Modelica標準庫里的異步電機模型過于復雜，為了便于學習，我用最基本的異步電機方程寫了一個Modelica模型，公式參照陳伯時的《電力拖動自動控制系統--運動控制系統》第3版的190頁到195頁的內容，實際的電機模型參數參照了Novotny和Lipo的《Vector Control and Dynamics of AC Drives》第78頁的一個例子參數并稍作修改。這個模型沒有使用dq坐標系。

本模型中使用的電機主要參數為：

• 額定電壓（相電壓）：220 V
• 額定頻率：50 Hz
• 極對數：2
• 轉動慣量：0.1 kg.m^2
• 定子電阻：0.531 Ohm
• 轉子電阻：0.408 Ohm
• 定子漏感：2.52 mH
• 轉子漏感：2.52 mH
• 互感：8.47 mH

上述參數可根據實際電機的參數進行修改，負載轉矩和負載慣量可根據實際仿真情況加以修改。

Modelica模型如下。

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"; parameter Resistance Rs = 0.531"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";initial equation Psi_A = 0; Psi_B = 0;Psi_C = 0;Psi_a = 0; Psi_b = 0;Psi_c = 0;phi = 0;w = 0;equationu_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);if time <= 100 thenu_A = 0;u_B = 0;u_C = 0;f_s = 0;Tl = 0;elsef_s = f_N; u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000); u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3);u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3); Tl = 10;end if;end SACIM;

在模型中，我們定義了電機的定子電壓方程（由于仿真軟件的時間單位是毫秒，所以所有求導操作前都乘以1000，下同）：

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);

轉子電壓方程（針對鼠籠轉子，如果采用繞線式轉子，可以把外接的電阻和電抗參數引入方程）：

0 = Rr * i_a + 1000 * der(Psi_a);0 = Rr * i_b + 1000 * der(Psi_b);0 = Rr * i_c + 1000 * der(Psi_c);

定子磁鏈方程：

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;

轉子磁鏈方程：

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;

電磁轉矩方程：

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));

轉子的角速度和機械角位移存在導數關系：

w = 1000 * der(phi_m);

下面兩個公式實現轉子電角度與機械角度，角速度和電機轉速之間的單位轉換。

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

電機的實際速度由電機的電磁轉矩、負載轉矩以及電機和負載的共同負載慣量決定(采用最簡化的剛體動力學模型，可逐漸擴展):

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

在此基礎上，我們就可以通過設定外部條件的變化來仿真電機的運行，如改變定子電壓和頻率，定子串電阻，轉子串電阻，改變負載大小等。
這里只給出了最簡單的額定電壓直接啟動的例子

if time <= 100 thenu_A = 0;u_B = 0;u_C = 0;f_s = 0;Tl = 0;elsef_s = f_N; u_A = u_N * 1.414 * sin(2*Pi*f_s*time/1000); u_B = u_N * 1.414 * sin(2*Pi*f_s*time/1000-2*Pi/3);u_C = u_N * 1.414 * sin(2*Pi*f_s*time/1000-4*Pi/3); Tl = 10;end if;

運行如下命令可進行模型的仿真：

simulate(SACIM,startTime=0,stopTime=2000)

轉載于:https://www.cnblogs.com/bingc/p/5274430.html

總結

以上是生活随笔為你收集整理的交流异步电机的Modelica模型的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。