MATLAB含风电场RX模型的系统潮流计算
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 success
display_results(bus_data, V, theta, wind_farms, wind_speeds);
else
fprintf('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;
end
end
fprintf('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;
end
function 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_out
P_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;
else
P_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_buses
if 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);
end
end
end
fprintf('\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 < tolerance
success = 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
try
correction = J \ mismatch_vector;
catch
fprintf('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);
end
if success
fprintf('潮流计算在 %d 次迭代后收敛\n', iterations);
else
fprintf('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_buses
P_calc = 0;
Q_calc = 0;
for j = 1:n_buses
V_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 == i
wind_speed = wind_speeds(i);
[P_wind, Q_wind] = wind_power_calculation(...
wind_farms(k), V(i), wind_speed);
break;
end
end
% 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) == 1
P_mismatch(i) = 0;
Q_mismatch(i) = 0;
end
% PV节点处理
if bus_data(i, 2) == 3
Q_mismatch(i) = 0;
end
end
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_buses
if bus_data(i, 2) ~= 1 % 非平衡节点
n_P = n_P + 1;
end
if bus_data(i, 2) == 2 % PQ节点
n_Q = n_Q + 1;
end
end
J = 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_buses
if bus_data(i, 2) == 1 % 跳过平衡节点
continue;
end
col = 1;
for j = 1:n_buses
if bus_data(j, 2) == 1 % 跳过平衡节点
continue;
end
if i == j
% 对角元素 ∂P/∂θ
J(row, col) = -Q_mismatch(i) - imag(Y_bus(i, i)) * V(i)^2;
else
% 非对角元素 ∂P/∂θ
V_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));
end
col = col + 1;
end
mismatch_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_buses
if bus_data(i, 2) ~= 2 % 只处理PQ节点
continue;
end
% Q-θ部分
col = 1;
for j = 1:n_buses
if bus_data(j, 2) == 1 % 跳过平衡节点
continue;
end
if i == j
% 对角元素 ∂Q/∂θ
J(row, col) = P_mismatch(i) - real(Y_bus(i, i)) * V(i)^2;
else
% 非对角元素 ∂Q/∂θ
V_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));
end
col = col + 1;
end
% Q-V部分
col = n_P + 1;
for j = 1:n_buses
if bus_data(j, 2) ~= 2 % 只处理PQ节点
continue;
end
if i == j
% 对角元素 ∂Q/∂V
J(row, col) = -Q_mismatch(i) + imag(Y_bus(i, i)) * V(i)^2;
J(row, col) = J(row, col) / V(i); % 除以V
else
% 非对角元素 ∂Q/∂V
V_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));
end
col = col + 1;
end
mismatch_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_buses
if bus_data(i, 2) ~= 1 % 非平衡节点
theta_new(i) = theta(i) + correction(idx);
idx = idx + 1;
end
end
% 更新电压幅值 (PQ节点)
for i = 1:n_buses
if bus_data(i, 2) == 2 % PQ节点
V_new(i) = V(i) + correction(idx);
idx = idx + 1;
end
end
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_id
has_wind_farm = true;
wind_speed = wind_speeds(bus_id);
[P_wind, Q_wind] = wind_power_calculation(...
wind_farms(k), V(i), wind_speed);
break;
end
end
if has_wind_farm
fprintf('%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);
else
fprintf('%2d %8.4f %8.4f %8.3f %8.3f %8s %8s\n', ...
bus_id, V(i), rad2deg(theta(i)), P_load, Q_load, '-', '-');
end
total_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;
end
fprintf('--------------------------------------------------------------------------------\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_scenarios
wind_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);
else
fprintf('%6.1f 计算失败\n', wind_speed);
end
end
% 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 success
voltages(i) = V(4);
status = '收敛';
else
voltages(i) = 0;
status = '发散';
end
fprintf('%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
7. 运行说明
-
运行主程序: 在MATLAB中运行
main.m -
查看结果:
- 控制台输出的潮流计算结果
- 自动生成的电压分布图
- 风速影响分析图
- 电压稳定性分析图
-
修改系统参数:
- 在
create_test_system.m中修改系统拓扑 - 调整风电场参数和风速设置
- 修改负荷数据和线路参数
- 在
8. 主要特性
- 完整的RX模型: 准确模拟风电场特性
- 牛顿-拉夫逊法: 可靠的潮流计算算法
- 可视化分析: 丰富的图形输出
- 稳定性评估: 电压稳定性分析
- 灵活配置: 易于修改系统参数
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