3) 扇区3 (θs = θ + 90 : 120～180) t1 = K ×Vβ
t2 = K ×(-√3 / 2 ×Vα - 1 / 2 ×Vβ) tU = 0
tV = t1 + t2 = K ×(-√3 / 2 ×Vα + 1 / 2 ×Vβ) = K ×Vq ×(√3 / 2 ×sinθ + 1 / 2 ×cosθ) tW = t2 = K ×(-√3 / 2 ×Vα - 1 / 2 ×Vβ) = K ×Vq ×(√3 / 2 ×sinθ - 1 / 2 ×cosθ)
4) 扇区4 (θs = θ + 90 : 180～240) t1 = K ×(-Vβ)
t2 = K ×(-√3 / 2 ×Vα + 1 / 2 ×Vβ) tU = 0
tV = t2 = K ×(-√3 / 2 ×Vα + 1 / 2 ×Vβ) = K ×Vq ×(√3 / 2 ×sinθ + 1 / 2 ×cosθ) tW = t1 + t2 = K ×(-√3 / 2 ×Vα - 1 / 2 ×Vβ) = K ×Vq ×(√3 / 2 ×sinθ - 1 / 2 ×cosθ)
5) 扇区5 (θs = θ + 90 : 240～300) t1 = K ×(-√3 / 2 ×Vα - 1 / 2 ×Vβ) t2 = K ×(√3 / 2 ×Vα - 1 / 2 ×Vβ)
tU = t2 = K ×(√3 / 2 ×Vα - 1 / 2 ×Vβ） = K × Vq×(-√3 / 2 ×sinθ - 1 / 2 ×cosθ) tV = 0
tW = t1 + t2 = -K ×Vβ = -K ×Vq ×cosθ
6) 扇区6 (θs = θ + 90 : 300～360) t1 = K ×(√3 / 2 ×Vα + 1 / 2 ×Vβ) t2 = K ×(-Vβ)
tU = t1 + t2 = K ×(√3 / 2 ×Vα - 1 / 2 ×Vβ)
= K ×Vq ×(-√3 / 2 ×sinθ - 1 / 2 ×cosθ) tV = 0
tW = t2 = -K ×Vβ
= -K ×Vq ×cosθ
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2.9.2
3 相调制的 U、V、W 波形 (Vd = 0 时) 空间向量运算 3相调制 UVW 波形 空間ベクトル演算 3 相変調 U、V、W 波形(Vd = 0)1.210.80.60.40.20-0.2
图 2-11 空间矢量运算 -- 3 相调制
UVW Vdc: DC 电压 T: PWM 半周期 K = √3 / Vdc ×T
tU、tV、tW: U、V、W 相的on時間 (半周期)
1) 扇区1 (θs = θ + 90 : 0～60) t1 = K ×(√3 / 2 ×Vα - 1 / 2 ×Vβ) t2 = K ×Vβ
tU = t1 + t2 + t3 / 2 = (T + t1 + t2) / 2 = K ×(Vq + √3 / 2 ×Vα + 1 / 2 ×Vβ) / 2 = K ×Vq ×(1 - √3 / 2 ×sinθ + 1 / 2 ×cosθ) / 2 tV = t2 + t3 / 2 = (T - t1 + t2) / 2 = K ×(Vq - √3 / 2 ×Vα + 3 / 2 ×Vβ) / 2 = K ×Vq ×(1 + √3 / 2 ×sinθ + 3 / 2 ×cosθ) / 2 tW = t3 / 2 = (T - t1 - t2) / 2 = K ×(Vq - √3 / 2 ×Vα - 1 / 2 ×Vβ) / 2 = K ×Vq ×(1 + √3 / 2 ×sinθ - 1 / 2 ×cosθ) / 2
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2) 扇区2 (θs = θ + 90 : 60～120) t1 = K ×(-√3 / 2 ×Vα + 1 / 2 ×Vβ) t2 = K ×( √3 / 2 ×Vα + 1 / 2 ×Vβ) tU = t2 + t3 / 2 = (T - t1 + t2) / 2 = K ×(Vq + √3 ×Vα) / 2 = K ×Vq ×(1 - √3 ×sinθ) / 2 tV = t1 + t2 + t3 / 2 = (T + t1 + t2) / 2 = K ×(Vq + Vβ) / 2 = K ×Vq ×(1 + cosθ) / 2
tW = t3 / 2 = (T - t1 - t2) / 2 = K ×(Vq - Vβ) / 2 = K ×Vq ×(1 - cosθ) / 2
3) 扇区3 (θs = θ + 90 : 120～180) t1 = K ×Vβ
t2 = K ×(-√3 / 2 ×Vα - 1 / 2 ×Vβ) tU = t3 / 2 = (T - t1 - t2) / 2 = (√3 / 2) ×Vα - (1 / 2) ×Vβ
= K ×Vq ×(1 - √3 / 2 ×sinθ - 1 / 2 ×cosθ) / 2 tV = t1 + t2 + t3 / 2 = (T + t1 + t2) / 2 = -(√3 / 2) ×Vα + (1 / 2) ×Vβ
= K ×Vq ×(1 + √3 / 2 ×sinθ + 1 / 2 ×cosθ) / 2 tW = t2 + t3 / 2 = (T - t1 + t2) / 2 = -(√3 / 2) ×Vα - (3 / 2) ×Vβ
= K ×Vq ×(1 + √3 / 2 ×sinθ - 3 / 2 ×cosθ) / 2
4) 扇区4 (θs = θ + 90 : 180～240) t1 = K ×(-Vβ)
t2 = K ×(-√3 / 2 ×Vα + 1 / 2 ×Vβ) tU = t3 / 2 = (T - t1 - t2) / 2 = (√3 / 2) ×Vα + (1 / 2) ×Vβ
= K ×Vq ×(1 - √3 / 2 ×sinθ + 1 / 2 ×cosθ) / 2 tV = t2 + t3 / 2 = (T - t1 + t2) / 2 = -(√3 / 2) ×Vα + (3 / 2) ×Vβ
= K ×Vq ×(1 + √3 / 2 ×sinθ + 3 / 2 ×cosθ) / 2 tW = t1 + t2 + t3 / 2 = (T + t1 + t2) / 2 = -(√3 / 2) ×Vα - (1 / 2) ×Vβ
= K ×Vq ×(1 + √3 / 2 ×sinθ - 1 / 2 ×cosθ) / 2
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5) 扇区5 (θs = θ + 90 : 240～300) t1 = -(√3 / 2) ×Vα - (1 / 2) ×Vβ t2 = (√3 / 2) ×Vα - (1 / 2) ×Vβ tU = t2 + t3 / 2 = (T - t1 + t2) / 2 = √3 ×Vα
= K ×Vq ×(1 - √3 ×sinθ) / 2 tV = t3 / 2 = (T - t1 - t2) / 2 = Vβ
= K ×Vq ×(1 + cosθ) / 2
tW = t1 + t2 + t3 / 2 = (T + t1 + t2) / 2 = -Vβ
= K ×Vq ×(1 - cosθ) / 2
6) 扇区6 (θs = θ + 90 : 300～360) t1 = (√3 / 2) ×Vα + (1 / 2) ×Vβ t2 = -Vβ
tU = t1 + t2 + t3 / 2 = (T + t1 + t2) / 2 = (√3 / 2) ×Vα - (1 / 2) ×Vβ
= K ×Vq ×(1 - √3 / 2 ×sinθ - 1 / 2 ×cosθ) / 2 tV = t3 / 2 = (T - t1 - t2) / 2 = -(√3 / 2) ×Vα + (1 / 2) ×Vβ
= K ×Vq ×(1 + √3 / 2 ×sinθ + 1 / 2 ×cosθ) / 2 tW = t2 + t3 / 2 = (T - t1 + t2) / 2 = -(√3 / 2) ×Vα - (3 / 2) ×Vβ
= K ×Vq ×(1 + √3 / 2 ×sinθ - 3 / 2 ×cosθ) / 2
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2.10
弱磁控制 印加電圧 (V) vs 誘起電圧 (E)施加电压 V 感应电压 E 1.510.50-0.5-1-1.5
图 2-12 施加电压与感应电压
VE向定子线圈施加电压 V后，转子开始旋转，产生感应电压 E。只要是V > E ，就会有电流流经定子线圈，产生旋转扭力。
V 的最大值为DC 电压，因此E 的最大值也是 DC 电压，此时马达的速度最大。这里，控制Id将转子的磁场减弱时，感应电压也会降低，电流增加，从而获得更高的速度。它称作弱磁控制。
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