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MATLAB含风电场RX模型的系统潮流计算

news 2025/10/15 11:40:42

MATLAB实现，用于计算含风电场RX模型的电力系统潮流

1. 主程序文件

main.m - 主程序

%% 含风电场RX模型的系统潮流计算
% 作者: MATLAB助手
% 功能: 实现含风电场的电力系统潮流计算clear; clc; close all;%% 系统参数设置
fprintf('=== 含风电场RX模型的系统潮流计算 ===\n\n');% 基准值
S_base = 100;   % MVA
V_base = 230;   % kV%% 创建测试系统
[bus_data, line_data, wind_farms] = create_test_system();%% 构建节点导纳矩阵
Y_bus = build_y_bus(bus_data, line_data);%% 潮流计算
% 风速设置
wind_speeds = containers.Map('KeyType', 'int32', 'ValueType', 'double');
wind_speeds(4) = 10.0;  % 节点4风速10m/s% 执行潮流计算
[V, theta, iterations, success] = power_flow_with_wind(...bus_data, line_data, Y_bus, wind_farms, wind_speeds);%% 显示结果
if successdisplay_results(bus_data, V, theta, wind_farms, wind_speeds);
elsefprintf('潮流计算未收敛！\n');
end%% 风速影响分析
analyze_wind_impact(bus_data, line_data, wind_farms);%% 电压稳定性分析
voltage_stability_analysis(bus_data, line_data, wind_farms);

2. 系统建模函数

create_test_system.m - 创建测试系统

function [bus_data, line_data, wind_farms] = create_test_system()
% 创建测试系统数据% 节点数据格式: [节点编号, 类型, V_set, theta_set, P_load, Q_load]% 类型: 1=平衡节点, 2=PQ节点, 3=PV节点bus_data = [1, 1, 1.05, 0,   0,    0;      % 平衡节点2, 2, 1.00, 0,   0.5,  0.2;    % PQ节点  3, 3, 1.02, 0,   0.3,  0.1;    % PV节点4, 2, 1.00, 0,   0.4,  0.15    % 风电场节点];% 线路数据格式: [从节点, 到节点, R, X, B/2, 变比]line_data = [1, 2, 0.01,  0.05,  0.0, 1.0;1, 3, 0.015, 0.06,  0.0, 1.0;2, 3, 0.02,  0.08,  0.0, 1.0;3, 4, 0.01,  0.04,  0.0, 1.0];% 风电场数据wind_farms = struct();wind_farms(1).bus = 4;              % 接入节点wind_farms(1).capacity = 100;       % 容量(MVA)wind_farms(1).power_factor = 0.9;   % 功率因数wind_farms(1).V_rated = 1.0;        % 额定电压(pu)fprintf('测试系统创建完成:\n');fprintf('- 节点数: %d\n', size(bus_data, 1));fprintf('- 线路数: %d\n', size(line_data, 1));fprintf('- 风电场: 节点 %d, 容量 %.1f MVA\n', ...wind_farms(1).bus, wind_farms(1).capacity);
end

3. 导纳矩阵构建

build_y_bus.m - 构建节点导纳矩阵

function Y_bus = build_y_bus(bus_data, line_data)
% 构建节点导纳矩阵n_buses = size(bus_data, 1);Y_bus = zeros(n_buses, n_buses);for i = 1:size(line_data, 1)from_bus = line_data(i, 1);to_bus = line_data(i, 2);R = line_data(i, 3);X = line_data(i, 4);B = line_data(i, 5);tap = line_data(i, 6);% 计算串联导纳Z = R + 1j * X;Y_series = 1 / Z;% 计算对地导纳Y_shunt = 1j * B;% 更新节点导纳矩阵if tap == 1% 普通线路Y_bus(from_bus, from_bus) = Y_bus(from_bus, from_bus) + Y_series + Y_shunt;Y_bus(to_bus, to_bus) = Y_bus(to_bus, to_bus) + Y_series + Y_shunt;Y_bus(from_bus, to_bus) = Y_bus(from_bus, to_bus) - Y_series;Y_bus(to_bus, from_bus) = Y_bus(to_bus, from_bus) - Y_series;else% 考虑变压器变比Y_bus(from_bus, from_bus) = Y_bus(from_bus, from_bus) + Y_series/tap^2 + Y_shunt;Y_bus(to_bus, to_bus) = Y_bus(to_bus, to_bus) + Y_series + Y_shunt;Y_bus(from_bus, to_bus) = Y_bus(from_bus, to_bus) - Y_series/tap;Y_bus(to_bus, from_bus) = Y_bus(to_bus, from_bus) - Y_series/tap;endendfprintf('节点导纳矩阵构建完成\n');
end

4. 风电场模型

wind_power_calculation.m - 风电场功率计算

function [P_wind, Q_wind] = wind_power_calculation(wind_farm, V, wind_speed)
% 计算风电场功率输出% 风速-功率特性曲线P_wind = wind_power_curve(wind_farm, wind_speed);% 计算无功功率phi = acos(wind_farm.power_factor);Q_wind = P_wind * tan(phi);% 电压修正V_ratio = V / wind_farm.V_rated;P_wind = P_wind * V_ratio^2;Q_wind = Q_wind * V_ratio^2;
endfunction P_wind = wind_power_curve(wind_farm, wind_speed)
% 风速-功率特性曲线cut_in = 3.0;    % 切入风速(m/s)rated = 12.0;    % 额定风速(m/s)cut_out = 25.0;  % 切出风速(m/s)if wind_speed < cut_in || wind_speed > cut_outP_wind = 0;elseif wind_speed < rated% 立方关系P_rated = wind_farm.capacity * wind_farm.power_factor;P_wind = P_rated * ((wind_speed - cut_in) / (rated - cut_in))^3;elseP_wind = wind_farm.capacity * wind_farm.power_factor;end
end

5. 潮流计算核心

power_flow_with_wind.m - 含风电场的潮流计算

function [V, theta, iterations, success] = power_flow_with_wind(...bus_data, line_data, Y_bus, wind_farms, wind_speeds)
% 含风电场的潮流计算% 参数设置max_iterations = 50;tolerance = 1e-6;n_buses = size(bus_data, 1);% 初始化电压和相角V = ones(n_buses, 1);theta = zeros(n_buses, 1);% 设置PV节点和平衡节点电压for i = 1:n_busesif bus_data(i, 2) == 1 || bus_data(i, 2) == 3  % 平衡节点或PV节点V(i) = bus_data(i, 3);if bus_data(i, 2) == 1  % 平衡节点theta(i) = bus_data(i, 4);endendendfprintf('\n开始潮流计算...\n');success = false;for iterations = 1:max_iterations% 计算功率不平衡量[P_mismatch, Q_mismatch] = calculate_power_mismatch(...bus_data, Y_bus, V, theta, wind_farms, wind_speeds);% 检查收敛max_mismatch = max([max(abs(P_mismatch)), max(abs(Q_mismatch))]);fprintf('迭代 %2d: 最大不平衡量 = %.6f\n', iterations, max_mismatch);if max_mismatch < tolerancesuccess = true;break;end% 构建雅可比矩阵[J, mismatch_vector] = build_jacobian(...bus_data, Y_bus, V, theta, P_mismatch, Q_mismatch);% 求解修正方程trycorrection = J \ mismatch_vector;catchfprintf('雅可比矩阵奇异！\n');break;end% 更新电压和相角[V, theta] = update_variables(...bus_data, V, theta, correction);endif successfprintf('潮流计算在 %d 次迭代后收敛\n', iterations);elsefprintf('潮流计算未收敛\n');end
end

calculate_power_mismatch.m - 计算功率不平衡量

function [P_mismatch, Q_mismatch] = calculate_power_mismatch(...bus_data, Y_bus, V, theta, wind_farms, wind_speeds)
% 计算功率不平衡量n_buses = size(bus_data, 1);P_mismatch = zeros(n_buses, 1);Q_mismatch = zeros(n_buses, 1);% 计算节点注入功率for i = 1:n_busesP_calc = 0;Q_calc = 0;for j = 1:n_busesV_i = V(i);V_j = V(j);theta_ij = theta(i) - theta(j);Y_ij = Y_bus(i, j);G_ij = real(Y_ij);B_ij = imag(Y_ij);P_calc = P_calc + V_i * V_j * (G_ij * cos(theta_ij) + B_ij * sin(theta_ij));Q_calc = Q_calc + V_i * V_j * (G_ij * sin(theta_ij) - B_ij * cos(theta_ij));end% 负荷功率P_load = bus_data(i, 5);Q_load = bus_data(i, 6);% 风电场功率P_wind = 0;Q_wind = 0;% 检查该节点是否有风电场for k = 1:length(wind_farms)if wind_farms(k).bus == iwind_speed = wind_speeds(i);[P_wind, Q_wind] = wind_power_calculation(...wind_farms(k), V(i), wind_speed);break;endend% 功率不平衡量P_mismatch(i) = P_wind - P_load - P_calc;Q_mismatch(i) = Q_wind - Q_load - Q_calc;% 平衡节点处理if bus_data(i, 2) == 1P_mismatch(i) = 0;Q_mismatch(i) = 0;end% PV节点处理if bus_data(i, 2) == 3Q_mismatch(i) = 0;endend
end

build_jacobian.m - 构建雅可比矩阵

function [J, mismatch_vector] = build_jacobian(...bus_data, Y_bus, V, theta, P_mismatch, Q_mismatch)
% 构建雅可比矩阵n_buses = size(bus_data, 1);% 确定方程数量n_P = 0;  % P方程数量n_Q = 0;  % Q方程数量for i = 1:n_busesif bus_data(i, 2) ~= 1  % 非平衡节点n_P = n_P + 1;endif bus_data(i, 2) == 2  % PQ节点n_Q = n_Q + 1;endendJ = zeros(n_P + n_Q, n_P + n_Q);mismatch_vector = zeros(n_P + n_Q, 1);% 填充雅可比矩阵和不平衡量向量row = 1;% P-θ部分 (n_P × n_P)for i = 1:n_busesif bus_data(i, 2) == 1  % 跳过平衡节点continue;endcol = 1;for j = 1:n_busesif bus_data(j, 2) == 1  % 跳过平衡节点continue;endif i == j% 对角元素 ∂P/∂θJ(row, col) = -Q_mismatch(i) - imag(Y_bus(i, i)) * V(i)^2;else% 非对角元素 ∂P/∂θV_i = V(i);V_j = V(j);theta_ij = theta(i) - theta(j);Y_ij = Y_bus(i, j);J(row, col) = V_i * V_j * (real(Y_ij) * sin(theta_ij) - imag(Y_ij) * cos(theta_ij));endcol = col + 1;endmismatch_vector(row) = P_mismatch(i);row = row + 1;end% P-V部分 (n_P × n_Q) 和 Q-θ部分 (n_Q × n_P)% Q-V部分 (n_Q × n_Q)for i = 1:n_busesif bus_data(i, 2) ~= 2  % 只处理PQ节点continue;end% Q-θ部分col = 1;for j = 1:n_busesif bus_data(j, 2) == 1  % 跳过平衡节点continue;endif i == j% 对角元素 ∂Q/∂θJ(row, col) = P_mismatch(i) - real(Y_bus(i, i)) * V(i)^2;else% 非对角元素 ∂Q/∂θV_i = V(i);V_j = V(j);theta_ij = theta(i) - theta(j);Y_ij = Y_bus(i, j);J(row, col) = -V_i * V_j * (real(Y_ij) * cos(theta_ij) + imag(Y_ij) * sin(theta_ij));endcol = col + 1;end% Q-V部分col = n_P + 1;for j = 1:n_busesif bus_data(j, 2) ~= 2  % 只处理PQ节点continue;endif i == j% 对角元素 ∂Q/∂VJ(row, col) = -Q_mismatch(i) + imag(Y_bus(i, i)) * V(i)^2;J(row, col) = J(row, col) / V(i);  % 除以Velse% 非对角元素 ∂Q/∂VV_i = V(i);V_j = V(j);theta_ij = theta(i) - theta(j);Y_ij = Y_bus(i, j);J(row, col) = -V_i * (real(Y_ij) * sin(theta_ij) - imag(Y_ij) * cos(theta_ij));endcol = col + 1;endmismatch_vector(row) = Q_mismatch(i);row = row + 1;end
end

update_variables.m - 更新变量

function [V_new, theta_new] = update_variables(bus_data, V, theta, correction)
% 更新电压和相角n_buses = size(bus_data, 1);V_new = V;theta_new = theta;idx = 1;% 更新相角 (所有非平衡节点)for i = 1:n_busesif bus_data(i, 2) ~= 1  % 非平衡节点theta_new(i) = theta(i) + correction(idx);idx = idx + 1;endend% 更新电压幅值 (PQ节点)for i = 1:n_busesif bus_data(i, 2) == 2  % PQ节点V_new(i) = V(i) + correction(idx);idx = idx + 1;endend
end

6. 结果分析和可视化

display_results.m - 显示结果

function display_results(bus_data, V, theta, wind_farms, wind_speeds)
% 显示潮流计算结果fprintf('\n=== 潮流计算结果 ===\n\n');fprintf('节点    电压(pu)    相角(度)    有功负荷    无功负荷    风电有功    风电无功\n');fprintf('--------------------------------------------------------------------------------\n');total_P_load = 0;total_Q_load = 0;total_P_wind = 0;total_Q_wind = 0;for i = 1:size(bus_data, 1)bus_id = bus_data(i, 1);P_load = bus_data(i, 5);Q_load = bus_data(i, 6);% 检查风电场P_wind = 0;Q_wind = 0;has_wind_farm = false;for k = 1:length(wind_farms)if wind_farms(k).bus == bus_idhas_wind_farm = true;wind_speed = wind_speeds(bus_id);[P_wind, Q_wind] = wind_power_calculation(...wind_farms(k), V(i), wind_speed);break;endendif has_wind_farmfprintf('%2d      %8.4f    %8.4f    %8.3f    %8.3f    %8.3f    %8.3f\n', ...bus_id, V(i), rad2deg(theta(i)), P_load, Q_load, P_wind, Q_wind);elsefprintf('%2d      %8.4f    %8.4f    %8.3f    %8.3f    %8s    %8s\n', ...bus_id, V(i), rad2deg(theta(i)), P_load, Q_load, '-', '-');endtotal_P_load = total_P_load + P_load;total_Q_load = total_Q_load + Q_load;total_P_wind = total_P_wind + P_wind;total_Q_wind = total_Q_wind + Q_wind;endfprintf('--------------------------------------------------------------------------------\n');fprintf('总计:                 %8.3f    %8.3f    %8.3f    %8.3f\n', ...total_P_load, total_Q_load, total_P_wind, total_Q_wind);fprintf('净注入:               %8.3f    %8.3f\n', ...total_P_wind - total_P_load, total_Q_wind - total_Q_load);% 绘制电压分布图figure;subplot(2, 1, 1);bar(1:size(bus_data, 1), V, 'b');xlabel('节点编号');ylabel('电压 (pu)');title('系统电压分布');grid on;subplot(2, 1, 2);bar(1:size(bus_data, 1), rad2deg(theta), 'r');xlabel('节点编号');ylabel('相角 (度)');title('系统相角分布');grid on;
end

analyze_wind_impact.m - 风速影响分析

function analyze_wind_impact(bus_data, line_data, wind_farms)
% 分析风速对系统的影响fprintf('\n=== 风速影响分析 ===\n\n');% 构建导纳矩阵Y_bus = build_y_bus(bus_data, line_data);% 不同风速场景wind_speeds = 5:2:15;n_scenarios = length(wind_speeds);voltages = zeros(n_scenarios, 1);P_wind_values = zeros(n_scenarios, 1);Q_wind_values = zeros(n_scenarios, 1);fprintf('风速(m/s)   电压(pu)   风电有功   风电无功\n');fprintf('--------------------------------------------\n');for i = 1:n_scenarioswind_speed = wind_speeds(i);wind_speeds_map = containers.Map('KeyType', 'int32', 'ValueType', 'double');wind_speeds_map(4) = wind_speed;  % 假设风电场在节点4% 执行潮流计算[V, theta, ~, success] = power_flow_with_wind(...bus_data, line_data, Y_bus, wind_farms, wind_speeds_map);if success% 获取风电场功率[P_wind, Q_wind] = wind_power_calculation(...wind_farms(1), V(4), wind_speed);voltages(i) = V(4);P_wind_values(i) = P_wind;Q_wind_values(i) = Q_wind;fprintf('%6.1f      %8.4f   %8.3f   %8.3f\n', ...wind_speed, V(4), P_wind, Q_wind);elsefprintf('%6.1f       计算失败\n', wind_speed);endend% 绘制影响曲线figure;subplot(1, 2, 1);plot(wind_speeds, voltages, 'bo-', 'LineWidth', 2, 'MarkerSize', 8);xlabel('风速 (m/s)');ylabel('节点电压 (pu)');title('风速对节点电压的影响');grid on;subplot(1, 2, 2);plot(wind_speeds, P_wind_values, 'ro-', 'LineWidth', 2, 'MarkerSize', 8);hold on;plot(wind_speeds, Q_wind_values, 'go-', 'LineWidth', 2, 'MarkerSize', 8);xlabel('风速 (m/s)');ylabel('功率 (pu)');title('风电功率特性');legend('有功功率', '无功功率', 'Location', 'best');grid on;
end

voltage_stability_analysis.m - 电压稳定性分析

function voltage_stability_analysis(bus_data, line_data, wind_farms)
% 电压稳定性分析fprintf('\n=== 电压稳定性分析 ===\n\n');% 构建导纳矩阵Y_bus = build_y_bus(bus_data, line_data);% 不同风电渗透率penetrations = 0.1:0.1:2.0;  % 从10%到200%n_cases = length(penetrations);voltages = zeros(n_cases, 1);convergence = false(n_cases, 1);fprintf('风电渗透率   电压(pu)   收敛状态\n');fprintf('----------------------------------\n');original_capacity = wind_farms(1).capacity;for i = 1:n_cases% 调整风电场容量wind_farms(1).capacity = original_capacity * penetrations(i);wind_speeds = containers.Map('KeyType', 'int32', 'ValueType', 'double');wind_speeds(4) = 10.0;  % 固定风速% 执行潮流计算[V, ~, ~, success] = power_flow_with_wind(...bus_data, line_data, Y_bus, wind_farms, wind_speeds);convergence(i) = success;if successvoltages(i) = V(4);status = '收敛';elsevoltages(i) = 0;status = '发散';endfprintf('%8.2f      %8.4f     %s\n', penetrations(i), voltages(i), status);end% 恢复原始容量wind_farms(1).capacity = original_capacity;% 绘制PV曲线figure;plot(penetrations, voltages, 'bo-', 'LineWidth', 2, 'MarkerSize', 6);xlabel('风电渗透率');ylabel('节点电压 (pu)');title('风电渗透率对电压稳定的影响 (PV曲线)');grid on;% 标记稳定极限divergence_point = find(~convergence, 1);if ~isempty(divergence_point)hold on;plot([penetrations(divergence_point), penetrations(divergence_point)], ...[0, max(voltages)], 'r--', 'LineWidth', 2);legend('PV曲线', '稳定极限', 'Location', 'best');end
end

参考代码含风电场RX模型的系统潮流计算 www.youwenfan.com/contentcnj/63616.html