第四周仿真作业

时间:2021-09-22 22:16:39

经过第四周关于交流电机的学习,我们通过对起调速特性的了解,进行仿真:

  • 控制电机带重物上升,从静止加速到800r/min
  • 保持800r/min匀速运动0.5s,
  • 减速到静止,保持静止状态0.5s,
  • 带重物下降,从静止达到600r/min
  • 保持600r/min匀速运动0.6s,
  • 减速到静止。
    (为了便于仿真,匀速和静止持续时间较短)

分析:这里,由于自耦降压启动具有K值方便直接调节的特点,所以我们采用此种启动方法。由于变频调速具有调速范围广、平滑性好、能耗小无级调速,故采用变频调速。制动采用相对方便的反接制动。

参数:我们需要设置K,a,b,c 4个参数,由于不方便计算,都是通过观察图像进行调试,从而得出近似值。我是将K先固定,通过调节a,使转速稳定时接近800,调节b,使其接近制动,调节c,使转速稳定时接近600.

从而我这里得出的参数K=0.8,a=0.54,b=0.07,c=0.405.

代码:

model SACIM "A Simple AC Induction Motor Model"
type Voltage=Real(unit="V");
type Current=Real(unit="A");
type Resistance=Real(unit="Ohm");
type Inductance=Real(unit="H");
type Speed=Real(unit="r/min");
type Torque=Real(unit="N.m");
type Inertia=Real(unit="kg.m^2");
type Frequency=Real(unit="Hz");
type Flux=Real(unit="Wb");
type Angle=Real(unit="rad");
type AngularVelocity=Real(unit="rad/s");

constant Real Pi = 3.1415926;

Current i_A"A Phase Current of Stator";
Current i_B"B Phase Current of Stator";
Current i_C"C Phase Current of Stator";
Voltage u_A"A Phase Voltage of Stator";
Voltage u_B"B Phase Voltage of Stator";
Voltage u_C"C Phase Voltage of Stator";
Current i_a"A Phase Current of Rotor";
Current i_b"B Phase Current of Rotor";
Current i_c"C Phase Current of Rotor";
Frequency f_s"Frequency of Stator";
Torque Tm"Torque of the Motor";
Speed n"Speed of the Motor";

Flux Psi_A"A Phase Flux-Linkage of Stator";
Flux Psi_B"B Phase Flux-Linkage of Stator";
Flux Psi_C"C Phase Flux-Linkage of Stator";
Flux Psi_a"a Phase Flux-Linkage of Rotor";
Flux Psi_b"b Phase Flux-Linkage of Rotor";
Flux Psi_c"c Phase Flux-Linkage of Rotor";

Angle phi"Electrical Angle of Rotor";
Angle phi_m"Mechnical Angle of Rotor";
AngularVelocity w"Angular Velocity of Rotor";

Torque Tl"Load Torque"; 

Resistance Rs"Stator Resistance";
parameter Resistance Rr=0.408"Rotor Resistance";
parameter Inductance Ls = 0.00252"Stator Leakage Inductance";
parameter Inductance Lr = 0.00252"Rotor Leakage Inductance";
parameter Inductance Lm = 0.00847"Mutual Inductance"; 
parameter Frequency f_N = 50"Rated Frequency of Stator";
parameter Voltage u_N = 220"Rated Phase Voltage of Stator";
parameter Real p =2"number of pole pairs";
parameter Inertia Jm = 0.1"Motor Inertia";
parameter Inertia Jl = 0.1"Load Inertia";
parameter Real K=0.8"starting rate";
parameter Real a=0.54"frequency rate";
parameter Real b=0.07"stable frequency rate"; 
parameter Real c=0.405"another frequency rate";
parameter Real P=0.7"stoping rate"; 

initial equation

Psi_A = 0; 
Psi_B = 0;
Psi_C = 0;
Psi_a = 0; 
Psi_b = 0;
Psi_c = 0;
phi = 0;
w = 0;

equation

u_A = Rs * i_A + 1000 * der(Psi_A);
u_B = Rs * i_B + 1000 * der(Psi_B);
u_C = Rs * i_C + 1000 * der(Psi_C);
= Rr * i_a + 1000 * der(Psi_a);
= Rr * i_b + 1000 * der(Psi_b);
= Rr * i_c + 1000 * der(Psi_c);

Psi_A = (Lm+Ls)*i_A + (-0.5*Lm)*i_B + (-0.5*Lm)*i_C + (Lm*cos(phi))*i_a + (Lm*cos(phi+2*Pi/3))*i_b + (Lm*cos(phi-2*Pi/3))*i_c;
Psi_B = (-0.5*Lm)*i_A + (Lm+Ls)*i_B + (-0.5*Lm)*i_C + (Lm*cos(phi-2*Pi/3))*i_a + (Lm*cos(phi))*i_b + (Lm*cos(phi+2*Pi/3))*i_c;
Psi_C = (-0.5*Lm)*i_A + (-0.5*Lm)*i_B + (Lm+Ls)*i_C + (Lm*cos(phi+2*Pi/3))*i_a + (Lm*cos(phi-2*Pi/3))*i_b + (Lm*cos(phi))*i_c;

Psi_a = (Lm*cos(phi))*i_A + (Lm*cos(phi-2*Pi/3))*i_B + (Lm*cos(phi+2*Pi/3))*i_C + (Lm+Lr)*i_a + (-0.5*Lm)*i_b + (-0.5*Lm)*i_c;
Psi_b = (Lm*cos(phi+2*Pi/3))*i_A + (Lm*cos(phi))*i_B + (Lm*cos(phi-2*Pi/3))*i_C + (-0.5*Lm)*i_a + (Lm+Lr)*i_b + (-0.5*Lm)*i_c;
Psi_c = (Lm*cos(phi-2*Pi/3))*i_A + (Lm*cos(phi+2*Pi/3))*i_B + (Lm*cos(phi))*i_C + (-0.5*Lm)*i_a + (-0.5*Lm)*i_b + (Lm+Lr)*i_c;

Tm =-p*Lm*((i_A*i_a+i_B*i_b+i_C*i_c)*sin(phi)+(i_A*i_b+i_B*i_c+i_C*i_a)*sin(phi+2*Pi/3)+(i_A*i_c+i_B*i_a+i_C*i_b)*sin(phi-2*Pi/3));

w = 1000 * der(phi_m);

phi_m = phi/p;
n= w*60/(2*Pi);

Tm-Tl = (Jm+Jl) * 1000 * der(w);
Tl = 10;

if time <= 100 then
u_A = 0;
u_B = 0;
u_C = 0;
f_s = 0;Rs = 0.531;
elseif time<=106 then
f_s = f_N*a;

Rs = 0.531;
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*K*a; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*K*a;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*K*a; 
elseif time<=1706 then
f_s = f_N*a;

Rs = 0.531;
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a; 
elseif time<=1756 then
f_s = f_N*a;Rs = 3;
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a;
elseif time<=2679 then
f_s = f_N*a;Rs = 0.531;
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a;
elseif time<=3196 then
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*b; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*b;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*b; 
f_s = f_N*b;Rs = 0.531;
elseif time<=3310 then
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*K*c; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*K*c;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*K*c; 
f_s = f_N*K*c;Rs = 0.531;

elseif time<=4560 then
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*c; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*c;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*c; 
f_s = f_N*c;Rs = 0.531;
elseif time<=4595.5 then
f_s = f_N*P*a;Rs = 2;
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a*P; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a*P;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a*P; 
elseif time<=5560 then
f_s = f_N*a;

Rs = 0.531;
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*a; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*a;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*a; 
else
u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000)*b; 
u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3)*b;
u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3)*b; 
f_s = f_N*b;Rs = 0.531;
end if;

end SACIM;

得出的仿真图像:第四周仿真作业