# Three-Phase Mutual Inductance Z1-Z0

Implement three-phase impedance with mutual coupling among phases

## Library

Simscape / Electrical / Specialized Power Systems / Power Grid Elements

## Description

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.

## Parameters

Positive-sequence parameters

The positive-sequence resistance R1, in ohms (Ω), and the positive-sequence inductance L1, in henries (H). Default is `[ 2 50e-3]`.

Zero-sequence parameters

The zero-sequence resistance R0, in ohms (Ω), and the zero-sequence inductance L0, in henries (H). Default is `[4 100e-3]`.

## Examples

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 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.