The integration of large-scale wind power into the electrical grid presents significant challenges due to its inherent intermittency and stochastic nature. These fluctuations can jeopardize grid stability, frequency regulation, and power quality, complicating the task for system operators. To mitigate these adverse effects and enhance the controllability of wind farm output, energy storage systems have emerged as a crucial enabling technology. Among various storage technologies, the cell energy storage system, particularly battery-based solutions, offers fast response, precise power control, and modular scalability, making it highly suitable for smoothing wind power and ensuring dispatchability.
This article delves into a sophisticated multi-objective optimal control strategy for a cell energy storage system co-located with a wind farm. The primary goals are twofold: first, to enable the combined wind-storage plant to accurately follow a pre-determined generation schedule issued by the grid operator, and second, to actively smooth the short-term power fluctuations of the wind farm itself. Crucially, this strategy also explicitly considers the operational health and longevity of the battery storage by optimizing its state of charge (SOC) and minimizing unnecessary cycling.
Analysis of the Combined Wind-Storage Power Plant
The topology of a typical co-located wind and cell energy storage system involves connecting both assets to a common point of interconnection, often the medium-voltage bus of the wind farm’s collector substation. The fundamental power balance at the grid connection point is given by:
$$P_{\text{grid}}(t) = P_{\text{wind}}(t) + P_{\text{bess}}(t)$$
where \(P_{\text{grid}}(t)\) is the total power delivered to the grid, \(P_{\text{wind}}(t)\) is the instantaneous power generated by the wind turbines, and \(P_{\text{bess}}(t)\) is the output power of the cell energy storage system (discharging is positive, charging is negative). The core function of the cell energy storage system is to provide a compensating power \(P_{\text{bess}}(t)\) that bridges the gap between the highly variable wind power and the desired, stable grid output.
The desired grid output \(P_{\text{grid, target}}(t)\) is shaped by two main requirements:
1. Schedule Tracking: To follow a day-ahead or intra-day generation plan \(P_{\text{plan}}(t)\) within a permitted tolerance band \(\varepsilon_1\).
2. Fluctuation Smoothing: To limit the rate of change of power, ensuring that variations over specific time windows (e.g., 1-minute and 10-minute) comply with grid codes.
Therefore, the required compensation from the cell energy storage system can be conceptually decomposed as:
$$P_{\text{bess}}(t) = P_{\text{bess, plan}}(t) + P_{\text{bess, smooth}}(t)$$
$$P_{\text{bess, plan}}(t) = P_{\text{plan}}(t) – P_{\text{wind}}(t) \quad \text{(within power and energy constraints)}$$
$$P_{\text{bess, smooth}}(t) = f(P_{\text{wind}}(t), P_{\text{grid, target}}(t))$$
The operation of the battery is governed by its state of charge dynamics:
$$SOC(t+\Delta t) = (1 – \rho) \cdot SOC(t) – \frac{\int_{t}^{t+\Delta t} P_{\text{batt}}(\tau) d\tau}{C_{\text{rate}}}$$
where \(SOC(t)\) is the state of charge at time \(t\), \(\rho\) is the self-discharge rate, \(C_{\text{rate}}\) is the rated energy capacity, and \(P_{\text{batt}}\) is the actual power at the battery terminals, related to \(P_{\text{bess}}\) by the power conversion system (PCS) efficiency:
$$P_{\text{batt}}(t) = \begin{cases}
F_{\text{char}} \cdot \eta_{\text{char}} \cdot P_{\text{bess}}(t), & P_{\text{bess}}(t) < 0 \text{ (charging)} \\
F_{\text{dis}} \cdot \frac{P_{\text{bess}}(t)}{\eta_{\text{dis}}}, & P_{\text{bess}}(t) > 0 \text{ (discharging)}
\end{cases}$$
Here, \(F_{\text{char}}\) and \(F_{\text{dis}}\) are charging/discharging flags (0 or 1), and \(\eta_{\text{char}}, \eta_{\text{dis}}\) are the charging and discharging efficiencies, respectively.
Establishing a Comprehensive Evaluation Index System
To quantitatively assess the performance of the wind-cell energy storage system, a set of evaluation metrics is established, covering schedule adherence, power quality, and battery health.
| Category | Metric | Formula / Description |
|---|---|---|
| Schedule Tracking | Instantaneous Accuracy \(\gamma_{\text{plan}}(t)\) | \(\gamma_{\text{plan}}(t) = 1 – \frac{|P_{\text{grid}}(t) – P_{\text{plan}}(t)|}{P_c(t)}\) where \(P_c\) is available capacity. |
| Average Tracking Accuracy \(\varphi_{\text{plan}}\) | \(\varphi_{\text{plan}} = 1 – \frac{1}{N}\sum_{t=1}^{N} (1 – \gamma_{\text{plan}}(t))^2\) | |
| Schedule Qualification Rate \(B_{\text{plan}}\) | \(B_{\text{plan}} = \frac{1}{N}\sum_{t=1}^{N} F(\gamma_{\text{plan}}(t) \ge 1-\varepsilon_1)\) where \(F\) is an indicator function. | |
| Power Fluctuation | Short-term Fluctuation Rate \(\gamma_{\text{flu}}(t)\) | \(\gamma_{\text{flu}}(t) = \frac{\max_{k \in [t-T, t]} P_{\text{grid}}(k) – \min_{k \in [t-T, t]} P_{\text{grid}}(k)}{S_c}\) \(T\) is time window (e.g., 10 min), \(S_c\) is installed capacity. |
| Average Smoothness \(\varphi_{\text{flu}}\) | \(\varphi_{\text{flu}} = \frac{1}{N}\sum_{t=1}^{N} \gamma_{\text{flu}}(t)\) | |
| Fluctuation Qualification Rate \(B_{\text{flu}}\) | \(B_{\text{flu}} = \frac{1}{N}\sum_{t=1}^{N} F(\varepsilon_2 – \gamma_{\text{flu}}(t) \ge 0)\) where \(\varepsilon_2\) is the grid code limit. | |
| Battery Health & Usage | Cumulative Charge/Discharge Energy | \(E_{\text{char}} = \sum |P_{\text{batt},t} \cdot T \cdot F(-P_{\text{batt},t})|\), \(E_{\text{dis}} = \sum |P_{\text{batt},t} \cdot T \cdot F(P_{\text{batt},t})|\) |
| Total Energy Throughput \(E_{\text{sum}}\) | \(E_{\text{sum}} = E_{\text{char}} + E_{\text{dis}}\). Related to battery aging. |
Multi-Objective Optimal Control Model Formulation
Based on the evaluation metrics, a multi-objective optimization model is constructed to determine the optimal power setpoint for the cell energy storage system at each control interval. The model aims to minimize a vector of conflicting objectives.
The primary objective is to track the generation schedule. A penalty function \(f_1\) is defined that increases when the instantaneous accuracy falls below the tolerance:
$$f_1(t) = \begin{cases}
0, & 1 – \gamma_{\text{plan}}(t) \le \varepsilon_1 \\
a_1\left(1 – e^{\frac{(\varepsilon_1 – (1-\gamma_{\text{plan}}(t)))^2}{b_1^2}}\right) + (1 – a_1), & 1 – \gamma_{\text{plan}}(t) > \varepsilon_1
\end{cases}$$
The second objective is to suppress power fluctuations. A similar penalty function \(f_2\) activates when the fluctuation rate exceeds the limit \(\varepsilon_2\):
$$f_2(t) = \begin{cases}
0, & \gamma_{\text{flu}}(t) \le \varepsilon_2 \\
a_2\left(1 – e^{\frac{(\varepsilon_2 – \gamma_{\text{flu}}(t))^2}{b_2^2}}\right), & \gamma_{\text{flu}}(t) > \varepsilon_2
\end{cases}$$
The third objective focuses on minimizing the depth and frequency of battery cycles within a single control step to reduce wear:
$$f_3(t) = \frac{\int_{t}^{t+T} |P_{\text{batt}}(\tau)| d\tau}{C_{\text{rate}}}$$
The fourth objective is to manage the State of Charge (SOC) of the cell energy storage system optimally. This involves keeping the SOC within a preferred range to avoid deep discharges or overcharges, thereby extending battery life. The SOC range is divided into zones (e.g., Over-discharge, Discharge Warning, Preferred Charge, Preferred Discharge, Charge Warning, Over-charge). The objective \(f_4\) is a piecewise function that assigns higher costs when operating in non-preferred zones. For example, during a charging command (\(P_{\text{bess}}<0\)):
$$f_{4,\text{char}}(SOC) = \begin{cases}
1, & SOC < SOC_{\text{min}} \\
\frac{SOC – SOC_a}{SOC_{\text{min}} – SOC_a}, & SOC_{\text{min}} \le SOC < SOC_a \\
0, & SOC_a \le SOC \le SOC_b \\
1 – \left[1 – \left(\frac{SOC – SOC_b}{SOC_{\text{max}} – SOC_b}\right)\right]^2, & SOC_b < SOC \le SOC_{\text{max}} \\
1, & SOC > SOC_{\text{max}}
\end{cases}$$
A symmetric function \(f_{4,\text{dis}}\) is defined for discharging commands. The overall fourth objective is \(f_4 = f_{4,\text{char}}\) or \(f_{4,\text{dis}}\) based on the power command direction.
The complete multi-objective optimization problem for the cell energy storage system is then:
$$\min \mathbf{F} = [f_1, f_2, f_3, f_4]^T$$
Subject to:
$$P_{\text{batt}} \le \min\left(P_{\text{dis}}^{\text{max}}, \frac{[(1-\rho)SOC – SOC_{\text{min}}]C_{\text{rate}}}{T}\right)$$
$$-P_{\text{batt}} \le \min\left(P_{\text{char}}^{\text{max}}, \frac{[SOC_{\text{max}} – (1-\rho)SOC]C_{\text{rate}}}{T}\right)$$
$$SOC_{\text{min}} \le SOC \le SOC_{\text{max}}$$
Solution and Decision-Making: NSGA-II and Fuzzy Comprehensive Evaluation
The formulated problem is a complex, non-linear, multi-objective optimization. To solve it in real-time, a two-stage approach is employed.
Stage 1: Generating the Pareto Front using NSGA-II. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is applied to find a set of non-inferior (Pareto-optimal) solutions. Each solution represents a possible power setpoint for the cell energy storage system with a unique trade-off among the four objectives. The algorithm works with a population of candidate solutions, applies genetic operators (selection, crossover, mutation), and uses non-dominated sorting and crowding distance to evolve the population toward the true Pareto front over multiple generations.
Stage 2: Selecting the Best Compromise Solution using Fuzzy Comprehensive Evaluation. Since the Pareto front contains many equally optimal solutions from a multi-objective standpoint, a decision-making method is needed to select the single best command for the cell energy storage system. A fuzzy comprehensive evaluation (FCE) method is used for this purpose.
- Define Evaluation Factors and Judgment Set: The four objective functions \((f_1, f_2, f_3, f_4)\) form the factor set \(U\). A judgment set \(V\) is defined with linguistic terms, e.g., \(V = \{\text{Poor (P)}, \text{Below Average (BA)}, \text{Average (A)}, \text{Good (G)}, \text{Excellent (E)}\}\).
- Determine Weight Vector: The relative importance of each objective is captured by a weight vector \(\mathbf{w} = [w_1, w_2, w_3, w_4]\), often determined via methods like the Analytic Hierarchy Process (AHP). For instance, schedule tracking might be assigned the highest weight.
- Establish Membership Matrix R: For each solution on the Pareto front, the value of each objective \(f_i\) is mapped to a degree of membership (between 0 and 1) for each grade in \(V\) using predefined membership functions (e.g., trapezoidal or Gaussian functions). This forms a matrix \(\mathbf{R}\) for each solution.
- Perform Fuzzy Synthesis: The comprehensive evaluation vector \(\mathbf{B}\) for a solution is calculated using a weighted aggregation operator: \(\mathbf{B} = \mathbf{w} \circ \mathbf{R}\). The element \(b_j\) in \(\mathbf{B}\) indicates the degree to which the solution belongs to the \(j\)-th grade in \(V\).
- Make Final Decision: A score vector \(\mathbf{S}\) is assigned to the judgment grades (e.g., S=[30, 55, 75, 90, 100] for P, BA, A, G, E). The final score \(G\) for a solution is \(G = \mathbf{B} \cdot \mathbf{S}^T\). The solution (i.e., the power command for the cell energy storage system) with the highest score \(G\) is selected as the optimal compromise and dispatched to the battery controllers.
Case Study and Performance Analysis
A simulation was conducted using 24-hour measured data from a 50 MW wind farm paired with a 10 MW / 20 MWh cell energy storage system. The control time step was 5 minutes. Three scenarios were compared:
- Scenario 1: Wind farm alone (No BESS).
- Scenario 2: BESS with a rule-based strategy focused primarily on schedule tracking and simple SOC management.
- Scenario 3: The proposed multi-objective optimal control strategy.
Key control and optimization parameters used in the simulation are summarized below:
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| \(P_{\text{char}}^{\text{max}}, P_{\text{dis}}^{\text{max}}\) | 10 MW | \(\eta_{\text{char}}, \eta_{\text{dis}}\) | 0.9 |
| \(SOC_0\) | 0.5 | \(SOC_{\text{min}}, SOC_{\text{max}}\) | 0.2, 0.9 |
| \(SOC_a, SOC_b, SOC_c\) | 0.4, 0.55, 0.7 | Schedule Tolerance \(\varepsilon_1\) | 0.1 (10%) |
| Fluctuation Limit \(\varepsilon_2\) | 0.15 (15% of capacity) | Weight Vector \(\mathbf{w}\) | [0.468, 0.281, 0.068, 0.183] |
The performance results for the three scenarios are quantitatively compared in the following table:
| Performance Metric | Scenario 1 (No BESS) | Scenario 2 (Rule-based BESS) | Scenario 3 (Proposed Strategy) |
|---|---|---|---|
| Schedule Tracking | |||
| Average Accuracy \(\varphi_{\text{plan}}\) | 91.38% | 93.73% | 92.71% |
| Qualification Rate \(B_{\text{plan}}\) | 70.83% | 96.53% | 100% |
| Power Fluctuation | |||
| Qualification Rate \(B_{\text{flu}}\) | 99.31% | 100% | 100% |
| Average Smoothness \(\varphi_{\text{flu}}\) | 0.044 | 0.028 | 0.033 |
| Battery Usage & Health | |||
| Total Charge Energy \(E_{\text{char}}\) | N/A | 16.092 MWh | 11.978 MWh |
| Total Discharge Energy \(E_{\text{dis}}\) | N/A | 8.022 MWh | 3.812 MWh |
| SOC Operating Range | N/A | 0.30 – 0.81 | 0.41 – 0.70 |
| Number of Charge/Discharge Cycles | N/A | 67 | 61 |
Analysis of Results:
- Schedule Tracking: The proposed strategy (Scenario 3) achieved a 100% qualification rate, meaning the combined output met the schedule tolerance at every single time step. While its average accuracy was slightly lower than Scenario 2, it avoided “over-compensation” and strategically used the cell energy storage system‘s energy budget to ensure compliance precisely when needed.
- Power Fluctuation: Both BESS scenarios successfully brought the fluctuation qualification rate to 100%. Scenario 2 resulted in a slightly smoother output on average, but this came at the cost of significantly higher battery usage.
- Battery Health & Longevity: This is where the proposed multi-objective strategy shows clear superiority. By explicitly including battery cycle stress (\(f_3\)) and SOC management (\(f_4\)) in the optimization, Scenario 3 reduced the total charge and discharge energy by approximately 25.6% and 52.5%, respectively, compared to Scenario 2. The SOC was maintained in a narrower, healthier band (0.41-0.70 vs. 0.30-0.81), reducing the depth of discharge (DoD) and associated degradation. The number of significant charge/discharge cycles was also reduced. These factors collectively contribute to a substantial extension of the operational lifespan of the cell energy storage system.
Conclusion
Integrating a cell energy storage system with a wind farm is a highly effective solution to the challenges of grid integration. This article has presented a comprehensive multi-objective optimal control framework that moves beyond simple, single-purpose control strategies. By simultaneously optimizing for generation schedule tracking, power fluctuation smoothing, battery cycle minimization, and optimal state-of-charge management, the proposed strategy delivers a balanced and technically superior performance.
The core of the method lies in formulating the real-time control of the cell energy storage system as a multi-objective problem, solving it efficiently using the NSGA-II algorithm to obtain a Pareto-optimal set of actions, and then employing a fuzzy comprehensive evaluation to select the best compromise command based on predefined operational priorities. Simulation results based on real-world data confirm that this approach not only guarantees excellent grid compliance (100% schedule qualification and fluctuation qualification) but also does so in a manner that significantly reduces the operational stress on the battery. By minimizing cumulative energy throughput and maintaining the SOC within a preferred range, the strategy effectively decelerates the aging process of the cell energy storage system, thereby improving the long-term economic viability of the wind-storage hybrid asset. This holistic approach to control is essential for maximizing the value and sustainability of storage assets in renewable energy integration.