# Wind Power Installed Capacity Forecast Based on a Two-Parameter Variable-Weight Buffer Operator and Subsidy Strategy Research

Authors: Ye Li; Xue Bai
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

Since the installed capacity of wind power is greatly affected by the subsidy policy, this paper predicts the installed wind power capacity in China under different policy scenarios. Firstly, a new two-parameter variable-weight buffer operator is proposed to quantify the impact of the policy shock, whose optimal parameters are obtained by the genetic algorithm, and combined with the grey GM(1,1) model to predict the installed capacity of wind power in China under the cessation of subsidy policy. Then, the GM(1,1) model with optimized background value is used to predict the installed capacity under continued subsidy. Finally, two policy subsidy strategy models are constructed based on the forecast data to simulate the future trend of wind power installed capacity under different subsidy policies and explore the strength of wind power subsidies in China during the “14th Five-Year Plan” period (2021–2025). The results show that both the GM(1,1) model based on the two-parameter variable-weight buffer operator and the GM(1,1) model with optimized background value have high fitting accuracy, with errors of 0.15% and 4.93%, respectively. Furthermore, in the case of the central government’s subsidy cancellation, the local government should take over the central government’s subsidy policy and adjust the subsidy intensity to 0.57–1 times of that during the “13th Five-Year Plan” period (2015–2020) to achieve the national planning target.


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## Body

## 1. Introduction

### 1.1. Background and Motivation

As the global energy crisis and environmental crisis continue to intensify, the transition of energy structure has become an urgent task, and electric energy substitution is the inevitable trend of energy structure transformation. The “14th Five-Year Plan” (2021–2025) is a critical period for China to build a new development pattern and transform its energy and power structure. As a clean energy with great potential, wind power has significant advantages such as no pollution, flexible investment, and low cost. It also plays a crucial part in facilitating the transformation of China’s energy structure and building a modern energy system. However, due to the instability and randomness of wind power, it is difficult to rely on the industry itself to achieve sustainable and high-quality development. Over the years, under the policy of high subsidies from the central government, the wind power industry in China has developed rapidly, with the installed capacity of wind power ranking first in the world for several years. As can be seen from Figure1, the development of the subsidy policy of wind power from 2011 to 2020 can be divided into two phases. The first phase is the subsidy-supported phase from 2011 to 2015, during which the wind power installed capacity grew at a high rate. The second phase is the subsidy withdrawal phase from 2015 to 2020. In 2015, the National Development and Reform Commission issued the Notice on Appropriate Adjustment of the Benchmark Feed-in Tariff for Onshore Wind Power, which reduced the benchmark tariff for wind power during the “13th Five-Year Plan” period. As a result, the growth of wind power installed capacity slowed down. By the way, the surge in wind power installed capacity in 2015 and 2020 is due to the decline in subsidies and the planned implementation of the desubsidization policy, respectively, resulting in a frenzy of “rush to install” in the wind power industry. Data show that by 2020, the cumulative installed capacity of wind power has reached 281.53 million kilowatts, an increase of 34.6% year on year, reaching the low-limit target of the “13th Five-Year Plan.” After the successful completion of the “13th Five-Year Plan,” China has ushered in a new target for installed wind power capacity during the “14th Five-Year Plan” period. Unfortunately, in May 2019, the National Development and Reform Commission issued a Notice on Improving the Feed-in Tariff Policy for Wind Power, clearly indicating that the central government will no longer subsidize newly approved onshore wind power projects from January 1, 2021. However, China’s wind power industry is in a critical period of growth, and a certain amount of subsidies must be maintained for further development. In the objective situation of eliminating the central financial subsidies, only the local government is suitable to relay the subsidy policy to create a stable policy environment for the development of wind power and help it pass the critical growth period smoothly.Figure 1
Installed capacity and growth rate of wind power from 2011 to 2020.At present, there are two issues. With the cancellation of the subsidy policy for wind power by the central government in 2021, whether China can complete the task of the “14th Five-Year Plan” for wind power installation; if not, how should the local government adjust the subsidy intensity when relaying the subsidy policy to ensure that the scale of wind power installation is completed in strict accordance with the target of the “14th Five-Year Plan.” Therefore, a scientific and accurate forecast of wind power installed capacity under the cessation and continuation of the subsidy policy during the “14th Five-Year Plan” period is of great significance for the local government to reasonably formulate subsidy policies and adjust subsidy intensity.


### 1.2. Literature Review

With wind power gradually becoming the mainstream form of new energy generation in China, the forecast of wind power at home and abroad has become a major hot spot. The grey prediction model, first proposed by Professor Deng [1] in 1982, has been widely applied in various fields, such as transportation [2, 3], tourism [4, 5], population [6, 7], automobile industry [8, 9], economics [10, 11], energy and environment [12, 13], and other important fields due to its advantages of simple structure and excellent performances. The GM(1,1) model is the core of the grey prediction model. Since wind power is disturbed by policy, weather, and other external factors, it is unstable and uncontrollable, and the sample data is limited. Therefore, the GM(1,1) model is highly suitable for wind power installed capacity forecasting. In recent years, many scholars have conducted in-depth studies on GM(1,1) models from different perspectives [14–16]. However, the prediction results in practical forecasting are often inconsistent with the conclusions of qualitative analysis, mainly because the system behavior data itself is distorted and deformed by the interference of various external factors [17]. Based on this, Liu [18] first proposed the concept of buffer operator, gave its axiomatic system, and constructed a class of practical buffer operators. In terms of the construction of buffer operators, there are many classical buffer operators whose designs and implications are shown in Table 1. In terms of the applications of the buffer operator, many scholars have applied buffer operator to the prediction of practical problems, such as the cumulative confirmed cases in different stages of COVID-19 [25], the production and sales of new energy vehicles prediction [26], residential solar energy consumption prediction [27], the main indicators of online shopping prediction [28], the output of shale gas prediction [29], etc. The construction and application of these buffer operators have contributed to the development of grey theory. Different prediction systems need to be matched with appropriate buffer operators to achieve effective prediction for systems with few data. Therefore, this paper constructs a new two-parameter variable-weight buffer operator to quantify the impact of the subsidy policy, and simulates and predicts the wind power installed capacity under the cessation of subsidy policy in China by combining the GM(1,1) model to address the issue whether China can complete the task of wind power installation in 2025.Table 1
Literature studies related to buffer operators.
Authors (year)CategoryDesign of buffer operatorsImplicationsLiu (1997) [18]Practical buffer operatorsxkd1=xk+xk+1+⋯+xn/n−k+1, xkd2=x1+x2+⋯+xk−1+kxk/2k−1The concept of buffer operator and its axiomatic system were first proposed, laying the foundation for the development of various buffer operatorsXu et al. (2014) [19] and Liu et al. (2016) [20]Variable-weight buffer operatorxkd1=λxn+1−λxk,xkd2=xk(xn/xk)α,0<α<1The effect of the buffer operator is adjusted by variable weights to improve the adaptability to more volatile sequencesJiang et al. (2020) [21]Logarithmically weakening buffer operatorxkd1=xk1+logxn/xk,xkd2=λxk1+logxn/xk+1−λxnThe operator combines the properties of logarithms to improve the prediction accuracy of the modelWu et al. (2018) [22]Fractional buffer operatorXDp/q=X1/n0⋯01/n1/n−1⋯0⋮⋮⋱⋮1/n1/n−1⋯1p/qThe fractional order buffer operator can not only generalize the weakening and strengthening buffer operator, but also make small adjustments to the buffering effectChen and Wu (2021) [23]Real order inverse cumulative generating operatorwxkr=r+n−2n−1xn0+r+n−3n−2xn−10+⋯+r+k−2k−1xk0/r+n−2n−1+r+n−3n−2+⋯+r+k−2k−1The operator allows finer adjustment of the weight distribution between the original data sequences by changing the order of the weakening buffer operatorHe and Wang (2022) [24]Seasonal weakening buffer operatorDS=1/nXAXBDiagATB−1−1DSeasonal weakening buffer operator can effectively handle modeling and prediction of seasonal shock disturbance systemsThe current studyTwo-parameter variable-weight buffer operatorxkd=xk⋅∑i=kn(iλ⋅xi)/∑i=kniλ⋅xkγThe operator not only unifies the weakening and strengthening buffer operator, but also its adaptability is enhanced by the coordinated variation of the two parametersIn addition, although domestic and foreign scholars have conducted extensive research on wind power forecasting, most of them are limited to improving the forecasting accuracy of grey models from different perspectives [30, 31], lacking a focus on governmental decision-making behavior in the wind power market. In fact, we should pay more attention to the government’s decision-making behavior in the wind power market and use the forecast information to provide a reference for decision-making behavior.


### 1.3. Contributions and Organizations

The main contributions of this study are drawn as follows.This paper proposes a new two-parameter variable-weight buffer operator to quantify the impact of policy shocks and provides accurate predictions of installed wind power capacity under different subsidy policy scenarios.To further improve the forecasting capability of the model, the genetic algorithm is employed to determine the optimal value of non-linear parameters.It is also a new idea to use predictive information to inform decision-making behavior by constructing subsidy strategy models based on predicted data, and the results can guide the government in formulating relevant policies.The remainder of this paper is organized as follows. Section2 describes the construction and parameter optimization of the two-parameter variable-weight buffer operator and the modeling steps of two GM(1,1) models. The forecast analysis of the wind power installed capacity under the cessation and continuation of China’s wind power subsidy policy is presented in Section 3. Section 4 constructs two subsidy strategy models based on the predicted values and measures the subsidy intensity of the local government. The last section summarizes the conclusions.


## 1.1. Background and Motivation

As the global energy crisis and environmental crisis continue to intensify, the transition of energy structure has become an urgent task, and electric energy substitution is the inevitable trend of energy structure transformation. The “14th Five-Year Plan” (2021–2025) is a critical period for China to build a new development pattern and transform its energy and power structure. As a clean energy with great potential, wind power has significant advantages such as no pollution, flexible investment, and low cost. It also plays a crucial part in facilitating the transformation of China’s energy structure and building a modern energy system. However, due to the instability and randomness of wind power, it is difficult to rely on the industry itself to achieve sustainable and high-quality development. Over the years, under the policy of high subsidies from the central government, the wind power industry in China has developed rapidly, with the installed capacity of wind power ranking first in the world for several years. As can be seen from Figure1, the development of the subsidy policy of wind power from 2011 to 2020 can be divided into two phases. The first phase is the subsidy-supported phase from 2011 to 2015, during which the wind power installed capacity grew at a high rate. The second phase is the subsidy withdrawal phase from 2015 to 2020. In 2015, the National Development and Reform Commission issued the Notice on Appropriate Adjustment of the Benchmark Feed-in Tariff for Onshore Wind Power, which reduced the benchmark tariff for wind power during the “13th Five-Year Plan” period. As a result, the growth of wind power installed capacity slowed down. By the way, the surge in wind power installed capacity in 2015 and 2020 is due to the decline in subsidies and the planned implementation of the desubsidization policy, respectively, resulting in a frenzy of “rush to install” in the wind power industry. Data show that by 2020, the cumulative installed capacity of wind power has reached 281.53 million kilowatts, an increase of 34.6% year on year, reaching the low-limit target of the “13th Five-Year Plan.” After the successful completion of the “13th Five-Year Plan,” China has ushered in a new target for installed wind power capacity during the “14th Five-Year Plan” period. Unfortunately, in May 2019, the National Development and Reform Commission issued a Notice on Improving the Feed-in Tariff Policy for Wind Power, clearly indicating that the central government will no longer subsidize newly approved onshore wind power projects from January 1, 2021. However, China’s wind power industry is in a critical period of growth, and a certain amount of subsidies must be maintained for further development. In the objective situation of eliminating the central financial subsidies, only the local government is suitable to relay the subsidy policy to create a stable policy environment for the development of wind power and help it pass the critical growth period smoothly.Figure 1
Installed capacity and growth rate of wind power from 2011 to 2020.At present, there are two issues. With the cancellation of the subsidy policy for wind power by the central government in 2021, whether China can complete the task of the “14th Five-Year Plan” for wind power installation; if not, how should the local government adjust the subsidy intensity when relaying the subsidy policy to ensure that the scale of wind power installation is completed in strict accordance with the target of the “14th Five-Year Plan.” Therefore, a scientific and accurate forecast of wind power installed capacity under the cessation and continuation of the subsidy policy during the “14th Five-Year Plan” period is of great significance for the local government to reasonably formulate subsidy policies and adjust subsidy intensity.


## 1.2. Literature Review

With wind power gradually becoming the mainstream form of new energy generation in China, the forecast of wind power at home and abroad has become a major hot spot. The grey prediction model, first proposed by Professor Deng [1] in 1982, has been widely applied in various fields, such as transportation [2, 3], tourism [4, 5], population [6, 7], automobile industry [8, 9], economics [10, 11], energy and environment [12, 13], and other important fields due to its advantages of simple structure and excellent performances. The GM(1,1) model is the core of the grey prediction model. Since wind power is disturbed by policy, weather, and other external factors, it is unstable and uncontrollable, and the sample data is limited. Therefore, the GM(1,1) model is highly suitable for wind power installed capacity forecasting. In recent years, many scholars have conducted in-depth studies on GM(1,1) models from different perspectives [14–16]. However, the prediction results in practical forecasting are often inconsistent with the conclusions of qualitative analysis, mainly because the system behavior data itself is distorted and deformed by the interference of various external factors [17]. Based on this, Liu [18] first proposed the concept of buffer operator, gave its axiomatic system, and constructed a class of practical buffer operators. In terms of the construction of buffer operators, there are many classical buffer operators whose designs and implications are shown in Table 1. In terms of the applications of the buffer operator, many scholars have applied buffer operator to the prediction of practical problems, such as the cumulative confirmed cases in different stages of COVID-19 [25], the production and sales of new energy vehicles prediction [26], residential solar energy consumption prediction [27], the main indicators of online shopping prediction [28], the output of shale gas prediction [29], etc. The construction and application of these buffer operators have contributed to the development of grey theory. Different prediction systems need to be matched with appropriate buffer operators to achieve effective prediction for systems with few data. Therefore, this paper constructs a new two-parameter variable-weight buffer operator to quantify the impact of the subsidy policy, and simulates and predicts the wind power installed capacity under the cessation of subsidy policy in China by combining the GM(1,1) model to address the issue whether China can complete the task of wind power installation in 2025.Table 1
Literature studies related to buffer operators.
Authors (year)CategoryDesign of buffer operatorsImplicationsLiu (1997) [18]Practical buffer operatorsxkd1=xk+xk+1+⋯+xn/n−k+1, xkd2=x1+x2+⋯+xk−1+kxk/2k−1The concept of buffer operator and its axiomatic system were first proposed, laying the foundation for the development of various buffer operatorsXu et al. (2014) [19] and Liu et al. (2016) [20]Variable-weight buffer operatorxkd1=λxn+1−λxk,xkd2=xk(xn/xk)α,0<α<1The effect of the buffer operator is adjusted by variable weights to improve the adaptability to more volatile sequencesJiang et al. (2020) [21]Logarithmically weakening buffer operatorxkd1=xk1+logxn/xk,xkd2=λxk1+logxn/xk+1−λxnThe operator combines the properties of logarithms to improve the prediction accuracy of the modelWu et al. (2018) [22]Fractional buffer operatorXDp/q=X1/n0⋯01/n1/n−1⋯0⋮⋮⋱⋮1/n1/n−1⋯1p/qThe fractional order buffer operator can not only generalize the weakening and strengthening buffer operator, but also make small adjustments to the buffering effectChen and Wu (2021) [23]Real order inverse cumulative generating operatorwxkr=r+n−2n−1xn0+r+n−3n−2xn−10+⋯+r+k−2k−1xk0/r+n−2n−1+r+n−3n−2+⋯+r+k−2k−1The operator allows finer adjustment of the weight distribution between the original data sequences by changing the order of the weakening buffer operatorHe and Wang (2022) [24]Seasonal weakening buffer operatorDS=1/nXAXBDiagATB−1−1DSeasonal weakening buffer operator can effectively handle modeling and prediction of seasonal shock disturbance systemsThe current studyTwo-parameter variable-weight buffer operatorxkd=xk⋅∑i=kn(iλ⋅xi)/∑i=kniλ⋅xkγThe operator not only unifies the weakening and strengthening buffer operator, but also its adaptability is enhanced by the coordinated variation of the two parametersIn addition, although domestic and foreign scholars have conducted extensive research on wind power forecasting, most of them are limited to improving the forecasting accuracy of grey models from different perspectives [30, 31], lacking a focus on governmental decision-making behavior in the wind power market. In fact, we should pay more attention to the government’s decision-making behavior in the wind power market and use the forecast information to provide a reference for decision-making behavior.


## 1.3. Contributions and Organizations

The main contributions of this study are drawn as follows.This paper proposes a new two-parameter variable-weight buffer operator to quantify the impact of policy shocks and provides accurate predictions of installed wind power capacity under different subsidy policy scenarios.To further improve the forecasting capability of the model, the genetic algorithm is employed to determine the optimal value of non-linear parameters.It is also a new idea to use predictive information to inform decision-making behavior by constructing subsidy strategy models based on predicted data, and the results can guide the government in formulating relevant policies.The remainder of this paper is organized as follows. Section2 describes the construction and parameter optimization of the two-parameter variable-weight buffer operator and the modeling steps of two GM(1,1) models. The forecast analysis of the wind power installed capacity under the cessation and continuation of China’s wind power subsidy policy is presented in Section 3. Section 4 constructs two subsidy strategy models based on the predicted values and measures the subsidy intensity of the local government. The last section summarizes the conclusions.


## 2. Methodology

### 2.1. Construction of Two-Parameter Variable-Weight Buffer Operator

Compared with the traditional buffer operator, the two-parameter variable-weight buffer operator constructed in this paper adds an exponential parameter to the sequentially decreasing weights of the old and new data as a flexible adjustment of the buffer strength. A power exponential parameter is also introduced to unify the weakening and strengthening buffer operators. The adaptability of the buffer operator to the data sequence is enhanced by the coordinated variation of these two parameters.Theorem 1.
AssumeX=x1,x2,…,xn,xk>0 is the raw data. Let(1)XD=x1d,x2d,…xnd,where(2)xkd=xk⋅kλxk+k+1λxk+1+⋯+nλxnkλ+k+1λ+⋯nλ⋅xkγ=xk⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xkγ,λ≥0, k=1,2,…,n, then(1)
Whenγ>0, whether X is a monotonically increasing sequence, a monotonically decreasing sequence, or an oscillating sequence, D is always the weakening operator.(2)
Whenγ<0, whether X is a monotonically increasing sequence, a monotonically decreasing sequence, or an oscillating sequence, D is always the strengthening operator.(3)
Whenγ=0, D is the constant operator.Proof.
ClearlyD satisfies axioms for buffer operator and thus D is a buffer operator.(1)
Whenγ>0, there are the following three cases.(a)
IfX is a monotonically increasing sequence, for i=k,k+1,…,n, we have xi≥xk, then(3)xkd=xk⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xkγ≥xk⋅∑i=kn(iλ⋅xk)∑i=kniλ⋅xkγ=xk.That is, whenX is a monotonically increasing sequence, D is the weakening buffer operator.(b)
IfX is a monotonically decreasing sequence, for i=k,k+1,…,n, we have xi≤xk, then(4)xkd=xk⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xk≤xk⋅∑i=kn(iλ⋅xk)∑i=kniλ⋅xk=xk.That is, whenX is a monotonically decreasing sequence, D is the weakening buffer operator.(c)
IfX is an oscillating sequence, let(5)xl=maxxk|k=1,2,…,n,xh=minxk|k=1,2,…,n.Then,(6)xld=xl⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xl≤xl⋅∑i=kniλ⋅xl∑i=kniλ⋅xl=xl,xhd=xh⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xh≥xh⋅∑i=kniλ⋅xh∑i=kniλ⋅xh=xh.Therefore, whenX is the oscillation sequence, D is the weakening buffer operator.(2)
Whenγ<0, as long as γ>0 becomes γ<0 in the proof of (1) and the inequality is reversed accordingly, the required result is obtained naturally.(3)
Obviously holds whenγ=0. Proof ends.


### 2.2. The GM(1,1) Model based on Two-Parameter Variable-Weight Buffer Operator

Compared with the traditional GM(1,1) model, the buffered operator-based GM(1,1) model adds two steps of buffer sequence generation and parameter search. The modeling process are described as follows:Step 1. Let the original non-negative data sequence be defined as(7)X0=x01,x02,…,x0n.Step 2. Buffering is carried out on the raw data sequence to obtain the buffered sequence:(8)X0D=x01d,x02d,…,x0nd,wherexkd=xk⋅kλxk+k+1λxk+1+⋯+nλxn/kλ+k+1λ+⋯nλ⋅xkγ = xk⋅∑i=kn(iλ⋅xi)/∑i=kniλ⋅xk.X0D=x01d,x02d,…,x0nd is also recorded as X′0=x′01,x′02,…,x′0n.Step 3. By accumulating the buffered sequence, a cumulative series is generated as follows:(9)X′1=x′11,x′12,…,x′1n.wherex1k=∑i=1kx0i,k=1,2,…,n.Step 4. The grey differential equation of the GM(1,1) model is(10)x′0k+az1k=b,k=1,2,…,n,wherea, b, and z1k are the development coefficient, endogenous control, grey scale, and background value, respectively, and z1k=0.5x′1k+0.5x′1k−1,k=2,3,…,n.Step 5. Parameters are estimated by least squares (LS) regression. Supposing that,(11)B=−z12−z13⋮−z1n11⋮1,Y=x02x03⋮x0n.The coefficient is(12)P=a,bT=BTB−1BTY.Step 6. The corresponding whitening differential equation is(13)dx′1dt+ax′1=b.Step 7. The time-response function of the GM(1,1) model is(14)x^′1k+1=x′01−bae−ak+ba,k=1,2,…,n.Step 8. Through the first-order inverse accumulated generating operation, the predicted values can be obtained:(15)x^′0k+1=x^′1k+1−x^′1k=1−eax′01−bae−ak,k=1,2,…,n.


### 2.3. Optimizing Factorsλ and γ Employing the Genetic Algorithm

Due to a complicated non-linear relationship between the weight-regulating factors and prediction error, the optimal values ofλ and γ are solved by the genetic algorithm (GA), and the mean absolute percentage error (MAPE) is used as an objective function of the optimization. The objective function, namely, the fitness function, is expressed as follows:(16)fitness=100%n∑i=1nx^i′−xi′xi′,s.t.P=a^,b^T=BTB−1BTYx^′1k+1=x′01−bae−ak+bax^′0k+1=x^′1k+1−x^′1k,k=1,2,…,n,where xi′ represents the forecast value and xi′ expresses the buffered data, namely, the modeling data.


### 2.4. The GM(1,1) Model with Improved Background Value

The background value is one of the key factors causing errors in the traditional GM(1,1) model, which is formulated asz1k=0.5x1k+0.5x1k−1, but most of the background value construction improvement methods are tedious [32]. In this paper, we refer to the reference to set the background value formula as a linear combination with parameters, namely, z1k=αx1k+1−αx1k−1. [33].Different from the model in Section2.3, the GM(1,1) model with improved background values is built directly based on the original data and the sequence of background value is replaced with z1k=αx1k+1−αx1k−1. Incidentally, the parameter α is also solved using the genetic algorithm. The modeling process can be expressed by the flowchart shown in Figure 2.Figure 2
The flowchart of the GM(1,1) model with improved background value.


## 2.1. Construction of Two-Parameter Variable-Weight Buffer Operator

Compared with the traditional buffer operator, the two-parameter variable-weight buffer operator constructed in this paper adds an exponential parameter to the sequentially decreasing weights of the old and new data as a flexible adjustment of the buffer strength. A power exponential parameter is also introduced to unify the weakening and strengthening buffer operators. The adaptability of the buffer operator to the data sequence is enhanced by the coordinated variation of these two parameters.Theorem 1.
AssumeX=x1,x2,…,xn,xk>0 is the raw data. Let(1)XD=x1d,x2d,…xnd,where(2)xkd=xk⋅kλxk+k+1λxk+1+⋯+nλxnkλ+k+1λ+⋯nλ⋅xkγ=xk⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xkγ,λ≥0, k=1,2,…,n, then(1)
Whenγ>0, whether X is a monotonically increasing sequence, a monotonically decreasing sequence, or an oscillating sequence, D is always the weakening operator.(2)
Whenγ<0, whether X is a monotonically increasing sequence, a monotonically decreasing sequence, or an oscillating sequence, D is always the strengthening operator.(3)
Whenγ=0, D is the constant operator.Proof.
ClearlyD satisfies axioms for buffer operator and thus D is a buffer operator.(1)
Whenγ>0, there are the following three cases.(a)
IfX is a monotonically increasing sequence, for i=k,k+1,…,n, we have xi≥xk, then(3)xkd=xk⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xkγ≥xk⋅∑i=kn(iλ⋅xk)∑i=kniλ⋅xkγ=xk.That is, whenX is a monotonically increasing sequence, D is the weakening buffer operator.(b)
IfX is a monotonically decreasing sequence, for i=k,k+1,…,n, we have xi≤xk, then(4)xkd=xk⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xk≤xk⋅∑i=kn(iλ⋅xk)∑i=kniλ⋅xk=xk.That is, whenX is a monotonically decreasing sequence, D is the weakening buffer operator.(c)
IfX is an oscillating sequence, let(5)xl=maxxk|k=1,2,…,n,xh=minxk|k=1,2,…,n.Then,(6)xld=xl⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xl≤xl⋅∑i=kniλ⋅xl∑i=kniλ⋅xl=xl,xhd=xh⋅∑i=kn(iλ⋅xi)∑i=kniλ⋅xh≥xh⋅∑i=kniλ⋅xh∑i=kniλ⋅xh=xh.Therefore, whenX is the oscillation sequence, D is the weakening buffer operator.(2)
Whenγ<0, as long as γ>0 becomes γ<0 in the proof of (1) and the inequality is reversed accordingly, the required result is obtained naturally.(3)
Obviously holds whenγ=0. Proof ends.


## 2.2. The GM(1,1) Model based on Two-Parameter Variable-Weight Buffer Operator

Compared with the traditional GM(1,1) model, the buffered operator-based GM(1,1) model adds two steps of buffer sequence generation and parameter search. The modeling process are described as follows:Step 1. Let the original non-negative data sequence be defined as(7)X0=x01,x02,…,x0n.Step 2. Buffering is carried out on the raw data sequence to obtain the buffered sequence:(8)X0D=x01d,x02d,…,x0nd,wherexkd=xk⋅kλxk+k+1λxk+1+⋯+nλxn/kλ+k+1λ+⋯nλ⋅xkγ = xk⋅∑i=kn(iλ⋅xi)/∑i=kniλ⋅xk.X0D=x01d,x02d,…,x0nd is also recorded as X′0=x′01,x′02,…,x′0n.Step 3. By accumulating the buffered sequence, a cumulative series is generated as follows:(9)X′1=x′11,x′12,…,x′1n.wherex1k=∑i=1kx0i,k=1,2,…,n.Step 4. The grey differential equation of the GM(1,1) model is(10)x′0k+az1k=b,k=1,2,…,n,wherea, b, and z1k are the development coefficient, endogenous control, grey scale, and background value, respectively, and z1k=0.5x′1k+0.5x′1k−1,k=2,3,…,n.Step 5. Parameters are estimated by least squares (LS) regression. Supposing that,(11)B=−z12−z13⋮−z1n11⋮1,Y=x02x03⋮x0n.The coefficient is(12)P=a,bT=BTB−1BTY.Step 6. The corresponding whitening differential equation is(13)dx′1dt+ax′1=b.Step 7. The time-response function of the GM(1,1) model is(14)x^′1k+1=x′01−bae−ak+ba,k=1,2,…,n.Step 8. Through the first-order inverse accumulated generating operation, the predicted values can be obtained:(15)x^′0k+1=x^′1k+1−x^′1k=1−eax′01−bae−ak,k=1,2,…,n.


## 2.3. Optimizing Factorsλ and γ Employing the Genetic Algorithm

Due to a complicated non-linear relationship between the weight-regulating factors and prediction error, the optimal values ofλ and γ are solved by the genetic algorithm (GA), and the mean absolute percentage error (MAPE) is used as an objective function of the optimization. The objective function, namely, the fitness function, is expressed as follows:(16)fitness=100%n∑i=1nx^i′−xi′xi′,s.t.P=a^,b^T=BTB−1BTYx^′1k+1=x′01−bae−ak+bax^′0k+1=x^′1k+1−x^′1k,k=1,2,…,n,where xi′ represents the forecast value and xi′ expresses the buffered data, namely, the modeling data.


## 2.4. The GM(1,1) Model with Improved Background Value

The background value is one of the key factors causing errors in the traditional GM(1,1) model, which is formulated asz1k=0.5x1k+0.5x1k−1, but most of the background value construction improvement methods are tedious [32]. In this paper, we refer to the reference to set the background value formula as a linear combination with parameters, namely, z1k=αx1k+1−αx1k−1. [33].Different from the model in Section2.3, the GM(1,1) model with improved background values is built directly based on the original data and the sequence of background value is replaced with z1k=αx1k+1−αx1k−1. Incidentally, the parameter α is also solved using the genetic algorithm. The modeling process can be expressed by the flowchart shown in Figure 2.Figure 2
The flowchart of the GM(1,1) model with improved background value.


## 3. Validation of the Two-Parameter Variable-Weight Buffer Operator

### 3.1. Evaluation Criteria

To investigate the validity and applicability of each grey prediction model, we select the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) as the evaluation criteria. The calculation formulas are expressed as follows.(17)RMSE=1n∑i=1ne2i,MAE=1n∑i=1nei,MAPE=1n∑i=1neix0i×100%,where ei=x0i−x^0i, x0i, and x^0i represent the actual and forecasted values, respectively. The classification of the prediction accuracy of MAPE is shown in Table 2.Table 2
The MAPE criterion for model examination [34].
MAPE (%)Forecasting abilityMAPE (%)Forecasting ability<10High forecasting20–50Reasonable forecasting10–20Good forecasting>50Weak forecasting


### 3.2. Case Study: U.S. Solar Power Generation Forecast

In this subsection, the observations of solar power generation in the United States from 2010 to 2020 are chosen as data samples, which are gathered from BP Statistical Review of World Energy (https://www.bp.com/statisticalreview). Subsequently, these sample data are divided into two sets, namely training set, and test set. The parameters in the two-parameter variable-weight buffer operator are optimally searched by the genetic algorithm. Figure 3 show the optimal value of the nonlinear parameters. It can be seen that the optimal parameter values are λ∗=0.917 and γ∗=0.309, respectively. Table 3 shows the fitted and predicted results of each model, and the computational results of evaluation metrics are listed in Table 4.Figure 3
Optimal parameter value.Table 3
The fitted and predicted values of each model in case study.
YearRaw dataGM(1,1)AWBO-GM(1,1)2-VWBO-GM(1,1)Fitted/predicted valuesErrors (%)Buffered dataFitted/predicted valuesErrors (%)Buffered dataFitted/predicted valuesErrors (%)Training set20103.019.1492.8729.37——18.35——20114.7413.3247.3933.1337.740.3523.0630.4432.0420129.0419.4221.0737.8743.550.1932.8135.678.71201316.0428.313.1043.6350.250.5543.8341.794.65201429.2241.264.6550.5357.990.6357.3448.9614.61201539.4360.158.5357.6366.920.2760.5557.375.25201655.4287.6812.3366.7477.231.0766.4667.211.13201778.069.1492.8778.0632.701.2978.0678.750.88Test set201894.31127.8135.52—89.125.50—92.272.172019107.97186.3172.55—102.844.75—108.100.122020133.97271.58102.72—118.6711.42—126.665.46Table 4
Computational results of each evaluation metric in case study.
ErrorGM (1,1)AWBO-GM (1,1)2-VWBO-GM (1,1)Training setRMSE4.900.404.60MAE4.170.333.61MAPE (%)27.130.629.61Test setRMSE93.448.544.39MAE83.159.793.16MAPE (%)70.267.232.58As can be seen from Table4, the GM(1,1) model has a large error in both the training and testing phases and cannot be directly used for prediction. The reason for the large error is that the U.S. solar power generation data changed abruptly in 2018, with a sudden drop in growth rate, and the traditional GM(1,1) model cannot accurately predict the abruptly changed data series. The GM(1,1) model based on the two-parameter variable-weight buffer operator has a MAPE of 9.61% and 2.58% in the training and test sets, respectively, and they both achieve high prediction accuracy according to the test criteria in Table 2. Usually, the simulation accuracy of the training set is high and the prediction accuracy of the test set is also high. The GM(1,1) model based on the average weakening buffer operator has the smallest simulation error but not the smallest prediction error, which is because the average weakening buffer operator may over-buffer the data resulting in high simulation accuracy and low prediction accuracy. In contrast, the GM(1,1) model based on the two-parameter variable-weight buffer operator has the highest prediction accuracy. In summary, the GM(1,1) model based on the two-parameter variable-weight buffer operator is relatively optimal.


## 3.1. Evaluation Criteria

To investigate the validity and applicability of each grey prediction model, we select the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) as the evaluation criteria. The calculation formulas are expressed as follows.(17)RMSE=1n∑i=1ne2i,MAE=1n∑i=1nei,MAPE=1n∑i=1neix0i×100%,where ei=x0i−x^0i, x0i, and x^0i represent the actual and forecasted values, respectively. The classification of the prediction accuracy of MAPE is shown in Table 2.Table 2
The MAPE criterion for model examination [34].
MAPE (%)Forecasting abilityMAPE (%)Forecasting ability<10High forecasting20–50Reasonable forecasting10–20Good forecasting>50Weak forecasting


## 3.2. Case Study: U.S. Solar Power Generation Forecast

In this subsection, the observations of solar power generation in the United States from 2010 to 2020 are chosen as data samples, which are gathered from BP Statistical Review of World Energy (https://www.bp.com/statisticalreview). Subsequently, these sample data are divided into two sets, namely training set, and test set. The parameters in the two-parameter variable-weight buffer operator are optimally searched by the genetic algorithm. Figure 3 show the optimal value of the nonlinear parameters. It can be seen that the optimal parameter values are λ∗=0.917 and γ∗=0.309, respectively. Table 3 shows the fitted and predicted results of each model, and the computational results of evaluation metrics are listed in Table 4.Figure 3
Optimal parameter value.Table 3
The fitted and predicted values of each model in case study.
YearRaw dataGM(1,1)AWBO-GM(1,1)2-VWBO-GM(1,1)Fitted/predicted valuesErrors (%)Buffered dataFitted/predicted valuesErrors (%)Buffered dataFitted/predicted valuesErrors (%)Training set20103.019.1492.8729.37——18.35——20114.7413.3247.3933.1337.740.3523.0630.4432.0420129.0419.4221.0737.8743.550.1932.8135.678.71201316.0428.313.1043.6350.250.5543.8341.794.65201429.2241.264.6550.5357.990.6357.3448.9614.61201539.4360.158.5357.6366.920.2760.5557.375.25201655.4287.6812.3366.7477.231.0766.4667.211.13201778.069.1492.8778.0632.701.2978.0678.750.88Test set201894.31127.8135.52—89.125.50—92.272.172019107.97186.3172.55—102.844.75—108.100.122020133.97271.58102.72—118.6711.42—126.665.46Table 4
Computational results of each evaluation metric in case study.
ErrorGM (1,1)AWBO-GM (1,1)2-VWBO-GM (1,1)Training setRMSE4.900.404.60MAE4.170.333.61MAPE (%)27.130.629.61Test setRMSE93.448.544.39MAE83.159.793.16MAPE (%)70.267.232.58As can be seen from Table4, the GM(1,1) model has a large error in both the training and testing phases and cannot be directly used for prediction. The reason for the large error is that the U.S. solar power generation data changed abruptly in 2018, with a sudden drop in growth rate, and the traditional GM(1,1) model cannot accurately predict the abruptly changed data series. The GM(1,1) model based on the two-parameter variable-weight buffer operator has a MAPE of 9.61% and 2.58% in the training and test sets, respectively, and they both achieve high prediction accuracy according to the test criteria in Table 2. Usually, the simulation accuracy of the training set is high and the prediction accuracy of the test set is also high. The GM(1,1) model based on the average weakening buffer operator has the smallest simulation error but not the smallest prediction error, which is because the average weakening buffer operator may over-buffer the data resulting in high simulation accuracy and low prediction accuracy. In contrast, the GM(1,1) model based on the two-parameter variable-weight buffer operator has the highest prediction accuracy. In summary, the GM(1,1) model based on the two-parameter variable-weight buffer operator is relatively optimal.


## 4. Empirical Analysis of Wind Power Installed Capacity Forecasting

### 4.1. Data Selection

The purpose of this paper is to explore the impact on the installed wind power capacity during the “14th Five-Year Plan” period if the wind power subsidy policy in China during the “13th Five-Year Plan” period (2015–2020) is continued, so the data on the wind power installed capacity from 2015 to 2020 (see Table5) are selected for forecasting. The data are obtained from the national macro monthly database in the CEInet statistics database (https://db.cei.cn/).Table 5
Installed capacity and growth rate of wind power from 2015–2020.
YearWind power installed capacity (million kilowatts)Growth rate (%)201513075—20161474712.7920171632510.7020181842712.8820192091513.5020202815334.61


### 4.2. Wind Power Installed Capacity Forecasting

Since the central government implemented the wind power desubsidization policy in early 2021, two situations need to be considered in predicting the wind power installed capacity during the “14th Five-Year Plan” period. One is that the local government does not take over the subsidy policy of the central government, and the other is that the local government takes over the subsidy policy of the central government.If the local government does not continue to implement the wind power subsidy policy, the wind power installed capacity in China during the “14th Five-Year Plan” period will no longer be affected by the subsidy policy during the “13th Five-Year Plan” period. Therefore, to quantify the impact of the subsidy policy, the two-parameter variable-weight buffer operator proposed in this paper is used to weaken the data from 2015–2020 before forecasting. The optimal values of the factorsλ and γ regulating the buffer strength are solved by the genetic algorithm. Then, the GM(1,1) model is established based on the buffered data to forecast the wind power installed capacity from 2021 to 2025. The steps are as follows:Step 1. The fitness function fitness=100%/6∑i=16x^i−xi/xi was constructed, where x^i denotes the predicted value and xi denotes the buffered data, i.e., the modeling data.Step 2. The computational program of the fitness function was written using MATLAB, and the Genetic Algorithm GUI window in Optimization Toolbox was opened to iteratively solve for the optimal parameters, the results of which are shown in Figure 4. It can be seen that the optimal parameters were λ∗=1.138 and γ∗=0.074, respectively.Step 3. The optimal parameters were substituted into the buffer operator, and then the GM(1,1) model based on a two-parameter variable-weight buffer operator was established, at which time the parameter estimates of the model were a^=a,bT=−0.08,18370.38T, and the corresponding time response equation was x^′1t+1=248328.75e0.08t−229629.75. The simulated results and errors are shown in Table 6.Figure 4
Optimal value parameters.If the local government continues to implement the central government’s wind power subsidy policy during the “14th Five-Year Plan” period, the GM(1,1) model with optimal background values is built directly based on the data of wind power installed capacity from 2015 to 2020. The optimal background value ofα∗=0.434 was obtained by the genetic algorithm, at which time the parameter estimates of the model were a^=a,bT=−0.17,10426T, and the time response equation was x^1t+1=74404.60e0.17t−61329.4.. The simulated results and errors are shown in Table 6.Table 6
Simulation results of wind power installed capacity in China.
YearContinuation of subsidyDiscontinuation of subsidyRaw dataSimulated valueRelative error (%)Buffered dataSimulated valueRelative error (%)201513075——18699——201614747137786.5720629206180.05201716325163230.0122239222870.22201818427193404.9524199240910.45201920915229139.5526041260420.00202028153271473.5728153281500.01From Table6, it can be further measured that the simulated average relative errors of the installed wind power capacity are 4.93% and 0.15% for the two scenarios of continuing and stopping subsidies, respectively, which are well fitted. The prediction results illustrate that the two-parameter variable-weight buffer operator flexibly adjusts the buffer strength through the coordinated changes of the two parameters, thus well quantifying the impact of policy shocks. Therefore, the GM(1,1) model based on buffered data can accurately fit the wind power capacity forecast under the continuation of the subsidy policy during the 14th Five-Year Plan. Meanwhile, the GM(1,1) model with optimized background values can also accurately predict the installed wind power capacity when the local government stop subsidies. The wind power installed capacity under the continuation and cessation of the subsidy policy during the 14th Five-Year Plan was predicted, respectively, and the forecast results are shown in Table 7.Table 7
Predicted value of wind power installed capacity from 2021–2025.
Year20212022202320242025Predicted value of continued subsidy (million kW)3216338106451475348963373Predicted value of stopped subsidy (million kW)3042832891355543843241544The forecast results show that, without continued subsidy policy from the local government, China’s wind power installed capacity will be 415.44 million kilowatts in 2025, failing to reach the national target of 540 million kilowatts. On the contrary, if the local government continues to subsidize, the wind power installed capacity will rise to 633.73 million kilowatts, which can exceed the planned target. Then, the comparison chart of forecast results of wind power installed capacity is drawn as shown in Figure5.Figure 5
Comparison chart of forecast results of wind power installed capacity.As can be seen from Figure5, in both cases, the data of wind power installed capacity during the “14th Five-Year Plan” period are on the increase, and the growth trend in the case of discontinued subsidy is significantly lower than that in the case of continued subsidy. In 2025, the national planning target value lies between the installed wind power capacity values for both policy scenarios. Therefore, to carry out regulatory work in accordance with the “14th Five-Year Plan,” the local government needs to relay the central government’s subsidy policy and adjust the intensity of subsidy within the appropriate range.


## 4.1. Data Selection

The purpose of this paper is to explore the impact on the installed wind power capacity during the “14th Five-Year Plan” period if the wind power subsidy policy in China during the “13th Five-Year Plan” period (2015–2020) is continued, so the data on the wind power installed capacity from 2015 to 2020 (see Table5) are selected for forecasting. The data are obtained from the national macro monthly database in the CEInet statistics database (https://db.cei.cn/).Table 5
Installed capacity and growth rate of wind power from 2015–2020.
YearWind power installed capacity (million kilowatts)Growth rate (%)201513075—20161474712.7920171632510.7020181842712.8820192091513.5020202815334.61


## 4.2. Wind Power Installed Capacity Forecasting

Since the central government implemented the wind power desubsidization policy in early 2021, two situations need to be considered in predicting the wind power installed capacity during the “14th Five-Year Plan” period. One is that the local government does not take over the subsidy policy of the central government, and the other is that the local government takes over the subsidy policy of the central government.If the local government does not continue to implement the wind power subsidy policy, the wind power installed capacity in China during the “14th Five-Year Plan” period will no longer be affected by the subsidy policy during the “13th Five-Year Plan” period. Therefore, to quantify the impact of the subsidy policy, the two-parameter variable-weight buffer operator proposed in this paper is used to weaken the data from 2015–2020 before forecasting. The optimal values of the factorsλ and γ regulating the buffer strength are solved by the genetic algorithm. Then, the GM(1,1) model is established based on the buffered data to forecast the wind power installed capacity from 2021 to 2025. The steps are as follows:Step 1. The fitness function fitness=100%/6∑i=16x^i−xi/xi was constructed, where x^i denotes the predicted value and xi denotes the buffered data, i.e., the modeling data.Step 2. The computational program of the fitness function was written using MATLAB, and the Genetic Algorithm GUI window in Optimization Toolbox was opened to iteratively solve for the optimal parameters, the results of which are shown in Figure 4. It can be seen that the optimal parameters were λ∗=1.138 and γ∗=0.074, respectively.Step 3. The optimal parameters were substituted into the buffer operator, and then the GM(1,1) model based on a two-parameter variable-weight buffer operator was established, at which time the parameter estimates of the model were a^=a,bT=−0.08,18370.38T, and the corresponding time response equation was x^′1t+1=248328.75e0.08t−229629.75. The simulated results and errors are shown in Table 6.Figure 4
Optimal value parameters.If the local government continues to implement the central government’s wind power subsidy policy during the “14th Five-Year Plan” period, the GM(1,1) model with optimal background values is built directly based on the data of wind power installed capacity from 2015 to 2020. The optimal background value ofα∗=0.434 was obtained by the genetic algorithm, at which time the parameter estimates of the model were a^=a,bT=−0.17,10426T, and the time response equation was x^1t+1=74404.60e0.17t−61329.4.. The simulated results and errors are shown in Table 6.Table 6
Simulation results of wind power installed capacity in China.
YearContinuation of subsidyDiscontinuation of subsidyRaw dataSimulated valueRelative error (%)Buffered dataSimulated valueRelative error (%)201513075——18699——201614747137786.5720629206180.05201716325163230.0122239222870.22201818427193404.9524199240910.45201920915229139.5526041260420.00202028153271473.5728153281500.01From Table6, it can be further measured that the simulated average relative errors of the installed wind power capacity are 4.93% and 0.15% for the two scenarios of continuing and stopping subsidies, respectively, which are well fitted. The prediction results illustrate that the two-parameter variable-weight buffer operator flexibly adjusts the buffer strength through the coordinated changes of the two parameters, thus well quantifying the impact of policy shocks. Therefore, the GM(1,1) model based on buffered data can accurately fit the wind power capacity forecast under the continuation of the subsidy policy during the 14th Five-Year Plan. Meanwhile, the GM(1,1) model with optimized background values can also accurately predict the installed wind power capacity when the local government stop subsidies. The wind power installed capacity under the continuation and cessation of the subsidy policy during the 14th Five-Year Plan was predicted, respectively, and the forecast results are shown in Table 7.Table 7
Predicted value of wind power installed capacity from 2021–2025.
Year20212022202320242025Predicted value of continued subsidy (million kW)3216338106451475348963373Predicted value of stopped subsidy (million kW)3042832891355543843241544The forecast results show that, without continued subsidy policy from the local government, China’s wind power installed capacity will be 415.44 million kilowatts in 2025, failing to reach the national target of 540 million kilowatts. On the contrary, if the local government continues to subsidize, the wind power installed capacity will rise to 633.73 million kilowatts, which can exceed the planned target. Then, the comparison chart of forecast results of wind power installed capacity is drawn as shown in Figure5.Figure 5
Comparison chart of forecast results of wind power installed capacity.As can be seen from Figure5, in both cases, the data of wind power installed capacity during the “14th Five-Year Plan” period are on the increase, and the growth trend in the case of discontinued subsidy is significantly lower than that in the case of continued subsidy. In 2025, the national planning target value lies between the installed wind power capacity values for both policy scenarios. Therefore, to carry out regulatory work in accordance with the “14th Five-Year Plan,” the local government needs to relay the central government’s subsidy policy and adjust the intensity of subsidy within the appropriate range.


## 5. Policy Subsidy Strategy

### 5.1. Subsidy Strategy Model

Subsidy intensity is a relatively abstract concept, so the central or local governments generally rely on historical experience when adjusting subsidy strategies, which is highly subjective [35]. To provide a quantitative basis for the central and local governments to formulate their subsidy strategies, two subsidy strategy models are constructed in this paper, as shown in Figures 6 and 7.Figure 6
Subsidy strategy model 1.Figure 7
Subsidy strategy model 2.From Figures6 and 7, it is assumed that point O is the first year of the impact of the subsidy policy, the segment OA represents the predictor of the continuation of the subsidy policy by the local government, the segment OB represents the national planning target, and the segment OC represents the predictor of the cessation of the subsidy policy. The coordinate axis is established at point C. The horizontal axis represents the year, and the vertical axis represents the intensity of the government subsidy, denoted by S. The subsidy intensity is SC=0. for point C, SA=1. for point A, and SB=BC/AC. for point B according to the linear relationship in the figure. Thus, the security subsidy strategy is SB≤R≤1. in Model 1 and R≥SB in Model 2.It should be noted that the periodic change of government subsidy policy is a prerequisite for using the subsidy strategy model, where model 1 applies to the case of excessive government subsidies and model 2 applies to that of insufficient government subsidies.


### 5.2. Subsidy Strategy for Wind Power Installed Capacity

Based on the predicted value of wind power installed capacity under the two subsidy policy scenarios, the specific subsidy intensity adjustment strategy is analyzed. For the sake of observation, the predicted values of wind power installed capacity from 2020 to 2025 are drawn as a partially enlarged graph (see Figure8), where point A is the predicted value of wind power installed capacity in 2025 when the local government continues to subsidize during the “14th Five-Year Plan,” point B is the planned target value of wind power installed capacity, and point C is the predicted value of wind power installed capacity in 2025 without subsidies. It can be seen that this algorithm is consistent with the subsidy strategy model 1.Figure 8
Quantitative analysis of the subsidy strength for the wind power installed capacity.To accomplish the national planning target, the local government must relay the central government’s subsidy policy, and the subsidy intensity must at least overlap with or exceed pointB. Therefore, section AB is a safe subsidy strategy zone. From the forecast results, we can see that the wind power installed capacities at points A and C are 6,337,300 kilowatts and 4,154,400 kilowatts, respectively. The national planning target for the wind power installed capacity during the “14th Five-Year Plan” period is 540 million kilowatts. According to model 1, the subsidy intensity at point B can be calculated as(18)SB=BCAC=54000−4154463373−41544=0.57.Therefore, the safety subsidy strategy is0.57≤R≤1, that is, to ensure the smooth completion of the “14th Five-Year Plan,” the local government should relay the subsidy policy in the event that the central government cancels the subsidy policy, and adjust the policy subsidy intensity to between 0.57 and 1 times of that during the “13th Five-Year Plan” period.


## 5.1. Subsidy Strategy Model

Subsidy intensity is a relatively abstract concept, so the central or local governments generally rely on historical experience when adjusting subsidy strategies, which is highly subjective [35]. To provide a quantitative basis for the central and local governments to formulate their subsidy strategies, two subsidy strategy models are constructed in this paper, as shown in Figures 6 and 7.Figure 6
Subsidy strategy model 1.Figure 7
Subsidy strategy model 2.From Figures6 and 7, it is assumed that point O is the first year of the impact of the subsidy policy, the segment OA represents the predictor of the continuation of the subsidy policy by the local government, the segment OB represents the national planning target, and the segment OC represents the predictor of the cessation of the subsidy policy. The coordinate axis is established at point C. The horizontal axis represents the year, and the vertical axis represents the intensity of the government subsidy, denoted by S. The subsidy intensity is SC=0. for point C, SA=1. for point A, and SB=BC/AC. for point B according to the linear relationship in the figure. Thus, the security subsidy strategy is SB≤R≤1. in Model 1 and R≥SB in Model 2.It should be noted that the periodic change of government subsidy policy is a prerequisite for using the subsidy strategy model, where model 1 applies to the case of excessive government subsidies and model 2 applies to that of insufficient government subsidies.


## 5.2. Subsidy Strategy for Wind Power Installed Capacity

Based on the predicted value of wind power installed capacity under the two subsidy policy scenarios, the specific subsidy intensity adjustment strategy is analyzed. For the sake of observation, the predicted values of wind power installed capacity from 2020 to 2025 are drawn as a partially enlarged graph (see Figure8), where point A is the predicted value of wind power installed capacity in 2025 when the local government continues to subsidize during the “14th Five-Year Plan,” point B is the planned target value of wind power installed capacity, and point C is the predicted value of wind power installed capacity in 2025 without subsidies. It can be seen that this algorithm is consistent with the subsidy strategy model 1.Figure 8
Quantitative analysis of the subsidy strength for the wind power installed capacity.To accomplish the national planning target, the local government must relay the central government’s subsidy policy, and the subsidy intensity must at least overlap with or exceed pointB. Therefore, section AB is a safe subsidy strategy zone. From the forecast results, we can see that the wind power installed capacities at points A and C are 6,337,300 kilowatts and 4,154,400 kilowatts, respectively. The national planning target for the wind power installed capacity during the “14th Five-Year Plan” period is 540 million kilowatts. According to model 1, the subsidy intensity at point B can be calculated as(18)SB=BCAC=54000−4154463373−41544=0.57.Therefore, the safety subsidy strategy is0.57≤R≤1, that is, to ensure the smooth completion of the “14th Five-Year Plan,” the local government should relay the subsidy policy in the event that the central government cancels the subsidy policy, and adjust the policy subsidy intensity to between 0.57 and 1 times of that during the “13th Five-Year Plan” period.


## 6. Conclusion

The purpose of this paper is to explore the future development of installed wind power capacity under different subsidy policies and to measure the strength of government subsidy policies during China’s “14th Five-Year Plan” period. Considering that the wind power installed capacity is strongly affected by government subsidy policy, a new two-parameter variable-weight buffer operator is proposed to quantify the impact of policy shocks in this paper. The weights in the buffer operator can be flexibly adjusted through the coordinated changes of the two parameters, and the optimal parameters are found by a genetic algorithm. The new buffer operator combined with the GM(1,1) model can well simulate the trend of installed wind power capacity without the subsidy policy. Meanwhile, the GM(1,1) model with optimized background values is used to simulate and forecast the installed wind power capacity under the continued subsidy scenario with high accuracy.Currently, China’s economy has entered a critical period of building a new development pattern and transforming its energy and power structure, which will drive the demand for a large amount of clean energy, including wind energy. In addition, wind energy is playing an increasingly important role in alleviating energy shortages and environmental degradation. However, the removal of subsidies by the central government will result in China’s installed wind power capacity falling short of expected targets. According to the policy subsidy strategy model constructed in this paper, to achieve the national “14th Five-Year Plan” for installed wind power capacity, the local government needs to continue the central government’s subsidy policy and adjust the subsidy intensity to at least 0.57 times of that during the “13th Five-Year Plan” period.Under the premise of ensuring high-precision forecasting, we focus on the government’s decision-making behavior in the wind power market to provide a basis for the local government to formulate the subsidy policy. However, this paper only considers the impact of government subsidy policy on the wind power installed capacity, and the analysis of subsidy strategy under multifactor conditions can be a further research direction in the future.



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*Source: 5380366-2022-03-27.xml*