MATLAB、Python 、 C 语言-SVPWM与PLL-PID算法代码实现

MATLAB、Python 和 C 语言实现 SVPWM 与 PLL-PID 算法解析

以下分别提供 SVPWM（空间矢量脉宽调制）和 PLL-PID（锁相环-比例积分微分）算法的实现代码及注释解析，涵盖 MATLAB、Python 和 C 语言。代码包含详细注释和实际应用示例。

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SVPWM 算法实现

MATLAB 实现

function [Ta, Tb, Tc] = svpwm(Valpha, Vbeta, Vdc, Ts)
    % 输入：Valpha, Vbeta - αβ坐标系电压分量；Vdc - 直流母线电压；Ts - 采样周期
    % 输出：Ta, Tb, Tc - 三相桥臂导通时间
    
    % 计算电压矢量幅值和角度
    Vref = sqrt(Valpha^2 + Vbeta^2);
    theta = atan2(Vbeta, Valpha);
    
    % 扇区判断
    sector = floor(theta / (pi/3)) + 1;
    
    % 计算基本矢量作用时间
    T1 = (sqrt(3)*Ts/Vdc) * (sin(sector*pi/3 - theta) * Vref);
    T2 = (sqrt(3)*Ts/Vdc) * (sin(theta - (sector-1)*pi/3) * Vref);
    T0 = Ts - T1 - T2;
    
    % 根据扇区分配导通时间
    switch sector
        case 1
            Ta = T1 + T2 + T0/2; Tb = T2 + T0/2; Tc = T0/2;
        case 2
            Ta = T1 + T0/2; Tb = T1 + T2 + T0/2; Tc = T0/2;
        % 其他扇区类似...
    end
end

Python 实现

import numpy as np

def svpwm(Valpha, Vbeta, Vdc, Ts):
    # 计算幅值和角度
    Vref = np.sqrt(Valpha**2 + Vbeta**2)
    theta = np.arctan2(Vbeta, Valpha)
    
    # 扇区判断
    sector = int(theta // (np.pi/3)) + 1
    
    # 计算T1, T2, T0
    T1 = (np.sqrt(3)*Ts/Vdc) * np.sin(sector*np.pi/3 - theta) * Vref
    T2 = (np.sqrt(3)*Ts/Vdc) * np.sin(theta - (sector-1)*np.pi/3) * Vref
    T0 = Ts - T1 - T2
    
    # 导通时间分配（示例为扇区1）
    if sector == 1:
        Ta = T1 + T2 + T0/2
        Tb = T2 + T0/2
        Tc = T0/2
    return Ta, Tb, Tc

C 语言实现

#include <math.h>

void svpwm(float Valpha, float Vbeta, float Vdc, float Ts, float *Ta, float *Tb, float *Tc) {
    float Vref = sqrt(Valpha*Valpha + Vbeta*Vbeta);
    float theta = atan2(Vbeta, Valpha);
    
    int sector = (int)(theta / (M_PI/3)) + 1;
    
    float T1 = (sqrt(3)*Ts/Vdc) * sin(sector*M_PI/3 - theta) * Vref;
    float T2 = (sqrt(3)*Ts/Vdc) * sin(theta - (sector-1)*M_PI/3) * Vref;
    float T0 = Ts - T1 - T2;
    
    // 扇区1示例
    if (sector == 1) {
        *Ta = T1 + T2 + T0/2;
        *Tb = T2 + T0/2;
        *Tc = T0/2;
    }
}

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PLL-PID 算法实现

MATLAB 实现

function [theta, Vd] = pll_pid(Valpha, Vbeta, Kp, Ki, Ts)
    % 输入：Valpha, Vbeta - αβ分量；Kp, Ki - PID参数；Ts - 采样时间
    % 输出：theta - 估计角度；Vd - d轴电压
    
    persistent integral_error prev_theta;
    
    % 初始化
    if isempty(integral_error)
        integral_error = 0;
        prev_theta = 0;
    end
    
    % 计算误差（基于反Park变换）
    error = -Valpha * sin(prev_theta) + Vbeta * cos(prev_theta);
    
    % PID控制
    integral_error = integral_error + error * Ts;
    delta_theta = Kp * error + Ki * integral_error;
    
    % 更新角度
    theta = prev_theta + delta_theta * Ts;
    prev_theta = theta;
    
    % 计算Vd（可选）
    Vd = Valpha * cos(theta) + Vbeta * sin(theta);
end

Python 实现

class PLL_PID:
    def __init__(self, Kp, Ki, Ts):
        self.Kp = Kp
        self.Ki = Ki
        self.Ts = Ts
        self.integral_error = 0
        self.prev_theta = 0
    
    def update(self, Valpha, Vbeta):
        # 计算误差
        error = -Valpha * np.sin(self.prev_theta) + Vbeta * np.cos(self.prev_theta)
        
        # PID更新
        self.integral_error += error * self.Ts
        delta_theta = self.Kp * error + self.Ki * self.integral_error
        
        # 角度更新
        theta = self.prev_theta + delta_theta * self.Ts
        self.prev_theta = theta
        
        # 计算Vd
        Vd = Valpha * np.cos(theta) + Vbeta * np.sin(theta)
        return theta, Vd

C 语言实现

typedef struct {
    float Kp, Ki, Ts;
    float integral_error;
    float prev_theta;
} PLL_PID;

void pll_pid_update(PLL_PID *pll, float Valpha, float Vbeta, float *theta, float *Vd) {
    // 计算误差
    float error = -Valpha * sin(pll->prev_theta) + Vbeta * cos(pll->prev_theta);
    
    // PID更新
    pll->integral_error += error * pll->Ts;
    float delta_theta = pll->Kp * error + pll->Ki * pll->integral_error;
    
    // 角度更新
    *theta = pll->prev_theta + delta_theta * pll->Ts;
    pll->prev_theta = *theta;
    
    // 计算Vd
    *Vd = Valpha * cos(*theta) + Vbeta * sin(*theta);
}

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应用示例

MATLAB SVPWM 控制三相逆变器

Vdc = 300; Ts = 1e-4;
[Ta, Tb, Tc] = svpwm(100, 50, Vdc, Ts); % 生成PWM信号

Python PLL-PID 同步电网电压

pll = PLL_PID(Kp=0.1, Ki=0.01, Ts=1e-4)
theta, Vd = pll.update(Valpha=220, Vbeta=0) # 跟踪电网相位

C 语言嵌入式实现

PLL_PID pll = {.Kp=0.1, .Ki=0.01, .Ts=1e-4};
float theta, Vd;
pll_pid_update(&pll, 220, 0, &theta, &Vd); // 实时更新角度

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关键注释解析

1. SVPWM：通过扇区判断和时间分配优化谐波性能。
2. PLL-PID：通过误差反馈和积分补偿实现相位精确跟踪。
3. 多语言差异：MATLAB适合快速验证，Python适合算法研究，C语言适合嵌入式部署。