Research on entropy weight variation evaluation method for wind power clusters based on dynamic layered sorting

0 Introduction

With the continuous increase in energy demand and environmental awareness,wind energy is gradually becoming a central energy choice in countries worldwide because it is a clean,relatively safe,cost-effective,and renewable energy source.Wind power clusters,a critical form of wind energy generation,have advantages such as low cost,environmental friendliness,and economies of scale,making them an important trend in wind energy development.However,owing to the spatial and temporal variations in factors such as wind speed and wind direction,the dispatching and allocation problems of wind power clusters have become increasingly complex.Accurate evaluation and rational allocation have become the key challenges in dispatching and allocating wind power clusters.

Currently,research on stratified scheduling strategies for wind power clusters lacks a unified evaluation standard and indicator system,making it difficult to objectively compare and evaluate the research outcomes.The existing evaluation methods include expert scoring,grey correlation analysis,principal component analysis,and entropy weighting.Among them,expert scoring [1] is subjective,and the evaluation results are easily influenced by personal preferences and experience.Grey correlation analysis [2] ignores the linear relationships between indicators.Principal component analysis [3] only considers indicators with larger variances,which may result in information loss.Some scholars have combined multiple methods,such as the combination of the analytic hierarchy process and the fuzzy evaluation method used in [4],for a comprehensive evaluation of the active power control effects of wind power clusters.The entropy method or its improved methods can consider the weights between multiple indicators,comprehensively measure the degree of dispersion and influence of different indicators,and have a certain degree of objectivity compared to expert scoring.For example,references [5-6] used the analytic hierarchy process and entropy weighting to determine the weights of various indicators for comprehensive decision making.Reference [7] proposed an entropy-weighted clustering method that considered the time variation and correlation between wind power generation and load to evaluate the stability and security of the system.A comprehensive multi-indicator analysis can compensate for the insufficient correlation between indicators and reduce the limitations of principal component analysis (PCA),which may lead to some loss of information.The classification and value assignment of data are based on the correlation between the quality indicators in [8],reducing the overall assignment error.However,these studies used only fixed weights for the calculation and did not consider changes in weights over time.In addition,owing to the large fluctuations in the wind power output,fixed-weight evaluation cannot accurately reflect the weight differences of different indicators at different times.Therefore,this study proposes an evaluation method for wind power cluster entropy weighting that considers the correlation between indicators and the dynamic properties of entropy weights,with the aim of objectively and accurately evaluating the dispatch performance of wind power clusters.The evaluation method addresses the problems of subjectivity in expert scoring,potential information loss in PCA,and the inability to accurately reflect the weight differences of different indicators at different times in a fixed-weight evaluation.

In addition,for the allocation strategies of wind power clusters,most existing research focuses on the wind farm level.Owing to the hierarchical relationship between wind power clusters and wind farms,the allocation method can adopt a hierarchical structure. [9-10] proposed active power-layered control strategies for wind power cluster groups at different spatial scales,which improved wind power absorption while realizing scheduling plans;however,there was no comprehensive consideration of other factors,such as turbine fatigue and output fluctuations,for sorting and scheduling.Numerous scholars have developed various sorting-based cluster allocation strategies and references [11-13] proposed scheduling and allocation strategies for wind power clusters based on the ranking of unit fatigue,health status,and unit control ability.However,on a time scale,the power limiting status of individual wind farms may repeatedly change in a short term,introducing additional scheduling fatigue.With the implementation of wind power prediction systems,dynamically arranging the day-ahead power output plan of wind power clusters according to the predicted power has become the industry mainstream [14-16].Wind power prediction and cluster hierarchical scheduling are carried out at both time and spatial scales,and dynamic model predictive control and optimization scheduling methods have been adopted to improve the accuracy and reliability of cluster control.The above-mentioned references result in increasing wind power absorption and reliability in wind power clusters,but lacks research on stability aspects,such as reducing the frequency of adjustments,scheduling fatigue,and output fluctuations.Frequent scheduling operations increase the grid load pressure,making the power system more vulnerable and unstable.Therefore,appropriate research is required to reduce the number of scheduling operations.Therefore,this paper proposes a power cluster allocation method based on dynamic hierarchical sorting that comprehensively considers the power-limiting degree in the last cycle,adjustment margin,and volatility.Simultaneously,it considers reducing the number of scheduling times to improve the scheduling performance of the wind power clusters.The proposed allocation method addresses the problems of hierarchical allocation methods that do not comprehensively consider multiple factors.Additionally,the dynamic performance of the sorting allocation method is low.

In summary,this paper proposes an evaluation method for wind power clusters based on entropy weighting combined with a dynamic layered sorting allocation method,which comprehensively considers the correlation between indicators and the dynamic performance of weight changes and reduces the frequency of adjustments through dynamic layered sorting.These methods are of significance and application value in scheduling and allocating practical wind power clusters.Through this study,the comprehensive level of wind farms can be better evaluated,providing scientific decision-making support for wind energy development and scheduling.

1 Evaluation method based on entropy weighting

1.1 Evaluation indicators

1.1.1 Degree of power limitation in the last cycle

where t denotes the current cycle.This indicator represents the difference margin between the actual and rated outputs of the wind farm in the last cycle,indicating the power generation level and potential power increase in the last cycle,which affects the dispatching range of the next cycle.A larger value of this indicator is preferable when the wind farm needs to increase its power,indicating a larger difference in fulfilling the rated power in the last cycle and the potential for a higher increase in output within the rated power range in the next cycle.Conversely,a smaller value is preferable when a wind farm needs to decrease its power consumption.

This indicator reflects the proportion of electricity that a wind farm was unable to generate in the previous cycle owing to grid demand or excess wind power.The greater the power limitation of a wind farm,the less it can fully tap into its power generation potential,thereby affecting the effective utilization of wind energy.By considering this indicator,the operational strategy of the power grid can be optimized,wind power rationing events can be reduced,and wind energy utilization efficiency can be improved.

1.1.2 Adjustment margin

The adjustment margin refers to the relative difference between the actual output in the last cycle and the instruction for the next cycle when the wind farm tracks the grid instructions.It represents the direction and margin of the adjustment in the next cycle based on the output level in the previous cycle (considering only the magnitude of the adjustment margin in this case).When the wind farm must increase its power,a larger adjustment margin is preferred,indicating that a higher output can be increased within the instruction range in the next cycle.Conversely,a larger decremental adjustment margin is preferred when a wind farm must decrease its power.

The adjustment margin refers to the generation capacity margin that a wind farm can use to respond to grid dispatch instructions while ensuring safe and stable operation.A larger regulation margin indicates that wind farms can flexibly increase or decrease their power generation to adapt to changes in grid demand.This indicator is crucial for power grid scheduling,particularly in the case of large load fluctuations in power systems.

1.1.3 Fluctuation rate

where gi(t) represents the standard deviation of the power of unit i over the past five cycles,which is used to measure the power fluctuation of the unit,represents the average power of unit i over the past five cycles.This indicator considers the fluctuations over five cycles and quantifies them as the fluctuation rate.A smaller fluctuation rate is preferred during the dispatching process,indicating a lower volatility in the power output.

The fluctuation of wind power is a special concern in wind power cluster scheduling.The high power fluctuation rate of wind farms means that their output power is unstable,which poses challenges to the scheduling and stable operation of the power grid.Volatility can be used to better understand the output stability of wind farms and take appropriate measures to balance the entire system.

1.2 Entropy weighting method and variable weighting theory

1.2.1 Entropy weighting method

The entropy weighting method is a decision-making method based on the principle of information entropy.It calculates the entropy weight of each indicator based on the degree of variation of each indicator,and then corrects the weight of each indicator using the entropy weight to obtain a more objective indicator weight.Information entropy is a measure of the degree of system disturbance and can be used to evaluate the degree of variance in various indicators.The smaller the degree of variation in the indicator,the greater the information entropy;the smaller the amount of information provided by the indicator,the smaller its weight.In other words,when we want to evaluate the comprehensive ability of a group of objects and evaluation indicators involving multiple factors,we need to use the entropy weight method to calculate the weights of each indicator and calculate the final evaluation indicators by weighting them.

The calculation steps are as follows:

1) Using the concept of information entropy,we assume a multi-attribute decision matrix M.

where {A1，A2，…，Am} represents the set of m wind farms,xmn represents the value of the n-th indicator for the m-th wind farm,m and n represent the number of wind farms and indicators,respectively,which are 10 wind farms and the three indicators mentioned in Section 1.1.

2) Normalization of indicator values.

3) Calculate the contribution of the i-th Wind Farm to the j-th Indicator Pij and their weight,which is considered as the probability used in the calculation of relative entropy,representing the continuity of the proportion.

4) Calculate the entropy value ej for the j-th indicator.

where ensures that 0 ≤ Ej ≤1has a maximum value of one.This equation shows that when the contributions of different wind farms under a certain indicator tend to be consistent,Ej tends to be one.In particular,when all contributions are equal,the effect of the attribute of the target in decision making can be ignored,meaning that the weight of the indicator is zero.As ej increases,the entropy value also increases,indicating that the amount of information obtained from the j-th indicator is less,and the degree of dispersion is greater.

5) Entropy weight wj for the j-th indicator

Since entropy and weight are negatively correlated,the information utility value 1 -ej is used for the calculation,and the entropy weight of each indicator is finally normalized,which is the weight occupied by each indicator.

1.2.2 Deterioration degree

To eliminate the influence of the correlation among various physical quantities,it is necessary to normalize the indicator values based on the concept of deterioration [17].The degree of deterioration describes the extent of deterioration in the actual power generation performance of a wind turbine compared with its fault-free state.Therefore,the better the indicator value,the smaller the degree of deterioration with a range of [0,1].

For indicators with a“smaller is better”type:

For indicators with a“larger is better”type:

where g(x) represents the deterioration degree of the indicator;x represents the actual value of the indicator;[α,β] represents the operational range of the indicator.The degree of deterioration is a normalization of (5),considering the influence of the numerical value of the indicator on the weight.It is normalized specifically for positive indicators (where larger values are better) and inverse indicators (where smaller values are better).Therefore,the degree of deterioration represents the standardized and normalized values of each indicator.

1.2.3 Variable weight theory

The variable weight theory reflects the balanced relationship between each indicator in the overall decisionmaking process by modifying the normal weights based on the deterioration of each indicator.In the comprehensive evaluation of wind-farm power-generation performance,if an indicator has a significantly higher value but a relatively smaller weight,its deterioration performance may be ignored in the overall evaluation,which has a significant impact on the accuracy of the performance assessment of the wind farm.Therefore,the variable weight theory was introduced to balance the horizontal correlation between the indicators and accurately evaluate the performance of the wind farm.The formula for the variable weight theory is as follows:

where represents the variable weight of indicator j,wj represents the normal weight of indicator j,gij represents the degree of deterioration of the indicator,T is the variable weight coefficient with a value of 0.5,n is the number of indicators.

1.2.4 Membership functions

To accurately quantify and analyze the performance,an accurate comprehensive evaluation of the object being assessed is required using membership functions.Fuzzy comprehensive evaluation is a highly effective multi-factor decision method to comprehensively evaluate the effects of multiple factors.Its characteristic is that the evaluation results are not absolutely positive or negative but are represented by a fuzzy set.The membership function is a mathematical tool used to represent fuzzy sets,and indicates the“degree of membership”of an element belonging to a certain fuzzy set.

In this study,a combination of triangular and trapezoidal functions is used as the membership functions,which are divided into four fuzzy sets {excellent,good,fair,and poor},as shown in Fig.1.(11) [17] is derived to formalize these functions,where g represents the degree of deterioration,and v represents the membership degrees of the four sets.This formula was used to calculate the membership degrees of various indicators.

Fig.1 Membership function corresponding to the degree of deterioration

1.3 Comprehensive evaluation process

The process of comprehensive evaluation is constructed based on the relevant theoretical formulas of entropy method,degree of deterioration,change-weight theory,and membership functions,as shown in Fig.2.The entropy method is used to calculate the equal weights of each indicator,and then the change-weight theory is combined with the degree of deterioration to obtain the changed weights.Subsequently,the membership functions are applied to determine the evaluation sets to which each indicator of the wind farm belongs.Finally,the comprehensive evaluation result of the cluster is obtained.Based on the number of wind farms and indicators in this paper,the values of m and n in the calculation process should be 10 and 3,respectively.

Fig.2 Comprehensive evaluation process

2 Wind farm clustering dynamic hierarchical sorting allocation

2.1 Objectives and constraints of dynamic hierarchical sorting

This study has two main objectives for the dynamic hierarchical sorting of wind farm clusters.First,it aims to adjust and control the total output power of each wind farm in real time based on the requirements of the wind farm cluster system dispatch to maintain consistency with the system demand and track the grid power instructions of the cluster.Second,wind farms are grouped and sorted based on their fluctuation indicators to reduce the scheduling and output fluctuations of individual wind farms and improve the reliability of instruction tracking.

To ensure the power supply stability of the entire windfarm cluster and make the control results more practical,the total output power of the wind farms should be maintained within a certain range.This can be achieved by setting the upper and lower limits of the total power,which imposes a power balance constraint on the wind farms.

where Pmin and Pmax indicate the upper and lower limits of the total power output of the wind farm cluster,respectively.

The dispatched power of each wind farm should be less than its installed capacity to ensure that the farms operate within a reasonable load range.Therefore,the capacity constraint for each wind farm is given by

where denotes the installed capacity (rated output power) of wind farm i.

Considering the physical constraints in the wind-farm cluster,the power-output constraint for each wind farm can be expressed as

where represent the minimum dispatched power,dispatched active power instruction,and forecasted power of wind farm i,respectively.The notation“min”indicates the minimum value among the given terms.

The wind farm has a limited capability to adjust its power output rate;therefore,it is necessary to restrict the rate of change in the output power.This is achieved by setting a speed slope that represents the capability of the wind farm to adjust its power output.Therefore,the speed regulation constraint for wind farm i is given by

where denotes the actual output power of wind farm i,di indicates the time interval (in the subsequent calculations,a 10-minute interval or 600 s is used),and k is the speed slope.Generally,the value of k is between 0.2 and 0.5,and in this case,a value of 0.3 is chosen.

The power fluctuation of a wind farm should be controlled within a certain range to minimize its impact on the system.This can be achieved by setting an upper limit on the power fluctuation.In this case,a power fluctuation limit coefficient of three was chosen,which represents the stability constraint for wind farm operation.Therefore,the constraint can be expressed as

where denotes the actual output power of wind farm i.

Additionally,to reduce the power tracking error for the cluster,the power error is defined as the difference between the actual cluster output power and the set point Pr,which should not exceed 1% Pr.

2.2 Dynamic clustering and sorting strategy for wind farm cluster

Currently,there is no strict definition for clustering windfarm clusters.However,they can generally be summarized as a collection of wind farms that are geographically close to each other and have complementary relationships in terms of their geographic locations or grid structures.

The proposed hierarchical clustering control comprises three levels:cluster,group,and wind farm.Based on the classification indicators,the individual wind farms within the cluster are grouped together,and several wind farms with the same indicator formed a group known as a field group.Within a field group,the individual wind farms are sorted based on indicators.Finally,through this clustering and sorting process,the wind farms are controlled in an orderly manner,as shown in Fig.3.This scheduling method reduces the number of wind-farm adjustments.Unlike proportional allocation,where all wind farms and units are adjusted when the cluster instruction changes (i.e.,power increases or decreases),the method proposed in this study adjusts only a subset of wind farms,reducing the number of wind farm adjustments and effectively diminishing action fatigue.

Fig.3 Architecture of the proposed hierarchical scheduling method

The definitions of clustering within the cluster and sorting within field groups are as follows:2.2.1 Clustering within the cluster

In the dynamic clustering process,the short-term power forecast values for the next four cycles,starting from the current time (t),are used as the basis for evaluating the power variation trend of each wind farm.This implies that forecast values are continuously updated over time,thereby exhibiting a certain degree of dynamism.Clustering within the cluster is performed based on the trend of the forecast values,specifically,the climb rate.However,it should be emphasized that these clusters are not fixed or static,as clustering is reevaluated based on the indicators for each cycle.The climb classification indicator for the wind farms is defined as follows:

The climb classification indicator for wind farms [18] is defined as

where sign() denotes the sign function, represents the forecasted power value of the wind farm for the n-th cycle,and is the power output value of the wind farm at time t.

Equation (17) describes the calculation of the climbing grouping indicator for a wind farm,which can assess its performance and variation trends.As the forecast values are continuously updated,and clustering is performed for each cycle,this process exhibits a certain level of dynamism.This implies that the power variation on a wind farm can be predicted more accurately,leading to more precise clustering.

Based on this definition,it can be observed that Ki ∈-[4,4].Based on Ki,the wind farm group was divided into uphill,transition,and downhill groups.The grouping indicators and their characteristics are listed in Table 1.

Table 1 Indicators and characteristics of climbing grouping

Therefore,based on this climbing rate indicator,the scheduling order for field groups when the power instruction changes is as follows:when the power needs to be increased,the climbing group is prioritized,followed by the transition group;when the power needs to be decreased,the descending group is prioritized,followed by the transition and climbing groups.However,it should be noted that during cluster power increase,the descending group exhibited a decreasing power trend and could not be directly adjusted to increase the power.

2.2.2 Sorting within field groups

Within the same wind farm cluster,the dispatch order of the wind farms was determined based on their load rates.The load rate δi of a wind farm is defined as the ratio of its actual power output to its installed capacity:

When the power of a cluster needs to be increased,priority is given to increasing the power of the wind farms with lower load rates within the groups.Conversely,when the power of a cluster needs to be decreased,priority is given to decreasing the power of wind farms with higher load rates within the groups.This approach ensures a more balanced power output among the wind farms within the cluster.

2.3 Hierarchical algorithm flow

The proposed dynamic hierarchical sorting algorithm for offshore wind farm clusters conducts dynamic clustering and sorting of wind farms within the cluster based on grouping indicators and the time-varying load rates of the wind farms.Based on the difference between the current output and the instructions,as well as the forecasted values of the wind farms,it determines whether the cluster needs to increase or decrease power.Scheduling was then conducted based on the grouping.The scheduling process is illustrated in Fig.4.

Fig.4 Layered scheduling flowchart of wind power cluster

3 Case study analysis

The case study was based on data from various wind farms in a large base located in the northwest China.The base layout contains ten wind farms,as shown in Fig.5.The wind speed data for each wind farm were obtained by fitting the data measured at the wind measurement towers to the hub-height wind speed using Windographer software.The wind speed is measured by anemometer towers in an actual wind power cluster;therefore,it is inherently reliable.The wind farm information and wind speed data are obtained from actual large-scale wind power clusters,which ensures the feasibility of the proposed allocation and evaluation methods in practical system applications.The power output of each wind farm is determined based on the wind speed,installed capacity,and power curve of the turbines.Information on the installed capacity of each wind farm at the base is presented in Table 2.

Table 2 Information of each wind farm in a wind power base

continue

Fig.5 Wind farm layout of the base

To analyze the effectiveness of the dynamic hierarchical sort allocation (DHSA),the case study uses data from a period of three days in the base.The wind speed data for each wind farm are shown in Fig.6.The case study has a time resolution of 10 min,with a total of 432 cycles.Three different methods were compared:proportional allocation (PA),comprehensive sorting allocation (CSA),and the clustering allocation method proposed in this paper.The base power instructions used for comparison are listed in Table 3.

Table 3 Power command settings

Fig.6 Wind speed data curve of each wind farm in the large base

3.1 Overall dispatch analysis

Based on the aforementioned power instructions,the comparison results of the three power-tracking methods are shown in Fig.7.The blue solid line represents the issued power instructions for the wind-farm cluster,the red line represents the power allocation curve using proportional allocation,the green line represents the power allocation curve using comprehensive sorting,and the black line represents the proposed power allocation curve.From the overall tracking performance,it can be observed that the three power allocation curves almost overlap.Under limited power and free power generation modes,they can closely follow power instructions.When the power instruction is too large,both methods operate in the maximum power generation mode,with some fluctuations depending on the wind speed.Thus,it can be concluded that the proposed method achieves the goal of power instruction tracking.

Fig.7 Output comparison between power command and two distribution methods

To quantitatively compare the performances of the different control methods,the average relative deviation (εMRE) and root mean square deviation (εRMSE) are used to evaluate the two methods.The average relative deviation was primarily used to evaluate the tracking performance of the grid-set value,whereas the root mean square deviation was used to evaluate the power fluctuation.The calculation formulas are as follows and the results are listed in Table 4,where N indicates the total number of simulation cycles.

Table 4 Average relative deviation and root mean square deviation of the two allocation methods

From the results in Table 4,it is evident that the proposed allocation method has a better average relative deviation and RMSE in tracking the power instruction than the proportional allocation and sorting allocation methods.This indicates an improvement in the tracking performance and power fluctuation,leading to enhanced stability of the cluster power output.

3.2 Load and fluctuation analysis

The fluctuation and load rate variations of the ten wind farms based on the actual wind speed simulation are shown in Fig.8.The red curve represents the cluster allocation curve proposed in this study.In the left half of the graph,purple and green curves represent the fluctuation rates of proportional and sorted allocations,respectively.In the right half of the graph,the orange and blue curves represent the load rates of proportional and sorted allocations,respectively.

Fig.8 Comparison of volatility and load rates of each wind farm under two distribution methods

Based on the fluctuation rate variations of the first five wind farms,it can be observed that cluster allocation prioritizes the increase in power for wind farms with lower load rates or the decrease in power for wind farms with higher load rates when there are changes in instructions.This was done to maximize the power increase or decrease within wind farms that are ranked higher in sorting,aiming to satisfy the instruction requirements.Consequently,larger fluctuations occurred during certain cycles.However,overall,both the proportional and sorted allocations showed relatively more fluctuations than the cluster allocation proposed in this study.The proposed cluster allocation reduces the number and frequency of actions within the wind-farm cluster,which can reduce fatigue loads and provide a more stable power output.

According to the load rate curves of the last five wind farms,there was little difference in the load rates under the three methods,and they all exhibit the same fluctuation trend.The variations are primarily concentrated in two stages,20 -35 h and 50 -60 h.In both stages,the red curve quickly reaches the required load rate for the next stage with minimal fluctuations.This requires fewer adjustments and maintains a more stable overall performance.By contrast,the orange and blue curves exhibit more fluctuations and higher fluctuation frequencies during the adjustment process.Consequently,they may increase the overall load fatigue.By comparison,it can be concluded that the proposed allocation method achieves a more stable load rate fluctuation,reduces the number of load rate variations or adjustments,and alleviates the fatigue load.This method is significant for maintaining a stable power output and reducing the fatigue load.

3.3 Comprehensive evaluation

Considering the data at the time of power reduction in the 300th cycle,a comprehensive evaluation of the performance of each wind farm at the base was conducted.

Based on the entropy method (5)– (9),constant weights can be obtained,as shown in Table 5.Entropy weights represent the relative importance of each criterion.From this,it can be observed that the adjustment margin has the greatest influence on the overall performance.As the adjustment margin is based on a comparison with the power instruction,it has the highest reference significance for achieving the instruction requirements,and therefore,has the highest entropy weight.However,the power limitation and fluctuation rate were considered based on the rated and actual power over multiple cycles,respectively.Therefore,their reference significance for tracking the instruction schedule is relatively low,leading to a smaller impact on the overall performance,and subsequently,a smaller entropy weight.

Table 5 Constant weight of three indicators

According to the definition of the degree of deterioration,the power limitation and fluctuation rate in the previous cycle belong to the“the smaller,the better”type of indicators,while the control margin belongs to the“the larger,the better”type of indicator.Based on the values of these indicators,the deterioration matrix can be determined,as shown in (21),in which a smaller degree of deterioration indicates better performance.However,there are significant differences in the values of these indicators among the wind farms.Therefore,a membership function is applied to fuzzily evaluate the degree of deterioration and determine the level of performance.

According to (11),the corresponding membership degrees for the degrees of deterioration are calculated.Taking wind farm 1 as an example,the membership matrix is obtained,as shown in (22).

From the equation,it can be observed that indicator 1 tends to be“poor”,indicator 2 tends to be“good”and“average”,and indicator 3 tends to be“excellent”.This means that wind farm 1 has a relatively poor power limitation,moderate control margin,and a good fluctuation rate.This is consistent with the definition of the degree of deterioration,in which a smaller deterioration value indicates better performance.

According to change-weight theory,the modified weight matrix is obtained by adjusting the entropy weight constant weight,as shown in (23).In this equation,weight calculations are performed for each indicator of each wind farm.Unlike entropy weighting,change-weight theory considers the correlation between indicators and performs weight calculations for individual indicators.In addition,the weights are updated in each period,making the results more precise and accurate.By contrast,the entropy weight considers the uniform weight of wind farms based on the probability of indicators,disregarding the differences and timeliness between different wind farms.

The above calculations have already performed individual fuzzy evaluations of the three indicators using membership functions and obtained the variable weights by considering their correlation through the change-weight theory.Therefore,by calculating the weighted average of the individual evaluations,comprehensive evaluation results for all indicators can be obtained.

A comparative analysis was performed using the traditional constant weight entropy method and PCA to validate the effectiveness of the proposed evaluation method.The comparison results are presented in Table 6 and Fig.9.

Table 6 Comparison of Results from Different Evaluation Methods

Fig.9 Comparison of results from different evaluation methods

These results demonstrate that the evaluation trends of the three methods were generally similar,indicating the feasibility and effectiveness of the proposed method for wind farm performance evaluation.Moreover,the evaluation results of the proposed method are positioned between those of the constant-weight entropy method and PCA,approaching a more balanced and informative level.However,because the comprehensive evaluation score can have both positive and negative values,the meaning of the comprehensive evaluation function may not be clear and the final evaluation may not be intuitive.Therefore,it is necessary to conduct a fuzzy quantification analysis of the comprehensive evaluation scores.Based on the results obtained from the proposed method in this study,In (24),U1 represents the weighted comprehensive evaluation vector for wind farm 1 according to the“excellent-good-fair-poor”scale for each indicator.By applying this evaluation to all ten wind farms,a comprehensive evaluation matrix U for the wind farm cluster was obtained.

Based on the results obtained from the method proposed in this study,matrix U contains ten rows that correspond to the ten wind farms and four columns that correspond to the membership degrees {excellent,good,fair,poor}.Based on the principle of maximum membership degree,wind farms 2,4,5,6,7,8,9,and 10 are evaluated as“excellent”in overall performance,wind farm 1,3 is evaluated as“good”.Wind farms rated as“fair”and“poor”are rated as zero.The comprehensive evaluation results were intuitive and accurate.Moreover,after using the proposed allocation method,the overall performance of the wind power base is good.This indicates that the allocation method effectively reduces the power fluctuation of the cluster because the evaluation criteria primarily focuses on tracking instructions and fluctuations in the scheduling process.Therefore,this study proves that the proposed allocation method has clear optimization effects in reducing power fluctuations and improving the stability of the power output of a cluster,which is of significant importance.By comparison,it can be observed that the proposed evaluation method has an accuracy similar to that of the constant weight entropy method and PCA.By using a membership function for the fuzzy quantitative analysis of the comprehensive score,intuitive and accurate comprehensive evaluation results can be obtained,which have good application prospects.

4 Conclusions

A comprehensive evaluation method based on an entropy-weighted wind farm cluster was proposed to address scheduling and allocation problems in wind farm clusters.This evaluation method considers the interrelationships between indicators and the dynamic nature of weight changes,thereby providing a comprehensive evaluation of the impact of allocation strategies on wind farms.Moreover,a dynamic hierarchical sorting allocation method within the cluster was introduced,enabling dynamic grouping and sorting based on actual needs over time through a three-tiered approach of a cluster-group-wind farm,which reduce the number of transfers.The model was validated and analyzed using data from a large-scale wind farm base comprising ten wind farms.Compared to traditional proportional and sorting allocation methods,the proposed allocation method reduces the number and frequency of control actions for wind farms while achieving instruction tracking.Moreover,it significantly decreases the frequency and magnitude of wind farm fluctuations and tracking deviations,verifying the feasibility and effectiveness of the proposed allocation method.

The proposed scheduling method has limitations,such as being limited by the accuracy of wind speed prediction and real-time data communication within the wind power cluster.Further research can be conducted on the selection of evaluation indicators and wind power forecasting,clustering,and sorting methods.

Acknowledgments

This study was supported by the National Natural Science Foundation of China (Grant No.52076038,U22B20112,No.52106238),and the Fundamental Research Funds for Central Universities (No.423162,B230201051).

Declaration of competing interests

The authors have no conflicts of interest to declare.