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Trackingdispatch of a combined windstorage system based on model predictive control and twolayer fuzzy control strategy
Protection and Control of Modern Power Systems volume 8, Article number: 58 (2023)
Abstract
To maximize improving the tracking wind power output plan and the service life of energy storage systems (ESS), a control strategy is proposed for ESS to track wind power planning output based on model prediction and twolayer fuzzy control. First, based on model predictive control, a model with deviations of gridconnected power from the planned output and the minimum deviation of the remaining capacity of the ESS from the ideal value is established as the target. Then, when the gridconnected power exceeds the allowable deviation band of tracking, the weight coefficients in the objective function are adjusted by introducing the first layer of fuzzy control rules, combining the state of charge (SOC) of the ESS with the dynamic tracking demand of the planned value of wind power. When the gridconnected power is within the tracking allowable deviation band, the second layer of fuzzy control rules is used to correct the charging and discharging power of the ESS to improve its ability to track the future planned deviation while not crossing the limit. By repeatedly correcting the charging and discharging power of the ESS, its safe operation and the multitasking execution of the wind power plan output tracking target are ensured. Finally, taking actual data from a wind farm as an example, tests on a simulation platform of a combined windstorage power generation system verify the feasibility and superiority of the proposed control strategy.
1 Introduction
Development of wind power is an effective way to accelerate the construction of a clean, lowcarbon, safe, and efficient energy system, and to achieve sustainable energy development and dualcarbon goals [1, 2]. However, the fluctuating and intermittent nature of wind power impacts on the safe and stable operation of power grids [3,4,5]. Power generation plans based on shortterm wind forecasts can stabilize the impact of variable wind power integration to a certain extent, but there are still large deviations between shortterm forecast power and actual wind power [6, 7]. Energy storage systems (ESS) can effectively compensate for the drawbacks of wind power generation and improve the tracking accuracy of windstorage cogeneration systems for planned power output [8, 9]. However, the tracking accuracy of ESS is limited by their service life, capacity, and control mechanisms [10,11,12,13]. Given these limitations, it is critical to study the optimal control strategies for windstorage systems [14, 15].
Many indepth studies have looked at applying ESS in tracking the output of wind power plans [16,17,18,19,20,21,22]. Energy storage improves the output of wind farm tracking and power generation through either post hoc realtime section or realtime advance optimization control. Under realtime section control, the ESS corrects the deviation between the actual wind power and the planned value at each moment in realtime.
Reference [23] studies the use of ESS in a wind farm to track shortterm planned output to improve wind farm tracking ability. In [24], an ESS control strategy containing five control coefficients is established and a particle swarm optimization algorithm is used to optimize and correct the charge and discharge control coefficients at each time in realtime. This improves the ability to control the ESS and track wind power planning. Reference [25] proposes a coordinated optimization control strategy combining online rolling optimization and realtime active power control. These reduce the number of energy storage charge and discharge conversions, and show improved ability to track planned output. Realtime section control adopts timely regulation without considering the future changes in the SOC of ESS batteries, while the control effect and economy of a windstorage system are affected by battery overcharge, overdischarge, and capacity underutilization.
The combination of realtime lead optimization control with ultrashortterm wind power prediction can achieve forwardlooking lead control. Reference [12] proposes energy storage SOC feedback control based on ultrashortterm wind power prediction and scenario analysis in order to reduce the number of energy storage commands and avoid excessive charging and discharging. In [26], an optimization model is constructed to reduce the fluctuation range and the charge and discharge depth of energy storage SOC. This model, combined with wind power prediction information, adopts realtime rolling optimization to track the generation schedule and use the full ESS capacity. In [27], ultrashortterm power prediction is used to minimize the ordered times of energy storage, while advance rolling optimization is realized in the assessment period. This improves the precision of a wind power tracking plan. In [28], the Kalman filter algorithm is used to enhance the minute level of ultrashortterm wind power prediction data so as to improve the finegrained power prediction. The algorithm, when combined with advanced rolling optimization, can accurately optimize the windstorage system’s power assessment and energy storage life. However, the effect of realtime advanced optimization control depends heavily on the accuracy of wind power prediction.
The model predictive control (MPC) algorithm has good robustness and antiinterference ability, and can better solve optimal control problems with a variety of uncertainties. A twostage stochastic MPC with the aim of determining the optimal ESS size is proposed in [29], whereas a new control strategy based on the MPC method to fulfill the committed energy production of wind farms is presented in [30]. However, the service life of the ESS is neglected. References [31, 32] apply MPC to windstorage systems and propose tracking scheduling instructions and minimizing energy storage output as control objectives. This improves the ability to schedule wind farm production. However, fixed values are used for the objective function weighting factors while no method is given for determining the weighting factors. In fact, the selection of weighting factors has a significant impact on MPC [33,34,35]. In the reviewed publications, MPC is used to determine the optimal ESS size and scheduling with the aim of reducing wind power forecast error. However, there is little research on improving the tracking capability of a windstorage system for future planned curve by optimizing the current residual capacity of ESS in advance.
Thus, it is clear that there is a lack of comprehensive consideration of wind power prediction error and uncertainty of energy storage SOC on future tracking accuracy, and that further research is needed on how to effectively balance the contradiction between ESS lifetime and wind power plan tracking capability. Therefore, this paper proposes a combined windstorage system tracking wind power plan control strategy based on MPC and doublelayer fuzzy control, with the aim of improving both the windstorage system tracking plan output and the ESS service life. The main contributions of this study can be summarized as:

(1)
An ESS tracking wind power plan control model is established based on the MPC method. An objective function is proposed to minimize the deviation of gridconnected power from the planned output and the deviation of ESS remaining capacity from the ideal value. Consequently, the deviation of gridconnected power from the planned curve is reduced, while the ESS lifetime is taken into account.

(2)
When the gridconnected power exceeds the tracking allowable deviation band, a method of using the first layer of fuzzy controller is proposed to correct the weight coefficients of the objective function to effectively resolve the contradiction between the deviations from the wind power plan and the energy storage overrun limit. The proposed method reduces the dead time and extends the service life of the ESS while improving the tracking of the planned curve.

(3)
Statistical factor analysis theory is used to construct the contradictory factors between the two variables of ESS offlimit power and planned power deviation in the future optimization period. When the gridconnected power is within the tracking allowable deviation band, a method of using the second layer of fuzzy control rules is used to correct the charging and discharging power of the ESS. Charging and discharging are carried out in advance to improve the ESS’s ability to track deviations from the future plan.
A simulation platform is developed for a combined windstorage power generation system, and the effectiveness of the proposed control strategy is verified considering a wind farm’s actual operating data. The rest of this paper is organized as follows: Sect. 2 describes the topology of the combined windstorage generation system and the creation of allowable deviation bands for generation schedule tracking. In Sect. 3, the ESS tracking wind power planning control model is established based on the MPC method, while in Sect. 4, a twolayer fuzzy control strategy is proposed. Case studies are presented in Sect. 5, and Sect. 6 concludes the paper.
2 Windstorage cogeneration system
Uncertain changes in wind speed lead to weak dispatchability of wind farm active power output. This increases the operational risk to the grid. The ability to schedule power production at a wind farm can be effectively improved by controlling the ESS charging and discharging power at the wind farm connection point. The topology of the windstorage cogeneration system is shown in Fig. 1. It mainly consists of a wind farm, an energy storage station, stepup transformers, converters, and an energy management system. These are connected to the main grid through transmission lines.
During actual grid dispatching, the power generation plan value P_{p} is formulated according to the wind power prediction value. The charging and discharging power P_{b} of the ESS is calculated through a suitable control strategy to compensate for the difference between the actual P_{w} and planned P_{p} wind power. Finally, the gridconnected power P_{g} of the windstorage cogeneration system is obtained. The power balance equation of the windstorage cogeneration system is:
For the forecasting of continuous states, in terms of mathematical solution, the time is usually discretized equally. Therefore, Eq. (1) is discretized to:
where P_{b}(i) and P_{w}(i) are the power of the ESS and the actual power of the wind power at the current moment, respectively. P_{g}(i + 1) denotes the power of windstorage cogeneration system at the next moment. When P_{b}(i) > 0, the ESS is charged and when P_{b}(i) < 0, the ESS is discharged.
The iterative equation for the State of Energy (SOE) after discretization is:
where C_{SOE}(i) denotes the residual ESS capacity at time i, and T_{c} and C_{rated} are the ESS control period and capacity, respectively. η is the ESS conversion efficiency.
According to the “Technical Regulations for Wind Power Forecasting” issued by the National Energy Administration in 2019 [36], the shortterm forecast accuracy rate should be greater than or equal to 80%. Thus, the allowable deviation band of generation plan tracking, i.e., the allowable error ranges between the actual power and the planned output curve, can be written [37] as:
where P_{u}(i) and P_{d}(i) are the upper limit and lower limit of the allowable deviation band, respectively. δ denotes the deviation band set coefficient, and P_{p}(i) refers to the planned value of wind power at time i.
The target is for the output from the combined windstorage power generation system to be within the planned range. As shown in Area I of Fig. 2, the ESS does not act when the actual power of the wind farm is within the allowable range. When the actual power exceeds the upper limit or lower limit of the deviation band and reaches Area II, the combined output of the wind and storage at the moment is controlled within Area I via the ESS by absorbing or releasing power.
According to the above analysis, the target power P_{a}(i) can be calculated as follows:
3 Control model of MPC energy storage system
Based on the above power balancing equation and SOE iteration equation, the MPC system model is created. Meanwhile, the MPC rolling optimization objective function and constraints are established by combining the target power sources, taking into account the energy storage lifetime and tracking capability, and transforming the power into a quadratic programming problem for solution.
3.1 Based on MPC system model
MPC is a class of methods that consider openloop optimal control in a finitetime domain, using the idea of rolling planning and advance control. The MPC for tracking the planned wind power output is shown in Fig. 3. At its core lies the timedomain rolling optimization process:

(1)
Establish the objective function and constraints.

(2)
Solve the optimization problem with constraints to obtain a sequence of control instructions for a future period using the values of state variables at the current moment.

(3)
Apply the 1st value of the control instruction sequence to the control system.

(4)
Scroll to the next moment and update the state variables to repeat the above process.
The schematic block diagram of the tracking plan with MPC is shown in Fig. 4. The MPC conducts realtime rolling optimization for system control. This is comprised of three parts: a prediction model, rolling optimization, and feedback correction.
The prediction model plays a fundamental role in model predictive control as it anticipates the future dynamic behavior of the system. Such a model relies on historical data and the current status of the system, incorporating future time domain system change trends and the impact of control instructions to forecast the system's dynamic behavior within a limited future time span. These prediction outcomes serve as inputs for the rolling optimization stage. Here, under the influence of specific optimization objectives, the control sequence that aligns the system's predicted trend most effectively with the optimization problem requirements is considered as the optimal control instruction.
Rolling optimization serves as the central element of MPC. Its core concept involves continuously integrating system prediction information and control sequences within a limited time window to perform realtime optimization based on the specific goals defined for the controlled system. The results obtained from this process are then used to guide the system's future outputs. At each time step, the initial component of the optimal control sequence that brings the system closest to the defined optimization goal is selected as the control input for the upcoming moment. Subsequently, the new measurements generated by the system at that moment refresh the initial state of the controlled system, and the cycle repeats itself through model prediction and rolling optimization. As time progresses, the prediction time horizon also advances until the desired control objective is achieved.
In each step, MPC uses the initial element of the previously solved optimal control sequence from the prior moment to interact with the system, yielding new system state information and outputs. This process effectively refreshes the rolling optimization problem. During this process, MPC establishes both feedforward and feedback components. On the one hand, the newly acquired system state information and the ongoing system prediction information at each time step are used as inputs for the feedforward component. If any changes are detected, they are fed back into the prediction model, enabling the recomputation of the optimal control sequence through rolling optimization, thus achieving feedforward correction. On the other hand, because feedforward control has limitations in addressing existing system errors, MPC introduces a feedback loop by inputting the discrepancy between the actual system output and the predicted output at each time step into the feedback component. This creates a closedloop system, allowing for feedback correction of the overall prediction error at that moment. This feedback mechanism enhances the robustness of the control strategy by addressing deviations that may have occurred.
From (2) and (3) and combined with the superposition theorem, the gridconnected power P_{g}(i) and the ESS residual capacity C_{SOE}(i) are selected to form the state variables, which are x(i) = [P_{g}(i),C_{SOE}(i)]^{T}. The ESS output P_{b}(i) is used as the control variable in the form of u(i) = P_{b}(i), while the ultrashortterm wind power P_{f}(i) is used as an input variable as r(i) = P_{f}(i). The ESS P_{g}(i) and C_{SOE}(i) are selected as the output variables as y(i) = [P_{g}(i),C_{SOE}(i)]^{T}. Then the state space equation of the windstorage cogeneration system is:
where \(\user2{A = }\left[ {\begin{array}{*{20}c} 0 & 0 \\ 0 & 1 \\ \end{array} } \right]\), \({\varvec{B}}_{1} = \left[ {\begin{array}{*{20}c} 1 \\ {  \eta T_{{\text{c}}} /C_{{{\text{rated}}}} } \\ \end{array} } \right]\), \({\varvec{B}}_{2} = \left[ {\begin{array}{*{20}c} 1 \\ 0 \\ \end{array} } \right]\), and \(\user2{C = }\left[ {\begin{array}{*{20}c} 1 & 0 \\ \end{array} } \right]\).
3.2 Objective function and constraints
From the perspective of extending the life of the ESS, the energy storage output is reduced while satisfying the tracking plan, and the SOE converges to the ideal value by introducing the storage SOE variation into the optimization process to improve the adaptability of ESS to future wind power changes. Therefore, the objective function is established with the deviation of gridconnected power from the planned output and the minimum deviation of ESS remaining capacity from the ideal value, as:
where C_{ideal} denotes the ideal ESS residual capacity, which is 0.5 times the rated capacity, and α and β denote the weight coefficients with α + β = 1.
The following charging and discharging power and SOC constraints should also be satisfied along with the MPC rolling optimization objective function.

(1)
ESS capacity constraints
Considering factors such as ESS service life and safety, the SOC should satisfy the inequality constraint equation of:
where E_{soc.min} and E_{soc.max} are the lower and upper limits of ESS SOC, respectively.

(2)
ESS power constraints
The unequal constraint condition of ESS charging power is:
where P_{rated} is the rated power of the ESS.
The unequal constraint condition of ESS discharge power is:
3.3 Energy storage target power solution based on MPC rolling optimization method
Using the MPC control principle and combining (7)–(11), the problem can be transformed into a quadratic programming form to obtain the sequence of control variables, i.e., the target power tracked by the ESS, in the present and future periods.
x(i) is the known actual state value at moment i. From (7), the state variable x(i + 1) at moment i + 1 can be obtained, and the state variable at moment i + 2 can be further calculated by x(i), as:
By analogy, an expression for the state variables at each moment can be obtained from x(i), all consisting of the known state and perturbation quantities, and the control variables to be solved. Let the sequence of state variables, the sequence of control variables, and the sequence of input quantities be divided as shown as:
As x(i) = x_{0}, Eq. (12) can be expanded as:
where the matrices of the coefficients are
Through matrix operations, all state variables in the optimization objective can be represented by control variables. Since the constant terms are not involved in the optimization and can thus be omitted, the objective function can be transformed into the standard quadratic programming form, as:
where H and f are the quadratic term and primary term parameter matrices of the control variable that need to be solved, respectively.
The optimal sequence of control variables U_{i} that satisfies the optimization conditions and constraints, i.e., the storage tracking target power P_{b}(i), P_{b}(i + 1)…P_{b}(i + k), can be obtained by mathematical solutions. In theory, if the real system model aligns perfectly with the established mathematical model and the predictions are highly accurate, substituting the control sequence into the actual system should yield results consistent with the theoretically predicted state variables. However, various factors, such as model inaccuracies and disturbances, necessitate the use of rolling optimization to enhance control precision. When determining the optimal power storage target, it is essential to recognize that prediction information closer to the current time tends to be more accurate. Therefore, during each optimization step, only the first element of the sequence is chosen for controlling the system. As time progresses, at each moment, the state sequence is refreshed for prediction, and this process is repeated iteratively to correct errors that may have accumulated during the control process, ultimately leading to improved control accuracy.
4 Weight coefficient adjustment based on twolayer fuzzy control
The MPC rolling optimization objective function was defined in Sect. 3 taking into account the multiobjective optimization problem in which the deviations of gridconnected power from the planned output capacity and ESS remaining capacity from the ideal value are minimized. In the optimization process, optimizing the ESS output capacity depends entirely on the SOE. Therefore, in this section, the relationship between the ESS output capacity C_{SOE} and the dynamic regulation coefficient α is calculated by designing a twolayer fuzzy controller. The ESS operating state and gridconnected power are determined by adjusting the weights of the two optimization parts.
4.1 Weight coefficient analysis
To further analyze the influence of the weight coefficients on the objective function, we make N = 1 in (8) and derive the derivative for J. Letting the derivative equal 0 allows for finding the ESS output power with the smallest objective function at the moment i + 1, i.e.:
As can be seen from (17), the ESS output power is controlled by α such that the larger α is, the closer the ESS residual capacity is to the ideal value, but the less effective the tracking plan curve is. On the contrary, if α is smaller, the tracking effect is better, but it could make the SOC overbound. Therefore, the following method is used here to dynamically adjust α in realtime.

(1)
At time i + 1, when the predicted ultrashortterm wind power exceeds the upper or lower limits of the planned deviation band, the combined output of windstorage should be ensured to be within the allowable deviation band of tracking. At the same time, the first layer fuzzy controller is used to correct α to keep the SOC from exceeding the limit.

(2)
At time i + 1, when the ultrashortterm wind power prediction is within the tracking allowable deviation band, it balances the contradiction between the planned power deviation and the ESS limit overrun in the future rolling optimization period. It improves the ability of the combined windstorage system to track deviations from future plans while ensuring ESS life. At this time, the second layer fuzzy controller is used to correct the charging and discharging power of the ESS, and the correction formula is given as:
$$P_{{\text{b}}}^{\prime} \left( {i + 1\left i \right.} \right) = P_{{\text{b}}} \left( {i + 1\left i \right.} \right) + \Delta k \times \delta P_{{\text{p}}} \left( {i + 1\left i \right.} \right)$$(18)
where \(P_{{\text{b}}}^{\prime} \left( {i + 1\left i \right.} \right)\) is the operation instruction after ESS correction at time i + 1 and ∆k is the correction coefficient.
4.2 First layer of fuzzy control
As the capacity and charge and discharge power of an ESS have certain ranges, if the SOC and charge and discharge power exceed their allowable ranges, the service life of the ESS can be seriously affected. Based on this, a first layer fuzzy controller is used to adjust the charging and discharging power of the ESS to maintain the SOC within the allowed working range. The fuzzy controller is designed as doubleinput and singleoutput, i.e., the inputs are the energy storage output P_{b}(i) and SOC at time i, and the output is α. The fuzzy control input and output membership functions are shown in Fig. 5.
The universe of fuzzy control input variable P_{b}(i) is [− 1,1], and the fuzzy set is {NB,NS,Z,PS,PB}, which sequentially represent values that are negative large, negative small, zero, positive small, or positive large. The universe of E_{soc}(i) is [0.2,0.8], and the fuzzy set is {VS,S,M,B,VB}, which in turn sequentially represent values that are small, slightly small, slightly large, or large. The domain of fuzzy control output variable α is [0,1], and the fuzzy set is {VS,S,M,B,VB}, which sequentially represent values that are very small, small, moderate, large, or very large. The first layer fuzzy control rules are shown in Table 1.
4.3 Second layer fuzzy control
Based on the ultrashortterm wind power forecast value and the wind power plan value, the future SOE is evaluated, and then the charging and discharging are carried out in advance to improve the ESS’s ability to track deviations from the future plan. The ESS offlimit power W(i + k) and the planned power deviation P_{d}(i + k) at each sampling point during the rolling optimization period are calculated as:
where k = 1,2,…,N and N takes the value of 8. The covariance and correlation coefficients of the offlimit power and planned power deviations calculated from historical data are less than 0. It can be concluded that W and P_{d} are negatively correlated, and the contradiction factor F of the two variables W and P_{d} can be constructed by the following method.
First, the matrix is constructed through:
where \(d_{ij}^{2}\) denotes the square of the Euclidean distance of the i^{th} and j^{th} objects in matrix Z, and Z is composed of the offlimit power and the planned power deviation. q is the number of rows in Z (q = 2), and l is the number of columns in Z (l = 8). z_{ir} is the element in row i and column r of Z, while h_{ij} is the element of matrix H.
After the eigenvalue decomposition of H, the following is obtained:
where U is the matrix with corresponding eigenvectors as columns and V is the diagonal matrix generated by the eigenvalues of H. Then the contradiction factor F for the two variables W and P_{d} can be expressed by:
A very large F indicates that the ESS is overproducing in the future rolling optimization period, i.e., E_{SOC} has exceeded E_{SOC.max} and the ESS should be discharged in advance. If F is very small, it means that the ESS has insufficient ability to track the planned output in the future rolling optimization period, i.e., E_{SOC} is lower than E_{SOC.min}, and the ESS needs to be charged in advance. If the spear F is moderate, the ESS is charged and discharged according to the original instructions. The input quantities of the second layer fuzzy controller are F and P_{b}(i), and the output quantity is ∆k. The fuzzy control input and output membership functions are shown in Fig. 6.
The universe of fuzzy control input variable P_{b}(i) is [1,1], and the fuzzy set is {L,LM,M,MH,H}, which sequentially represent values that are negative large, negative small, zero, positive small, or positive large. The universe of F is [0.2,0.2], and the fuzzy set is {VS,S,B,VB}, which sequentially represent values that are small, slightly small, slightly large, or large. The universe of fuzzy control output variable ∆k is [1,1], and the fuzzy set is {NB,PB,N,Z,P,PH,NH}, which sequentially represent minimum, small, slightly small, moderate, slightly large, large, or maximum values. The fuzzy control rules are shown in Table 2, and Fig. 7 shows the specific process of the proposed control strategy.
5 Simulation analysis of numerical examples
The example scenario is based on the measured wind power data of a wind farm with an installed capacity of 50 MW, and the experiments are conducted to simulate integrated control in the combined windstorage power generation system, as shown in Fig. 8.
The topological structure, system functions, and secondary parameters of the simulation platform refer to the actual engineering design, as shown in Fig. 9. The platform consists of an energy storage station energy management system, a wind farm SCADA system, a reactive power compensation monitoring system, a boosterstation integrated automation system, and a system for the integrated intelligent monitoring of automatic power generation, voltage control, etc.
In this paper, the simulation parameters are mainly set by referring to the methods in [38] and [39]. In realworld engineering applications within China's power grid, the planned power generation curve is evaluated at 5min intervals. Therefore, we also opt for a 5min sampling period. Table 3 lists the main wind farm and ESS parameter settings. To illustrate the feasibility and superiority of the proposed control strategy (Scheme 4), it is compared with MPC control Schemes 1, 2 and 3, and Table 4 shows the settings of the four control methods.
5.1 Evaluation index
The advantages and disadvantages are evaluated based on the following four indicators: power prediction accuracy P_{re}, maximum tracking deviation P_{d.max}, ESS dead time T_{d}, and ESS output coefficient C_{b}. Each of the indicators is descripted as follows.

(1)(1)
Power prediction accuracy P_{re}
$$P_{re} = \left(1  \frac{{\sqrt {\frac{1}{n}\sum\limits_{i = 1}^{n} {\left[ {P_{w} (i)  P_{p} (i)} \right]^{2} } } }}{Cap}\right) \times 100\%$$(26)
where n is the number of samples, and Cap is the startup capacity of the wind farm.

(2)(2)
Maximum tracking deviation P_{d.max}
$$P_{d.max} = \max \left {P_{{\text{g}}} \left( i \right)  P_{{\text{p}}} \left( i \right)} \right$$(27)where T_{d} is the time when the energy storage SOC exceeds the set safety threshold.

(3)(3)
ESS dead time T_{d}
$$\begin{gathered} T_{{\text{d}}} = T_{{\text{s}}} \times \sum\limits_{i = 0}^{N  1} {\left[ {h\left( {\frac{{E_{{{\text{SOC}}}} \left( i \right)}}{{E_{{{\text{SOC}}.\min }} }}} \right)\bigcup {h\left( {\frac{{E_{{{\text{SOC}}.\max }} }}{{E_{{{\text{SOC}}}} \left( i \right)}}} \right)} } \right]} \hfill \\ \begin{array}{*{20}c} {} & {h\left( x \right)} \\ \end{array} = \left\{ \begin{gathered} 1,x \ge 1 \hfill \\ 0,x < 1 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$$(28)where T_{d} is the time when the energy storage SOC exceeds the set safety threshold.

(4)(4)
ESS output coefficient C_{b}
$$C_{b} = \sqrt {\frac{1}{T  1}\sum\limits_{i = 1}^{T  1} {\left[ {E_{{{\text{SOC}}}} \left( i \right)  0.5} \right]^{2} } }$$(29)where T is the number of sampling periods in the energy storage output cycle. The smaller the value of C_{b}, the larger the output capacity.
5.2 Analysis of simulation results
The curves of the actual and planned wind power values selected in this paper are shown in Fig. 10. Taking the planned wind power in Fig. 10 as a reference, Fig. 11 displays the effect of the power generation planning curves of the windstorage joint output tracking for the four control methods, and Table 5 shows the evaluation indices for the different control schemes.
As can be seen from Fig. 11, Schemes 1, 2 and 3 can largely ensure the joint output of windstorage to be within the allowable deviation band of tracking for most of the time, while Scheme 4 fully meets the requirements. Table 5 shows that, compared to without energy storage, the prediction accuracies of the four control schemes with energy storage increase by 10.43%, 5.35%, 8.32%, and 11.31%, respectively, while the maximum tracking deviations decrease by 34.79%, 18.25%, 40.41%, and 58.08%, respectively. In summary, Scheme 4 has the best tracking effect, followed by Schemes 1, 3 and then 2.
The energy storage SOC variation curves in Fig. 12 show that Scheme 1 ESS is in a high energy state during the two time periods of 80–200 min and 710–850 min. This decreases its charging capacity. Table 5 also shows that Scheme 1 ESS dead time is as long as 170 min, and the capacity coefficient is 0.226. These do not support the ESS for tracking the planned capacity in the future. Scheme 2 takes the minimum deviation of ESS remaining capacity from the ideal value as the optimization target, and the SOC change curve is gradually adjusted toward 0.5. Although the ESS overrun limit is avoided, the tracking effect is poor. Figure 12 shows that the Scheme 3 ESS is in a high energy state during the time period of 145–200 min, which decreases its charging capacity. Table 5 also shows that Scheme 3 ESS dead time is 55 min, and the capacity coefficient is 0.197. These reduce the ability of ESS to track planned power output. Combined with the ESS power in Fig. 13, Scheme 4 improves the ability of the ESS to track the future planned curve by dynamically adjusting the weighting coefficient and charging and discharging in advance. Compared with Scheme 1, Scheme 4 reduces the dead time and extends the service life of the ESS while improving the tracking of the planned curve. Compared with Scheme 2, Scheme 3 ESS output capacity is slightly reduced, but the ability to track the wind power planning curve is greatly improved. Compared with Scheme 3, Scheme 4 reduces the dead time and output coefficient while improving the tracking of the planned curve. Therefore, compared with Schemes 1, 2 and 3, the proposed method effectively balances the conflict between energy storage crossing limit and wind power plan tracking, and verifies the superiority of the proposed method.
5.3 Parameter analysis
In the process of constructing the proposed method, the determined rated power P_{rated}, rated capacity C_{rated}, and the size of the ESS deviation band setting coefficient δ have great impact on the tracking effect. Therefore, it is necessary to analyze the influence of relevant parameter changes on the control effect of the proposed method.

(1)(1)
Influence of ESS power rating
For the ESS rated capacity C_{rated} = 20 MW·h and the deviation band set coefficient δ = 0.2, the change rule of the evaluation index of each control scheme with different power ratings of ESS is compared, as shown in Fig. 14.
From Fig. 14, it is seen that ESS dead time and output coefficient are less affected by the rated power in Schemes 2 and 4, but more affected in Scheme 1. Compared with Scheme 1, the tracking effect of Scheme 4 is better when the rated ESS power is greater than 6.5 MW. Compared with Scheme 2, although the output capacity of Scheme 4 is slightly lower, its power prediction accuracy is much higher. Compared with Scheme 3, Scheme 4 also has better tracking effect and ESS output capacity. Therefore, as the rated power of ESS increases, the tracking effects of the four control schemes become better, while the control effect of Scheme 4 is the best.

(2)(2)
Impact of ESS rated capacity
For the ESS rated power P_{rated} = 10 MW and the deviation band coefficient of δ = 0.2, Fig. 15 shows the change rules of the evaluation indices for each control scheme with different rated ESS capacities.
As is seen from Fig. 15, as the ESS rated capacity increases, its dead time decreases substantially and the output capacity also decreases for the four control schemes. Compared with Schemes 1, 2 and 3, Scheme 4 has the best tracking effect, mainly because it considers the influence of the current ESS residual capacity on the future tracking ability and ensures that the ESS charging and discharging ability can cope with possible future wind power schedule deviations. That is, the proposed control method can appropriately reduce the required ESS capacity.

(3)(3)
Impact of the deviation band setting coefficient
For ESS rated power of P_{rated} = 10 MW and rated capacity of C_{rated} = 20 MW·h, the change rule of the evaluation index of each control scheme with different deviation band coefficients is compared, as shown in Fig. 16.
With increasing deviation band coefficients, the requirement of tracking wind power plan output is relaxed, which reduces the ESS charging and discharging energy. The ESS dead time and output coefficient presented in Fig. 16 show that the tracking is worsened with each of the three control schemes, although wind power prediction accuracy and maximum tracking deviation show that Scheme 4 is still better than Schemes 1, 2 and 3. Therefore, the proposed method is superior.
6 Conclusion
In this paper, a power control strategy based on model prediction and doublelayer fuzzy control is proposed for a combined windstorage system to track wind power plan output that not only tracks wind power plan deviations but also increases the ESS’s ability to track future plan deviations. From the findings, we can draw the following conclusions.

(1)
An objective function is proposed to minimize the deviation of gridconnected power from the planned output, and the deviation of ESS remaining capacity from the ideal value. At the same time, a method of using the first layer of fuzzy controller is proposed to correct the weight coefficients of the objective. Compared with Schemes 1, 2 and 3, the power prediction accuracy in Scheme 4 is increased by 97.43%, 96.55%, and 93.75%, respectively. Compared with Schemes 1 and 3, Scheme 4 reduces the dead time by 180 min and 55 min, respectively. Thus, the proposed method reduces the dead time and extends the service life of the ESS while improving the tracking of the planned curve.

(2)
Statistical factor analysis theory is used to construct the contradictory factors between the two variables of ESS offlimit power and planned power deviation in the future optimization period. A method of using the second layer of fuzzy control rules is proposed to correct the charging and discharging power of the ESS. Compared with Schemes 1, 2 and 3, the maximum tracking deviation in Scheme 4 is decreased by 35.71%, 48.72%, and 29.64%, respectively. Compared with Scheme 1 and 3, the ESS output coefficient in Scheme 4 is decreased by 35.84% and 26.40%, respectively. Hence, charging and discharging are carried out in advance to improve the utilization level of the ESS and the ESS’s ability to track deviations from the future plan.

(3)
The effectiveness of the proposed control strategy is affected by the ESS’s rated power, rated capacity and deviation band setting coefficient. However, under the same conditions, the comprehensive index of the proposed control strategy is better than the indices under Schemes 1, 2 and 3, and effectively offsets the conflict between the planned wind power output tracking and the excess of the ESS. The proposed control method can appropriately reduce the required ESS capacity, so as to improve ESS economy.
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References
Lin, Z. J., Chen, H. Y., Wu, Q. W., et al. (2020). Meantracking model based stochastic economic dispatch for power systems with high penetration of wind power. Energy, 193(5), 1–13.
Su, Y., & Teh, J. (2023). Twostage optimal dispatching of AC/DC hybrid active distribution systems considering network flexibility. Journal of Modern Power Systems and Clean Energy, 33(1), 52–65.
Dui, X. W., Zhu, G. P., & Yao, L. Z. (2018). Twostage optimization of battery energy storage capacity to decrease wind power curtailment in gridconnected wind farms. IEEE Transactions on Power Systens, 33(3), 3296–3305.
Li, X. J., Ma, R., Gan, W., et al. (2022). Optimal dispatch for battery energy storage station in distribution network considering voltage distribution improvement and peak load shifting. Journal of Modern Power Systems and Clean Energy, 10(1), 131–139.
He, G. N., Chen, Q. X., Kang, C. Q., et al. (2016). Optimal bidding strategy of battery storage in power markets considering performancebased regulation and battery cycle life. IEEE Transactions on Smart Grid, 7(5), 2359–2367.
Jiang, Q., & Hong, H. (2013). Waveletbased capacity configuration and coordinated control of hybrid energy storage system for smoothing out wind power fluctuations. IEEE Transactions on Power Systems, 28(2), 1363–1372.
Siqueira, D., Maria, S. L., & Wei, P. (2021). Control strategy to smooth wind power output using battery energy storage system: A review. Journal of Energy Storage, 35, 102252–102263.
Guo, T. T., Liu, Y. B., Zhao, J. B., Zhu, Y. W., et al. (2020). A dynamic waveletbased robust wind power smoothing approach using hybrid energy storage system. International Journal of Electrical Power & Energy Systems, 116, 105579.
Choopani, K., Effatnejad, R., & Hedayati, M. (2020). Coordination of energy storage and wind power plant considering energy and reserve market for a resilience smart grid. Journal of Energy Storage, 30, 101542–101550.
Teixeira, T. P., & Borges, C. L. T. (2021). Operation strategies for coordinating battery energy storage with wind power generation and their effects on system reliability. Journal of Modern Power Systems and Clean Energy, 9(1), 190–198.
Zhai, Y. J., Zhang, J. W., Tian, Z. W., et al. (2021). Reseaarch on the application of superconducting magenetic energy stogage in the wind power generation system for smoothing wind power fluctuations. IEEE Transactions on Applied Superconductivity., 31(5), 1–5.
Zhou, Y., Yan, Z., & Li, N. H. (2017). A novel state of charge feedback strategy in wind power smoothing based on shortterm forecast and scenario analysis. IEEE Transactions on Sustainable Energy, 8(2), 870–876.
Barra, P. H. A., De Carvalho, W. C., Menezes, T. S., et al. (2021). A review on wind power smoothing using highpower energy storage systems. Renewable & Sustainable Energy Reviews, 137, 110455.
Dong, J. J., Gao, F., Guan, X. H., et al. (2017). Storage sizing with peakshaving policy for wind farm based on cyclic Markov chain model. IEEE Transactions on Sustainable Energy., 8(3), 978–989.
Roy, P., Liao, Y., & He, J. B. (2023). Economic dispatch for gridconnected wind power with batterysupercapacitor hybrid energy storage system. IEEE Transactions on Industry Applications, 59(1), 1118–1128.
Guo, Z. J., Wei, W., Shahidehpour, M., et al. (2023). Twotimescale dynamic energy and reserve dispatch with wind power and energy storage. IEEE Transactions on Sustainable Energy, 14(1), 490–503.
Sewnet, A., Khan, B., Gide, I., et al. (2022). Mitigating generation schedule deviation of wind farm using battery energy storage system. Energies, 15(5), 1768.
Emara, D., Ezzat, M., Abdelaziz, A. Y., et al. (2021). Novel control strategy for enhancing microgrid operation connected to photovoltaic generation and energy storage systems. Electronics, 10(11), 1261.
Rong, S., Chen, X. G., Guan, W. L., et al. (2019). Coordinated dispatching stragery of multiple energy sources for wind power consumption. Journal of Modern Power Systems and Clean Energy, 7(6), 1461–1471.
Rayit, N. S., Chowdhury, J. I., & BaltaOzkan, N. (2021). Technoeconomic optimisation of battery storage for gridlevel energy services using curtailed energy from wind. Energy Storage, 39, 102641.
Li, J. H., Wang, S., Ye, L., et al. (2018). A coordinated dispatch method with pumpedstorage and batterystorage for compensating the variation of wind power. Protection and Control of Modern Power Systems., 3(1), 21–34.
Dhiman, H. S., & Deb, D. (2020). Wake management based life enhancement of battery energy storage system for hybrid wind farms[J]. Renewable & Sustainable energy reviews, 130, 109912.
Nguyen, C. L., & Lee, H. H. (2017). Optimal power control strategy for wind farm with energy storage system. Journal of Electrical Engineering Technology, 12(2), 726–737.
Moghaddam, I. N., Chowdhury, B. H., & Mohajeryami, S. (2018). Predictive operation and optimal sizing of battery energy storage with high wind energy penetration. IEEE Transactions on Industrial Electronics, 65(8), 6686–6692.
Li, Q., Choi, S. S., Yuan, Y., et al. (2011). On the determination of battery energy storage capacity and shortterm power dispatch of a wind farm. IEEE Transactions on Sustainable Energy, 2(2), 148–158.
Shi, J., Wang, L., Le, W. J., et al. (2019). Hybrid Energy Storage System (HESS) optimization enabling very shortterm wind power generation scheduling based on output feature extraction. Applied Energy, 256, 113915.
Zhang, X. S., Yuan, Y., Hua, L., et al. (2017). On generation schedule tracking of wind farms with battery energy storage systems. IEEE Transactions on Sustainable Energy, 8(1), 341–353.
Kani, S. A. P., Wild, P., & Saha, T. K. (2020). Improving predictability of renewable generation through optimal battery sizing. IEEE Transactions on Sustainable Energy, 11(1), 37–47.
Baker, K., Hug, G., & Li, X. (2016). Energy storage sizing taking into account forecast uncertainties and receding horizon operation. IEEE Transactions on Sustainable Energy, 8(1), 331–340.
Moghaddam, I. N., Chowdhury, B. H., & Mohajeryami, S. (2017). Predictive operation and optimal sizing of battery energy storage with high wind energy penetration. IEEE Transactions on Industrial Electronics, 65(8), 6686–6695.
Esmaeili S., Amini M., Khorsandi A., et al. (2021). Marketoriented optimal control strategy for an integrated energy storage system and wind farm. in 2021 29th Iranian Conference on Electrical Engineering (ICEE), Tehran, Iran, Islamic Republic of, 407–411.
Guo, T. T., Zhu, Y. W., Liu, Y. B., et al. (2020). Twostage optimal MPC for hybrid energy storage operation to enable smooth wind power integration. IET Renewable Power Generation, 14(13), 2477–2486.
Sun, Y. S., Tang, X. S., Sun, X. Z., et al. (2019). Model predictive control and improved lowpass filtering strategies based on wind power fluctuation mitigation. Journal of Modern Power Systems and Clean Energy, 7(3), 512–524.
Long, B., Liao, Y., Chong, K. T., et al. (2021). Enhancement of frequency regulation in AC microgrid: A fuzzyMPC controlled virtual synchronous generator. IEEE Transactions on Smart Grid, 12(4), 3138–3149.
Tang, L., Xu, W., Wang, X., Dong, D., et al. (2021). Weighting factors optimization of model predictive control based on fuzzy thrust constraints for lLinear induction machine. IEEE Transactions on Applied Superconductivity, 31(8), 1–5.
National Energy Board. NB/T102052019 Technical rules for wind power forecasting. Beijing: StandardPress of China, 2019
Oskouei, M. Z., & Yazdankha, A. S. H. (2017). The role of coordinated load shifting and frequencybased pricing strategies in maximizing hybrid system profit. Energy, 135(15), 370–381.
Zhang, F., Meng, K., Zhao, X., et al. (2017). Battery ESS planning for wind smoothing via variableinteval reference modulation and selfadaptive SOC control strategy. IEEE Transactions on Sustainable Energy, 8(2), 695–707.
Shi J., Lee W. J., Liu X. F. (2017). Generation scheduling optimization of windenergy storage system based on wind power output fluctuation featuers. in 2017 IEEE/IAS 53rd Industral and Commercial Power Systems Technical conference(I&CPS), Niagara Falls, ON, Canada, 1–7.
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Funding
This work was supported by the Major Science and Technology Project of Hunan Province (2020GK1013); Project of Natural Science Foundation of Hunan Province (2023JJ50344); Project of Educational Commission of Hunan Province (22C0512).
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All authors contributed to the research, read and approved the manuscript. Formal analysis: TGY; Investigation: JYY; Supervision: L. F. LUO; Writingoriginal draft: J. Y. YANG; Writingreview and editing: L. F. LUO; Data curation: LI PENG. All authors have readand approved the fnal manuscript.
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Yang, J., Yang, T., Luo, L. et al. Trackingdispatch of a combined windstorage system based on model predictive control and twolayer fuzzy control strategy. Prot Control Mod Power Syst 8, 58 (2023). https://doi.org/10.1186/s41601023003346
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DOI: https://doi.org/10.1186/s41601023003346