WPT无线电能传输公式推导、编程计算、仿真验证全过程

主要分为5大模块，分别为无补偿,SS,SP,PP,PS，每个模块对应有公式推导，matlab编程计算相关参数以及将计算参数和仿真验证观察是否对应。

先给定参数：

(1)电感:L1=1e-05H,L2=1e-05H (2)互感:M=6e-06H (3)电阻:R1=0.8?,R2=0.8? (4)输入电源:电压,频率,内阻:U1=500v,f=85000Hz,Rs=0.01? (5)负载:RL=20?

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1、无补偿

1.1 公式推导

列网孔方程：

1.2 matlab编程参数计算

1.3 仿真验证

2 SS补偿电路

2.1 公式推导

1.2 编程计算参数

syms Rs R1 R2 w M n RL I1 I2 Vs Z1 Z2 KI1 KI2 V2 L1 C1 L2 C2  Iin
Rs=0.1;
R1=0.8;
R2=0.8;
w=2.*pi.*85000;
M=6e-06;
Vs=70.7;
L1=1e-05;
L2=1e-05;
RL=20;

C1=1/(w^2.*L1);
C2=1/(w^2.*L2);

Z1=R1+Rs;%原边阻抗
Z2=R2+RL;%副边阻抗

I1=(Vs.*Z2)./(Z1.*Z2+w.^2.*M.^2);%原边电流
I2=(-w.*M.*Vs)./(Z1.*Z2+w.^2.*M.^2);%副边电流

KI1=abs(I1);%原边电流
KI2=abs(I2);%副边电流

P1=Vs.*KI1;%输入功率
P2=KI2^2.*RL;%输出功率

V2=P2/KI2;%输出电压
n=((w.*M)^2.*RL)./((Rs+R1).*(RL+R2)^2+(w.*M)^2.*(RL+R2));%效率

n 
P2
P1
C1
C2
I1
I2
V2

1.3 仿真验证

3 PS补偿电路

3.1 公式推导

3.1 编程参数计算

3.3 仿真验证结果

4 SP补偿电路

4.1 公式推导

4.2 编程计算参数

?

syms Rs R1 R2 w M n RL I1 I2 Vs Z1 Z2 KI1 KI2 KI3 V2 L1 C1 L2 C2 Zf IL
Rs=0.01;
R1=0.8;
R2=0.8;
w=2.*pi.*85000;
M=6e-06;
Vs=500;
L1=1e-05;
L2=1e-05;
RL=20;

C1=1./((w.^2.*L1)-((w.^2.*M.^2)./L2));
C2=1./(w.^2.*L2);

Z2=1./((1i.*w.*C2)+(1./RL))+R2+1i.*w.*L2; %副边阻抗
Zf=(w.^2.*M.^2)./Z2;  %反射阻抗
Z1=R1+1i.*w.*L1+1./(1i.*w.*C1);%原边阻抗

I1=(Vs.*Z2)./(Z1.*Z2+w.^2.*M.^2);
I2=(1i.*w.*M.*Vs)./(Z1.*Z2+w.^2.*M.^2);%副边电流

IL=I2./(1+1i.*w.*C2.*RL);
KI1=abs(I1);%原边电流
KI2=abs(I2);%副边电流
KI3=abs(IL);%电阻电流

P1=Vs.*KI1;%输入功率
P2=KI3.^2.*RL;
V2=P2/KI3;%输出电压
n=P2./P1;

n
P2
P1
C1
C2
KI1
KI2
KI3
V2

4.3 仿真验证?

5 PP补偿电路?

5.1 公式推导

5.2 编程计算参数

C2=(RL^2+(RL^2-4*w^2*L2^2)^0.5)/(2*w^2*RL^2*L2);
Zf=w.^2.*M.^2*(1+w^2*RL^2*C2^2)/(R2+RL+w^2*RL^2*C2^2*R2);

C1=L1/(w^2*L1^2+(Zf+R1)^2);


Vs=(R1+1i.*w.*L1).*I1+1i.*w.*M.*I2;
Vs=(I0-I1).*(1./(1i.*w.*C1));
0=1i.*w.*M.*I1+RL.*IL+(R2+1i.*w.*L2).*I2;
0 =RL.*IL+(IL-I2).*(1./(1i.*w.*C2));


Z1=R1+1i.*w.*L1;
Z2=R2+1i.*w.*L2+RL./(1+1i.*w.*RL.*C2);

I1=Vs.*Z2./(Z1.*Z2+w.^2.*M.^2);
I0=1i.*w.*C1.*Vs+I1;
I2=(-1i.*w.*M.*Vs)./(Z1.*Z2+w.^2.*M.^2);
IL=I2./(1+1i.*w.*C2.*RL);
IL=(-1i.*w.*M.*Vs)./(1+1i.*w.*C2.*RL)./(Z1.*Z2+w.^2.*M.^2);

5.3 仿真验证

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