The transition towards a high proportion of renewable energy within power systems presents significant challenges related to the uncertainty and intermittency of sources like photovoltaic (PV) generation. This variability can lead to severe temporal and spatial imbalances in power distribution, ultimately threatening grid stability. As an effective solution, the combined operation of energy storage systems (ESS) with renewable generation is becoming a key trend in the evolution of modern distribution networks. For end-users, particularly in residential communities, deploying integrated PV and energy storage systems prior to construction requires rational planning and optimal configuration to maximize economic benefits and system efficiency. The core of this economic assessment is intimately linked to the service life and degradation characteristics of the energy storage battery.
This work focuses on the optimal configuration of PV-ESS for residential communities. We establish a dynamic loss model for the energy storage battery that accurately accounts for the impacts of both the number of charge-discharge cycles and the depth of discharge (DOD) on battery life. Subsequently, a configuration optimization model is developed with the dual objectives of maximizing the system’s average annual net profit and minimizing the load peak-valley difference. The model is solved using a multi-objective particle swarm optimization algorithm, and the operational strategies and economic performance under different scenarios are compared and analyzed through simulation.
Dynamic Degradation Model for the Energy Storage Battery
The capacity of an energy storage battery gradually decays over its service life due to various factors. To accurately evaluate the long-term benefits and schedule the replacement of the energy storage battery, a refined life loss model is essential. While factors like operating temperature and charge/discharge rates play a role, this study focuses primarily on the two most critical operational parameters: the depth of discharge (DOD) and the cumulative number of charge-discharge cycles.
Battery State of Health (SOH) Model
The State of Health (SOH) is defined based on the available capacity of the energy storage battery relative to its initial rated capacity. Typically, an energy storage battery is considered to have reached its end of service for primary application when its SOH degrades to 80%.
$$S_{off} = S_R \times 80\%$$
$$SOH = \frac{S_{Now}}{S_R} \times 100\%$$
where \(S_{off}\) is the available capacity at end-of-life, \(S_R\) is the initial rated capacity, \(S_{Now}\) is the current available capacity, and \(SOH\) is the State of Health. The relationship between SOH and the degree of life loss \(\Gamma_{loss}\) (where 0 represents new and 1 represents SOH=80%) can be derived from experimental data. A fitted function is obtained as follows:
$$SOH(t) = f(\Gamma_{loss}) = k_1 e^{k_2 \Gamma_{loss}} + k_3 e^{k_4 \Gamma_{loss}}$$
where \(k_1\), \(k_2\), \(k_3\), and \(k_4\) are fitting coefficients. To simplify the model and accelerate computation, this nonlinear relationship is piecewise linearized. The Self-Optimal Piecewise Linearization (SO-PWL) method is applied to obtain segments that closely approximate the original curve.
$$SOH(t) – SOH(t-1) = \partial_j \cdot \Gamma_{loss}(t)$$
For the \(j\)-th segment, the linear relationship can be expressed as:
$$SOH(t) = a_j \Gamma_{loss}(t) + b_j$$
where \(\partial_j\) is the capacity decay coefficient, and \(a_j\), \(b_j\) are the coefficients for the \(j\)-th linear segment.
Battery Life Decay Model
The cycle life of an energy storage battery is highly dependent on the Depth of Discharge (DOD). The relationship between the remaining cycle life \(N_{life}\) and DOD can be characterized by an exponential function derived from manufacturer data.
$$N_{life}(DOD) = \begin{cases}
\alpha_0 e^{\alpha_1 DOD(t)} + \alpha_2 e^{\alpha_3 DOD(t)} & DOD > 0 \\
+\infty & DOD = 0
\end{cases}$$
where \(\alpha_0\) to \(\alpha_3\) are fitting parameters for the energy storage battery life equation. The incremental life loss \(\Gamma_{loss}(t)\) at time \(t\) is related to the change in the battery’s State of Charge (SOC). The SOC is defined as \(SOC(t) = 1 – DOD(t)\). The mapping function \(f[SOC(t)]\) is defined based on the reciprocal of the cycle life.
$$\Gamma_{loss}(t) = f[SOC(t)] – f[SOC(t-1)]$$
$$f[SOC(t)] = \frac{1}{2}\left[ \frac{1}{N_{life}(1)} + \frac{1}{N_{life}(1-SOC(t))} \right]$$
Applying the SO-PWL method to \(f[SOC(t)]\) allows for an efficient and accurate linear calculation of \(\Gamma_{loss}(t)\) based on the operating SOC, which is crucial for integrating battery degradation into the optimization model.
PV-ESS Optimal Configuration Model
Objective Functions
The optimization aims to achieve two primary goals: maximizing economic return and improving grid friendliness by peak shaving.
1. Maximize Average Annual Net Profit (\(f_1(x)\)):
The net profit considers revenues from energy arbitrage and PV surplus sales, minus the total costs including initial investment, operation & maintenance (O&M), plus the residual value from battery recycling.
$$F = \min\{ -f_1(x), f_2(x) \}$$
$$f_1(x) = \frac{C_E + C_{re} – f_{in} – f_{mt}}{N}$$
where \(C_E\) is the total electricity sales revenue over the energy storage battery lifespan, \(C_{re}\) is the recycling revenue, \(f_{in}\) is the initial investment cost, \(f_{mt}\) is the total O&M cost, and \(N\) is the service life in years.
- Initial Investment Cost: \(f_{in} = f_p + f_E + f_{PV} = k_p P_R + k_s S_R + k_{PV} S_{PV}\)
- O&M Cost: \(f_{mt} = \sum_{t=1}^{N} (k_{m.ESS}^t P_R + k_{m.PV}^t S_{PV})\)
- Electricity Sales Revenue:
– From ESS arbitrage: \(C_{E1} = N \cdot \sum_{t=1}^{24} 365 \cdot \lambda(t) \cdot [B_{dis}(t)P_{dis}(t)\Delta t_{dis} – B_{ch}^{grid}(t)P_{ch}^{grid}(t)\Delta t_{ch}]\)
– From PV surplus: \(C_{E2} = N \cdot \sum_{t=1}^{24} 365 \cdot \lambda(t) \cdot [P_{PV}(t) – P_{ch}(t)] \Delta t\) - Recycling Revenue: \(C_{re} = \gamma \cdot f_E\) where \(\gamma\) is the recycling coefficient.
2. Minimize Load Peak-Valley Difference (\(f_2(x)\)):
This objective aims to flatten the load profile by using the ESS to shift energy from off-peak to peak periods.
$$f_2(x) = \max[P_{load}(t) – P_{dis}(t)] – \min[P_{load}(t) + P_{ch}^{grid}(t)]$$
Constraints
The optimization is subject to the following operational and physical constraints:
1. Power Balance:
\(P_{dis}(t) – P_{ch}^{grid}(t) + P_{grid}(t) = P_{load}(t)\)
2. ESS Service Life:
\(0 \leq N \leq N_{max}\)
3. ESS Charge/Discharge Power Limits:
\(0 \leq P_{ch}(t) \leq P_R B_{ch}(t); \quad 0 \leq P_{dis}(t) \leq P_R B_{dis}(t)\)
4. State of Charge (SOC) Dynamics and Limits:
\(SOC(t) = SOC(t-1) + \frac{\mu_{ch}B_{ch}(t)P_{ch}(t)\Delta t_{ch} – \frac{B_{dis}(t)P_{dis}(t)\Delta t_{dis}}{\mu_{dis}}}{S_R}\)
\(SOC_{min} \leq SOC(t) \leq SOC_{max}; \quad SOC(0) = SOC(n)\)
5. PV Installation Capacity Limit:
\(0 \leq S_{PV} \leq S_{PV}^{max}\)
6. ESS Mode Exclusion (no simultaneous charge/discharge):
\(0 \leq B_{ch}(t) + B_{dis}(t) \leq 1\)
Solution Methodology
The configuration variables include the ESS rated capacity \(S_R\), rated power \(P_R\), and the PV installed capacity \(S_{PV}\). The problem involves multiple constraints and two conflicting objectives, making it a multi-objective optimization challenge. The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is employed for its efficiency in parallel search, simplicity, and rapid convergence. The algorithm iteratively updates particle positions (potential solutions) based on individual and global best positions, ultimately generating a Pareto front of non-dominated optimal solutions from which a final configuration can be selected.
Case Study and Analysis
Basic Data and Parameter Settings
To ensure representativeness, comprehensive typical daily data is synthesized. PV output profiles for different seasons and weather conditions (sunny/cloudy) are weighted using the Analytic Hierarchy Process (AHP). Similarly, residential load profiles for summer and non-summer seasons on both weekdays and weekends are weighted using the Entropy Weight Method to create a composite typical daily load curve. Key parameters for the Lithium Iron Phosphate (LFP) energy storage battery and system costs are listed in the table below.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Unit Power Cost, \(k_p\) (\$/kW) | 1,351 | Chg./Disch. Efficiency, \(\mu_{ch}\), \(\mu_{dis}\) | 0.9 |
| Unit PV Cost, \(k_{PV}\) (\$/kW) | 4,000 | Recycling Coefficient, \(\gamma\) | 0.09 |
| Unit Capacity Cost, \(k_s\) (\$/kWh) | 1,500 | Max Service Life, \(N_{max}\) (years) | 25 |
| Min SOC, \(SOC_{min}\) | 30% | Life Model Coefficient, \(\alpha_0\) | 5,496 |
| Max SOC, \(SOC_{max}\) | 90% | Life Model Coefficient, \(\alpha_1\) | -3.747 |
The time-of-use electricity prices are also defined for peak, flat, and off-peak periods.
Scenario Definition
Three operational scenarios are defined to analyze the impact of the battery degradation model and grid interaction:
- Scenario 1: Basic configuration. ESS charges only from PV and discharges to meet peak loads. Battery degradation is not considered in scheduling.
- Scenario 2: Advanced configuration. The dynamic energy storage battery degradation model is integrated into the optimization. ESS operation is still limited to PV charging.
- Scenario 3: Grid-connected configuration. The dynamic degradation model is used, and the ESS is allowed to perform “arbitrage” by purchasing cheap grid electricity during off-peak hours to discharge during peak hours, in addition to using PV.
Configuration Results and Analysis
The optimization results for the three scenarios are summarized below:
| Configuration Result | Scenario 1 | Scenario 2 | Scenario 3 |
|---|---|---|---|
| Avg. Annual Net Profit (\$10k) | 82.58 | 118.20 | 126.31 |
| ESS Rated Capacity (kWh) | 1,443.00 | 1,209.00 | 1,118.16 |
| ESS Rated Power (kW) | 129.27 | 178.48 | 165.17 |
| PV Installed Capacity (kW) | 212.40 | 246.32 | 260.27 |
| System Configuration Cost (\$10k) | 318.9 | 304.0 | 295.2 |
| PV Annual Sales Revenue (\$10k) | 1.83 | 1.80 | 9.80 |
| Max. Projected Service Life (years) | 24.60 | 14.40 | 13.92 |
| Optimal Peak-Valley Difference (kW) | 285.88 | 263.44 | 177.02 |
| Reduction in Peak-Valley Difference | 33.2% | 38.4% | 58.6% |
Key Findings:
- Comparing Scenario 1 and 2 demonstrates the value of the dynamic energy storage battery degradation model. Although it projects a shorter, more realistic service life, it guides a more cost-effective configuration (lower capacity, higher power) that significantly increases net annual profit and enhances peak-shaving capability.
- Comparing Scenario 2 and 3 reveals the benefits of grid interaction. Allowing the ESS to perform energy arbitrage (Scenario 3) further boosts economic returns and dramatically improves load flattening, reducing the peak-valley difference by 58.6%. The increased revenue from selling more PV surplus to the grid is a major contributor. The trade-off is a slightly shorter projected battery life due to more intensive use.
- The configuration results suggest that if the primary goal is to maximize the consumption of locally generated PV power, Scenario 2 is preferable. However, if maximizing economic return and providing significant grid support through peak shaving are the priorities, then the grid-connected configuration of Scenario 3 is optimal.
Conclusion
This study presents a comprehensive framework for the optimal configuration of PV and energy storage battery systems in residential communities. The core contribution is the development and integration of a dynamic energy storage battery life loss model that accurately reflects degradation based on operational cycling and depth of discharge. This model enables a more precise prediction of the energy storage battery‘s service life and a more realistic economic assessment.
The multi-objective optimization, considering both economics and load profile smoothing, provides a balanced solution for planning. Case study results demonstrate that while incorporating the battery degradation model leads to a more conservative life estimate, it results in a more profitable and effective system design. Furthermore, operating the residential ESS in a grid-connected mode that allows for energy arbitrage offers the best combination of high economic returns and superior peak-shaving performance, making it the recommended strategy when regulations permit. This model provides a valuable and practical reference for the planning and investment decision-making of distributed PV-ESS in residential areas.