# Documentation

Implement three-phase dynamic load with active power and reactive power as function of voltage or controlled from external input

## Library

Fundamental Blocks/Elements

## Description

The Three-Phase Dynamic Load block implements a three-phase, three-wire dynamic load whose active power P and reactive power Q vary as function of positive-sequence voltage. Negative- and zero-sequence currents are not simulated. The three load currents are therefore balanced, even under unbalanced load voltage conditions.

The load impedance is kept constant if the terminal voltage V of the load is lower than a specified value Vmin. When the terminal voltage is greater than the Vmin value, the active power P and reactive power Q of the load vary as follows:

`$\begin{array}{c}P\left(s\right)={P}_{0}{\left(\frac{V}{{V}_{0}}\right)}^{{n}_{p}}\frac{1+{T}_{p1}s}{1+{T}_{p2}s}\\ Q\left(s\right)={Q}_{0}{\left(\frac{V}{{V}_{0}}\right)}^{{n}_{q}}\frac{1+{T}_{q1}s}{1+{T}_{q2}s},\end{array}$`

where

• V0 is the initial positive sequence voltage.

• P0 and Qo are the initial active and reactive powers at the initial voltage Vo.

• V is the positive-sequence voltage.

• np and nq are exponents (usually between 1 and 3) controlling the nature of the load.

• Tp1 and Tp2 are time constants controlling the dynamics of the active power P.

• Tq1 and Tq2 are time constants controlling the dynamics of the reactive power Q.

For a constant current load, for example, you set np to 1 and nq to 1, and for constant impedance load you set np to 2 and nq to 2.

## Parameters

Nominal L-L voltage and frequency

Specifies the nominal phase-to-phase voltage, in volts RMS, and nominal frequency, in hertz, of the load. Default is ```[ 500e3 60 ]```.

Active and reactive power at initial voltage

Specifies the initial active power, Po, in watts, and initial reactive power, Qo, in vars, at the initial voltage, Vo. Default is ```[50e6 25e6]```.

When you use the Machine Initialization tool of the powergui block to initialize the dynamic load and start simulation in steady state, these parameters are automatically updated according to the P and Q points specified for the load.

When you use the Load Flow tool of the powergui block to initialize the dynamic load, these parameters represent the P and Q reference powers used by the load flow.

Initial positive-sequence voltage Vo

Specifies the magnitude and phase of the initial positive-sequence voltage of the load. Default is `[0.994 -11.8]`.

When you use the Load Flow tool or the Machine Initialization tool of the powergui block to initialize the dynamic load and start simulation in steady state, this parameter is automatically updated using the values computed by the load flow.

External control of PQ

If selected, the active power and reactive power of the load are defined by an external Simulink® vector of two signals. By default, the check box is cleared.

[np nq]

Specifies the np and nq parameters that define the nature of the load. Default is ` [1.3 2]`.

Time constants [Tp1 Tp2 Tq1 Tq2]

Specifies the time constants controlling the dynamics of the active power and the reactive power. Default is ```[0 0 0 0]```.

Minimum voltage Vmin

Specifies the minimum voltage at which the load dynamics commences. The load impedance is constant below this value. Default is `0.7`.

Filtering time constant

Specifies the time constant, in seconds, of the current filter of the Three-Phase Dynamic Load block. Default is `1e-4`.

## Inputs and Outputs

If External control of PQ is selected, a Simulink input, labeled `PQ`, appears. This input is used to control the active and reactive powers of the load from a vector of two signals [P, Q].

The `m` output is a vector containing the following three signals:

• positive-sequence voltage (pu)

• active power P (W)

• reactive power Q (vars)

## Examples

The `power_dynamicload` model uses a Three-Phase Dynamic Load block connected on a 500 kV, 60 Hz power network.

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