仿真作业
对于老师所给的交流电机模型，其正常工作时，旋转磁场的转速
n0=60f/p=1500r/min
一般情况下，三相异步电动机的额定转速nN=(0.94~0.985) n0，运行老师所给的电机模型，知该电机的额定转速约为1490r/min
- 启动方法的选择
总体要求是，在保证电流较小的情况下，拥有较大的启动转矩。
参考书P70几种常用启动方法的比较可知，在启动电流相同的情况下，自耦变压器降压启动的启动转矩较大。Y-△降压启动也有良好的启动特性，但考虑到自耦变压器降压启动的K值可变，选择性更多，利于后面进行调节，因此选用自耦变压器降压启动的启动。
选取K=0.8
2. 调速方法的选择
要求满足相应速比进行调速。
选用变频调速，因为其调速范围广，且能保证电机的机械特性硬度不变，在n=0时有较大的启动转矩，利于启动。
具体频率比的值要通过调试得出。
3. 制动方法的选择
依题意，采取倒拉制动的制动效果会好于能耗制动，选用倒拉制动，但与此同时，倒拉制动并不能自动在n=0时停止，因此需要及时进行控制。
启动阶段为t=100-102ms，t=1200ms时转速稳定在800r/min
匀速运动0.5s，从t=1200ms至t=1700ms
从1700ms开始倒拉制动至转速为0。从t=2675ms至t=3175ms保持静止。
从t=3175ms开始反向加速，t=3950ms时转速稳定在600r/min
匀速运动0.6s,从t=3950ms至t=4550ms
从4550ms开始制动，至5550ms制动至静止。
整个过程耗时5550ms，期间转矩Tm始终控制在182以下。
代码如下：
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 = 1"Load Inertia";
parameter Real K=0.8"starting rate";
parameter Real a=0.544"frequency rate";
parameter Real b=0.0685"stable frequency rate";
parameter Real c=0.3893"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);
0 = Rr * i_a + 1000 * der(Psi_a);
0 = Rr * i_b + 1000 * der(Psi_b);
0 = 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 = 15;
if time <= 100 then
u_A = 0;
u_B = 0;
u_C = 0;
f_s = 0;
Rs = 0.531;
elseif time<=102 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<=1695 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<=1740 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<=2660 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<=3165 then
f_s = f_N*b;
Rs = 0.531;
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;
elseif time<=3300 then
f_s = f_N*K*c;
Rs = 0.531;
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;
elseif time<=4540 then
f_s = f_N*c;
Rs = 0.531;
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;
elseif time<=4580.5 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<=5550 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
f_s = f_N*b;
Rs = 0.531;
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;
end if;
end SACIM;
图像如下：
整个过程耗时5550ms，期间转矩Tm始终控制在182以下。