基于遗传算法的33节点配电网网络重构MATLAB实现

1. 主程序文件

% 33节点配电网网络重构 - 遗传算法优化
clear; clc; close all;

%% 参数设置
pop_size = 50;          % 种群大小
max_gen = 100;          % 最大迭代次数
pc = 0.8;               % 交叉概率
pm = 0.1;               % 变异概率
elite_rate = 0.1;       % 精英保留比例

%% 加载33节点系统数据
network_data = load_33_node_system();

%% 初始化种群
population = initialize_population(pop_size, network_data);

%% 遗传算法主循环
best_fitness = zeros(max_gen, 1);
avg_fitness = zeros(max_gen, 1);
best_individual = [];

fprintf('开始33节点配电网网络重构优化...\n');

for gen = 1:max_gen
    % 计算适应度
    fitness = calculate_fitness(population, network_data);
    
    % 记录最优解
    [best_fit, best_idx] = min(fitness);
    best_fitness(gen) = best_fit;
    avg_fitness(gen) = mean(fitness);
    
    if gen == 1 || best_fit < best_fitness(max(1, gen-1))
        best_individual = population(best_idx, :);
    end
    
    % 选择操作
    new_population = selection(population, fitness, elite_rate);
    
    % 交叉操作
    new_population = crossover(new_population, pc, network_data);
    
    % 变异操作
    new_population = mutation(new_population, pm, network_data);
    
    population = new_population;
    
    % 显示进度
    if mod(gen, 10) == 0
        fprintf('代数 %d: 最优损耗 = %.4f kW, 平均损耗 = %.4f kW\n', ...
                gen, best_fit, avg_fitness(gen));
    end
end

%% 结果显示
fprintf('\n=== 优化结果 ===\n');
fprintf('最优网络损耗: %.4f kW\n', best_fitness(end));
fprintf('重构方案开关状态:\n');

% 显示最优开关状态
display_switch_status(best_individual, network_data);

% 绘制收敛曲线
plot_convergence(best_fitness, avg_fitness);

% 验证网络连通性
is_radial = check_radial_constraint(best_individual, network_data);
fprintf('网络辐射状约束: %s\n', string(is_radial));

%% 潮流计算验证最终结果
final_loss = power_flow_analysis(best_individual, network_data);
fprintf('最终潮流计算损耗: %.4f kW\n', final_loss);

2. 33节点系统数据加载

function network_data = load_33_node_system()
    % 33节点配电网系统参数
    network_data.num_nodes = 33;
    network_data.num_branches = 32;
    network_data.base_V = 12.66;  % kV
    network_data.base_S = 10;     % MVA
    
    % 节点负荷数据 (kW + jkVar)
    network_data.loads = [
        0,      0;      % 节点1 (平衡节点)
        100,    60;     % 节点2
        90,     40;     % 节点3
        120,    80;     % 节点4
        60,     30;     % 节点5
        60,     20;     % 节点6
        200,    100;    % 节点7
        200,    100;    % 节点8
        60,     20;     % 节点9
        60,     20;     % 节点10
        45,     30;     % 节点11
        60,     35;     % 节点12
        60,     35;     % 节点13
        120,    80;     % 节点14
        60,     10;     % 节点15
        60,     20;     % 节点16
        60,     20;     % 节点17
        90,     40;     % 节点18
        90,     40;     % 节点19
        90,     40;     % 节点20
        90,     40;     % 节点21
        90,     40;     % 节点22
        90,     50;     % 节点23
        420,    200;    % 节点24
        420,    200;    % 节点25
        60,     25;     % 节点26
        60,     25;     % 节点27
        60,     20;     % 节点28
        120,    70;     % 节点29
        200,    600;    % 节点30
        150,    70;     % 节点31
        210,    100;    % 节点32
        60,     40      % 节点33
    ] / 1000;  % 转换为MW
    
    % 支路数据 [起始节点, 终止节点, 电阻(ohm), 电抗(ohm)]
    network_data.branches = [
        1,  2,  0.0922,  0.0470;
        2,  3,  0.4930,  0.2511;
        3,  4,  0.3660,  0.1864;
        4,  5,  0.3811,  0.1941;
        5,  6,  0.8190,  0.7070;
        6,  7,  0.1872,  0.6188;
        7,  8,  0.7114,  0.2351;
        8,  9,  1.0300,  0.7400;
        9,  10, 1.0440,  0.7400;
        10, 11, 0.1966,  0.0650;
        11, 12, 0.3744,  0.1238;
        12, 13, 1.4680,  1.1550;
        13, 14, 0.5416,  0.7129;
        14, 15, 0.5910,  0.5260;
        15, 16, 0.7463,  0.5450;
        16, 17, 1.2890,  1.7210;
        17, 18, 0.7320,  0.5740;
        2,  19, 0.1640,  0.1565;
        19, 20, 1.5042,  1.3554;
        20, 21, 0.4095,  0.4784;
        21, 22, 0.7089,  0.9373;
        3,  23, 0.4512,  0.3083;
        23, 24, 0.8980,  0.7091;
        24, 25, 0.8960,  0.7011;
        6,  26, 0.2030,  0.1034;
        26, 27, 0.2842,  0.1447;
        27, 28, 1.0590,  0.9337;
        28, 29, 0.8042,  0.7006;
        29, 30, 0.5075,  0.2585;
        30, 31, 0.9744,  0.9630;
        31, 32, 0.3105,  0.3619;
        32, 33, 0.3410,  0.5362
    ];
    
    % 联络开关位置 (可操作的开关)
    network_data.tie_switches = [9, 15, 21, 27, 32];  % 支路编号
    
    % 分段开关位置
    network_data.section_switches = setdiff(1:network_data.num_branches, ...
                                          network_data.tie_switches);
end

3. 种群初始化

function population = initialize_population(pop_size, network_data)
    % 初始化种群，确保辐射状结构
    population = zeros(pop_size, length(network_data.tie_switches));
    
    for i = 1:pop_size
        % 随机生成可行的开关组合
        valid = false;
        while ~valid
            % 随机选择要闭合的联络开关数量 (通常为1-3个)
            num_close = randi([1, 3]);
            close_switches = randperm(length(network_data.tie_switches), num_close);
            
            % 生成染色体
            individual = zeros(1, length(network_data.tie_switches));
            individual(close_switches) = 1;
            
            % 检查辐射状约束
            if check_radial_constraint(individual, network_data)
                population(i, :) = individual;
                valid = true;
            end
        end
    end
end

4. 适应度计算

function fitness = calculate_fitness(population, network_data)
    % 计算种群中每个个体的适应度（网络损耗）
    pop_size = size(population, 1);
    fitness = zeros(pop_size, 1);
    
    for i = 1:pop_size
        % 进行潮流计算得到网络损耗
        power_loss = power_flow_analysis(population(i, :), network_data);
        
        % 适应度为网络损耗的倒数（最小化问题）
        fitness(i) = power_loss;
        
        % 如果违反约束，施加惩罚
        if ~check_radial_constraint(population(i, :), network_data)
            fitness(i) = fitness(i) + 1000;  % 惩罚项
        end
    end
end

5. 潮流计算

function total_loss = power_flow_analysis(individual, network_data)
    % 前推回代法进行潮流计算
    try
        % 构建当前开关状态下的网络拓扑
        [branch_status, ~] = build_network_topology(individual, network_data);
        
        % 初始化电压
        V = ones(network_data.num_nodes, 1) * network_data.base_V;
        delta_V = inf;
        tolerance = 1e-6;
        max_iter = 100;
        iter = 0;
        
        while delta_V > tolerance && iter < max_iter
            V_old = V;
            
            % 回代计算电流
            I = calculate_currents(V, network_data.loads, branch_status, ...
                                 network_data.branches);
            
            % 前推计算电压
            V = update_voltages(I, branch_status, network_data.branches, ...
                              network_data.base_V);
            
            delta_V = max(abs(V - V_old));
            iter = iter + 1;
        end
        
        % 计算总损耗
        total_loss = calculate_power_loss(I, branch_status, network_data.branches);
        
    catch
        % 如果潮流计算不收敛，返回大值作为惩罚
        total_loss = 10000;
    end
end

function I = calculate_currents(V, loads, branch_status, branches)
    % 计算各支路电流
    num_nodes = length(V);
    I = zeros(size(branches, 1), 1);
    
    % 从末端节点向前计算电流
    for i = size(branches, 1):-1:1
        if branch_status(i) == 0  % 开关断开
            continue;
        end
        
        from_node = branches(i, 1);
        to_node = branches(i, 2);
        
        % 负荷电流
        S_load = loads(to_node, 1) + 1j * loads(to_node, 2);
        I_load = conj(S_load / V(to_node));
        
        % 下游支路电流之和
        downstream_current = 0;
        for j = i+1:size(branches, 1)
            if branches(j, 1) == to_node && branch_status(j) == 1
                downstream_current = downstream_current + I(j);
            end
        end
        
        I(i) = I_load + downstream_current;
    end
end

function V = update_voltages(I, branch_status, branches, base_V)
    % 更新节点电压
    num_nodes = max(branches(:, 2));
    V = ones(num_nodes, 1) * base_V;
    
    for i = 1:size(branches, 1)
        if branch_status(i) == 0  % 开关断开
            continue;
        end
        
        from_node = branches(i, 1);
        to_node = branches(i, 2);
        
        R = branches(i, 3);
        X = branches(i, 4);
        
        % 电压降
        voltage_drop = I(i) * (R + 1j * X);
        V(to_node) = V(from_node) - voltage_drop;
    end
end

function total_loss = calculate_power_loss(I, branch_status, branches)
    % 计算总网损
    total_loss = 0;
    
    for i = 1:size(branches, 1)
        if branch_status(i) == 1  % 只计算闭合支路
            R = branches(i, 3);
            total_loss = total_loss + abs(I(i))^2 * R;
        end
    end
    
    total_loss = real(total_loss) * 1000;  % 转换为kW
end

6. 遗传操作函数

function new_population = selection(population, fitness, elite_rate)
    % 锦标赛选择
    pop_size = size(population, 1);
    elite_size = round(pop_size * elite_rate);
    
    new_population = zeros(size(population));
    
    % 精英保留
    [~, elite_idx] = mink(fitness, elite_size);
    new_population(1:elite_size, :) = population(elite_idx, :);
    
    % 锦标赛选择剩余个体
    tournament_size = 3;
    for i = elite_size+1:pop_size
        contestants = randperm(pop_size, tournament_size);
        [~, best_idx] = min(fitness(contestants));
        new_population(i, :) = population(contestants(best_idx), :);
    end
end

function new_population = crossover(new_population, pc, network_data)
    % 单点交叉
    pop_size = size(new_population, 1);
    
    for i = 1:2:pop_size-1
        if rand < pc
            % 选择交叉点
            cross_point = randi([1, size(new_population, 2)-1]);
            
            % 执行交叉
            temp1 = new_population(i, :);
            temp2 = new_population(i+1, :);
            
            new_population(i, :) = [temp1(1:cross_point), temp2(cross_point+1:end)];
            new_population(i+1, :) = [temp2(1:cross_point), temp1(cross_point+1:end)];
            
            % 检查约束，如果不满足则恢复
            if ~check_radial_constraint(new_population(i, :), network_data)
                new_population(i, :) = temp1;
            end
            if ~check_radial_constraint(new_population(i+1, :), network_data)
                new_population(i+1, :) = temp2;
            end
        end
    end
end

function new_population = mutation(new_population, pm, network_data)
    % 位变异
    pop_size = size(new_population, 1);
    chrom_length = size(new_population, 2);
    
    for i = 1:pop_size
        if rand < pm
            original = new_population(i, :);
            valid = false;
            attempts = 0;
            
            while ~valid && attempts < 10
                % 随机选择变异位
                mut_point = randi(chrom_length);
                new_population(i, mut_point) = 1 - new_population(i, mut_point);
                
                % 检查约束
                if check_radial_constraint(new_population(i, :), network_data)
                    valid = true;
                else
                    new_population(i, :) = original;
                    attempts = attempts + 1;
                end
            end
        end
    end
end

7. 约束检查函数

function is_radial = check_radial_constraint(individual, network_data)
    % 检查网络是否为辐射状结构
    [branch_status, active_branches] = build_network_topology(individual, network_data);
    
    % 构建连通性矩阵
    num_nodes = network_data.num_nodes;
    adjacency = zeros(num_nodes);
    
    for i = 1:length(branch_status)
        if branch_status(i) == 1
            from = network_data.branches(i, 1);
            to = network_data.branches(i, 2);
            adjacency(from, to) = 1;
            adjacency(to, from) = 1;
        end
    end
    
    % 使用BFS检查连通性和辐射状
    visited = false(1, num_nodes);
    queue = 1;  % 从根节点开始
    visited(1) = true;
    parent = zeros(1, num_nodes);
    
    while ~isempty(queue)
        current = queue(1);
        queue(1) = [];
        
        neighbors = find(adjacency(current, :));
        for neighbor = neighbors
            if ~visited(neighbor)
                visited(neighbor) = true;
                parent(neighbor) = current;
                queue(end+1) = neighbor;
            elseif neighbor ~= parent(current)
                % 发现环
                is_radial = false;
                return;
            end
        end
    end
    
    % 检查是否所有节点都连通
    if all(visited)
        is_radial = true;
    else
        is_radial = false;
    end
end

function [branch_status, active_branches] = build_network_topology(individual, network_data)
    % 根据染色体构建网络拓扑
    branch_status = ones(network_data.num_branches, 1);  % 默认所有支路闭合
    
    % 设置联络开关状态
    for i = 1:length(network_data.tie_switches)
        switch_idx = network_data.tie_switches(i);
        branch_status(switch_idx) = individual(i);
    end
    
    active_branches = find(branch_status == 1);
end

8. 结果显示函数

function display_switch_status(individual, network_data)
    % 显示开关状态
    fprintf('联络开关状态:\n');
    for i = 1:length(network_data.tie_switches)
        switch_idx = network_data.tie_switches(i);
        status = individual(i);
        fprintf('开关 %d (支路%d-%d): %s\n', i, ...
                network_data.branches(switch_idx, 1), ...
                network_data.branches(switch_idx, 2), ...
                iif(status == 1, '闭合', '断开'));
    end
    
    fprintf('\n活动的支路:\n');
    [branch_status, active_branches] = build_network_topology(individual, network_data);
    for i = 1:length(active_branches)
        branch_idx = active_branches(i);
        fprintf('支路 %d: 节点%d - 节点%d\n', branch_idx, ...
                network_data.branches(branch_idx, 1), ...
                network_data.branches(branch_idx, 2));
    end
end

function plot_convergence(best_fitness, avg_fitness)
    % 绘制收敛曲线
    figure;
    plot(1:length(best_fitness), best_fitness, 'b-', 'LineWidth', 2);
    hold on;
    plot(1:length(avg_fitness), avg_fitness, 'r--', 'LineWidth', 2);
    xlabel('迭代次数');
    ylabel('网络损耗 (kW)');
    title('遗传算法收敛曲线');
    legend('最优解', '平均解');
    grid on;
end

function result = iif(condition, true_val, false_val)
    % 内联if函数
    if condition
        result = true_val;
    else
        result = false_val;
    end
end

参考代码 微电网遗传算法优化 www.3dddown.com/csa/60783.html

说明

1. 运行主程序：直接运行主程序文件即可开始优化过程
2. 参数调整：可以根据需要调整种群大小、迭代次数等参数
3. 结果解读：程序会输出最优的开关配置方案和相应的网络损耗

特点

• 编码方案：采用二进制编码表示开关状态
• 约束处理：确保网络始终保持辐射状结构
• 潮流计算：使用前推回代法进行精确的潮流分析
• 收敛性：包含精英保留策略，保证算法收敛性