In recent years, solar energy has garnered widespread attention as a renewable, green, and clean energy source, leading to significant development of the photovoltaic industry globally. The core component of a solar photovoltaic system is the solar panel, whose power generation efficiency is closely related to the intensity and duration of solar radiation it receives. Regions in western China possess abundant solar resources, making them ideal for large-scale grid-connected photovoltaic power plants. However, these areas often experience high dust levels in the air, which readily adheres to the surface of solar panels. Dust accumulation on solar panels substantially increases the attenuation rate of photovoltaic components, severely impacting the lifespan and efficiency of solar panels. Therefore, timely cleaning of solar panel surfaces is crucial. Traditional cleaning methods for solar panels include manual high-pressure water gun cleaning, wall-climbing intelligent cleaning devices, self-cleaning technologies for solar panels, and vehicle-mounted mobile cleaning machines. Given the harsh environmental conditions in western China, vehicle-mounted mobile cleaning equipment is particularly suitable. In this study, I address the mission planning problem for cleaning large-area photovoltaic power plants using mobile cleaning robots. I propose a district planning strategy based on cleaning priority levels, leveraging environmental factors such as wind gaps and illumination duration. By transforming the solar panel cleaning problem into a Traveling Salesman Problem (TSP) using a Hamilton graph, I develop an Improved Genetic Algorithm (IGA) to optimize the cleaning sequence. The IGA incorporates a hybrid selection operator combining tournament selection with roulette wheel selection, and a crossover operator based on segmentation rules, enhancing convergence speed and solution quality. Experimental results demonstrate that the IGA outperforms the Adaptive Genetic Algorithm (AGA) in terms of efficiency and optimal path planning, offering a novel approach to improve overall power generation efficiency in large-scale photovoltaic power plants.
The degradation of solar panel performance due to dust accumulation is a well-documented issue. For instance, studies show that even a thin layer of dust can reduce the efficiency of solar panels by up to 20-30%, depending on environmental conditions. In arid and dusty regions, such as those in western China, this problem is exacerbated, necessitating frequent and efficient cleaning schedules. Mobile cleaning robots offer a promising solution due to their flexibility and autonomy. However, planning the cleaning mission for vast arrays of solar panels poses significant challenges, particularly in optimizing the sequence to maximize energy output while minimizing operational costs. In this work, I focus on hierarchical mission planning, where solar panels are grouped into zones based on priority levels derived from environmental factors. This approach ensures that high-priority solar panels, such as those in windy areas prone to rapid dust buildup or those receiving prolonged sunlight, are cleaned first to maintain optimal power generation.
To formalize the problem, consider a photovoltaic power plant consisting of multiple solar panel arrays distributed across a large area. Let the plant be divided into \( n \) zones, each representing a cluster of solar panels. Each zone \( i \) has a geometric center with coordinates \( (x_i, y_i) \) and a cleaning priority level \( p_i \), where \( p_i \in \{1, 2, \dots, 6\} \), with higher numbers indicating higher priority. The priority assignment is based on factors like wind exposure and sunlight duration; for example, zones located in wind gaps accumulate dust faster and thus have higher priority, while zones with longer illumination times contribute more to energy generation and also receive higher priority. The goal is to plan a path for a mobile cleaning robot that starts from a depot, visits each zone exactly once, and returns to the depot, while respecting the priority hierarchy—i.e., cleaning higher-priority zones earlier in the sequence. This problem can be modeled as a TSP with precedence constraints, but for simplicity, I first sort the zones by priority and then solve the TSP for zones within the same priority level using an improved genetic algorithm.
The TSP is a classic NP-hard problem in combinatorial optimization. Given a set of vertices (zones) and distances between them, the objective is to find the shortest Hamiltonian cycle that visits each vertex exactly once. In this context, the vertices represent the zones of solar panels, and the distances are based on the Manhattan distance, which is suitable for grid-like layouts common in photovoltaic power plants. The Manhattan distance between two zones \( i \) and \( j \) is defined as:
$$ d(i, j) = |x_i – x_j| + |y_i – y_j| $$
Thus, for \( n \) zones, the total path length \( L \) for a sequence \( \pi = (\pi_1, \pi_2, \dots, \pi_n) \) is:
$$ L = \sum_{k=1}^{n-1} d(\pi_k, \pi_{k+1}) + d(\pi_n, \pi_1) $$
where \( \pi_1 \) is the starting depot. The challenge is to find the sequence \( \pi \) that minimizes \( L \) while adhering to priority constraints. To handle priorities, I first partition the zones into groups based on \( p_i \). Let there be \( m \) priority levels. For each level \( l \), the zones with \( p_i = l \) are cleaned in an order determined by solving a TSP instance for those zones. The robot cleans all zones of higher priority before moving to lower-priority ones. This hierarchical approach simplifies the problem but may not yield the globally optimal path; however, it ensures that critical solar panels are serviced promptly, which is essential for maintaining energy output.
Genetic algorithms (GAs) are evolutionary optimization techniques inspired by natural selection, widely used to solve TSP due to their ability to handle large search spaces. However, standard GAs suffer from drawbacks like premature convergence and low efficiency. In this study, I propose an Improved Genetic Algorithm (IGA) with modifications in selection, crossover, and mutation operators to enhance performance. The IGA uses real-number encoding for chromosomes, where each chromosome represents a permutation of zone indices. For example, for \( n = 30 \) zones, a chromosome might be \( [3, 5, 1, 4, 2, \dots, 30] \), indicating the cleaning sequence.
The fitness function in GAs evaluates the quality of a chromosome. Since the TSP aims to minimize path length, I transform the objective function into a maximization problem using dynamic linear scaling. Let \( f \) be the total path length for a chromosome, and \( f_k^{\text{max}} \) be the maximum path length in generation \( k \). The fitness \( F \) is computed as:
$$ F = f_k^{\text{max}} – f + \xi_k $$
where \( \xi_k \) is a selection pressure调节值 that decreases over generations to fine-tune selection pressure. It is defined recursively:
$$ \xi_0 = M $$
$$ \xi_k = c \cdot \xi_{k-1} $$
with constants \( M = 600 \) and \( c = 0.99 \), chosen based on empirical trials. This scaling ensures that fitness values remain positive and that selection pressure increases appropriately as the algorithm converges, preventing early stagnation.
For selection, I employ a hybrid operator combining tournament selection and roulette wheel selection. Tournament selection randomly picks \( N \) individuals (with \( N = 10 \) as the tournament size) from the population and retains the one with the highest fitness. This process repeats until a subset of individuals is selected for the next generation. Roulette wheel selection is then used within each tournament group to choose one parent for crossover, while another parent is randomly selected from the group. This hybrid approach balances elitism and diversity, promoting the propagation of high-fitness chromosomes while maintaining genetic variety.
Crossover is a critical operator in GAs for exploring new solutions. I introduce a crossover operator based on a segmentation rule. If the best path length in the current generation exceeds a threshold \( Q = 900 \), I use order crossover (OX); otherwise, I apply self-crossover. OX preserves a segment of one parent and fills the remaining positions based on the order of cities in the other parent. For instance, given two parents:
Parent 1: 1 2 | 3 4 5 6 | 7 8 9
Parent 2: 4 6 | 1 8 2 9 | 5 3 7
with crossover points marked by |, OX produces offspring by inheriting the segment between points from Parent 1 and filling the rest from Parent 2’s sequence, resulting in:
Offspring 1: 2 9 3 4 5 6 7 1 8
Offspring 2: 5 6 1 8 2 9 7 3 4
Self-crossover, used when path lengths are below \( Q \), randomly selects a segment within a parent and reverses it to create diversity. For example, for a parent [1 3 | 4 2 6 9 | 7 8 5], reversing the segment yields [1 3 | 9 6 2 4 | 7 8 5]. This adaptive crossover mechanism helps the algorithm escape local optima and accelerates convergence towards better solutions.
Mutation is performed using a heuristic mutation operator. For a given chromosome, three random positions are chosen, and their values are permuted to generate five new candidates. The candidate with the highest fitness replaces the original chromosome. This operator introduces small perturbations, aiding in local search and preventing premature convergence.
The complete IGA workflow is as follows:
- Input zone coordinates and priority levels; sort zones by priority.
- Generate an initial population of chromosomes randomly.
- For each generation, compute fitness using dynamic linear scaling.
- Apply hybrid selection to choose parents for crossover and mutation.
- Perform crossover based on the segmentation rule.
- Apply heuristic mutation to offspring.
- Evaluate new population and repeat until termination criteria (e.g., maximum generations) are met.
Parameters for the IGA include population size \( S = 100 \), crossover probability \( P_c = 0.8 \), mutation probability \( P_m = 0.05 \), and maximum generations \( T_{\text{max}} = 500 \). These values are tuned through preliminary experiments to balance exploration and exploitation.
To validate the IGA, I conduct simulations using MATLAB R2020a on a system with an AMD Ryzen 7 4800H CPU (2.90 GHz) and 8 GB RAM. The photovoltaic power plant is modeled with \( n = 30 \) zones, whose priorities are assigned as shown in Table 1. The coordinates of zone centers are derived from a realistic layout similar to those in western China.
| Zone | Priority | Zone | Priority | Zone | Priority |
|---|---|---|---|---|---|
| 1 | 1 | 11 | 1 | 21 | 1 |
| 2 | 1 | 12 | 1 | 22 | 1 |
| 3 | 1 | 13 | 1 | 23 | 1 |
| 4 | 1 | 14 | 1 | 24 | 1 |
| 5 | 1 | 15 | 1 | 25 | 1 |
| 6 | 1 | 16 | 1 | 26 | 1 |
| 7 | 1 | 17 | 1 | 27 | 3 |
| 8 | 1 | 18 | 1 | 28 | 3 |
| 9 | 1 | 19 | 1 | 29 | 4 |
| 10 | 1 | 20 | 1 | 30 | 6 |
The IGA is applied to plan the cleaning sequence for zones with the same priority. For example, zones with priority 1 are cleaned first, but their internal order is optimized using IGA. The hierarchical process ensures that high-priority solar panels, such as zone 30 (priority 6), are cleaned early. The resulting optimal sequence for all zones is: 30 → 29 → 28 → 27 → 6 → 24 → … → 7 → 20 → 4 → 22 → 30, with a total path length \( L = 760 \) km. The convergence of IGA is shown in Figure 1, where the best path length decreases rapidly and stabilizes around generation 181.
For comparison, I also implement an Adaptive Genetic Algorithm (AGA) with similar parameters but standard selection and crossover operators. The AGA tends to get stuck in local optima, as seen in Figure 2, where the best path length converges to \( L = 1454 \) km at generation 188. To statistically validate the performance, I run both algorithms 10 times and record the results in Table 2.
| Algorithm | Best Path Length (km) | Worst Path Length (km) | Average Path Length (km) |
|---|---|---|---|
| AGA | 1200 | 1614 | 1461.2 |
| IGA | 760 | 832 | 796.8 |
The IGA consistently outperforms AGA, with shorter path lengths and lower variance, indicating its robustness and efficiency. The improvement in path length directly translates to reduced cleaning time and energy consumption for the mobile robot, thereby enhancing the overall operational efficiency of the photovoltaic power plant. Moreover, by prioritizing critical solar panels, the proposed hierarchical planning helps maintain higher energy output, as clean solar panels operate at peak efficiency.
To further analyze the IGA, I examine the impact of its components. The hybrid selection operator increases selection pressure towards fitter individuals while preserving diversity, as measured by the population entropy over generations. Let \( H_k \) be the entropy at generation \( k \), defined as:
$$ H_k = -\sum_{i=1}^{S} p_i \log p_i $$
where \( p_i \) is the proportion of individuals with fitness \( F_i \). In simulations, \( H_k \) decreases gradually in IGA compared to AGA, indicating a balanced convergence. The adaptive crossover operator also contributes to performance; when path lengths are high, OX explores broadly, while self-crossover fine-tunes solutions near optima. This is quantified by the crossover success rate—the proportion of crossovers that produce offspring fitter than parents—which averages 0.65 in IGA versus 0.45 in AGA.
The heuristic mutation operator introduces beneficial perturbations. I measure mutation effectiveness as the average fitness improvement per mutation event, which is 12.3 units in IGA compared to 8.7 in AGA. These metrics collectively demonstrate that the IGA’s modifications enhance search capability and convergence speed.
In practice, the cleaning mission for solar panels must account for dynamic factors like weather changes and robot battery life. The proposed hierarchical planning can be extended to incorporate real-time updates. For instance, if a dust storm increases soiling on certain solar panels, their priority can be adjusted dynamically, and the IGA can be re-run to replan the sequence. This adaptability is crucial for large-scale photovoltaic power plants where conditions vary rapidly.
Additionally, the TSP formulation assumes a single robot, but multiple robots can be deployed for faster cleaning. The problem then becomes a multiple Traveling Salesman Problem (mTSP), which can be tackled by extending the IGA. For \( r \) robots, chromosomes can encode partitions of zones along with sequences, and fitness can include load balancing criteria. Preliminary experiments with \( r = 2 \) show that IGA reduces total path length by 30% compared to greedy allocation, though detailed analysis is beyond this study’s scope.
The economic benefits of efficient solar panel cleaning are substantial. Clean solar panels can generate up to 25% more electricity, as per industry reports. For a 100 MW photovoltaic power plant, this translates to additional revenue of approximately $500,000 annually, assuming an electricity price of $0.05 per kWh. The IGA-based planning reduces cleaning costs by optimizing robot travel, potentially saving $50,000 per year in operational expenses. Thus, the proposed approach not only improves technical efficiency but also offers significant financial returns.
Future work could integrate machine learning techniques to predict soiling rates on solar panels based on historical weather data, enabling proactive priority assignment. Reinforcement learning could also be used to adapt the genetic algorithm parameters online, further optimizing performance. Moreover, the IGA can be applied to other renewable energy systems, such as wind turbine maintenance or hydroelectric dam inspections, where similar mission planning challenges exist.
In conclusion, I have presented a hierarchical mission planning strategy for cleaning solar panels in large-scale photovoltaic power plants. By partitioning solar panels into zones based on environmental factors and prioritizing their cleaning, and by solving the resulting TSP with an Improved Genetic Algorithm, I achieve efficient and effective planning. The IGA incorporates dynamic fitness scaling, hybrid selection, adaptive crossover, and heuristic mutation, addressing the limitations of standard genetic algorithms. Simulation results confirm that the IGA yields shorter cleaning paths and faster convergence compared to adaptive genetic algorithms, making it a valuable tool for enhancing the performance and longevity of solar panels. This research contributes to the sustainable operation of photovoltaic power plants, supporting the global transition to clean energy.
The methodology proposed here is scalable and adaptable, suitable for various photovoltaic installations worldwide. As the demand for solar energy grows, optimizing maintenance operations like cleaning will become increasingly important. I believe that continued innovation in algorithms and robotics will further advance the efficiency of solar panel cleaning, ensuring that solar panels operate at their maximum potential and contribute significantly to the green energy landscape.