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402 - Three-Phase Inverter¶

Three-phase voltage source inverter (VSI) for motor drives and grid-tied applications.

Overview¶

Three-phase VSIs are the backbone of: - AC motor drives (industrial, EV) - Grid-tied solar/wind inverters - Active power filters - STATCOM/FACTS devices

Topology¶

Two-Level VSI¶

      +Vdc ───┬────────┬────────┬───
              │        │        │
             S1       S3       S5
              │        │        │
              A        B        C ─── Three-phase
              │        │        │     output
             S2       S4       S6
              │        │        │
      GND ───┴────────┴────────┴───

Space Vector PWM (SVPWM)¶

Switching States¶

State	S1	S3	S5	Vector
V0	0	0	0	Zero
V1	1	0	0	Active
V2	1	1	0	Active
V3	0	1	0	Active
V4	0	1	1	Active
V5	0	0	1	Active
V6	1	0	1	Active
V7	1	1	1	Zero

SVPWM Algorithm¶

Calculate reference vector in α-β frame
Identify sector (1-6)
Calculate dwell times for adjacent vectors
Generate switching sequence

Key Equations¶

DC Bus Utilization: - Sine PWM: $\(V_{LL,max} = \frac{\sqrt{3}}{2} V_{dc} \approx 0.866 \cdot V_{dc}\)$ - SVPWM: $\(V_{LL,max} = \frac{V_{dc}}{\sqrt{3}} \cdot \frac{2}{\sqrt{3}} = \frac{2}{\sqrt{3}} \cdot 0.5 \cdot V_{dc}\)$

15% more DC bus utilization with SVPWM

Clarke Transform: $\(\begin{bmatrix} v_\alpha \\ v_\beta \end{bmatrix} = \frac{2}{3}\begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2} \\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \end{bmatrix} \begin{bmatrix} v_a \\ v_b \\ v_c \end{bmatrix}\)$

Design Parameters¶

Parameter	Motor Drive	Grid-Tied
DC Bus	300-800V	700-1500V
Switching Freq	5-20 kHz	10-50 kHz
Dead Time	1-3 µs	0.5-2 µs
Output Filter	Motor inductance	LCL filter

Control Architecture¶

                    ┌─────────────┐
Speed ref ─────────►│   Speed     │
                    │   Control   │
Speed fb ──────────►│   (PI)      │
                    └──────┬──────┘
                           │ iq*
                    ┌──────▼──────┐
                    │   Current   │
id*, iq* ──────────►│   Control   │───► PWM
                    │   (PI)      │
id, iq fb ─────────►│             │
                    └─────────────┘

Simulation Exercises¶

Implement SVPWM modulator
Compare with sinusoidal PWM
Observe common-mode voltage
Implement dead-time compensation