generating robust schedules of maintenance tasks, which can resist the uncertainty of maintenance demand with limited historical data. The proposed model minimizes the utilization of maintenance resources, while ensure that the uncertain maintenance demand has been fully met; Bai ¹² proposed a novel variant based on evolutionary PSO (EPSO). EPSO combines the idea of evolutionary computing and exploring capability of particles such that system parameters can self-evolve intelligently to adapt different problems; Barış ¹³ developed a sophisticated wind speed forecasting model. This model utilizes Robust Empirical Mode Decomposition (REMD) to decompose wind speed data into Intrinsic Mode Functions (IMFs), which are then integrated into a Long Short-Term Memory (LSTM) network. The LSTM architecture is optimized through the parameters estimated by the African Vulture Optimizer (AVO) algorithm, which is based on the Tents Chaos Map; Altan ¹⁴ presents the development of an advanced hybrid wind speed forecasting model that synergistically combines Long Short-Term Memory (LSTM) networks with decomposition techniques. The Grey Wolf Optimizer (GWO) is utilized to optimize the estimation of Intrinsic Mode Functions (IMFs), derived from the decomposition process. This approach has led to a marked improvement in the precision of wind speed predictions, which is vital for the effective harnessing of wind energy resources.

Due to the large number of turbines within a wind farm, there is a risk of the curse of dimensionality. The reason is that intelligent optimization algorithms tend to fall into local optimal solutions, which significantly reduces the optimization effectiveness. Therefore, intelligent optimization algorithms are rarely applied to the active power optimization scheduling of wind farms in a real scenario. The optimization of power scheduling is typically based on a comprehensive evaluation of the power regulation capabilities of wind turbines, taking into account their various operational states and characteristics. This is followed by a classification and ranking of these turbines based on the aforementioned evaluation. The comprehensive evaluation of turbine operating states based on various parameters has been highlighted in many studies. Some investigators calculated the weight of comprehensive indicators by using a combination of fuzzy weight analysis and entropy weight methods based on the data collected from the wind turbine Supervisory Control and Data Acquisition (SCADA) system. ¹⁵

Active power scheduling methods based on turbine state evaluations are explored. These methods classify turbines according to their output characteristics and operating states, allowing for the allocation of active power scheduling commands to the turbine layer based on these classifications. Compared to intelligent optimization algorithms, turbine state evaluation methods exhibit significantly lower computational complexity, making them more applicable for real-time power scheduling in wind farms. However, existing approaches primarily emphasize tracking accuracy of power commands, often neglecting other operational optimization aspects such as reducing turbine loads, lowering operational costs, and balancing turbine load fatigue.^16,17 To address these issues, researchers have proposed a novel Hierarchical Model Predictive Control (HMPC) strategy aimed at enhancing wind power scheduling and accommodation. ¹⁸ This strategy can be employed to classify turbines based on their output characteristics and operating states, with the objective of allocating active power scheduling commands to the turbine layer based on the classes. Compared with the methods based on intelligent optimization algorithms, the active power scheduling methods based on turbine state evaluations exhibit significantly lower computational complexity, which endows them with higher applicability to real-time power scheduling of wind farms. Nevertheless, the primary objective of existing active power scheduling methodologies based on turbine state assessments is to enhance the precision of power commands. However, there is a paucity of research exploring the potential of these techniques to reduce turbine loads, minimize wind farm operational costs, balance turbine load fatigue and optimize other aspects of operational efficiency.

Therefore, in response to the limited power operation mode of wind farms, an active power optimization scheduling method is proposed based on turbine state evaluations. This method aims to accurately track the wind farm's power commands with low computational complexity while attenuating turbine power fluctuations and reducing fatigue damage differences among turbines. Furthermore, this method may reduce operation and maintenance costs and achieve optimized operational control of wind farms.

This study introduces a power scheduling algorithm that operates on a per-cycle basis, utilizing a ranking system based on the aggregated degradation metrics for power modulation—both increases and decreases. The primary objective is to optimize power distribution. This is complemented by a state-based classification of turbines, which guides the determination of power commands to ensure the wind farm's accurate adherence to the total power directive. Our approach circumvents the conventional reliance on iterative optimization techniques like particle swarm optimization and genetic algorithms, opting for a strategic dispatch based on the degradation index rankings. This not only facilitates an optimized power scheduling across turbines but also ensures precision in tracking the overall power directive by considering the individual power modulation capabilities of each turbine.

The methodology for implementation encompasses three principal strategies:

1. The development of an integrated turbine scoring system that includes metrics such as the comprehensive fatigue coefficient, power fluctuation coefficient, curtailment rate, and power regulation margin of the turbines. The fuzzy entropy approach is employed to calculate the comprehensive degradation indices for power upregulation and downregulation, enabling a prioritized ranking for optimization.

2. A detailed classification of turbines based on their operational status to evaluate their respective power modulation capabilities.

3. Within each power dispatch cycle, the power output of turbines is modulated in accordance with the ranking derived from the comprehensive degradation indices. This strategy is designed to prioritize the optimal allocation of power, minimizing adjustments to turbines with higher degradation indices to achieve a more balanced distribution of fatigue and other metrics. Additionally, leveraging the classified status of each turbine, the power command is tailored to the modulation capacity of each unit, ensuring precise adherence to the wind farm's overall power directive.

Indicator definitions

To optimize wind farm operation by accurately tracking power commands while reducing fatigue differences and power fluctuation levels among turbines, the following four evaluation indicators are selected in this study.

Comprehensive turbine fatigue coefficient

To optimize the fatigue balance in wind farm operation, considering that the comprehensive fatigue of turbine components is influenced by the active power output and turbulence factors, a comprehensive turbine fatigue coefficient $f_a^i$ is introduced to quantify the fatigue damage caused during turbine operation. The calculation method is shown in equation (1), ¹⁹

$$f_a^i(t)=f_a^i(t_0)+\frac{{\int }_{t_0}^t{P}_i(t)\mathrm{dt}}{P_{\mathrm{rate}}^i{T}_{\mathrm{ser}}^i(1+M_{\mathrm{rep}}^i)}+D_{\mathrm{dis}}\frac{{\int }_{t_0}^t{I}_{\mathrm{eff}}^i(t)\mathrm{dt}}{T_{\mathrm{ser}}^i(1+M_{\mathrm{rep}}^i)}$$

(1)

where, $f_a^i$ (t₀) represents the cumulative fatigue coefficient of turbine i at time t₀, with an initial value of 0; The second term represents the operational fatigue caused by the turbine's operation, which is 0 when the turbine does not operate; The third term represents the fatigue caused by turbulence; $P_i\left(t\right)$ represents the current output power of turbine i; $P_{\mathrm{rate}}^i$ represents the rated power of turbine i; $T_{\mathrm{ser}}^i$ represents the designed lifetime of turbine i; $M_{\mathrm{rep}}^i$ represents the maintenance compensation coefficient of turbine i; $D_{\mathrm{dis}}$ represents the turbulence fatigue equivalent coefficient of the wind farm; $I_{\mathrm{eff}}^i$ (t) represents the effective turbulence intensity of turbine i at time t, which consists of the wake turbulence intensity $I_w^i$ (t) and the ambient turbulence intensity $I_a^i$ (t), as calculated in equation (2), ²⁰

$$\{\begin{array}{l}{I}_{\mathrm{ref}}^i\left(t\right)=\sqrt{I_a^i{(t)}^2+I_w^i{(t)}^2}\\ I_a^i\left(t\right)\frac{I_{ref}(0.75\cdot v_i(t)+5.6)}{v_i(t)}\\ I_w^i\left(t\right)\frac{1}{S_i}\sqrt{1.2\cdot C_T^i(t)}\end{array}$$

(2)

where, $I_{\mathrm{ref}}^i$ represents the reference value of turbulence intensity at a wind speed of 15 m/s at the hub height. According to the wind turbine design standards published by the International Electrotechnical Commission, this value is set to 0.15 for conventional onshore wind farms. ²¹ $v_i$ represents the wind speed at the hub height of turbine i; $S_i$ represents the swept area of the rotor of turbine i; $C_T^i$ represents the thrust coefficient of turbine i.

Turbine power fluctuation coefficient

To reduce periodic power fluctuations of wind turbines, thereby improving operational stability and reducing operational fatigue, the turbine power fluctuation coefficient is defined as an evaluation indicator. The power fluctuation coefficient $g_i$ for turbine ii can be calculated as follows,

$$g_i(t)=\sum _{n_0=1}^{N_0}\sqrt{{(P_i(t-n_0·T)-P_i^a)}^2}$$

(3)

$$P_i^a(t)=\frac{1}{N_0}\sum _{n_0=1}^{N_0}{P}_i(t-n_0·T)$$

(4)

where, g_i(t) and P_i^a( t) represent the standard deviation (SD) and the mean of the power of turbine i calculated based on the most recent N₀ historical periods from the current time t, respectively. The smaller the SD, the smaller the power fluctuation of the turbine. T represents the control period.

Turbine curtailment rate

The turbine curtailment rate can serve as an indicator reflecting the power regulation capability of a turbine. When the curtailment rate is lower, the turbine has a stronger capability to down-regulate its power but a weaker capability to up-regulate its power. Conversely, when the curtailment rate is higher, the turbine has a weaker capability to down-regulate its power but a stronger capability to up-regulate its power. The turbine curtailment rate is defined as the difference between 1 and the proportion of the turbine’s current actual power output to its current theoretical maximum power output. It can be calculated as follows,

$${\delta }_i(t)=1-\frac{P_i(t)}{P_{\mathrm{mppt}}^i(t)}$$

(5)

where, ${\delta }_i(t)$ represents the curtailment rate of turbine i; $P_i(t)$ represents the current power output of turbine i; $P_{\mathrm{mppt}}^i(t)$ represents the current theoretical maximum power output of turbine i according to the Maximum Power Point Tracking (MPPT) strategy, which can be determined through the interpolation from the turbine’s power curve based on the current wind speed.

Turbine power regulation margin

The turbine power regulation margin is the most direct indicator reflecting the turbine’s power regulation capability. It can be divided into the power up-regulation margin and the power down-regulation margin. Specifically, the power up-regulation margin is the difference between the turbine’s predicted power value for the next cycle and its current power value, which can be calculated as equation (6). The power down-regulation margin is the difference between the turbine’s current power value and its lower limit for power curtailment, which can be calculated as equation (7).

Power up-regulation margin: $\mathrm{\Delta }{P}_{\mathrm{up}}^i$ :

$$\mathrm{\Delta }{P}_{\mathrm{up}}^i(t)=P_{\max }^i(t+T)-P_i(t)$$

(6)

Power down-regulation margin $\mathrm{\Delta }{P}_{\mathrm{dw}}^i$ :

$$\mathrm{\Delta }{P}_{\mathrm{dw}}^i(t)=P_i(t)-P_{\min }^i$$

(7)

where, $P_{\max }^i(t+T)$ represents the predicted power value for turbine i in the next cycle, that is, the maximum power the turbine can achieve in the next cycle; $P_{\min }^i$ represents the lower limit for power curtailment of turbine i.

Comprehensive evaluations of turbine control capabilities based on the fuzzy entropy method

The significance of each evaluation indicator varies within a comprehensive evaluation system. Indicator weights can reflect the significance of corresponding indicators within an evaluation system. The larger the weight, the greater the impact of the corresponding indicator on the overall evaluation system. In terms of the entropy method, the concept of entropy from information theory is utilized to measure the degree of dispersion of indicators. The greater the dispersion of an indicator, the smaller its entropy value, indicating a greater impact on the comprehensive evaluation results and hence a larger weight for the corresponding indicator. ²² Firstly, the weight of each indicator is determined using the entropy method. Then, the fuzzy membership function method is employed to calculate the comprehensive score of each turbine. In this study, the comprehensive deterioration degree of wind turbines is used as the comprehensive evaluation score for turbines.

Since the state parameters of wind turbines change in each control cycle, the calculated values of indicator parameters also change accordingly. Therefore, before the power is allocated to turbines in each cycle, it is necessary to re-determine the weight of each indicator for turbines and the comprehensive scores of turbines, followed by the re-ranking based on these scores, Supplementary description: The flowchart of Fuzzy entropy calculation is shown in Figure 1.

Figure 1.

Fuzzy entropy calculation flowchart.

Determination of indicator weights

Assume that the number of wind turbines in the wind farm is n, and m evaluation indicators are selected for each turbine. The sample data for each cycle are organized into a sample data matrix X ∈R^n×m, as shown in equation (8),

$${\mathbf{X}}_{n\times m}=\left[\begin{array}{c}{x}_{11}{x}_{12}\cdots x_{1m}\hfill \\ \multicolumn{1}{c}{x_{21}{x}_{22}\cdots x_{2m}}\\ \multicolumn{1}{c}{⋮⋮\ddots ⋮}\\ \multicolumn{1}{c}{x_{n1}{x}_{n2}\cdots x_{\mathrm{nm}}}\end{array}\right]$$

(8)

where, $x_{\mathrm{ij}}$ (i∈[1, 2, …, n], j∈[1, 2, …, m]) represents the j-th evaluation indicator of turbine i.

Next, the sample data are normalized using the deterioration degree function. Depending on the indicator type, the deterioration degree function includes the following three forms. ⁶

Smaller-the-better indicators

For smaller-the-better indicators, the lower the value, the better the corresponding performance of the turbine, and thus the smaller the deterioration degree.

$$\begin{array}{c}\multicolumn{1}{c}{x_{\mathrm{ij}}^{\prime }=\{\begin{array}{c}0x_{\mathrm{ij}}<x_{min}\hfill \\ \multicolumn{1}{c}{\frac{x_{\mathrm{ij}}-x_{min}}{x_{max}-x_{min}},x_{min}\le x_{\mathrm{ij}}\le x_{max}}\\ \multicolumn{1}{c}{1x_{\mathrm{ij}}>x_{max}}\end{array}}\end{array}$$

(9)

where, $x_{max}$ and $x_{min}$ represent the maximum and minimum values of the j-th indicator among all turbines in the current cycle, respectively; $x_{\mathrm{ij}}\prime$ ∈[0, 1] represents the deterioration degree of $x_{\mathrm{ij}}$ .

Range indicators

For indicators with an optimal value range, the deterioration degree is smallest when the indicator value is within this optimal range. The deterioration degree function for moderate indicators can be defined as follows,

$$\begin{array}{c}\multicolumn{1}{c}{x_{\mathrm{ij}}^{\prime }=\{\begin{array}{c}1x_{\mathrm{ij}}<x_{min}\mathrm{or}{x}_{\mathrm{ij}}>x_{max}\hfill \\ \multicolumn{1}{c}{\frac{x_{\mathrm{ij}}-x_{min}}{x_a-x_{min}}{x}_{min}\le x_{\mathrm{ij}}<x_a}\\ \multicolumn{1}{c}{0,x_a\le x_{\mathrm{ij}}\le x_b}\\ \multicolumn{1}{c}{\frac{x_{\mathrm{ij}}-x_b}{x_{max}-x_b}{x}_b<x_{\mathrm{ij}}\le x_{max}}\end{array}}\end{array}$$

(10)

where, $x_a$ and $x_b$ represent the lower and upper bounds of the optimal value range for the j-th indicator.

Larger-the-better indicators

For larger-the-better indicators, the higher the value, the better the corresponding performance of the turbine, and thus the smaller the deterioration degree.

$$\begin{array}{c}\multicolumn{1}{c}{x_{ij\prime }=\{\begin{array}{c}1x_{\mathrm{ij}}<x_{min}\hfill \\ \multicolumn{1}{c}{\frac{x_{max}-x_{\mathrm{ij}}}{x_{max}-x_{min}},x_{min}\le x_{\mathrm{ij}}\le x_{max}}\\ \multicolumn{1}{c}{0x_{\mathrm{ij}}>x_{max}}\end{array}}\end{array}$$

(11)

After the deterioration degree is calculated, the resulting sample data matrix is denoted as X ′∈R^n×m,

$$X\prime =\left[\begin{array}{c}{x\prime }_{11}{x\prime }_{12}\cdots {x\prime }_{1m}\hfill \\ \multicolumn{1}{c}{{x\prime }_{21}{x\prime }_{22}\cdots {x\prime }_{2m}}\\ \multicolumn{1}{c}{⋮⋮\ddots ⋮}\\ \multicolumn{1}{c}{{x\prime }_{n1}{x\prime }_{n2}\cdots {x\prime }_{\mathrm{nm}}}\end{array}\right]$$

(12)

As reported in previous studies, the sample data are typically organized into a single sample data matrix for turbine indicators. However, considering the evaluation differences of turbine indicators during up-regulation and down-regulation of power in wind farms, sample data matrices are separately organized for up-regulation X _up∈R^n×4 and down-regulation X _dw∈R^n×4 based on the defined four indicators, which can be expressed as follows,

$${\mathit{X}}_{\mathit{up}}=\left[\begin{array}{c}{f}_1{g}_1{\delta }_1\mathrm{\Delta }{P}_{\mathit{up}}^1\hfill \\ \multicolumn{1}{c}{f_2{g}_2{\delta }_2\mathrm{\Delta }{P}_{\mathit{up}}^2}\\ \multicolumn{1}{c}{⋮⋮⋮⋮}\\ \multicolumn{1}{c}{f_n{g}_n{\delta }_n\mathrm{\Delta }{P}_{\mathit{up}}^n}\end{array}\right]$$

(13)

$${\mathit{X}}_{\mathit{dw}}=\left[\begin{array}{c}{f}_1{g}_1{\delta }_1\mathrm{\Delta }{P}_{\mathit{dw}}^1\hfill \\ \multicolumn{1}{c}{f_2{g}_2{\delta }_2\mathrm{\Delta }{P}_{\mathit{dw}}^2}\\ \multicolumn{1}{c}{⋮⋮⋮⋮}\\ \multicolumn{1}{c}{f_n{g}_n{\delta }_n\mathrm{\Delta }{P}_{\mathit{dw}}^n}\end{array}\right]$$

(14)

The types of deterioration degree for the indicators defined above are classified in the up-regulation sample data matrix and the down-regulation sample data matrix, as shown in Table 1. Based on the classification in Table 1, the deterioration degrees for each indicator in X _up and X _dw are calculated. The resulting up-regulation sample data matrix and down-regulation sample data matrix after calculating the deterioration degrees are denoted as X ′_up∈R^n×4 and X ′_dw∈R^n×4, respectively.

Table.1.

Classification of indicator deterioration degree types.

Sample matrix		Up-regulation matrix	Down-regulation matrix
Comprehensive fatigue coefficient		Smaller-the-better	Larger-the-better
Power fluctuation coefficient		Smaller-the-better	Smaller-the-better
Wind abandonment rate		Larger-the-better	Smaller-the-better
Power regulation margin	Up-regulation margin	Larger-the-better	—
	Down-regulation margin	—	Larger-the-better

After obtaining the sample data matrices with calculated deterioration degrees, the entropy method is used to calculate the weight coefficient for each indicator. These weight coefficients form the weight coefficient matrix W ∈R^1×m, as shown in equation (15),

$$\mathit{W}=[w_1,w_2,...,w_m]$$

(15)

Based on the method for calculating the indicator weight coefficients, the weight coefficient matrices for X ′_up and X ′_dw are calculated and denoted as W _up∈R^1×4 and W _dw∈R^1×4, respectively.

Comprehensive score calculation

After the weight coefficient for each indicator is determined, the comprehensive deterioration degree of each wind turbine is calculated based on fuzzy theory. Using the sample data matrix X ′, which contains n turbines and mm indicators, as an example, the deterioration degree of each indicator can be divided into four levels: Low, Medium-Low, Medium-High, and High. The higher the deterioration degree level, the lower the power regulation capability of the turbine. The fuzzy membership functions for these four levels are represented using semi-trapezoidal and triangular functions. The membership functions for the four levels of each indicator are denoted as M₁, M₂, M₃, and M₄, which can be expressed as follows,

$$\begin{array}{c}\multicolumn{1}{c}{M_1(x{\prime }_{\mathrm{ij}})=\{\begin{array}{c}1\hfill \\ \multicolumn{1}{c}{\frac{{x\prime }_{\mathrm{ij}}-b}{a-b}}\\ \multicolumn{1}{c}{0}\end{array},\begin{array}{c}{x\prime }_{\mathrm{ij}}\le a\hfill \\ \multicolumn{1}{c}{a<{x\prime }_{\mathrm{ij}}<b}\\ \multicolumn{1}{c}{{x\prime }_{\mathrm{ij}}\ge b}\end{array}}\end{array}$$

(16)

$$\begin{array}{c}\multicolumn{1}{c}{M_2\left({x\prime }_{\mathrm{ij}}\right)=\{\begin{array}{c}0\hfill \\ \multicolumn{1}{c}{\frac{{x\prime }_{\mathrm{ij}}-a}{b-a}}\\ \multicolumn{1}{c}{\frac{{x\prime }_{\mathrm{ij}}-c}{b-c}}\end{array},\begin{array}{c}{x\prime }_{\mathrm{ij}}\le a\mathrm{o}\mathrm{r}{x\prime }_{\mathrm{ij}}\ge c\hfill \\ \multicolumn{1}{c}{a<{x\prime }_{\mathrm{ij}}<b}\\ \multicolumn{1}{c}{b\le {x\prime }_{\mathrm{ij}}<c}\end{array}}\end{array}$$

(17)

$$\begin{array}{c}\multicolumn{1}{c}{M_3\left({x\prime }_{\mathrm{ij}}\right)=\{\begin{array}{c}0\hfill \\ \multicolumn{1}{c}{\frac{{x\prime }_{\mathrm{ij}}-b}{c-b}}\\ \multicolumn{1}{c}{\frac{{x\prime }_{\mathrm{ij}}-d}{c-d}}\end{array},\begin{array}{c}{x\prime }_{\mathrm{ij}}\le b\mathrm{o}\mathrm{r}{x\prime }_{\mathrm{ij}}\ge d\hfill \\ \multicolumn{1}{c}{b<{x\prime }_{\mathrm{ij}}<c}\\ \multicolumn{1}{c}{c\le {x\prime }_{\mathrm{ij}}<d}\end{array}}\end{array}$$

(18)

$$\begin{array}{c}\multicolumn{1}{c}{M_4(x{\prime }_{\mathrm{ij}})=\{\begin{array}{c}0\hfill \\ \multicolumn{1}{c}{\frac{{x\prime }_{\mathrm{ij}}-c}{d-c}}\\ \multicolumn{1}{c}{1}\end{array},\begin{array}{c}{x\prime }_{\mathrm{ij}}\le c\hfill \\ \multicolumn{1}{c}{c<{x\prime }_{\mathrm{ij}}<d}\\ \multicolumn{1}{c}{{x\prime }_{\mathrm{ij}}\ge d}\end{array}}\end{array}$$

(19)

where, $a$ , $b$ , $c$ , and $d$ represent the boundaries for the four levels, taking values of 0, 1/3, 2/3, and 1, respectively. According to the definitions in equations (16) to (19), the membership functions for each level are illustrated in Figure 2.

Figure 2.

Illustration of membership functions for each level.

To ensure that turbines with higher degradation levels receive higher degradation scores, scoring weights for the “Low,”“Medium-Low,”“Medium-High,” and “High” levels are set to 0.1, 0.2, 0.3, and 0.4, respectively. Therefore, the degradation score sc_ij for turbine i under indicator j is calculated as follows,

$$s{c}_{\mathrm{ij}}=0.1M_1(x{\prime }_{\mathrm{ij}})+0.2M_2(x{\prime }_{\mathrm{ij}})+0.3M_3(x{\prime }_{\mathrm{ij}})+0.4M_4(x{\prime }_{\mathrm{ij}})$$

(20)

Based on that, the degradation score set Sc_i for turbine i with respect to each indicator can be expressed as follows,

$$S{c}_i=[S{c}_{i1},S{c}_{i2},\cdots ,S{c}_{\mathrm{im}}]$$

(21)

Using the calculated weight matrix and the score set, the comprehensive degradation φ_i for turbine i is determined as follows,

$${\phi }_i=W·{\mathrm{Sc}}_i^{\mathrm{T}}$$

(22)

Finally, φ_i is transformed into the final comprehensive degradation ${\phi }_i\prime$ ranging from 0 to 100 using the following equation,

$${{\phi }^{\prime }}_i=\frac{{\phi }_i}{{\sum }_{i=1}^n{\phi }_i}\times 100\%$$

(23)

After W_up is combined with W_dw, the comprehensive degradation for both power up-regulation and down-regulation can be obtained using the above indicator comprehensive scoring method. When power up-regulation is required in the wind farm, turbines are ranked based on their comprehensive degradation for power up-regulation. Since turbines with lower degradation scores for power up-regulation have stronger power up-regulation capabilities, they are prioritized for scheduling. Similarly, when power down-regulation is required in the wind farm, turbines are ranked based on their comprehensive degradation for power down-regulation. Turbines with lower degradation scores for power down-regulation have stronger power down-regulation capabilities and are thus prioritized for scheduling.

Active power optimization scheduling of wind farms

Constraints

Wind farm power fluctuation constraint

According to the State Grid's maximum wind farm power variation standards, the power fluctuation limits within 1 min and 10 min for wind farms with different installed capacities are listed in Table 2.

Table 2.

Wind farm power fluctuation limits.

Installed capacity of wind farm (MW)	1 min power fluctuation limit (MW)	10 min power fluctuation limit (MW)
<30	3	10
30~150	Installed capacity/10	Installed capacity/3
>150	15	50

Wind turbine power limitation constraint

The frequent start-stop operation of wind turbines can reduce their operational safety and stability. Therefore, a minimum power limit is usually set to prevent turbines from being shut down due to an excessive power reduction. To prevent a high wind abandonment rate while ensuring sufficient downward power adjustment margin, the minimum power limit $P_{min}$ for each wind turbine is set as follows,

$$P_{min}=0.2P_{\mathrm{rate}}$$

(24)

where, $P_{\mathrm{rate}}$ represents the rated power of the turbine.

Power command tracking accuracy constraint

To ensure high precision in tracking the power command for the wind farm, the actual power output of the wind farm should deviate by no more than 1% from the power command $P_{\mathrm{cmd}}$ at any given time. This constraint can be expressed as follows,

$${\sum }_{i=1}^n{P}_i-P_{\mathrm{cmd}}\le 1\%P_{\mathrm{cmd}}$$

(25)

Classification of wind turbine states

The power regulation capability of wind turbines varies depending on their operational states. The factors for the classification of turbine states include the start-stop state $P_{min}$ , the cut-in power $P_{\mathrm{in}}$ (i.e., the power corresponding to the cut-in wind speed on the power curve), the real-time power $P_i\left(t\right)$ , and the predicted power ${P_i}_{max}(t+T)$ .

Firstly, turbines are classified into stopped turbines and operating turbines based on their real-time start-stop state recorded by the SCADA system. If the turbine's start-stop state is $s_i=0$ , it indicates that the turbine is stopped due to faults, maintenance, or other reasons, resulting in zero power up-regulation and down-regulation capabilities. For operating turbines with $s_i=1$ , their states are further classified based on the relationship between real-time power, predicted power, minimum power limit, and cut-in power. On that basis, the power regulation capability for each state can be determined. The classification of the operational states of wind turbines is shown in Figure 3.

Figure 3.

Schematic diagram for the classification of wind turbine operating states.

Figure 3 illustrates seven different operational states of wind turbines. For the turbine ii, its power regulation capabilities in different states include passive power down-regulation $P_{{\mathit{i}}_{\mathrm{p}}}$ , power up-regulation capability $P_{{\mathit{i}}_{\mathbf{s}}}$ , and active power down-regulation capability $P_{{\mathit{i}}_{\mathbf{a}}}$ , the Characteristics of 7 state classes are shown in Table 3.

Table 3.

Characteristics of 7 state classes.

State	Characteristics
1	The turbine unit is in standby mode, where the power forecast remains below Pin, and it will continue to remain in standby mode in the next cycle. The turbine unit's power cannot be further up-regulated or down-regulated.	$\{\begin{array}{l}{P}_{\mathrm{p}}^i=0\hfill \\ P_{\mathrm{s}}^i=0\hfill \\ P_{\mathrm{a}}^i=0\hfill \end{array}$
2	The forecasted power exceeds Pin, allowing the unit to be grid-connected in the next cycle. The turbine unit has a certain capability to up-regulate the power but cannot down-regulate it.	$\{\begin{array}{l}{P}_{\mathrm{p}}^i=0\hfill \\ P_{\mathrm{s}}^i=P_{\max }^i\left(t+T\right)\hfill \\ P_{\mathrm{a}}^i=0\hfill \end{array}$
3	The real-time power of the unit exceeds Pin, but the forecasted power is less than Pin, indicating that the unit will be in standby mode in the next cycle. The turbine unit will passively down-regulate the power, unable to actively up-regulate or down-regulate the power.	$\{\begin{array}{l}{P}_{\mathrm{p}}^i=P_i\left(t\right)\hfill \\ P_{\mathrm{s}}^i=0\hfill \\ P_{\mathrm{a}}^i=0\hfill \end{array}$
4	The forecasted power of the unit ranges from Pin to Pmin, which is less than the real-time power. The turbine unit will passively down-regulate the power by a certain amount and cannot actively up-regulate or down-regulate the power.	$\{\begin{array}{l}{P}_{\mathrm{p}}^i=P_i\left(t\right)-P_{\max }^i\left(t+T\right)\hfill \\ P_{\mathrm{s}}^i=0\hfill \\ P_{\mathrm{a}}^i=0\hfill \end{array}$
5	The real-time power of the unit ranges from Pin to Pmin, while the forecasted power exceeds the real-time power. The turbine unit has a certain capability to up-regulate the power but cannot actively down-regulate the power due to the real-time power being less than Pmin.	$\{\begin{array}{l}{P}_{\mathrm{p}}^i=0\hfill \\ P_{\mathrm{s}}^i=P_{\max }^i\left(t+T\right)-P_i\left(t\right)\hfill \\ P_{\mathrm{a}}^i=0\hfill \end{array}$
6	The real-time power of the unit ranges from Pin to Pmin, and the forecasted power exceeds the real-time power. The turbine unit has a certain capability to up-regulate or down-regulate the power.	$\{\begin{array}{l}{P}_{\mathrm{p}}^i=0\hfill \\ P_{\mathrm{s}}^i=P_{\max }^i\left(t+T\right)-P_i\left(t\right)\hfill \\ P_{\mathrm{a}}^i=P_i\left(t\right)-P_{\min }\hfill \end{array}$
7	Both the real-time power and forecasted power of the unit exceed Pmin, and the forecasted power is less than the real-time power. The turbine unit can passively down-regulate the power; meanwhile, it maintains a certain capability to down-regulate the power, but cannot up-regulate the power.	$\{\begin{array}{l}{P}_{\mathrm{p}}^i=P_i\left(t\right)-P_{\max }^i\left(t+T\right)\hfill \\ P_{\mathrm{s}}^i=0\hfill \\ P_{\mathrm{a}}^i=P_i\left(t\right)-P_{\min }\hfill \end{array}$

Active power scheduling algorithm

Determination of unit ranking and classification

Based on the comprehensive degradation evaluation method of unit indicators, the comprehensive degradation of unit power up-regulation and down-regulation is determined for the current cycle. Since lower degradation indicates a stronger power regulation capability, the power up-regulation and down-regulation comprehensive degradation of units are ranked separately in ascending order. This determines the ascending power control sequence L_up and descending power control sequence L_dw of wind turbine units.

Based on the classification of unit power generation states, the passive power down-regulation, potential power up-regulation, and actively down-regulated power of each unit are determined.

Calculation of the overall power adjustment ΔP

Firstly, the power difference dP between the overall real-time power of the wind farm and the power command P_cmd(t+T) is calculated for the next control cycle, which can be expressed as follows,

$$\mathrm{dP}=\sum _{i=1}^n{P}_i\left(t\right)-P_{\mathrm{cmd}}(t+T)$$

(26)

Then, the total amount of passive power down-regulation from the units in the wind farm is considered to determine the overall power adjustment $\mathrm{dP}\prime$ , which can be expressed as follows,

$$\mathrm{dP}\prime =\mathrm{dP}-\sum _{i=1}^n{P}_{\mathrm{P}}^i$$

(27)

Finally, the adjustment of $\mathrm{dP}\prime$ is made according to the grid's power fluctuation constraints on the wind farm. Assuming the power fluctuation limit for a certain wind farm is $\delta P$ , the wind farm's overall power adjustment $\mathrm{\Delta }P$ can be determined as follows,

$$\begin{array}{c}\multicolumn{1}{c}{\mathrm{\Delta }P=\{\begin{array}{c}-\delta P\hfill \\ \multicolumn{1}{c}{\mathrm{dP}\prime }\\ \multicolumn{1}{c}{\delta P}\end{array},\begin{array}{c}|\mathrm{dP}\prime |>\delta P\mathrm{an}\mathrm{d}\mathrm{dP}\prime <0\hfill \\ \multicolumn{1}{c}{|\mathrm{dP}\prime |\le \delta P}\\ \multicolumn{1}{c}{|\mathrm{dP}\prime |>\delta P\mathrm{an}\mathrm{d}\mathrm{dP}\prime >0}\end{array}}\end{array}$$

(28)

Determining the Wind Farm's Need for Power up-regulation or Down-regulation

When $\mathrm{\Delta }P<0$ , it indicates that the wind farm needs to up-regulate the power by $\left|\mathrm{\Delta }P\right|$ based on the current overall power to reach the power command in the next cycle. When $\mathrm{\Delta }P\ge 0$ it indicates that the wind farm needs to down-regulate the power by $\mathrm{\Delta }P$ based on the current overall power to reach the power command in the next cycle. The specific process is illustrated in Figure 4.

Figure 4.

Flowchart of active power optimization scheduling algorithms for wind farms.

Example analysis

Parameter settings

The wind speed data from the SCADA system of a wind farm in northwest China recorded from 00:00 on February 10, 2016, to 23:50 on February 10, 2016, with a data collection period of 10 min, are selected for analysis. The wind farm consists of 25 units of 2MW wind turbine, with a total installed capacity of 50 MW. The cut-in wind speed for the units is 3 m/s, corresponding to a cut-in power of 19.86 kW, and the cut-out wind speed is 25 m/s.

In this example, the optimization period is set to be the same as the data collection period, that is, $T=10$ min. The data recording period contains a total of 144 optimization cycles. The power fluctuation constraint within a 10-min interval in the wind farm is set to 16 MW, and the lower limit of the power restriction for wind turbines is set to $P_{min}=0.4$ MW. The maintenance compensation coefficient for the units is set to 0.5. During the optimization control period, all units are in operation. In the simulation experiment, the power prediction values of wind turbines are obtained by reading the wind speed of the next control cycle of the units and then interpolating the power curve.

Example results

Power tracking accuracy under different power limitation levels

The power limitation level ${\eta }_{\mathrm{f}}$ for the wind farm in the next cycle is defined as the proportion of the overall power scheduling instruction of the wind farm in the next cycle to the overall power prediction,

$${\eta }_{\mathrm{f}}=P_{\mathrm{cmd}}(t+T)/\sum _{i=1}^n{P}_{max}^i(t+T)$$

(29)

Firstly, the power tracking accuracy is analyzed for different power limitation levels of the wind farm, which is set at 0.9, 0.6, and 0.3, respectively. According to the proposed wind farm active power optimization scheduling method, the overall power for 144 control cycles of the wind farm and the corresponding overall power command are shown in Figure 5. Figures 5(a), 4(c), and 5(e) respectively illustrate the real-time power $P_{\mathrm{wf}}$ (red solid line) and the corresponding power command $P_{\mathrm{cmd}}$ (blue dashed line) for ${\eta }_{\mathrm{f}}$ set at 0.9, 0.6, and 0.3. It can be observed that the proposed method can effectively track and control $P_{\mathrm{cmd}}$ under different power limitation levels. Larger tracking errors occur during the low wind speed period, primarily concentrated in control cycles 70 to 110. This is because a large number of units are in standby mode during the low wind speed period, making it impossible to implement power up-regulation to reduce tracking errors. Figure 6(b), (d), and (f) illustrate the percentage tracking errors of the wind farm for ${\eta }_{\mathrm{f}}$ set at 0.9, 0.6, and 0.3, respectively (red solid line). During cycles 70 to 110, some cycles exceed the permissible error limit, with noticeably higher error values for ${\eta }_{\mathrm{f}}=0.9$ . During the low wind speed period, the overall power of the wind farm is small, resulting in larger percentage errors but smaller actual power deviations. In other control cycles, due to better wind conditions, the units have stronger power adjustment capabilities, and hence the power tracking error can be controlled within the permissible range. Additionally, since it is permissible to force some units into standby mode to achieve overall power down-regulation, the wind farm does not exceed the permissible error limit.

Figure 5.

Power tracking performance under different power limitation levels.

Figure 6.

Power tracking performance under different strategies.

The analysis indicates that there are the following situations where tracking errors exceed the permissible value.

• (1) After the wind farm forces some units into standby mode to achieve overall power down-regulation, if all units in the field lack enough secondary power reserve to compensate for the excessive power reduction during the low wind speed period, $P_{\mathrm{wf}}$ will ultimately be lower than $P_{\mathrm{cmd}}$ .

• (2) When the wind farm up-regulates the overall power by increasing the power output of certain units, if the units are in state 2 and the power reference value issued to the units is lower than P_in, these units will remain in standby mode and cannot increase power output, ultimately resulting in $P_{\mathrm{wf}}$ lower than $P_{\mathrm{cmd}}$ .

Optimization effect analysis

To analyze the optimization effect of the proposed wind farm active power optimization scheduling method based on unit state evaluation (referred to as the optimization method) on unit fatigue damage and power fluctuations within the wind farm, the optimization method is compared with the following two control strategies.

• Strategy 1: Proportional Allocation. Different from conventional proportional allocation methods, this strategy allocates power based on the proportion of each unit's power prediction for the next cycle to the total power prediction of the wind farm, aiming to better consider the power adjustment margin of each unit.

$$P_{\mathrm{ref}}^i(t+T)=s_i·P_{\mathrm{cmd}}(t+T)\frac{P_{max}^i(t+T)}{\sum _{i=1}^n{s}_i·P_{max}^i(t+T)}$$

(30)

• Strategy 2: Sequential Method. This strategy is still based on the unit classification method for power scheduling. However, different from the optimization method, the sequential method does not prioritize unit scheduling based on unit comprehensive deterioration. During the power instruction scheduling process, the wind farm performs power up-regulation or down-regulation control in sequential order according to the unit numbers.

The tracking performance of the wind farm with respect to P_cmd under three schemes is illustrated in Figure 6, where the power limit factor η_f for the wind farm is set to 0.8 in all cases. Figure 6(a) illustrates the overall power for each period under different schemes. To better compare the tracking accuracy of different schemes, Table 4 provides statistics on the Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE) for each scheme.

Table 4.

Wind farm power tracking errors under different strategies.

Error metric	Optimization method	Sequential method	Proportional allocation
MAE (kW)	760.68	761.07	782.49
MAPE	0.1176	0.1177	0.1413
RMSE (kW)	1.1167 × 103	1.1169 × 103	1.1224×103

According to Table 4, the MAE, MAPE, and RMSE for the optimization method are 760.68 kW, 0.1176, and 1.1167 × 10³kW, respectively, which are slightly larger than those of the sequential method but significantly larger than those of the proportional allocation method. Figure 6(b) illustrates the percentage tracking error for each scheme, indicating that the tracking deviations of all three schemes are concentrated during the low wind speed period in the wind farm. Specifically, the tracking error of the sequential method is almost identical to that of the optimization method, while the proportional allocation method exhibits significantly larger tracking errors. This suggests that both the sequential and optimization methods, which employ the classification of units by taking account of power regulation margins, can effectively reduce tracking errors with respect to the power command.

The power fluctuation and fatigue allocation among units under different schemes are shown in Figure 7. Figure 7(a) illustrates the power fluctuation coefficients calculated based on the generated power of each unit over 144 control cycles for different schemes, while Figure 7(b) illustrates the cumulative fatigue coefficients of each unit at the end of the 144th control cycle. Correspondingly, the SD of the cumulative fatigue coefficients and power fluctuation coefficients among units at the end of the 144th control cycle for different schemes is listed in Table 5. A smaller SD indicates less variability among units. It can be observed that after the 144th control cycle, the SD of the cumulative fatigue among units under the optimization, sequential, and proportional allocation methods is 3.0074 × 10⁻⁴, 3.8958 × 10⁻⁴, and 3.9016 × 10⁻⁴, respectively. The optimization method effectively reduces the difference in fatigue damage among units compared with the other two schemes. Moreover, the SD of the power fluctuation coefficients among units under the optimization, sequential, and proportional allocation methods is 0.0705, 0.0782, and 0.0781, respectively. The optimization method significantly reduces the difference in power fluctuations among units compared with the other two schemes. Figure 7(c) illustrates the SD of the fatigue coefficients among units for different schemes over each cycle. It can be observed that with an increase in control cycles, the difference in fatigue among units under different schemes presents an increasing trend, with the fatigue difference under the optimization method consistently lower than the others.

Figure 7.

Power fluctuation and fatigue allocation among units under different schemes.

Table 5.

Standard deviation of cumulative fatigue and power fluctuation among units.

Method	Cumulative fatigue SD	Power fluctuation SD
Optimization	3.0074 × 10−4	0.0705
Sequence	3.8958 × 10−4	0.0782
Proportion	3.9016 × 10−4	0.0781

Under different schemes, the power generation of each unit in each control period is shown in Figure 8, with the label "#i" in the top left corner of each subfigure indicating the corresponding unit number. When using the proportional allocation method (shown as magenta dashed lines) for intra-field power scheduling, the power fluctuations of each unit are relatively large. With the sequential method (shown as blue dashed lines), as units are always scheduled by the wind farm in sequence according to their numbers, units with lower numbers exhibit larger power fluctuations, while those with higher numbers show the smallest fluctuations due to less scheduling among the three schemes. The wind farm effectively reduces the overall power fluctuations of each unit using the optimization method (shown as red solid lines) compared with proportional and sequential allocation. The comparison of the power of units WT1 to WT18 under the three schemes reveals that units under the optimization method exhibit smoother power fluctuations; The comparison of the power of units WT19 to WT25 under the three schemes reveals that although the power fluctuations of units under the optimization method are slightly larger than those under the sequential method, they are still significantly smaller than those under the proportional allocation method. The result consistent with the pattern described in Figure 7(a), indicates that the proposed optimization method can effectively reduce overall power fluctuations of each unit and decrease differences in power fluctuations between units.

Figure 8.

Power generation of each unit under different schemes.

Overall, the proposed wind farm active power optimization scheduling method based on unit state evaluations can effectively track power commands under different power limitation levels. Furthermore, it can significantly reduce power fluctuation differences between wind turbine units, load fatigue differences, and overall power fluctuations of each unit, thereby reducing wind farm operational costs.

Conclusion

Intelligent optimization algorithms and unit state evaluation methods are primarily employed in current research on active power scheduling of wind farms under power-limited operation. The former can achieve operational optimization for wind farms. However, the long calculation time and high dependence on the model accuracy of intelligent optimization algorithms are not conducive to real-time control applications. The latter is efficient in the calculation process but currently has deficiencies in wind farm operational optimization. In response to these problems, this paper investigates an active power optimization scheduling method for wind farms based on unit state evaluations, in an attempt to achieve operational optimization control of wind farms with lower computational complexity. More specifically, the following achievements are made in this study.

• (1) Indicators in the comprehensive unit scoring system are defined, including the comprehensive fatigue coefficient, power fluctuation coefficient, wind curtailment rate, and power regulation margin of units. Using these indicators, the fuzzy entropy method is applied to calculating the comprehensive deterioration degrees for power up-regulation and down-regulation of each unit, which are then used for optimized ranking.

• (2) Based on the power generation state of each unit, a detailed classification is performed to determine the power regulation capabilities of various unit types, ensuring the tracking accuracy of the overall power command of the wind farm. Active power optimization scheduling under power limitation is implemented based on the unit state classification and the ranked comprehensive deterioration degrees for power up-regulation and down-regulation.

• (3) The historical data recorded by the SCADA system of a wind farm in Northwest China is used for the simulation analysis to verify the effectiveness of the proposed active power optimization scheduling method. The results demonstrate that the proposed method can effectively track the power commands of the wind farm under different power limitation levels. When the power limitation degree of the wind farm is 0.8, the proposed optimization method achieves power tracking, with the MAE, MAPE, and RMSE being 760.6784 kW, 0.1176, and 1.1167 × 10³kW, respectively, presenting higher tracking accuracy than the sequential and proportional allocation methods. The SD of the cumulative fatigue and power fluctuation coefficient between units under the optimization method is 3.0074 × 10⁻⁴ and 0.0705, respectively, all indicators have experienced a minimum reduction of 9.85%, both significantly lower than those under the sequential and proportional allocation methods. In conclusion, the proposed method can effectively reduce the power fluctuation differences and load fatigue differences between units, as well as the overall power fluctuations of each unit, thereby reducing the operational and maintenance costs of the wind farm.