Energy-Storage Optimization Strategy for Reducing Wind Power Fluctuation via Markov Prediction and PSO Method

Abstract

Wind power penetration ratios of power grids have increased in recent years; thus, deteriorating power grid stability caused by wind power fluctuation has caused widespread concern. At present, configuring an energy storage system with corresponding capacity at the grid connection point of a large-scale wind farm is an effective solution that improves wind power dispatchability, suppresses potential fluctuations, and reduces power grid operation risks. Based on the traditional energy-storage battery dispatching scheme, in this study, a multi-objective hybrid optimization model for joint wind-farm and energy-storage operation is designed. The impact of two new aspects, the energy-storage battery output and wind-power future output, on the current energy storage operation are considered. Wind-power future output assessment is performed using a wind-power-based Markov prediction model. The particle swarm optimization algorithm is used to optimize the wind-storage grid-connected power in real time, to develop an optimal operation strategy for an energy storage battery. Simulations incorporating typical daily wind power data from a several-hundred-megawatt wind farm and rolling optimization of the energy storage output reveal that the proposed method can reduce the grid-connected wind power fluctuation, the probability of overcharge and over-discharge of the stored energy, and the energy storage dead time. For the same smoothing performance, the proposed method can reduce the energy storage capacity and improve the economic efficiency of the wind-storage joint operation.

1. Introduction

As a result of the rapid development of wind power technology worldwide, there is a high likelihood of wind power being adopted for core power generation units in future power systems [1,2]. However, because of the randomness and uncertainty of wind power, wind power fluctuations are expected to induce instantaneous power imbalances in such future power grids. This will result in deterioration of the grid frequency and voltage quality, and may even endanger the power system stability [3,4,5,6]. Therefore, to improve the wind power penetration ratios of power grids and to maintain power system stability, an optimization scheme to reduce the power fluctuation of grid-connected wind power sources should be investigated.

A large number of studies have shown that an energy storage system is an effective means of alleviating wind power fluctuations, peak cutting, and valley filling, and of improving wind power dispatchability [7,8,9]. Experts from different countries have also performed many studies on energy-storage system control strategies. For example, Jiang et al. [10] previously proposed a dual-layer control strategy for a battery energy storage system (BESS), to mitigate the wind-power output fluctuation and to reduce the number of charge and discharge cycles. Furthermore, Shi et al. [11] analyzed the fluctuation features of wind power output in both the time and frequency domains. Hence, they defined the wind scenario with the largest power fluctuation based on quantization index clustering. The energy storage output was scheduled accordingly and the wind power dispatchability was improved. In some studies [12,13,14], dispatching strategies for a hybrid energy storage system to smooth wind power fluctuations were proposed. In that approach, the characteristics of multiple energy storage approaches are combined and coordinated to smoothen the wind power fluctuations. In the related studies, the smoothing capability of the energy storage system was found to be improved, and the system service life was also extended. Previously, Lamsal et al. [15] adopted the Kalman filter approach to eliminate bias errors in forecasted data. They evaluated the influence of wind and photovoltaic power fluctuations on load, so as to adjust the output of the energy storage system. Recently, the energy storage state-of-energy (SOE) indicator was divided into different output regions and a state-of-charge (SOC) feedback control for the energy storage system in certain regions was proposed [16,17]. The influence of the charge and discharge power on the energy storage battery life was estimated, and it was found that the economic efficiency of wind-storage joint operation was improved [18,19]. Overall, although different strategies have been proposed, a basic consensus has been reached; that is, use of an energy storage system can increase the wind power dispatchability. Furthermore, joint operation of a wind-storage system could improve the wind-power utilization rate and reduce the impact of wind farms on the grid.

In recent years, to further improve wind power dispatchability and reduce the impact of its randomness, wind power prediction technology has been developed extensively. Sahin and Sen [20] have reviewed the common wind power prediction methods in considerable detail, and evaluated the current research directions, challenges, and future developments. Hence, they have concluded that significant improvements to wind power prediction technology are still required, and are expected to have great research significance. Other researchers [21,22,23,24] have performed multi-step prediction for future wind speeds by calculating the Markov state transition matrix based on the Markov property in the wind speed change process and using historical wind speed data. The wind power at a wind farm is strongly correlated with the wind speed; thus, the Markov prediction model has also been applied for wind power prediction [25,26]. With the increasing maturity of traditional machine learning techniques and the development of deep learning methods, models related to these methods have been successfully applied to wind power prediction and the prediction performance has continuously improved. Relevant examples involve application of the least squares support vector machine [26], naive Bayesian model [27], neural network model [28], ensemble recurrent neural network [29], and echo state networks and long short-term memory [30]. In particular, considering the impact of future wind power on the optimization process employed for current wind-storage operation, Huo et al. [31] and Han et al. [32] proposed a strategy for real-time cost optimization of wind-storage dispatching considering the wind forecast uncertainties and forecast error features, respectively. Reasonable dispatching of energy storage systems on multiple time scales was realized. The model predictive control method has also been successfully introduced to economic wind-storage operation and energy management and dispatching, yielding effective improvements in wind farm dispatchability [33,34,35]. Note that, in models of the wind-storage system, its operation process is characterized as a dynamic optimization process. In other words, the most economic and reliable operation scheme is realized while satisfying basic constraints. Thus, various researchers [36,37,38,39] have used the colony optimization algorithm to realize energy management strategies for microgrids incorporating renewable energy and battery storage systems; hence, the operating costs of the full power systems have been optimized.

In the currently available literature, assessment and optimization of the smoothing ability of energy storage systems during real-time operating processes, or the influence of the future wind power output on the current energy storage output, are rarely discussed. In this paper, a multi-objective hybrid optimization model for a wind-storage joint operation strategy is proposed. Firstly, an assessment model of the energy-storage battery output level and a mathematical model of the future output influence of wind power are defined. A multi-objective hybrid optimization model is constructed. Then, the Markov chain (MC) approach is used for wind power prediction, and the particle swarm optimization (PSO) algorithm is applied to generate a real-time rolling optimization strategy for the energy storage output. Finally, simulation results demonstrate that the method proposed in this paper yields a superior smoothing effect and better prevention of energy storage entry to the dead zone compared to the traditional approach, and effectively improves the reliability and economic efficiency of a wind-storage system.

The remainder of this paper is organized as follows: Section 2 describes the structure of the wind/storage system and the optimization objective design for the wind-storage operation model. Section 3 presents the wind power prediction method based on Markov model and the wind-storage optimization strategy using the PSO algorithm. Section 4 presents the numerical simulation results and related discussion. Finally, Section 5 summarizes the conclusions of this paper.

2. Problem Description

2.1. System Description

In wind power generation systems, random and uncertain changes in wind speed can induce fluctuations in the active wind power. Large active wind power fluctuations impact the main grid and affect the power grid stability. By integrating a BESS at the points of common coupling (PCC) of the connected grid, the charge and discharge process of the controller can effectively smooth the connected-grid power fluctuation. Such a solution could also help increase wind power penetration ratios of power grids. The structure of a typical wind power generation system is shown in Figure 1. This system generally consists of several wind turbines, BESS, power electronic converters, and power transmission lines connected to the main power grid.

It is well known that an effective control strategy means lower energy storage capacity, longer service time, and shorter payback period [5]. Thus, the BESS power management unit (PMU) used to smoothen the grid-connected wind power is a key component of the wind-storage power generation system design. The purpose of this study is to design a PMU operation strategy that considers the energy storage smoothing ability and the future output prediction, and to use this strategy to reasonably smooth the grid-connected wind power.

2.2. Mathematical Model for Reducing Wind Power Fluctuation

It is apparent from Figure 1 in Section 2.1 that the power balance equation between wind farm, BESS and grid of the wind-storage hybrid system satisfies the relation

$$P_G(t)=P_W(t)+P_B(t),$$

(1)

where $P_G(t)$ represents the grid-connected power at time t, $P_W(t)$ is the wind farm output power at t, and $P_B(t)$ represents the output power of the energy storage battery. The energy change of the energy storage system satisfies the relation

$$E_B(t+1)=E_B(t)+P_B(t)\Delta T,$$

(2)

where $E_B(t)$ represents the stored energy at t and $\Delta T$ is the sampling time. When $P_B(t)>0$ and <0, the energy storage system is charging and discharging, respectively. At t, the remaining energy state of the energy storage battery $\mathrm{SOE}(t)$ is expressed as the ratio of the stored energy to the battery capacity, i.e., $\mathrm{SOE}(t)=E_B(t)/Q$, where $Q$ represents the capacity of the energy storage battery.

The wind power fluctuation smoothing achieved using traditional battery energy storage, $P_B(t)$, and the changes in SOE are shown in Figure 2. The grid-connected power $P_G(t-1)$ obtained at time t − 1 in real time, as well as $P_W(t)$, are used to estimate the power fluctuation caused by the grid-connected wind power at time t, such that

$$\Delta P_G(t)=P_W(t)-P_G(t-1),$$

(3)

where $\Delta P_G(t)$ represents the grid-connected power fluctuation. When $|\Delta P_G(t)|<\delta$, that is, when the wind power satisfies the power requirements for grid connection, the energy storage battery has no output. This is to reduce consumption of the stored energy, as shown for the 0–t₄, t₄–t₆, t₈–t₉, t₁₁–t₁₂, t₁₅–t₁₆, and t₁₇–t₁₈ time periods in Figure 2. When $\Delta P_G(t)<-\delta$, the energy storage battery is discharging to supplement the grid-connected power. To minimize consumption of the stored energy, usually $P_B(t)=P_W(t)-P_G(t-1)+\delta$, as shown for the t₁–t₂, t₃–t₄, t₉–t₁₁, and t₁₆–t₁₈ time periods in Figure 2. When $\Delta P_G(t)>\delta$, the energy storage battery is charging, and $P_B(t)=P_W(t)-P_G(t-1)-\delta$, as shown for the t₂–t₃, t₆–t₈, t₁₂–t₁₅, and t₁₉–t₂₀ time periods in Figure 2. The parameter $\delta$ represents the range of active wind power fluctuations that are permitted to be connected to the grid.

Figure 2 shows that there are still some problems with incorporation of energy storage for wind power fluctuation smoothing. (1) If the SOE upper and lower limits of the energy storage system are $[{\mathrm{SOE}}^{L1},{\mathrm{SOE}}^{U1}]$ or the energy storage capacity is infinite, this scheme is feasible. However, in reality, the energy storage capacity is limited. If the upper and lower limits of the SOE are $[{\mathrm{SOE}}^{L2},{\mathrm{SOE}}^{U2}]$, then, during the t₁₄–t₁₇ time period of the energy storage SOE curve in Figure 2, P_B is limited. Thus, the grid-connected power exceeds the allowable range of power fluctuation, which impacts the grid. This time period is defined as the energy storage “dead zone time.” However, if the energy storage discharge power is appropriately increased in the t₈–t₁₀ time period in region A, so as to restore the energy storage residual energy state to the state of maximum charge and the battery discharge capacity (SOE = 0.5), part of the influence of the dead zone can be eliminated. (2) In region B of Figure 2, which corresponds to the t₁–t₄ time period, the stored energy is charged and discharged frequently; this behavior has a detrimental influence on the service life of the energy storage battery.

Therefore, in this paper, a multi-objective operation optimization strategy for the energy storage battery is designed, which considers the energy storage output capability, predicts the influence of the future wind power output, and minimizes the energy storage output. This strategy can be applied to smooth grid-connected wind power fluctuations.

We assume that the optimization variable $X=\left[x_1,x_2\right]=\left[P_G(t),P_G(t+1)\right]$. Then, the index J₁, which represents the objective of controlling $\Delta P_G(t)$ within the allowable range, is expressed as in Equation (4). Furthermore, the index J₂, which represents the objective of minimizing P_B, is expressed as in Equation (5), and index J₃, which represents the energy storage output capability, is expressed as in Equation (6). The index J₄, which represents the predicted influence of the future wind power output is expressed as in Equation (7).

$$J_1=c_1(P_w(t)-P_G(t-1)),$$

(4)

$$J_2=c_2(P_w(t)-P_G(t)),$$

(5)

$$J_3=c_3(\mathrm{SOE}(t)+(P_w(t)-P_G(t))\Delta T/Q),$$

(6)

$$\begin{array}{c}{J}_4=c_1{(P_G(t+1)-P_G(t))}^2+c_2{({\widehat{P}}_w(t+1)-P_G(t+1))}^2+\dots \\ c_3{(\widehat{\mathrm{SOE}}(t+1)+({\widehat{P}}_w(t+1)-P_G(t+1))\Delta T/Q)}^2,\end{array}$$

(7)

where c₁ is the cost function of $\Delta P_G(t)$, as shown in Figure 3a; c₂ is the cost function of P_B, as shown in Figure 3b; and c₃ is the cost function of the energy storage output capability, as shown in Figure 3c. The energy storage output capability area is appropriately divided to generate an energy storage output capability assessment. In addition, ${\widehat{P}}_w(t+1)$ represents the predicted wind power and $\widehat{\mathrm{SOE}}(t+1)$ represents the energy storage state SOE at t + 1, after a period $\Delta T$ of operation at an energy storage output of $P_B(t)=P_W(t)-P_G(t)$ at time t.

A hybrid optimization objective J for the energy storage battery is then established according to Equations (4)–(7), for smoothing of the grid-connected wind power fluctuations. This objective is expressed in Equation (8), in which α represents the weight of the energy storage output capability as the optimization objective, β represents the weight of the predicted future energy storage output, and (α, β) ∈ [0, 1]. J₁ and J₂ are the optimization objectives of the traditional approach; that is, minimization of the energy storage output while satisfying the grid-connected power requirements. Thus, different objectives are optimized by setting the (α, β) values. It should also be noted that some parameters and variables in the objective function have partial constraints, which affect the optimization process. The constraints are given in Equation (9).

$$objectiveJ=J_1+J_2+\alpha \times J_3+\beta \times J_4,$$

(8)

$$s.t.\{\begin{array}{c}0\le P_G(t)\le P_{G,\max },\\ {\mathrm{SOE}}^L\le \mathrm{SOE}(t)\le {\mathrm{SOE}}^U,\end{array}$$

(9)

where ${\mathrm{SOE}}^L$ and ${\mathrm{SOE}}^U$ are respectively the lower and upper charge and discharge limits of the energy storage battery, and $P_{G,\max }$ is the maximum grid-connected power.

The indices of the grid-connected wind power smoothing performance were as follows [18]:

$$\Delta P_{G,\max }=\max (|\{\Delta P_G(t),t=1,2,\dots ,T-1\}|),$$

(10)

$$\Delta P_{G,mean}=\frac{1}{T-1}{\displaystyle \sum _{t=1}^{T-1}|\Delta P_G(t)|},$$

(11)

$$Q_G={\displaystyle \sum _{t=0}^{T-1}{P}_G(t)\Delta T},$$

(12)

$$Q_B={\displaystyle \sum _{t=0}^{T-1}|P_B(t)|\Delta T},$$

(13)

$$T_d=\Delta T{\displaystyle \sum _{t=0}^{T-1}[h(\mathrm{SOE}(t)\ge {\mathrm{SOE}}^U)\cup h(\mathrm{SOE}(t)\le {\mathrm{SOE}}^L)]},$$

(14)

$$Ca{p}_{ESS}=\sqrt{\frac{1}{T-1}{\displaystyle \sum _{t=0}^{T-1}{(\mathrm{SOE}(t)-0.5)}^2}},$$

(15)

where $\Delta P_{G,\max }$ and $\Delta P_{G,mean}$ represent the maximum and mean value of wind power fluctuation, respectively, they are indicating the smoothing levels of the energy storage battery. The smaller these values, the better the smoothing performance and the lower the impact on the power grid. $Q_G$ and $Q_B$ are, respectively, the grid-connected energy and the battery output on the typical days. A larger $Q_G$ represents a greater energy output to the grid and a higher wind power utilization rate. A larger $Q_B$ indicates more changes in the energy storage battery output and a greater impact on the energy storage battery cycle life. Further, $T_d$ represents the energy storage dead time. A larger $T_d$ value means a longer time of excessive charge and discharge of the energy storage, and more serious damage to the energy storage battery life. It also indicates a larger potential influence of wind power fluctuation on the power grid, where $h(x)=1\times (x\ge 0)+0\times (x<0)$. Finally, $Ca{p}_{ESS}$ is the output capacity assessment of the energy storage battery on a typical day. A lower $Ca{p}_{ESS}$ indicates a stronger charge and discharge level of the energy storage battery throughout the day.

3. Proposed Approach with Markov Prediction and PSO Method

3.1. Markov Prediction Model

The actual operation processes of most physical systems are stochastic. The wind speed and wind active power also follow this rule [20,21,22,23,24,25]. A stochastic process is a real-time process that can be described using a set of random variables, which are related to another variable, such as time t.

An MC is an analytical representation of a stochastic process. It is assumed that there is a discrete stochastic process $\left\{S_n,n=0,1,2,\dots \right\}$ in a discrete state-space $\left\{0,1,2,\dots \right\}$. It can be stated that $S_n$ is a discrete Markov process if it has the following attributes: The conditional probability distribution of any future state $S_{n+1}$ is independent of the past states $\left\{S_0,S_1,\dots ,S_{n-1}\right\}$ and only determined by the current state $S_n$. The discrete Markov process is expressed as

$$P\left\{S_{n+1}=j|S_n=i,S_{n-1}=i-1,\dots ,S_0=i_0\right\}=P_{i,j},$$

(16)

where $P_{i,j}$ represents the probability that the future state j is in the current hypothetical state i, with i and j representing the states of random variables in the state space.

In general, in an MC, random variables and time are discrete. A finite number of discrete states and a set of transition probabilities Π (t, t + 1) are used to define the probability of transitioning from one state to another in each step. The one-step transition probability between all states can be arranged in a “one-step state transition matrix”, the general form of which can be expressed as

$$\mathsf{\Pi }(t,t+1)=\left[\begin{array}{cccc}{P}_{1,1}& P_{1,2}& & P_{1,n}\\ P_{2,1}& P_{2,2}& & P_{2,n}\\ & & & \\ P_{n,1}& P_{n,2}& & P_{n,n}\end{array}\right],$$

(17)

where $P_{i,j}$ is the probability of transitioning from state i to state j in a time step. Further, $P_{i,j}=f_{i,j}/{\displaystyle {\sum }_{j=1}^K{f}_{i,j}}$, where $f_{i,j}$ is the total number of one-step transitions of state i to state j and K represents the number of states. The probability of all elements should be in the range of 0 to 1, and the sum of the probabilities in each row is 1. By using the one-step state transition matrix expressed in Equation (17) and the Markov properties, the n-step state transition matrix can be described as follows:

$$\mathsf{\Pi }(t,t+n)={\mathsf{\Pi }}^n(t,t+1).$$

(18)

In the wind power prediction process presented in this paper, the state transition matrix is constructed by recording the wind power historical data. The specific one-step prediction steps are as follows.

(1) Wind power discretization: In accordance with the wind farm installed capacity (the maximum wind power output), the number of state variables n is selected. The state description $\left\{S_n,n=0,1,2,\dots \right\}$ is obtained by dividing the overall wind power into equal intervals. The average of each wind power interval is defined as the power characterization of this state.

(2) State transition matrix calculation: The state evolution process of the wind power historical time series data is defined according to the corresponding interval range of each state. The one-step transition matrix $\mathsf{\Pi }(t,t+1)$ of the wind power is calculated according to Equation (17).

(3) Rolling prediction: The current state i is calculated according to the current wind power situation at time t. The maximum probability $P_{i,j}$ in the i-th row of the one-step transition matrix is found. This indicates that, when in the current state i, the wind power will transit to state j with maximum probability in the next moment. The average of the wind power interval corresponding to state j is regarded as the predicted wind power value at time t + 1. The prediction process is completed by continuously rolling t.

In this paper, the optimization objective functions expressed in Equations (7) and (8) in Section 2.2 define the cost functions for one-step prediction only. Therefore, it is only necessary to complete the one-step prediction. If the multi-step prediction results of the prediction part are increased in the optimization objective, a one-step state transition matrix must be used in the prediction process. The n-step state transition matrix is calculated according to Equation (18) in order to perform the prediction.

3.2. Coordinated Control Strategy Using the PSO Method

The heuristic optimization algorithm is an effective means of solving nonlinear and non-convex optimization problems. In 1995, Kenney and Eberhart proposed a global search swarm intelligence optimization algorithm by observing the migratory and group behaviors of birds during foraging [40,41]. Compared with the other optimization techniques, such as the genetic algorithm (GA) and simulated annealing (SA), PSO has higher search speed, fewer set parameters, and stronger optimization ability. It has been widely used in various optimization scenarios.

The main concept behind the PSO algorithm is determination of the optimal solution of a complex problem through initialization and iteration over a set of random particles. In the PSO algorithm, each particle represents a potential solution, characterized by three indices; namely, the position, velocity, and fitness function value. The particle fitness function value characterizes the strengths and weaknesses of the particle position. The position of the particle with the optimal fitness is marked as the optimal particle position. The position of each particle is updated according to its historical positions and the global optimal position, such that each individual particle is at the optimal position in the search space. The specific update equation is given in Equation (19). The algorithm is presented as pseudo code in

Table 1. Pseudo code of particle swarm optimization (PSO) algorithm.

PSO algorithm

1: Define PSO parameters, such as w, c1, c2, N, and intermax. The fitness function is f(•).

2: Install iter = 1 and initialize Xi(iter) and vi(iter), where X ∈ nR, i ∈ 1, 2, …, N.

3: Calculate Ji, best = f(Xi), Xi, best = Xi(iter), [Jbest, min, p] = min{ Ji, best }, and Xbest = Xp(iter).

4: While inter < intermax, inter = inter + 1 and i = 0.

5: While i < N, i = i + 1. Update Xi(iter) according to the following formula: vi(iter) = w × vi(iter − 1) + k1 × rand × (Xi, best − Xi(iter − 1)) + k2 × rand × (Xbest − Xi(iter − 1)); Xi(iter) = Xi(iter − 1) + vi(iter).

6: If f(Xi(iter)) < Ji, best, Xi, best = Xi(iter) and Ji, best = f(Xi(iter)); End.

7: If f(Xi(iter)) < Jbest, Xbest = Xi(iter) and Jbest = f(Xi(iter)); End.

8: End

9: End

.

$$\{\begin{array}{c}{\mathsf{\nu }}_i(iter)=w\times {\mathsf{\nu }}_i(iter-1)+k_1\times r_1\times (X_{i,best}-X_i(iter-1))+k_2\times r_2\times (X_{best}-X_i(iter-1)),\\ X_i(iter)=X_i(iter-1)+{\mathsf{\nu }}_i(iter),\end{array}$$

(19)

where iter represents the number of particle iterations, 1 < iter < inter_max; inter_max represents the maximum number of iterations of the algorithm; i = 1, 2, …, N; N represents the number of particles in each iteration; X_{i, best} represents the historical optimal position value of each particle; X_best represents the global optimal position value of all particles in the 1–iter iterations; ω, k₁, and k₂ are the parameters of the PSO algorithm, being the inertia parameter, the self-optimal learning factor, and the global optimal learning factor, respectively; and r₁ and r₂ are random numbers in the range of [0, 1].

Where J_{i, best} means f(X_{i, best}), the historical optimal position value of each particle represents the fitness function value. J_best means f(X_best), the global optimal position value of all particles from 1 to iter iterations represents the fitness function. Fitness function is Equation (8). p represents index of min{ J_{i, best} } among all particles in some inter.

In this study, the power PSO algorithm was used to optimize the output of the wind-storage hybrid system. The wind-storage grid-connected hybrid optimization objective J was defined as the particle fitness function. The wind-storage grid-connected power values at t and t + 1, $\left[P_G(t),P_G(t+1)\right]$, were defined as indicating the particle position. Note that the dynamic rolling optimization objective function is given by Equation (8). Hence, the optimal grid-connected power at t was calculated. The optimal energy storage operation scheme was obtained through combination with the wind-power future output. In the proposed scheme, α = β = 1; that is, the influence of P_B and the influence of the probable future P_W (i.e., P_predict,W(t + 1) in Figure 4) on P_B were considered. The active wind power prediction was completed using the Markov model of the wind power state transition matrix. The optimization process of the proposed scheme is shown in Figure 4.

4. Numerical Simulation Results and Discussion

4.1. Numerical Simulation Parameters

A wind-storage simulation system was designed on the MATLAB simulation platform (R2016b, Mathworks, Natick, MA, USA), so as to verify the effectiveness of the proposed method. The data used in the simulation were actual wind power data from a several-hundred-MW wind farm in China. The other simulation parameters are listed in

Table 2. Simulation parameters.

Simulation Parameters	Value	PSO Parameters	Value
Sampling time ΔT	1 min	Number of particles N	30
Allowable power fluctuation δ	2.5 MW	Maximum iteration number iter	100
Energy storage rated power Pbe	5 MW	Inertia factor ω	0.5
Energy storage battery capacity Q	2 MWh	Learning factor k1	2
Energy storage initial value SOE	0.5	Learning factor k2	2
Energy storage upper limit SOEU	0.9	Markov state number K	50
Energy storage lower limit SOEL	0.1	Wind power prediction length	1

. The cost function values of optimization objectives (4) to (7) were c₁ = 10, c₂ = 1, c₃ = [α_1, α_2, α_3, α_4, α₅] = [0, 5, 10, 20, 50].

To further compare the influence of the energy storage output capability and the wind power future output on the operation of the energy storage battery, the values of α and β were changed and the effects were compared. The different conditions considered in this study are listed in

Table 3. Method descriptions.

Parameters	Method 1	Method 2	Method 3
Energy storage output level adjustment parameter α	0	1	1
Future wind power output influence parameter β	0	0	1

. Note that α = β = 0 corresponds to the traditional method of wind power fluctuation smoothing with an energy storage battery. Further, the case of α = 1 and β = 0 corresponds to the optimization operation method for an energy storage battery after consideration of the energy storage output capability. Finally, α = β = 1 corresponds to the optimization operation scheme for wind-storage power generation proposed in this paper, with the objective of considering both the energy storage output capability and predicting the influence of the future wind power output.

For K = 50, as in Table 2, and the annual historical wind power data, the wind power one-step state transition matrix could be calculated, as shown in Figure 5.

It is apparent from Figure 5 that the high-probability transition processes are concentrated on the matrix diagonal. This indicates that, unlike photovoltaic power generation for which sudden changes in illumination may occur, the wind power does not suddenly drop to zero. In other words, wind power generation has a greater inertia. The one-step state transition probabilities differ for different states, which reflects the excessive wind power that occurs during the wind power changing process with time.

In the simulation numerical examples described in Section 4.2 and Section 4.3 of this paper, wind power data for two different cases (Cases 1 and 2, March 15 and October 15, respectively) corresponding to a typical day in spring and fall, respectively, were used to verify the energy storage optimization operation strategy. Wind power data obtained with a 1-min sampling time from a wind farm supplying hundreds of MW were used in both numerical examples. The smoothing performance of the energy storage battery with different optimization objectives and under different energy storage capacity and grid power fluctuation requirements (Table 3) were compared.

4.2. Case 1

Based on the actual wind power data of a typical day (March 15) in spring obtained from the wind farm, along with the simulation parameters listed in Table 2, the changes in the grid-connected power of the wind-storage power generation system P_G, the grid-connected active power fluctuations ΔP_G, and the energy storage battery SOE were compared under different optimization objectives, i.e., different (α, β) parameters. The results are shown in Figure 6.

The following results are apparent from Figure 6a,b. (1) In the case of raw wind power without energy storage smoothing, the active wind power fluctuation reached a maximum of 10 MW in 1 min. After incorporating the energy storage system, the wind-storage grid-connected power essentially met the 2.5 MW grid-connected power fluctuation requirement. (2) Comparison of the energy storage smoothing effects under different optimization objectives reveals that the wind-storage grid-connected power satisfied the requirement throughout the day when the proposed method (Method 3) was employed. However, for the other methods, the grid-connection requirements could not be satisfied in some time periods (such as sampling points of 600 to 720). The dead time of Method 2, however, was significantly smaller than that of Method 1. From comparison with Figure 6c, it is apparent that the energy storage battery reached the upper charging limit and entered the “dead zone”; thus, it was unable to continue to smooth the wind power. The results reveal that the proposed optimization process considering the energy storage battery output capability (Method 2) could effectively reduce the probability of the energy storage entering the dead zone. With consideration of the influence of the future wind power output (Method 3), the optimization strategy for the energy storage operation could further reduce the probability of the energy storage entering the dead zone, while also improving the wind power fluctuation smoothing capability of energy storage.

The optimization processes of the different optimization objectives were analyzed during the 667–681 sampling period, as shown in Figure 7.

It is apparent from Figure 7 that, at different sampling points (679 and 680), all three optimization objectives completed the convergence process under PSO. When deciding the grid-connection power at the 679-sampling point, the grid-connected power at the 678-sampling point was approximately 82.5 MW using the three methods and the wind power output at the 679-sampling point was 91 MW; thus, the power fluctuation was approximately 9.5 MW. At this point, the energy storage SOE values for Methods 1 and 2 were close to the upper charging limit. To reduce the impact on the power grid, the energy storage battery was charged to the upper limit. At the 680-sampling point, the upper charging limit was reached. At the 679-sampling point, the grid-connected power fluctuations of the two methods were still approximately 6.5 and 5 MW. With consideration of the energy storage output capability and the influence of the future wind power output (as proposed in this paper), the energy storage SOE still exhibited a strong charging and discharging capability at the 679-sampling point. Thus, the grid-connection power fluctuation requirement of 2.5 MW could be satisfied.

To further explain the advantages of the proposed method, Q ∈ {1, 2, 4 MW} and δ ∈ {1, 1.5, 2.5 MW} were changed. The results obtained using different methods are shown as follows. Figure 8 and Figure 9 present the ΔP_G and energy storage SOE changes. Figure 10 and Figure 11 show the frequency (time) of the energy storage battery SOE at different intervals during a typical day. The horizontal axis number is i. The vertical axis represents the number of energy storage SOE ∈ [i × 0.1, (i + 1) × 0.1). The specific assessment indices were calculated by combining Equations (14)–(19), as detailed in

Table 4. Assessment criteria under different Q.

Energy Storage Battery Capacity	Method	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathbf{max}}$ (MW)	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ (MW)	${\mathit{Q}}_{\mathit{G}}$ (MWh)	${\mathit{Q}}_{\mathit{B}}$ (MWh)	${\mathit{T}}_{\mathit{d}}$ (min)	$\mathit{C}\mathit{a}{\mathit{p}}_{\mathit{E}\mathit{S}\mathit{S}}$
Q1	Method 1	7.844	1.655	1278.75	11.222	45	0.217
	Method 2	8.076	1.642	1278.69	12.120	5	0.173
	Method 3	6.278	1.632	1278.66	12.516	2	0.155
Q2	Method 1	8.235	1.645	1278.35	11.538	33	0.228
	Method 2	5.079	1.631	1278.76	12.569	2	0.142
	Method 3	2.500	1.623	1278.74	12.607	0	0.120
Q3	Method 1	2.500	1.627	1277.62	11.882	0	0.235
	Method 2	2.500	1.623	1278.52	12.343	0	0.107
	Method 3	2.500	1.624	1278.71	12.632	0	0.094

and

Table 5. Assessment criteria under different δ.

Allowable Power Fluctuation	Method	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathbf{max}}$ (MW)	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ (MW)	${\mathit{Q}}_{\mathit{G}}$ (MWh)	${\mathit{Q}}_{\mathit{B}}$ (MWh)	${\mathit{T}}_{\mathit{d}}$ (min)	$\mathit{C}\mathit{a}{\mathit{p}}_{\mathit{E}\mathit{S}\mathit{S}}$
δ1	Method 1	6.891	0.899	1279.05	27.150	44	0.211
	Method 2	7.107	0.876	1278.82	27.867	25	0.180
	Method 3	6.053	0.867	1278.78	27.952	7	0.167
δ2	Method 1	8.015	1.187	1278.94	20.508	21	0.191
	Method 2	7.303	1.176	1278.94	21.144	10	0.164
	Method 3	6.142	1.159	1278.82	21.607	1	0.146
δ3	Method 1	8.235	1.655	1278.35	11.538	33	0.228
	Method 2	5.079	1.631	1278.76	12.569	2	0.142
	Method 3	2.500	1.623	1278.74	12.607	0	0.120

.

From Figure 8 and Figure 10, as well as the comparison results presented in Table 4, the following conclusions could be drawn.

(1) From the wind-storage operation indices presented in Figure 8 and Table 4, it was found that under different energy storage capacities and compared with the other methods, $\Delta P_{G,\max }$ and $\Delta P_{G,mean}$ were reduced significantly when the method proposed in this paper was adopted. Although the output energy $Q_B$ from the charge and discharge of the energy storage battery increased, $T_d$ was greatly reduced. The wind-storage grid-connection reliability was enhanced.

(2) From the $Ca{p}_{ESS}$ index results in Figure 10 and Table 4, it is apparent that the frequency of the energy storage battery SOE entering the overcharge and over-discharge areas was reduced significantly using the proposed the method, while the grid-connection requirements were satisfied. The energy storage battery output level could be maintained effectively.

(3) Comparison of the operation indices in Table 4 reveals that, when Q = 2 MW, the operation assessment index obtained from the proposed method (Method 3) was basically the same as those for Methods 1 and 2 at Q = 4 MW. This indicates that use of the proposed method to smooth wind power fluctuation can appropriately reduce the energy storage capacity, optimize the wind storage input cost, and improve the economic efficiency.

It is apparent from Figure 9 and Figure 11 and Table 5 that the influence of the active power fluctuation of the wind-storage system intensified under the same energy storage capacity, as the power grid had a higher requirement for the wind-storage grid-connected power fluctuation. The total energy output of the energy storage battery increased. Thus, the energy storage capacity must be increased to smooth this influence. Combining the conclusions drawn from Figure 8 and Table 4, it is apparent that the proposed energy storage optimization operation method, which considers the energy storage battery output capability and the influence of future wind power, could more easily and economically satisfy the increasingly strict power-grid requirements for active power at a given energy storage battery capacity.

4.3. Case 2

In order to verify the applicability of the proposed method, actual wind power data from the wind farm on a typical day (October 15) in fall were used for the comparison experiment. The simulation parameters were unchanged. The changes in P_G, ΔP_G, and the energy storage battery SOE are shown in Figure 12.

It is apparent from Figure 12a,b that, in the absence of an energy storage system (raw wind power), the grid-connected wind power fluctuation reached 10 MW. For the energy storage operation scheme based on the traditional method, i.e., α = 0, β = 0, the grid-connected power fluctuation of the wind-storage system was reduced significantly. However, some sampling points showing fluctuations larger than the required grid-connected power fluctuation of 2.5 MW remained. Under the proposed method, the wind-storage grid-connected power satisfied the requirements throughout the day. It is apparent from Figure 12c that, with use of the proposed energy storage operation scheme, the energy storage battery SOE was maintained in the range of 0.25–0.75, indicating a stronger ability for wind power fluctuation smoothing.

Different wind-storage optimization operation schemes were compared for different energy storage capacities and grid-connected power fluctuation requirements. The results are shown in Figure 13, Figure 14, Figure 15 and Figure 16. The specific indices are listed in

Table 6. Assessment criteria under different Q.

Energy Storage Battery Capacity	Method	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathbf{max}}$ (MW)	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ (MW)	${\mathit{Q}}_{\mathit{G}}$ (MWh)	${\mathit{Q}}_{\mathit{B}}$ (MWh)	${\mathit{T}}_{\mathit{d}}$ (min)	$\mathit{C}\mathit{a}{\mathit{p}}_{\mathit{E}\mathit{S}\mathit{S}}$
Q1	Method 1	7.748	1.655	618.47	13.72	56	0.227
	Method 2	3.599	1.638	618.37	14.87	6	0.194
	Method 3	2.500	1.634	618.36	15.09	0	0.172
Q2	Method 1	3.980	1.640	618.15	13.98	21	0.191
	Method 2	2.500	1.640	618.49	14.50	0	0.131
	Method 3	2.500	1.635	618.46	14.67	0	0.113
Q3	Method 1	2.500	1.637	617.97	14.09	0	0.117
	Method 2	2.500	1.639	618.34	14.33	0	0.082
	Method 3	2.500	1.628	618.44	14.75	0	0.070

and

Table 7. Assessment criteria under different δ.

Allowable Power Fluctuation	Method	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathbf{max}}$ (MW)	$\mathsf{\Delta }{\mathit{P}}_{\mathit{G},\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ (MW)	${\mathit{Q}}_{\mathit{G}}$ (MWh)	${\mathit{Q}}_{\mathit{B}}$ (MWh)	${\mathit{T}}_{\mathit{d}}$ (min)	$\mathit{C}\mathit{a}{\mathit{p}}_{\mathit{E}\mathit{S}\mathit{S}}$
δ1	Method 1	6.582	0.890	618.76	31.34	62	0.226
	Method 2	5.682	0.865	618.74	32.73	17	0.197
	Method 3	3.651	0.856	618.70	33.43	1	0.184
δ2	Method 1	3.987	1.164	618.84	24.11	31	0.220
	Method 2	3.469	1.147	618.69	25.18	1	0.173
	Method 3	1.500	1.150	618.57	25.82	0	0.157
δ3	Method 1	3.980	1.640	618.15	13.98	21	0.191
	Method 2	2.500	1.640	618.49	14.50	0	0.131
	Method 3	2.500	1.635	618.46	14.67	0	0.113

. Figure 13 and Figure 14 and Table 6 present the operation results under different energy storage capacities, whereas Figure 15 and Figure 16 and Table 7 give the operation results under different grid-connected active power requirements.

From the operation results for the wind farm during a typical day in fall, as detailed in Figure 13, Figure 14, Figure 15 and Figure 16 and Table 6 and Table 7, the same conclusions can be made regarding use of the proposed method as those obtained from the operation results during a typical day in spring. By considering the energy storage battery output capability, predicting the future wind power output, and operating the wind-storage system by rolling the PSO optimization in real time, the dead time of the energy storage battery could be reduced while the wind-storage grid-connected power was smoothened. The energy storage charge and discharge could be maintained at a high level. Compared with the traditional operation methods for an energy storage battery, the proposed method could reduce the energy storage capacity while satisfying the same smoothing index requirement, and improve the economic efficiency of the wind-storage power generation. In addition, under the same capacity, the proposed method could satisfy stricter grid-connected power fluctuation requirements and reduce the influence of power fluctuation on the power grid.

5. Conclusions

With the rapid development of wind power generation and the increased wind power penetration ratio of power grids worldwide, the influence of wind power fluctuation on power grids has become more serious. In this paper, a real-time rolling optimization control strategy for a wind-storage hybrid system was proposed to improve the smoothing capability of the energy storage system, increase the wind power penetration ratio, and enhance the wind-power utilization rate at a given energy storage capacity, or to reduce the energy storage configuration capacity and optimize the economic efficiency of the wind-storage system while maintaining the same smoothing ability.

For the first time, the influence of the energy storage output capability level and the future wind power output on the current energy storage operation were considered when establishing the optimization objectives. The traditional wind power fluctuation smoothing requirement and the energy storage output reduction objective were combined to form a hybrid optimization objective. The Markov model was then used to effectively predict the wind power. The PSO algorithm was adopted for rolling optimization of the wind-storage grid-connected power in real time, thereby completing the control of energy storage output. The simulation results showed the following: (a) The real-time rolling optimization strategy of the energy storage system output that considered the energy storage output capability increased the wind power fluctuation smoothing ability of the energy storage, reduced the energy storage time for entering the dead zone and the impact of the power fluctuation on the power grid, and reduced the probability of the energy storage battery entering intervals of deep charge and discharge cycles; (b) with consideration of the influence of the future wind power output (determined based on Markov prediction) in the optimization process, the optimization operation performance of the energy storage system was further improved.

In this study, the influence of one-step prediction of the wind power only was considered, and the constraint conditions of the wind-storage system optimization process were fairly simple. Further investigation will be required to develop a multi-step prediction optimization process for a wind-storage system based on predictive model error analysis under complex constraints.