In the face of global fossil energy depletion and escalating environmental pollution, the construction of photovoltaic-energy storage microgrids in highway service areas presents a promising solution. This approach not only facilitates green and low-carbon electricity consumption but also enables independent power supply in remote regions, enhancing the self-coordination capability of service area energy systems. In this study, I focus on addressing the critical issues in microgrid development for highway systems, which traditionally revolve around site selection, capacity determination, and investment decisions for roadside photovoltaic projects. However, existing research rarely treats service areas as independent microgrid entities. Therefore, I establish a typical architecture for highway service area microgrid systems and propose an optimization model for solar panel dust cleaning maintenance. Based on this, I develop a capacity planning model for photovoltaic-energy storage microgrids under solar panel dust cleaning regimes. Utilizing the Non-dominated Sorting Genetic Algorithm II (NSGA-II), I solve a multi-objective optimization problem aimed at minimizing total system investment and operational costs while maximizing microgrid energy autonomy. By computing the Pareto optimal solution boundary, I derive optimal capacities for photovoltaics, energy storage, and grid connection lines under varying levels of energy self-sufficiency for highway service areas.
The microgrid system for highway service areas, as conceptualized in this research, comprises distributed photovoltaic generation, energy storage, and loads—primarily electric vehicle charging loads and residential electricity consumption. Given the variability in supply-demand balance under different meteorological scenarios, it remains essential to connect to the main grid as a backup and operational safeguard. The core components are modeled mathematically to facilitate optimization. The photovoltaic array model leverages the photovoltaic effect of solar panel components to convert solar energy into electrical power. The output depends on solar radiation intensity, ambient temperature, and standard test conditions. The fundamental equation is expressed as:
$$P_{pv}(t) = P_{stc} \frac{I_{r,t}}{I_{stc}} [1 + a_T (T_t – T_{stc})]$$
Here, \(P_{stc}\) represents the output under standard test conditions, \(I_{r,t}\) is the actual solar radiation intensity at time \(t\), \(I_{stc} = 1 \, \text{kW/m}^2\) is the standard radiation intensity, \(a_T\) is the power temperature coefficient of the solar panel, \(T_t\) is the temperature of the solar panel at time \(t\), and \(T_{stc} = 25 \, ^\circ\text{C}\). When neglecting other influencing factors, the photovoltaic output can be simplified to:
$$P_{pv}(t) = P_{stc} \frac{I_t}{I_{stc}}$$
where \(I_t\) denotes the maximum solar radiation intensity reaching the ground without external influences. The shading coefficient \(\eta_t\), which accounts for power loss due to factors like dust accumulation on solar panels, is calculated as:
$$\eta_t = \frac{P_{pv} – P’_{pv}}{P_{pv}}$$
with \(P’_{pv}\) being the actual output under external influences such as dust on solar panels.
For energy storage, I employ battery banks as the storage system, with electrochemical storage serving to rapidly store and release energy to track load variations. The multi-period energy coupling model for storage is given by:
$$E_{bess}(t) = (1 – s) E_{bess}(t-1) + \left( \eta_{ch} P^{ch}_{bess}(t) – \frac{P^{dis}_{bess}(t)}{\eta_{dis}} \right) \cdot \Delta t$$
In this equation, \(E_{bess}(t)\) is the stored energy in the storage system at time \(t\), \(s\) is the self-discharge rate of the battery unit, \(\eta_{ch}\) and \(\eta_{dis}\) are the charging and discharging efficiencies respectively, \(P^{ch}_{bess}(t)\) and \(P^{dis}_{bess}(t)\) represent the charging and discharging powers at time \(t\), and \(\Delta t\) is the time step. The state of charge (SOC), a key parameter indicating remaining battery capacity, is defined as:
$$\text{SOC}(t) = \frac{E_{bess}(t)}{E_{rate}}$$
where \(E_{rate}\) is the rated capacity of the battery energy storage system.
A critical aspect of highway microgrid construction is the optimization of solar panel dust cleaning maintenance. In remote highway areas, dust generated from construction and vehicle operation on roadbeds, pavements, and slopes readily accumulates on solar panels, impairing their performance and increasing cleaning costs. Thus, determining an appropriate cleaning cycle for solar panels is vital. I formulate a time-varying prediction model for photovoltaic power loss rate relative to dust accumulation time:
$$\eta(\theta) = \eta^* \times (1 – e^{-\theta / \theta_c})$$
Here, \(\eta^*\) is the asymptotic value of power loss rate under dust accumulation, \(\eta(\theta)\) is the power loss rate at dust accumulation time \(\theta\) (in days), and \(\theta_c\) is the time constant. The daily cost of electricity loss due to dust on solar panels is:
$$e_d = P_{pv} \times \eta(\theta) \times T_d \times l_g$$
where \(P_{pv}\) is the installed capacity of the photovoltaic plant, \(T_d\) is the daily average utilization hours of the plant, and \(l_g\) is the grid feed-in tariff for photovoltaic power. The single cleaning maintenance cost for the photovoltaic plant is:
$$e_c = P_{pv} \times S \times l_c$$
with \(S\) being the area per unit capacity of solar panels and \(l_c\) the cleaning cost per unit area of solar panels. The total minimum cost combining electricity loss from dust and cleaning maintenance is:
$$\min C_{MVP} = \left( \int_0^{t_c} e_d \, d\theta + e_c \right) \cdot \frac{t_{all}}{t_c}$$
where \(t_c\) is the cleaning cycle, \(t_{all}\) is the statistical period (typically one year), and the integral represents total electricity loss cost over one cleaning cycle. Integrating these equations provides cleaning cycles and maintenance costs for solar panels as inputs to the planning model.
For capacity planning of the highway service area microgrid, I consider investment and operational costs for photovoltaics, energy storage, and grid connection lines. The objective function aims to minimize total costs including grid electricity purchase, maximize revenue from grid electricity sales, minimize load shedding penalty costs, and minimize total system investment and operational costs. Simultaneously, I maximize the energy autonomy of the microgrid, defined as the proportion of electricity self-consumed. Thus, the overall objective functions are:
$$\min f = C_{In} + C_{Ma} + C_{grid} – C_{ongrid} + C_{ab}$$
$$\max \eta_{ser} = \frac{\int_0^{8760} [P_{load}(t) – P_{grid}(t)] \, dt}{\int_0^{8760} P_{load}(t) \, dt}$$
In these expressions, \(C_{In}\), \(C_{Ma}\), \(C_{grid}\), \(C_{ongrid}\), and \(C_{ab}\) denote system investment cost, maintenance cost, grid electricity purchase cost, grid electricity sales revenue, and load shedding penalty cost, respectively. \(P_{load}(t)\) and \(P_{grid}(t)\) are the load demand power and power purchased from the grid at time \(t\), and \(\eta_{ser}\) is the energy autonomy rate.
The capacity planning model for highway service area microgrids is multi-objective, multivariate, and nonlinear. To solve it, I employ an improved NSGA-II algorithm. The multi-objective functions serve as fitness functions, and the solution process involves iterative computation of photovoltaic output, net load, energy exchange strategies based on storage SOC and grid connection capacity, and determination of storage charging/discharging power, grid power exchange, and load shedding. The flowchart illustrates this process, ensuring convergence to optimal solutions. NSGA-II is well-suited for such problems due to its ability to handle non-dominated sorting and crowding distance for diversity preservation.
In a case study of a large highway service area in Eastern China, all solar panels are 545 W monocrystalline silicon modules with dimensions of 2.384 m × 1.303 m. Parameters include cleaning maintenance cost per unit area of solar panels at 0.5 CNY/m², daily average utilization hours at 5 h, grid feed-in tariff at 0.55 CNY/kWh, and cleaning cycle as decision variable optimized via genetic algorithm over [0, 365] days. The optimal cleaning cycle for 545 W solar panels is 21 days, with annual total dust cleaning maintenance cost of 59.661 CNY. For the capacity planning model, maximum developable photovoltaic capacity around the service area is 4.046 MW, planning period is 20 years, discount rate is 10%, energy storage uses lithium iron phosphate batteries with 95% charge/discharge efficiency, 0.02% self-discharge rate, and load shedding penalty cost of 1.2 CNY/kWh.
Using MATLAB, I implement the improved NSGA-II with population size 100, maximum iterations 500, crossover rate 0.7, and mutation rate 0.3. The Pareto optimal solution boundary, shown graphically, exhibits uniform and widespread distribution, offering ample information for trade-offs between minimal total system cost and maximal energy autonomy. The lowest total system cost is 3.924 million CNY, covering grid connection investment, maintenance, and electricity purchase costs. Optimal configuration results for microgrid photovoltaic-energy storage capacity at autonomy rates of 40%, 60%, and 80% are summarized in the table below.
| Parameter | \(\eta_{ser} = 40\%\) | \(\eta_{ser} = 60\%\) | \(\eta_{ser} = 80\%\) |
|---|---|---|---|
| Solar Panel Model (W) | 545 | 545 | 545 |
| Number of Solar Panels in Service Area | 3028 | 4679 | 7202 |
| Battery Rated Power Capacity (kW) | 144.9 | 571.9 | 885.4 |
| Battery Rated Energy Capacity (kWh) | 289.8 | 1843.3 | 3622.5 |
| Grid Connection Line Rated Capacity (kW) | 860 | 532 | 402.1 |
| Solar Panel Dust Cleaning Maintenance Cost (10⁴ CNY) | 18.07 | 27.92 | 42.97 |
| System Annual Comprehensive Cost (10⁴ CNY) | 394.80 | 418.92 | 489.54 |
When the service area installs 3028 solar panels, the energy autonomy rate is 40%, indicating low self-sufficiency. With 7202 solar panels, autonomy increases to 80%. The grid connection line rated capacity decreases from near maximum load demand to about 400 kW, while energy storage configuration grows, stabilizing at 885.4 kW/3600 kWh. Notably, solar panel dust cleaning maintenance costs constitute 5% to 10% of the system’s annual comprehensive cost, highlighting the economic impact of dust management on solar panel efficiency. This underscores the importance of integrating dust cleaning optimization into microgrid planning, as neglecting it can lead to suboptimal performance and higher costs.
To further elaborate on the models, let’s delve into the mathematical formulations. The photovoltaic output model is crucial for accurate capacity planning. The power temperature coefficient \(a_T\) typically ranges from -0.3% to -0.5% per °C for silicon solar panels, affecting output in varying climates. Dust accumulation on solar panels reduces radiation transmittance, modeled via the shading coefficient. Empirical studies show that dust deposition on solar panels can cause power losses of up to 20% if not cleaned regularly, hence the need for the dust cleaning model. The time constant \(\theta_c\) in the power loss model depends on local dust properties and environmental conditions; for highway areas, it may be lower due to higher dust generation. Optimizing the cleaning cycle \(t_c\) involves balancing the integral of daily loss costs against periodic cleaning costs, a classic maintenance scheduling problem.
The energy storage model incorporates efficiency losses and self-discharge, which are critical for long-term energy management. The SOC constraints ensure battery longevity and safety, typically limited between 20% and 90%. In the capacity planning model, the objective functions are conflicting: minimizing costs often reduces autonomy, and vice versa. NSGA-II handles this by generating a Pareto front, allowing decision-makers to select configurations based on priorities. The algorithm’s steps include initialization, fitness evaluation, non-dominated sorting, crowding distance calculation, selection, crossover, and mutation. For this study, I adapted it to handle continuous variables for photovoltaic capacity (number of solar panels), storage power/energy, and grid connection capacity.
In the case study, additional parameters include solar radiation data from local meteorological stations, load profiles based on historical service area usage, and electricity price fluctuations. The genetic algorithm for dust cleaning optimization uses a fitness function based on \(C_{MVP}\), with cleaning cycle as a real-coded gene. Results show that for 545 W solar panels, the 21-day cycle minimizes total cost, but this may vary with panel type and location. Sensitivity analysis could explore impacts of dust accumulation rates or cleaning costs. For capacity planning, the Pareto front reveals that increasing autonomy from 40% to 80% raises system cost by approximately 24%, primarily due to more solar panels and storage. However, this enhances energy security and reduces grid dependence, valuable in remote areas.
The integration of dust cleaning maintenance into capacity planning is a novel aspect. Traditional models often assume constant photovoltaic efficiency, but in reality, solar panel performance degrades with dust, especially in arid or high-traffic zones. By incorporating the dust cleaning model, I account for this degradation, leading to more realistic capacity decisions. For instance, if dust cleaning is neglected, the required photovoltaic capacity might be underestimated, resulting in unmet load or higher grid purchases. The model shows that dust cleaning costs are a small but significant portion of overall costs, justifying regular maintenance. Moreover, autonomous operation reduces grid vulnerability, crucial for highway service areas during outages.
Future work could extend this research by considering demand response strategies, where loads are adjusted based on supply availability. For example, electric vehicle charging can be shifted to periods of high photovoltaic output, further optimizing autonomy and cost. Additionally, hybrid systems with wind power or other renewables could be incorporated. The dust cleaning model could be refined with real-time monitoring data from solar panels, enabling dynamic cleaning schedules. Economic factors like inflation or changing electricity tariffs might also be included. The NSGA-II algorithm could be compared with other multi-objective optimizers, such as MOEA/D or SPEA2, to assess efficiency and solution quality.
In conclusion, this study establishes a comprehensive framework for optimizing solar panel dust cleaning and capacity planning in highway service area photovoltaic-energy storage microgrids. By developing mathematical models for photovoltaic output, energy storage, dust-induced power loss, and multi-objective optimization, I provide a method to determine optimal configurations balancing cost and autonomy. The case study demonstrates practical applicability, with results showing optimal cleaning cycles for solar panels and capacity sets for different autonomy levels. This approach leverages distributed photovoltaic resources along highways to enhance energy self-sufficiency and system reliability, offering theoretical support and reference for demonstration projects in highway service area microgrid construction. The emphasis on solar panel maintenance underscores the importance of operational considerations in planning, ensuring long-term performance and sustainability.