A Wind Power Fluctuation Smoothing Control Strategy for Energy Storage Systems Considering the State of Charge

Abstract

With the significant increase in the scale of energy storage configuration in wind farms, improving the smoothing capability and utilization of energy storage has become a key focus. Therefore, a wind power fluctuation smoothing control strategy is proposed for battery energy storage systems (BESSs), considering the state of charge (SOC). First, a BESS smoothing wind power fluctuation system model based on model predictive control (MPC) is constructed. The objective function aims to minimize the deviation of grid-connected power from the target power and the deviation of the BESS’s remaining capacity from the ideal value by comprehensively considering the smoothing effect and the SOC. Second, when the wind power’s grid-connected power exceeds the allowable fluctuation value, the weight coefficients in the objective function are adjusted in real time using the first layer of fuzzy control rules combined with SOC partitioning. This approach smooths wind power fluctuations while preventing overcharging and overdischarging of the BESS. When the grid-connected power is within the allowable fluctuation range, the charging and discharging power of the BESS is further refined using a second layer of fuzzy control rules. This enhances the BESS’s capability and utilization for smoothing future wind power fluctuations by preemptively charging and discharging. Finally, the proposed control strategy is simulated using MATLAB R2021b with actual operational data from a wind farm as a case study. Compared to the traditional MPC control method, the simulation results demonstrate that the proposed method effectively controls the SOC within a reasonable range, prevents the SOC from entering the dead zone, and enhances the BESS’s ability to smooth wind power fluctuations.

1. Introduction

In the context of “peak carbon” and “carbon neutrality”, wind power has rapidly developed in recent years owing to its mature technology [1]. However, its power fluctuations can easily impact the power system, increasing the burden on frequency regulation and scheduling and, in severe cases, threatening its safe and stable operation [2,3]. Therefore, it is essential to implement measures to mitigate wind power fluctuations on the grid.

The rapid development of energy storage technology has provided essential technical support for mitigating wind power fluctuations. Technologies such as lithium iron phosphate batteries, all-vanadium redox flow batteries, and power-type storage like flywheel energy storage and superconducting magnetic energy storage have been applied to suppress wind power fluctuations [4,5]. These applications have effectively reduced the degree of power fluctuations in the grid [6]. However, the smoothing effectiveness of these battery energy storage systems (BESSs) is limited by factors such as service life, capacity, and control mechanisms [7,8,9]. Given these limitations, it is critical to study optimal control strategies for battery storage systems [10,11].

Extensive domestic and international research has been conducted on using energy storage to smooth wind power fluctuations. Various algorithms, such as low-pass filtering, wavelet packet decomposition, and ensemble empirical modal decomposition, are employed to obtain the grid-connected component [6,12]. For instance, a previous study [13] utilized first-order low-pass filtering to smooth wind power, with the energy storage system partially compensating for the filtered high-frequency fluctuations. However, the strong nonlinear characteristics of wind power make determining the filtering time constant challenging. Additionally, there is a phase lag in the smoothing process, which can increase the burden on the energy storage system by introducing a trend component. Reference [14] employed wavelet packet decomposition to break down wind power into high-, medium-, and low-frequency components, matching the power response to the characteristics of the corresponding energy storage resources. Reference [15] proposed a wind power smoothing strategy based on adaptive wavelet packets, enabling the power smoothing requirements to be met under different fluctuation scenarios. However, the choice of the wavelet base influences the effectiveness of wavelet packet decomposition. At the same time, empirical modal decomposition and its improved methods, such as ensemble empirical and variational modal decomposition, have been successfully applied in wind power smoothing control strategies. These methods adaptively constrain the power command based on the state of the energy storage system, keeping the state of charge within a reasonable range while meeting grid-connected power fluctuation requirements [15,16]. For instance, References [17,18] use ensemble empirical modal decomposition to obtain the grid-connected component. However, the decomposition effect is significantly influenced by the decomposition parameters, which are challenging to select accurately.

With the development of intelligent technology, methods such as fuzzy theory and neural networks are increasingly being used in the energy storage control process [19,20]. For example, a previous study [21] employs fuzzy empirical modal decomposition to break down wind power into low-frequency and high-frequency components. In this approach, the energy storage battery absorbs the high-frequency component to smooth wind power fluctuations, while the low-frequency component is directly connected to the grid. Another study [22] introduces an adaptive linear neuron-based coordinated control method utilizing a small-capacity battery energy storage system to achieve wind power smoothing. Meanwhile, a published study [23] presents a fuzzy adaptive Kalman filtering-based control strategy for energy storage systems utilizing an all-vanadium liquid current battery as the energy storage device. This approach effectively controls the state of energy of the battery while extending the lifetime of the energy storage system.

Researchers have discovered that the future output power of wind power significantly influences the current optimal output power of energy storage. With the increasing maturity of wind speed and wind power forecasting techniques, energy storage control methods considering the variation in predicted wind power have become crucial [24,25,26]. Reference [27] establishes a rolling optimization model with multiple forecast periods, advancing the overall optimization level and scheduling decisions. References [28,29,30] use model predictive control (MPC) in energy storage systems to derive an optimal control sequence for a given period. Reference [31] incorporates future wind power fluctuations and current energy storage states into a fuzzy controller to effectively control energy storage output, yielding favorable results. Meanwhile, a previous study [32] designs a hybrid energy storage strategy combining energy-type battery storage and power-type storage capacitors. It employs MPC to mitigate wind power fluctuations. It utilizes the Hilbert–Huang Transform to determine the cut-off frequency of the energy-type battery storage and power-type storage capacitor, thereby adjusting the power distribution of the hybrid energy storage system. In other studies [33,34], a dual battery energy storage system is designed based on the technical characteristics of the batteries. This design ensures that the two groups of batteries operate in different charging and discharging states, allowing them to alternately suppress wind power’s positive and negative fluctuations.

Based on the abovementioned analyses, it is evident that few studies have considered the influence of a BESS’s current residual capacity on future smoothing capability. Additionally, effectively balancing the trade-off between wind power fluctuation smoothing capability and avoiding state of charge (SOC) overruns requires further investigation. Therefore, this study proposes a control strategy for a BESS to smooth wind power fluctuations based on MPC and fuzzy control. The goal is to enhance the BESS’s wind power fluctuation smoothing capability and prevent SOC from entering dead zones. In summary, compared to current methods, this study offers two primary contributions:

(1)

We have constructed a system model for smoothing wind power fluctuations using a BESS based on MPC. We propose an objective function aimed at minimizing the deviation of grid-connected power from the target power and the deviation of the residual capacity of the BESS from the ideal value in the wind storage cogeneration system. This objective function comprehensively considers the smoothing effect of the BESS while preventing SOC from overrunning the limit and entering the dead zone.

(2)

We propose a method for adjusting the BESS’s charging and discharging power using two-layer fuzzy control rules. By integrating the smoothing effect and SOC interval division, we employ the first layer of fuzzy control rules to dynamically adjust the weight coefficients of the objective function in real time. This enhancement improves the BESS’s ability to smooth wind power fluctuations while preventing SOC from exceeding the limit and entering the dead zone. Additionally, the second layer of fuzzy control rules is utilized to proactively adjust the BESS’s charging and discharging power, thereby enhancing its ability to smooth future wind power fluctuations.

The proposed control strategy’s accuracy and efficiency are validated through MATLAB simulation using real operating data from a wind farm as an illustration. The paper is structured as follows. The topology of the wind storage cogeneration system, grid power fluctuation requirements, and storage SOC partitioning are described in Section 2. Section 3 develops the BESS smoothing wind power fluctuation control model employing the MPC method. Section 4 introduces a two-layer fuzzy control strategy to adjust BESS charging and discharging power. Section 5 presents case studies. Section 6 offers the research conclusion.

2. Wind Storage Cogeneration System and Power Relation

The variability in wind speed introduces fluctuations in the active power output of wind farms, which can disrupt the stable operation of the grid [35]. Integrating a BESS at the grid connection point of wind farms allows for the effective smoothing of these power fluctuations. By controlling the BESS’s charging and discharging power and maintaining its residual capacity within a reasonable range, the fluctuation of grid-connected power can be mitigated [36,37].

2.1. Wind Storage Cogeneration Systems and Grid-Connected Power Fluctuation Requirements

The wind storage cogeneration system’s structure, shown in Figure 1, primarily comprises the wind farm, energy storage station, boosting station, and energy management system. The energy management system is responsible for making decisions regarding energy management for the energy storage system. It bases these decisions on the state of energy (SOE) at the end of the current period t and the wind power grid-connected power target, as well as the actual wind power during the subsequent period t + 1. Then, it sends commands to the BESS to control energy storage, either releasing or absorbing power, to mitigate wind power fluctuations during the t + 1 period.

Referring to Figure 1, the power balance equation and the SOE iterative equation for the wind storage cogeneration system are presented as Equations (1) and (2):

$$P_{\mathrm{g}}(i+1)=P_{\mathrm{b}}(i)+P_{\mathrm{w}}(i)$$

(1)

where P_b(i) is the output power of the energy storage, P_w(i) is the output wind power, and P_g(i + 1) is the combined output of wind and storage.

$$C_{\mathrm{SOE}}(i+1)=C_{\mathrm{SOE}}(i)-\eta P_{\mathrm{b}}(i)\times T_{\mathrm{c}}/C_{\mathrm{rated}}$$

(2)

where C_SOE(i) is the residual capacity of the BESS at time i, while T_c and C_rated are the BESS control period and capacity, respectively.

The “Technical Rule for Connecting Wind Farm to Power System” of China has established regulations regarding the allowable variation limits of active power for wind farms with varying installed capacities [38,39], as illustrated in

Table 1. Maximum variation in active power in wind farm.

Wind Farm Installation Capacity/MW	10 min Active Power Change Maximum Limit/MW	1 min Active Power Change Maximum Limit/MW
<30	10	3
30–150	Installed capacity/3	Installed capacity/10
>150	50	15

. Proposed fluctuation ranges for wind power with 1 and 10 min time scales are specified.

For example, considering a wind farm with an installed capacity of 50 MW and a data acquisition time step of 1 min, the allowable fluctuation ranges for 1 and 10 min at time i are depicted in Equations (3) and (4).

$$\{\begin{array}{l}{P}_{\mathrm{g}1.\min }(i)=P_g\left(i\right)-\frac{1}{10}{C}_{\mathrm{install}}\\ P_{\mathrm{g}1.\max }(i)=P_g\left(i\right)+\frac{1}{10}{C}_{\mathrm{install}}\end{array}$$

(3)

$$\{\begin{array}{l}{P}_{\mathrm{g}10.\min }(i)=\underset{\Delta t=0,\cdot \cdot \cdot ,9}{\max }{P}_g\left(i-\Delta i\right)-\frac{1}{3}{C}_{\mathrm{install}}\\ P_{\mathrm{g}10.\max }(i)=\underset{\Delta t=0,\cdot \cdot \cdot ,9}{\mathrm{m}\mathrm{in}}{P}_g\left(i-\Delta i\right)+\frac{1}{3}{C}_{\mathrm{install}}\end{array}$$

(4)

where P_g1.min(i) and P_g1.max(i) are the lower and upper limits, respectively, of the allowable fluctuation range for grid-connected power within 1 min. Similarly, P_g10.min(i) and P_g10.max(i) are the lower and upper limits, respectively, of the allowable fluctuation range for grid-connected power within 10 min. Additionally, C_install is the installed capacity of the wind farms.

The allowable range of grid-connected power at the moment i can be expressed as:

$$\begin{array}{l}{P}_{\mathrm{g}}(i)\in \left[P_{\mathrm{g}.\min }(i),P_{\mathrm{g}.\max }(i)\right]\\ \begin{array}{ccc}& & \end{array}=\left[P_{\mathrm{g}1.\min }(i),P_{\mathrm{g}1.\max }(i)\right]{\displaystyle \cap \left[P_{\mathrm{g}10.\min }(i),P_{\mathrm{g}10.\max }(i)\right]}\end{array}$$

(5)

Based on the abovementioned analysis, the target power, denoted as P_a(i), can be calculated as follows:

$$P_{\mathrm{a}}(i)=\{\begin{array}{l}{P}_{\mathrm{g}.\max }(i)\begin{array}{cc}& P_{\mathrm{w}}(i)\ge P_{\mathrm{g}.\max }(i)\end{array}\\ P_{\mathrm{w}}(i)\begin{array}{cc}& P_{\mathrm{g}.\min }(i)<P_{\mathrm{w}}(i)<P_{\mathrm{g}.\max }(i)\end{array}\\ P_{\mathrm{g}.\min }(i)\begin{array}{cc}& P_{\mathrm{w}}(i)\le P_{\mathrm{g}.\min }(i)\end{array}\end{array}$$

(6)

2.2. SOC Partitioning for BESS

To ensure that the grid-connected power of the wind storage combined generation system adheres to the power fluctuation limits by controlling the BESS output, it is essential to maintain the SOC within a reasonably balanced interval during BESS operation. This prevents the SOC from staying excessively high or low for extended periods. For example, for lithium batteries, cycling at 80% of the depth of discharge doubles the cycle life of the battery, and the lower the depth of charge and discharge, the longer the cycle life [8]. Moreover, to maximize the BESS’s compensation capability for wind power, the BESS should have ample charge/discharge margins. Thus, it is necessary to partition the SOC of the energy storage battery, as depicted in Figure 2. The SOC for the BESS is divided into five sequential intervals:

(1)

Discharge dead zone [0%, E_SOC.min]: This interval indicates that the SOC of the BESS is critically low, nearing complete depletion. In this interval, the BESS cannot discharge further and should not be permitted. Immediate charging is necessary to prevent prolonged depletion, which could compromise the battery’s lifespan.

(2)

Discharge warning interval [E_SOC.min, E_{SOC.min-alert}]: This interval indicates that the SOC of the BESS is low and has surpassed the overdischarge warning threshold. During this phase, discharge operations must be conducted cautiously to prevent the SOC from entering the discharge dead zone.

(3)

Normal charging and discharging interval [E_{SOC.min-alert}, E_{SOC.max-alert}]: This interval indicates a favorable SOC range for the BESS. In this interval, the SOC of the BESS is considered healthy, allowing for a margin of capacity for charging and discharging operations.

(4)

Charge warning interval [E_{SOC.min-alert}, E_SOC.max]: This interval indicates that the SOC of the BESS is high and has surpassed the overcharging warning threshold. During this phase, charging operations must be performed cautiously to prevent the SOC from entering the charging dead zone.

(5)

Charging dead zone [E_SOC.max, 100%]: This interval indicates that the SOC of the BESS is excessively high, nearing theoretical full charge. In this interval, the BESS loses its charging capability and must not undergo further charging. Immediate discharge is necessary to prevent prolonged full charge, which could significantly impact the service life of the energy storage battery.

3. BESS Smoothing Wind Power Fluctuation Model Based on MPC

The control model of the MPC-based wind storage cogeneration system is constructed by integrating the MPC control principle with the iterative equations governing power balance and SOE. Simultaneously, the MPC rolling optimization objective function and constraints are formulated based on two main objectives: smoothing wind power fluctuations and preventing SOC overruns, utilizing the previously determined target power values.

3.1. Fundamentals of the MPC Algorithm

Compared to traditional control algorithms such as PID, MPC can address complex issues such as multivariable constrained optimal control, which are challenging to solve otherwise. It has advantages such as minimal requirements on control model accuracy, excellent dynamic control effects, and robustness. MPC operates as a closed-loop optimal control system comprising three fundamental elements: a prediction model, rolling optimization, and feedback correction. The basic structure of MPC is depicted in Figure 3.

The predictive model is a cornerstone of MPC, playing a crucial role in describing the dynamic behavior of a system. Its primary function is to predict the future dynamics of the controlled system. In contrast, the rolling optimization component is the core of MPC. Unlike conventional discrete optimization algorithms, predictive control does not rely on a fixed and unchanging global optimization objective. Instead, it adopts a time-forward rolling finite time-domain optimization approach. This method involves an online iterative optimization process conducted continuously rather than being executed offline in a single instance. The MPC feedback correction primarily comprises two components: feed-forward and feedback links. As time progresses, the system continuously updates its current state, future control, and historical information at each new moment. During this updating process, the current state information and future control information are generated and used as inputs to the feed-forward link of the system. Meanwhile, the updated historical information forms the feedback link of the system.

3.2. MPC-Based Wind Storage Cogeneration System

Alternatively referred to as rolling time domain optimal control, MPC is an algorithm for optimal control in the time domain based on models. This approach operates within a closed-loop system. Unlike some methods, MPC is not heavily reliant on the precision of the model, enabling it to tackle challenges such as uncertainty, nonlinearity, and time variation in industrial control settings. It effectively addresses complex issues pertaining to the structure, parameters, and environmental factors encountered in industrial control processes. Consequently, MPC has found extensive practical applications in industrial control systems. The primary difference between the MPC optimization strategy and traditional optimal control algorithms lies in their respective approaches to optimization. MPC employs a rolling, finite time domain optimization strategy instead of a fixed global optimization index. At its core, MPC relies on a rolling optimization concept, illustrated in Figure 4. The process is as follows: ① At the current moment, denoted as i, and the current state represented by x(i), predictions are made about the future state considering current and future constraints. This leads to the derivation of a sequence of control instructions spanning moments i + 1, i + 2, …, i + N. ② The initial value from this sequence is selected and implemented in the control system. ③ Upon reaching time i + 1, the state quantity is updated to x(i + 1), initiating a repetition of the abovementioned steps.

The block diagram illustrating the smoothing wind power fluctuation MPC is depicted in Figure 5. This MPC framework comprises three main components: ① Prediction at the current moment estimates the future output power of the wind power system within the upcoming rolling cycle based on historical data and future wind power inputs. ② Using the defined objective function and constraints, a sequence of control commands for the energy storage system is derived for the rolling cycle. These commands are then executed during the first moment of the rolling cycle. ③ In subsequent rolling cycles, the control commands from the previous moment are integrated to update the state variables, and the process is iterated accordingly.

For the wind storage cogeneration system aimed at mitigating wind power fluctuations, we address the issue by employing Equations (1) and (2), coupled with the superposition principle. This approach enables us to construct the state variable x(i) = [P_g(i), C_SOE(i)]^T, with the BESS output u(i) = P_b(i) as the control variable and the ultra-short-term rolling prediction of the wind power r(i) = P_f(i) as the input variable. At the same time, the grid power and the remaining capacity of the storage system are selected as the output variable y(i) = [P_g(i), C_SOE(i)]^T. Then, the MPC system model is established.

$$\{\begin{array}{l}\mathit{x}(i+1)=\mathit{A}\mathit{x}(i)+{\mathit{B}}_{1}u(i)+{\mathit{B}}_{2}r(i)\\ \mathit{y}(i)=\mathit{C}\mathit{x}(i)\end{array}$$

(7)

where $\mathit{A}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, ${\mathit{B}}_1=\left[\begin{array}{c}1\\ -T_{\mathrm{c}}/C_{\mathrm{rated}}\end{array}\right]$, ${\mathit{B}}_2=\left[\begin{array}{c}1\\ 0\end{array}\right]$, and $\mathit{C}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$.

According to the MPC principle, in conjunction with the state space Equation (7), the output for the subsequent moment can be derived as:

$$\{\begin{array}{l}{P}_{\mathrm{g}}\left(i+k|i\right)=P_{\mathrm{g}}\left(i\right)+{\displaystyle \sum _{t=1}^k{\mathit{u}}^{\mathrm{T}}\left(i+k|i\right)+}\\ \begin{array}{ccc}\begin{array}{cccc}& & & \end{array}& & \end{array}{\displaystyle \sum _{t=1}^k{P}_{\mathrm{f}}\left(i+k|i\right)\begin{array}{cc}& k=1,2,\cdot \cdot \cdot ,N\end{array}}\\ C_{SOE}\left(i+k|i\right)=C_{SOE}\left(i+k-1|i\right)-\\ \begin{array}{cc}\begin{array}{cc}\begin{array}{ccccc}& & & & \end{array}& \end{array}& \eta P_{\mathrm{b}}\left(i+k|i\right)\times T_{\mathrm{c}}/C_{\mathrm{rated}}\end{array}\end{array}$$

(8)

where P_g(i) is the real-time grid-connected power measurement at time i, and P_g(i + k|i) is the predicted grid-connected power at time i for the subsequent moment i + k. P_f(i + k|i) is the active power output increment of wind power within the period [i + (k − 1), i + k]. N is the MPC step size. C_SOE(i + k|i) is the remaining capacity of the BESS at time i to obtain the future time i + k. P_b(i + k|i) is the future BESS output power at time i + k. u^T(i + k|i) is the optimal control sequence derived by solving over a time period, as shown in Equation (9).

$$\begin{array}{l}{\mathit{u}}^{\mathrm{T}}\left(i+k|i\right)=[u\left(i+1\right),u\left(i+2\right),\cdot \cdot \cdot ,\\ \begin{array}{ccccc}& & & & \end{array}\begin{array}{ccc}& & \end{array}u\left(i+N\right)]\begin{array}{cc}& k=1,2,\cdot \cdot \cdot ,N\end{array}\end{array}$$

(9)

Let u(i + 1) denote the output power of the BESS at time i + 1. Following this, update the grid-connected power and SOE and proceed to the next time to solve the optimization process.

3.3. Objective Function and Constraints

In this paper, with the primary goal of smoothing wind power to align with grid demand, the reduction of energy storage power is approached from the standpoint of protecting the energy storage battery. Simultaneously, energy storage’s smoothing capacity is considered to enhance grid security. Consequently, an objective function is formulated to minimize the difference between grid-connected power and the target power while minimizing the deviation of the BESS’s residual capacity from the ideal value.

$$\begin{array}{l}\min J=\left(1-\lambda \left(i\right)\right){{\displaystyle \sum _{k=1}^{N-1}\left[P_g\left(i+k|i\right)-P_a\left(i+k|i\right)\right]}}^2+\\ {\begin{array}{cccc}& & & \lambda \left(i\right){\displaystyle \sum _{k=1}^N\left[C_{SOE}\left(i+k|i\right)-C_{\mathrm{ideal}}\right]}\end{array}}^2\end{array}$$

(10)

where C_ideal is the ideal residual capacity of the BESS, calculated as 0.5 times the rated capacity, and λ(i) is the weight coefficient.

Owing to technical and economic constraints, the control of the energy storage system during practical operations is predominantly constrained by factors such as charging and discharging power limitations and capacity constraints.

(1)

BESS power constraints

To ensure the safe operation of the BESS, strict limitations are imposed on the maximum charge and discharge power. These limitations are determined considering the current energy state of the BESS. The maximum charge and discharge power limits are as follows.

$$0<P_{\mathrm{c}}(i)\le \min \left\{P_{\mathrm{rated}},\frac{(E_{SOC.\max }-E_{SOC}(i))C_{\mathrm{rated}}}{T_s}\right\}$$

(11)

$$\max \left\{-P_{\mathrm{rated}},\frac{(E_{SOC.\min }-E_{SOC}(i))C_{\mathrm{rated}}}{T_s}\right\}\le P_{\mathrm{d}}(i)<0$$

(12)

where P_rated is the rated power of the BESS. P_c(i) and P_d(i) are the maximum charge and discharge power allowable for the BESS at the given moment.

(2)

BESS capacity constraints

Owing to the impact of charge and discharge depth on the lifespan of the BESS, the SOC of the energy storage system is strictly constrained at any given time. This constraint aims to enhance the battery’s lifespan and decrease the overall cost of the energy storage system.

$$E_{SOC.\min }\le E_{SOC}(i)\le E_{SOC.\max }$$

(13)

where E_soc.min and E_soc.max are the lower and upper limits of the BESS state of charge, respectively.

4. Charging and Discharging Power Correction for BESS Based on Two-Layer Fuzzy Control

As depicted in Equation (10), the control of BESS output power is governed by λ(i). A larger λ(i) brings the BESS residual capacity closer to the ideal value, albeit at the expense of reduced effectiveness in smoothing wind power fluctuations. Conversely, a smaller λ(i) enhances the smoothing effect but risks overbounding the SOC. To address this, a first-level fuzzy control dynamically adjusts λ(i) in real time. Additionally, to enhance the BESS’s smoothing capability for future wind power, a second layer of fuzzy control strategy corrects the charging and discharging power of the BESS. The control block diagram, integrating MPC and fuzzy control, is illustrated in Figure 6.

4.1. Single-Layer Fuzzy Control Strategy

Fuzzy control leverages computer systems to emulate human control experiences, mimicking the human brain’s handling of uncertainty, reasoning, and management of imprecise models or uncertain systems [24]. Unlike conventional control methods, fuzzy control does not rely on precise mathematical models of the controlled object. Instead, it demonstrates remarkable applicability to dynamic or highly nonlinear systems, exhibiting strong adaptability to variations in processes and parameters [40]. Given the complex nature of wind energy cogeneration systems, fuzzy control effectively addresses the limitations of traditional control methods, offering simplicity and high efficiency.

At time i + 1, when the grid-connected power surpasses the permitted fluctuation threshold and the energy storage SOE approaches the ideal value, prioritizing combined wind and storage power becomes imperative to ensure they remain within the acceptable fluctuation range. This is achieved by introducing a pair of fuzzy controllers to diminish the weighting coefficient λ(i). Conversely, if the energy storage SOE is exceptionally low or high, λ(i) is adjusted upward to prevent the BESS from breaching its operational limits. The inputs to the fuzzy controller consist of the storage state (E_SOC(i)) and storage power (P_b(i)) at time i, while the outputs are the weighting coefficients λ(i). The membership functions corresponding to the input and output variables are illustrated in Figure 7.

The input variable P_b(i) spans a fuzzy set domain of [−1, 1], with the chosen linguistic set {NB, NS, Z, PS, PB}, corresponding to “negative large value”, “negative small value”, “zero value”, “positive small value”, and “positive large value”, respectively. The variable E_SOC(i) operates within a fuzzy set domain of [0, 1], using the linguistic set {VS, S, M, B, VB}, denoting “very small value”, “small value”, “moderate”, “large value”, and “very large value”, respectively. The output variable λ(i) is defined within the fuzzy set domain [0, 1], employing the linguistic set {VS, S, M, B, VB}, indicating “very small value”, “small value”, “moderate”, “large value”, and “very large value”, respectively. The fuzzy inference rules for the fuzzy controller are outlined in

Table 2. Fuzzy reasoning of front fuzzy controller.

ESOC(i)	Pb(i)
	PB	PS	Z	NS	NB
VS	VB	VB	B	M	M
S	B	B	M	M	S
M	S	VS	VS	VS	S
B	S	M	M	B	B
VB	M	M	B	VB	VB

.

4.2. Two-Layer Fuzzy Control Strategy

At time i + 1, when the wind power fluctuation remains within the permissible range, the second layer of the fuzzy controller intervenes to rectify the magnitude of BESS charge and discharge power. This correction aims to enhance the BESS’s smoothing capability for future wind power by preemptively adjusting its capacity. The formula for correcting the charging and discharging power is depicted in (14).

$$P_{\mathrm{b}}^{\prime }\left(i+1|i\right)=P_{\mathrm{b}}\left(i+1|i\right)+\Delta k\times \left(P_{\mathrm{w}}(i+1)-P_{\mathrm{g}}(i)\right)$$

(14)

where $P_{\mathrm{b}}^{\prime }\left(i+1|i\right)$ is the corrected BESS output power, and ∆k is the correction factor.

Using the ultra-short-term wind power forecast, the storage charge state is assessed, and predictions for both the storage overflow limit Q(i + k) and the grid power fluctuation P_r(i + k) are made for each sampling point within the future rolling optimization period. These predictions are calculated using Equations (15) and (16), as shown below.

$$Q\left(i+k\right)=\{\begin{array}{l}\left(E_{\mathrm{SOC}}\left(i+k\right)-E_{\mathrm{SOC}.\max }\right)\times C_{\mathrm{rated}}\\ \begin{array}{ccc}& & \begin{array}{cccc}& & & \end{array} E_{\mathrm{SOC}}\left(i+k\right)>E_{\mathrm{SOC}.\max }\end{array}\\ \left(E_{\mathrm{SOC}.\min }-E_{\mathrm{SOC}}\left(i+k\right)\right)\times C_{\mathrm{rated}}\\ \begin{array}{cccc}& & & \begin{array}{ccc}& & \end{array} E_{\mathrm{SOC}}\left(i+k\right)<E_{\mathrm{SOC}.\min }\end{array}\end{array}$$

(15)

$$P_{\mathrm{r}}\left(i+k\right)=P_g\left(i+k\right)-P_a\left(i+k\right)$$

(16)

The covariance and correlation coefficient of Q and P_r calculated from historical data yield a value less than zero, indicating a negative correlation between the two variables. To address the contradiction between adhering to limits and smoothing wind power fluctuations—specifically, maximizing wind power fluctuation smoothing while ensuring the longevity of the energy storage device—the operational directives for the energy storage device need to be revised. Leveraging statistical factor analysis theory, the H-matrix is constructed using Equations (17)–(19).

$$h_{ij}=\frac{1}{2}\left(\frac{1}{q}{\displaystyle \sum _{j=1}^q{d}_{ij}^2+\frac{1}{q}{\displaystyle \sum _{i=1}^q{d}_{ij}^2-d_{ij}^2-I}}\right)$$

(17)

$$I=\frac{1}{q^2}{\displaystyle \sum _{i=1}^q{\displaystyle \sum _{j=1}^q{d}_{ij}^2}}$$

(18)

$$d_{ij}^2={{\displaystyle \sum _{r=1}^l\left(z_{ir}-z_{jr}\right)}}^2$$

(19)

where $d_{ij}^2$ is the square of the Euclidean distance between the i-th object and the j-th object in the matrix Z; Z_ik is the element of the k-th column of the i-th row in the matrix Z. The matrix Z comprises the transcendental limit and the planned power deviation, constituting a matrix with two rows and eight columns, denoted as q = 2 and l = 8. h_ij is an element of the matrix H.

The matrix H is obtained by eigenvalue decomposition:

$$\mathit{H}=\mathit{U}\mathit{V}{\mathit{U}}^{\mathrm{T}}$$

(20)

where V is the diagonal matrix formed by the eigenvalues of the matrix H, and U is the matrix with the corresponding eigenvectors arranged as columns.

The contradictory factors reflecting the two variables Q and P_r are extracted by Equation (21) and denoted as F.

$$F=\mathit{U}\sqrt{\mathit{V}}$$

(21)

If the value of F is large, it suggests that the BESS lacks sufficient charging capacity for the future rolling optimization period, requiring advance discharge of the BESS. Conversely, if F is small, it indicates insufficient discharge capacity for the BESS in the future rolling optimization period, requiring advance charging of the BESS. When F assumes a medium value, the BESS operates according to its original instructions for charging and discharging. Utilizing F as one input to the second-level fuzzy controller, the other input is defined as P_b(i), with the output being the correction factor ∆k. The membership functions for the fuzzy control input and output are illustrated in Figure 8.

The input variable P_b(i) has a fuzzy set domain of [−1, 1], utilizing the linguistic set {L, LM, M, MH, H}, representing “negative large value”, “negative small value”, “zero”, “positive small value”, and “positive large value”, respectively. The input variable F spans a fuzzy set domain of [−0.2, 0.2], employing the linguistic set {VS, S, B, VB}, denoting “negative large value”, “negative small value”, “positive small value”, and “positive large value”, respectively. The output variable’s fuzzy set range is [−1, 1], employing the linguistic set {NB, PB, N, Z, P, PH, NH}, indicating “very negative small value”, “negative small value”, “slightly negative small value”, “zero”, “slightly positive large value”, “positive large value”, and “very positive large value”, respectively. The fuzzy inference rules for the second-level fuzzy controller are depicted in

Table 3. Fuzzy inference table of the second layer fuzzy controller.

F	Pb(i)
	L	LM	M	MH	H
VS	NB	PB	P	NH	P
S	PB	N	Z	PH	Z
B	P	PH	Z	N	PB
VB	PH	NH	PB	PB	NB

.

In summary, the specific flow of the control strategy proposed in this paper is depicted in Figure 9, with the following specific steps:

Step 1:

Establish a target value for smoothing wind power fluctuations and initialize the parameters.

Step 2:

The MPC model for the wind storage cogeneration system is established with the short-term predicted wind power as the input variable, the future finite time domain’s incremental storage active power as the control variable, the current output power of the storage system as the initial value, and the grid-connected power and remaining capacity of the storage system as the output variables.

Step 3:

Define the objective function incorporating the deviation of the energy storage system’s remaining capacity from the ideal value and minimizing the difference between the grid-connected power and the target power. Establish the necessary constraints.

Step 4:

Check if the grid-connected power at time i + 1 surpasses the permissible fluctuation value. If it does not, proceed directly to step 6; otherwise, move to step 5.

Step 5:

The objective function’s weight coefficient λ(i) is adjusted using the first layer fuzzy controller.

Step 6:

The second layer of the fuzzy controller is employed to rectify the BESS output power.

Step 7:

Optimize the sequence of control variables within the constraint of N future periods using the CPLEX solver.

Step 8:

Extract the first control variable and compute the BESS power at time i + 1, along with the corresponding output in the model.

Step 9:

Compute the BESS power for i + 1 moments.

Step 10:

Utilize the actual output of the BESS at time i + 1 as the initial value for the optimization model. Then, return to step 2 and iterate through the rolling optimization process until completion.

5. Algorithm Analysis

This study’s experimental data consist of one day of continuous actual wind power data from a 50 MW wind farm, sampled at 1 min intervals, yielding 1440 sampling points.

Table 4. Simulation parameters.

Parameters	Symbol	Value and Units
Installed capacity of wind farms	Cinstall	50 MW
Cycle of control	Tc	1 min
Rated capacity of BESS	Crated	5 MW·h
Rated capacity of BESS	Prated	10 MW
Cycle of control	Ts	1 min
Optimize interval length	N	15
Charge dead zone boundary	ESOC.max	0.8
Discharge dead zone boundary	ESOC.min	0.2
Charge warning interval boundary	ESOC.max-alert	0.7
Discharge warning interval boundary	ESOC.min-alert	0.3

details the key parameter settings for the wind farm and the BESS. Among them, the setting of BESS-related parameters mainly refers to lithium-ion batteries. To showcase the effectiveness and superiority of the proposed control strategy, it is compared with the MPC method (Scheme 1), which focuses on minimizing power fluctuations. The method proposed in this paper (Scheme 2) is evaluated against Scheme 1 to highlight its advantages.

5.1. Evaluation Index

To assess the impact of the suggested control strategy, we have chosen three key indicators for evaluation. First, to gauge its ability to smooth power fluctuations, we evaluate the absolute mean value of grid-connected power fluctuations, reflecting how effectively the BESS can mitigate wind power fluctuations. Second, to consider energy storage longevity, we examine the BESS input dead time index, which gives an insight into the lifespan of the BESS. We use the BESS power output coefficient indicators to evaluate the BESS’s power output capacity.

(1)

Average absolute value of power fluctuation ∆P_g.mean.

$$\Delta P_{\mathrm{g}}(i)=\left|P_{\mathrm{g}}(i+1)-P_{\mathrm{g}}(i)\right|$$

(22)

$$\Delta P_{\mathrm{g}.\mathrm{mean}}=\frac{1}{N-1}{\displaystyle \sum _{i=0}^{N-1}\Delta P_{\mathrm{g}}(i)}$$

(23)

∆P_g(i) represents the absolute value of the grid-connected wind power fluctuation at time i. ∆P_g.mean is the average absolute value of wind power grid-connected fluctuation at time i. ∆P_g.mean provides a comprehensive measure of energy storage’s ability to smooth wind power fluctuations throughout the dispatch day. A lower ∆P_g.mean indicates a better smoothing effect because it signifies a reduced overall fluctuation level.

(2)

BESS enters dead time T_d.

$$\begin{array}{l}{T}_{\mathrm{d}}=T_{\mathrm{s}}\times {\displaystyle \sum _{i=0}^{N-1}\left[h\left(\frac{E_{\mathrm{SOC}}\left(i\right)}{E_{\mathrm{SOC}.\min }}\right){\displaystyle \cup h\left(\frac{E_{\mathrm{SOC}.\max }}{E_{\mathrm{SOC}}\left(i\right)}\right)}\right]}\\ \begin{array}{cc}& h\left(x\right)\end{array}=\{\begin{array}{l}1,x\ge 1\\ 0,x<1\end{array}\end{array}$$

(24)

where T_d is the time when the energy storage SOC surpasses the designated safety threshold.

(3)

BESS output capacity evaluation coefficient C_b.

$$C_b=\sqrt{\frac{1}{T-1}{\displaystyle \sum _{i=1}^{T-1}{\left[E_{\mathrm{SOC}}\left(i\right)-0.5\right]}^2}}$$

(25)

where C_b is the BESS output capacity evaluation coefficient, with a smaller value indicating a larger output capacity. T is the number of sampling periods in the energy storage output cycle.

5.2. Analysis of Simulation Results

In the simulation, a 1 min power fluctuation of 2 MW and a 10 min power fluctuation of 6 MW are set. Different control schemes yield varied actual output grid-connected power for the wind farm, as depicted in Figure 10.

Table 5. Evaluation indices.

Control Scheme	∆Pg.mean/MW	Td/min	Cb
Without BESS	0.92	—	—
Scheme 1	0.74	123	0.19
Scheme 2	0.61	0	0.13

provides a comparison of specific indicators. Scheme 2 significantly reduces grid-connected wind power fluctuations, with a 33.7% reduction in the average absolute value of power fluctuation compared to the system lacking energy storage. Similarly, Scheme 1 reduces the absolute mean of grid-connected power fluctuation by 19.6% compared to Scheme 1 without energy storage. Thus, Scheme 1 exhibits an increased average absolute value of power fluctuation compared to Scheme 2, indicating a less effective smoothing effect.

The 1 min power fluctuation is depicted in Figure 11, while the 10 min power fluctuation is illustrated in Figure 12. It is evident from the figures that the smoothing effect of control Scheme 2 surpasses that of control Scheme 1. Specifically, in the absence of energy storage, the maximum power fluctuation value for 1 min is 8.1 MW, with 173 crossing limit points; for 10 min, the maximum power fluctuation value is 29.4 MW, with 495 crossing limit points. In control Scheme 1, the maximum power fluctuation value for 1 min is 7 MW, with 59 crossing points; for 10 min, it is 21.3 MW, with 231 crossing points. In control Scheme 2, the maximum power fluctuation value for 1 min is 4.1 MW, with 44 crossing points; for 10 min, it is 18.9 MW, with 165 crossing points. These results highlight the significant improvement of the proposed method over the traditional MPC method in terms of smoothing the grid-connected power of wind power.

The energy storage SOC variation curve in Figure 13 indicates that for Scheme 1, the BESS experiences high energy states during the periods of 165–173, 203–217, 254–259, and 863–882, leading to a decrease in its charging capacity. Conversely, it enters low energy states during the periods of 330–338, 345–355, 442–458, 581–586, 712–723, and 746–764 min, decreasing its discharging capacity. Table 5 also reveals that in Scheme 1, the BESS dead time extends to 123 min, with a capacity coefficient of 0.19, indicating inadequate support for smoothing wind power fluctuations in the future. Examining the BESS power in Figure 14, Scheme 2 enhances the BESS’s capability to smooth future wind power fluctuations by dynamically adjusting weighting coefficients and implementing advanced charging and discharging strategies. Compared to Scheme 1, Scheme 2 reduces the BESS dead time by 123 min and decreases the output coefficient by 31.6%. By decreasing dead time while enhancing power fluctuation smoothing, Scheme 2 effectively balances the conflict between energy storage constraints and wind power fluctuation smoothing. This validates the superiority of the proposed method over Scheme 1.

Based on the SOC partitioning of the BESS outlined in Section 2.2,

Table 6. Time distribution of SOC in different interval segments for the two control schemes.

Control Scheme	Discharge Dead Zone/min	Discharge Warning Interval/min	Normal Charging and Discharging Interval/min	Charge Warning Interval/min	Charging Dead Zone/min
Scheme 1	73	155	929	233	50
Scheme 2	0	103	1230	107	0

presents the time distribution of the BESS SOC in different interval segments for the two control schemes. In control Scheme 1, the time for the SOC to enter the discharge dead zone is 73 min and for the charging dead zone is 50 min. Additionally, the time for the SOC to be in the discharge warning interval is 155 min and in the charging warning interval is 233 min. Furthermore, the SOC spends 929 min in the normal charging and discharging interval. In control Scheme 2, the SOC did not enter the charging and discharging dead zone. The time for the SOC to be in the discharge warning interval is 103 min and in the charging warning interval is 107 min. Moreover, the SOC spends 1230 min in the normal charging and discharging interval. Compared with control Scheme 1, control Scheme 2 notably diminishes the time of SOC in the dead and warning zones and maintains a relatively reasonable depth of charging and discharging. This enhancement enhances the BESS’s ability to smooth the wind power fluctuation.

6. Conclusions

To improve the dispatchability of the wind storage cogeneration system, this paper introduces an objective function aimed at minimizing the deviation of grid power from the target power and the residual capacity of the ESS from the ideal value. This objective function considers preventing SOC overruns while effectively smoothing wind power fluctuation. The conclusions drawn from this approach are as follows:

(1)

The method employs a first layer of fuzzy control to adjust the weight coefficients of the objective function, thereby enhancing the ESS’s ability to smooth wind power fluctuations while reducing the instances of the BESS entering dead and warning zones. Compared to control Scheme 1, control Scheme 2 exhibits a 17.7% decrease in the absolute mean value of wind grid-connected power fluctuations. Additionally, the time for SOC to enter the dead and warning intervals is reduced by 123 and 278 min, respectively. Consequently, control Scheme 2 effectively maintains SOC within a reasonable range and significantly improves the smoothing performance of the BESS for wind power.

(2)

A method is introduced to adjust the charging and discharging power of the BESS using the second layer of fuzzy control, thereby enhancing the BESS’s capacity to mitigate future wind power fluctuations. Compared to control Scheme 1, control Scheme 2 demonstrates a decrease of 31.6% in the BESS output coefficient. Consequently, control Scheme 2 effectively allocates sufficient chargeable capacity to smooth future wind power fluctuations by implementing advanced charging and discharging strategies.

(3)

Compared to control Scheme 1, the control method presented in this paper, utilizing fuzzy control rules to adjust charge and discharge power, leads to a certain increase in BESS charge and discharge cycles. Additionally, the effectiveness of the proposed control method is influenced by the accuracy of wind power predictions. Further research will explore the impact of wind power prediction errors on control effects and potential solutions. Additionally, battery charging and discharging strategies that consider the service life of BESS and the effective smoothing of wind power fluctuations will be investigated. These efforts aim to advance the efficient integration of energy storage systems with new energy sources.