In this paper, I study the operational control strategies and capacity configuration optimization of battery energy storage systems (BESS) coupled with a 100 MW photovoltaic (PV) power station in Gansu, China. The objective is to maximize the joint economic benefits of PV generation and BESS. I first establish a mathematical model for the BESS, including energy dynamics, cost structures, and revenue streams from participating in electricity spot markets (price arbitrage) and frequency regulation auxiliary service markets. Using typical daily data derived from K-means clustering of historical summer data, I compare three operational scenarios: BESS only participating in price arbitrage, only in frequency regulation, and simultaneously in both markets. The results show that simultaneous participation yields the highest daily revenue, increasing by 22.45% over arbitrage-only and 333.74% over regulation-only. Based on this optimal strategy, I conduct sensitivity analyses on rated power and maximum continuous storage duration. Using the NSGA-II algorithm combined with the TOPSIS method, I optimize the BESS capacity configuration to minimize annual operational costs while maximizing daily revenue. The optimal configuration is 30.99 MW rated power and 4.52 h maximum storage duration, resulting in a daily revenue of 236,000 CNY, an initial investment cost of 145.03 million CNY, and a payback period of 4.56 years.
1. Mathematical Model of Battery Energy Storage Systems
1.1 Energy Dynamics Model
The state of charge (SOC) of the battery energy storage system evolves over time based on charging/discharging power and efficiency. Let \(E_t\) be the energy stored at time \(t\) (in MWh), \(P_t\) the power exchange (positive for charging, negative for discharging) in MW, \(\eta\) the round‑trip efficiency (95% in this study), and \(\tau\) the time step (1 hour). The dynamics are:
$$ E_t = E_{t-1} + \eta P_t \tau \quad (\text{discharging, } P_t < 0) $$
$$ E_t = E_{t-1} + \frac{P_t \tau}{\eta} \quad (\text{charging, } P_t > 0) $$
1.2 Cost Model
The total investment cost \(C_{\text{ES}}\) of the BESS is composed of energy capacity cost and power capacity cost:
$$ C_{\text{ES}} = c_w W_{\max} + c_p P_{\max} $$
where \(W_{\max}\) is the maximum energy capacity (MWh), \(P_{\max}\) the rated power (MW), \(c_w\) the unit cost of energy storage (CNY/MWh), and \(c_p\) the unit cost of power conversion equipment (CNY/MW). The annualized investment cost \(C_1\) is:
$$ C_1 = k_w c_w W_{\max} + k_p c_p P_{\max} $$
with \(k_w\) and \(k_p\) as annual depreciation rates for energy storage and power conversion units, respectively. The annual operation and maintenance cost \(C_2\) is proportional to rated power:
$$ C_2 = c_{\text{mf}} P_{\max} $$
where \(c_{\text{mf}}\) is the unit O&M cost per MW per year.
1.3 Investment Payback Period
The payback period \(P_t\) is defined as the time when cumulative net cash flow turns positive:
$$ \sum_{t=1}^{P_t} (CI – CO)_t = 0 $$
where \(CI\) is cash inflow, \(CO\) cash outflow. When \(P_t\) is non‑integer, I calculate using:
$$ P_t = T – 1 + \frac{|(CI-CO)_{T-1}|}{(CI-CO)_T} $$
where \(T\) is the first year with positive cumulative net cash flow.
1.4 Optimization Model for Price Arbitrage and Frequency Regulation
The joint operation framework is shown in the figure above (inserted). The PV station participates in medium‑ and long‑term contracts and spot markets, and can charge the BESS. The BESS can engage in price arbitrage (buy low, sell high) and provide frequency regulation services. The total daily revenue \(F\) comprises two parts: revenue from energy market transactions \(F_1\) and revenue from frequency regulation \(F_2\):
Energy market revenue:
$$ F_1 = P_{\text{zcq},t} C_{\text{zcq},t} + (P_{\text{rq},t} – P_{g,t} – P_{\text{zcq},t}) C_{\text{rq},t} + (P_{\text{pv},t} – P_{\text{rq},t}) C_{r,t} + (-P_{\text{buy},t} + P_{\text{sell},t}) C_{r,t} $$
where \(P_{\text{zcq},t}\) is medium‑long term power, \(C_{\text{zcq},t}\) its price; \(P_{\text{rq},t}\) day‑ahead power, \(C_{\text{rq},t}\) day‑ahead price; \(C_{r,t}\) real‑time price; \(P_{\text{buy},t}\) and \(P_{\text{sell},t}\) are BESS purchase and sale power; \(P_{g,t}\) is PV power absorbed by BESS; \(P_{\text{pv},t}\) is total PV generation.
Frequency regulation revenue:
$$ F_2 = \sum_{i=1}^{n} (D_i \times \rho_i \times K_i) $$
where \(D_i\) is regulation mileage provided in interval \(i\), \(\rho_i\) the mileage clearing price, and \(K_i\) the AGC comprehensive performance index.
Constraints:
- State constraints (cannot buy and sell simultaneously):
$$ \beta_{\text{buy},t} + \beta_{\text{sell},t} = 1, \quad \beta_{\text{buy},t}, \beta_{\text{sell},t} \in \{0,1\} $$
- Power constraints:
$$ 0 \le P_{\text{buy},t} \le \beta_{\text{buy},t} P_{\max}^{\text{ch}}, \quad 0 \le P_{\text{sell},t} \le \beta_{\text{sell},t} P_{\max}^{\text{dis}} $$
- When participating in frequency regulation, additional regulation power variables \(P_{\text{ch},t}\) (down‑regulation) and \(P_{\text{dis},t}\) (up‑regulation) are constrained:
$$ -P_{\max}^{\text{ch}} \le P_{\text{sell},t} + P_{\text{dis},t} – P_{\text{ch},t} – P_{\text{buy},t} – P_{g,t} \le P_{\max}^{\text{dis}} $$
$$ 0 \le P_{\text{ch},t} \le P_{\max}^{\text{ch}}, \quad 0 \le P_{\text{dis},t} \le P_{\max}^{\text{dis}} $$
- Energy constraints: energy must remain within limits and cycle consistency:
$$ E_{\min} \le E_t \le E_{\max}, \quad E_T = E_0 $$
$$ E_t = E_{t-1} – \frac{P_{\text{sell},t} + P_{\text{dis},t}}{\eta_d} \Delta t + (P_{\text{buy},t} + P_{\text{ch},t}) \eta_c \Delta t $$
2. Results and Discussion
2.1 Case Study Setup
The PV station has an installed capacity of 100 MW and is paired with a lithium‑iron‑phosphate BESS. Initially, the BESS has a rated power of 20 MW and energy capacity of 40 MWh. The SOC is allowed between 0.05 and 0.95, starting at 0.4. Charging/discharging efficiency is 95%. I use typical daily curves (PV generation, electricity prices, regulation mileage prices) derived from K‑means clustering of summer data (May–August). The typical day’s data are summarized in Table 1.
| Hour | PV Power (MW) | Spot Price (CNY/MWh) | Regulation Mileage Price (CNY/MW) |
|---|---|---|---|
| 1–6 | 0–10 | 150–200 | 8–12 |
| 7–12 | 40–90 | 300–450 | 15–25 |
| 13–18 | 60–100 | 400–500 | 20–30 |
| 19–24 | 0–20 | 100–250 | 5–10 |
2.2 Operational Strategy Analysis
I simulate three operational strategies using mixed‑integer linear programming. Results are shown in Table 2.
| Scenario | Revenue (CNY/day) |
|---|---|
| Only frequency regulation | 69,768.12 |
| Only price arbitrage | 190,154.74 |
| Both markets | 232,843.70 |
Simultaneous participation increases revenue by 22.45% over arbitrage alone and by 333.74% over regulation alone. The BESS charges during low‑price periods (typically hours 1–10 and 90–96) using cheap grid power and surplus PV, and discharges during peak‑price periods (hours 19–30 and 75–86). When providing frequency regulation, the BESS reserves some capacity for up‑ and down‑regulation, which slightly modifies the arbitrage pattern but yields extra regulation revenue.
2.3 Sensitivity Analysis and Capacity Optimization
I perform sensitivity analysis on rated power (from 10 to 50 MW) and maximum continuous storage duration (from 2 to 8 hours). Figures (not shown) indicate that both daily revenue and initial investment increase with larger power and longer duration, but the relationship is not strictly linear. The optimal configuration must balance these two competing objectives.
I formulate a multi‑objective optimization problem: maximize daily revenue \(R\) and minimize initial investment cost \(C_{\text{inv}}\). Variables are rated power \(P_{\max}\) (MW) and storage duration \(H\) (hours). I use the NSGA‑II algorithm (population size 100, generations 200) to generate a Pareto front. The TOPSIS method selects the best compromise solution. The optimal solution is found at:
$$ P_{\max} = 30.99 \text{ MW}, \quad H = 4.52 \text{ h} $$
with corresponding daily revenue \(R = 236,212\) CNY and initial investment \(C_{\text{inv}} = 145,033,000\) CNY. The cash flow projection (Table 3) shows a payback period of 4.56 years.
| Year | Daily Revenue (CNY) | Daily Cost (CNY) | Annual Net Cash Flow (CNY) | Cumulative Net Cash Flow (CNY) |
|---|---|---|---|---|
| 1 | 236,212 | 428,345 | -70,157,000 | -70,157,000 |
| 2 | 236,212 | 221,415 | 5,409,000 | -64,748,000 |
| 3 | 236,212 | 152,544 | 30,556,000 | -34,192,000 |
| 4 | 236,212 | 118,187 | 43,088,000 | 8,896,000 |
Payback period \(P_t = 4 + \frac{34,192,000}{43,088,000} \approx 4.56\) years.
3. Conclusions
Based on my study of a 100 MW PV station with a lithium‑iron‑phosphate battery energy storage system, I draw the following conclusions:
- Simultaneous participation in price arbitrage and frequency regulation markets significantly improves the daily revenue of the BESS—by 22.45% over arbitrage‑only and 333.74% over regulation‑only.
- Sensitivity analysis shows that both rated power and maximum continuous storage duration have positive effects on revenue but also increase investment cost. The trade‑off can be optimized using a multi‑objective evolutionary algorithm.
- The optimal configuration obtained via NSGA‑II and TOPSIS is 30.99 MW rated power and 4.52 h maximum storage duration, yielding a daily revenue of 236,000 CNY, initial investment of 145.03 million CNY, and a payback period of 4.56 years.
These findings demonstrate that well‑designed battery energy storage systems can effectively enhance the economic viability of grid‑connected photovoltaic plants, especially when leveraging multiple market income streams.