Implement three-phase impedance with mutual coupling among phases

Fundamental Blocks/Elements

The Three-Phase Mutual Inductance Z1-Z0 block implements a three-phase balanced inductive and resistive impedance with mutual coupling between phases. This block performs the same function as the three-winding Mutual Inductance block. For three-phase balanced power systems, it provides a more convenient way of entering system parameters in terms of positive- and zero-sequence resistances and inductances than the self- and mutual resistances and inductances.

**Positive-sequence parameters**The positive-sequence resistance R1, in ohms (Ω), and the positive-sequence inductance L1, in henries (H).

**Zero-sequence parameters**The zero-sequence resistance R0, in ohms (Ω), and the zero-sequence inductance L0, in henries (H).

The `power_3phmutseq10`

example
illustrates the use of the Three-Phase Mutual Inductance Z1-Z0 block
to build a three-phase inductive source with different values for
the positive-sequence impedance Z1 and the zero-sequence impedance
Z0. The programmed impedance values are Z1 = 1+j1 Ω and Z0 =
2+j2 Ω. The Three-Phase Programmable Voltage Source block is
used to generate a 1-volt, 0-degree, positive-sequence internal voltage.
At t = 0.1 s, a 1- volt, 0-degree, zero-sequence voltage is added
to the positive-sequence voltage. The three source terminals are short-circuited
to ground and the resulting positive-, negative-, and zero-sequence
currents are measured using the Discrete 3-Phase Sequence Analyzer
block.

The current waveforms and their sequence components (magnitude and phase) are displayed on the Scope block. The resulting waveforms are shown on the following figure.

The polar impedance values are $${Z}_{1}=\sqrt{2}\angle {45}^{\circ}\Omega $$ and $${Z}_{0}=2\sqrt{2}\angle {45}^{\circ}\Omega $$.

Therefore, the positive- and zero-sequence currents displayed on the scope are

$$\begin{array}{c}{I}_{1}=\frac{{V}_{1}}{{Z}_{1}}=\frac{1}{\sqrt{2}\angle {45}^{\circ}}=0.7071A\angle -{45}^{\circ}\\ {I}_{0}=\frac{{V}_{0}}{{Z}_{0}}=\frac{1}{2\sqrt{2}\angle {45}^{\circ}}=0.3536A\angle -{45}^{\circ}\end{array}$$

The transients observed on the magnitude and the phase angle of the zero-sequence current when the zero-sequence voltage is added (at t = 0.1 s) are due to the Fourier measurement technique used by the Discrete 3-Phase Sequence Analyzer block. As the Fourier analysis uses a running average window of one cycle, it takes one cycle for the magnitude and phase to stabilize.

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