# Three-Phase Dynamic Load

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.

## Dialog Box and 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.

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.

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

If you use the Load Flow tool of Powergui 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.

When you use the Load Flow tool or the Machine Initialization tool of Powergui to initialize the dynamic load and start simulation in steady state, these two parameters are automatically updated according to 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.

Parameters [np nq]

Specifies the np and nq parameters that define the nature of the load.

Time constants [Tp1 Tp2 Tq1 Tq2]

Specifies the time constants controlling the dynamics of the active power and the reactive power.

Minimum voltage Vmin

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

## 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); and reactive power Q (vars).

## Example

The `power_dynamicload` model uses a Three-Phase Dynamic Load block connected on a 500 kV, 60 Hz power network. The network is simulated by its Thevenin equivalent (voltage source behind a R-L impedance corresponding to a three-phase short-circuit level of 2000 MVA). The source internal voltage is modulated in order to simulate voltage variation during a power swing. As the dynamic load is a nonlinear model simulated by current sources, it cannot be connected to an inductive network (R-L in series). Therefore, a small resistive load (1 MW) has been added in parallel with the dynamic load.

In order to start the simulation in steady state, you must specify the correct initial positive-sequence voltage Vo (magnitude and phase) corresponding to the desired Po and Qo values. You use the load flow utility to find this voltage and initialize the dynamic load. Open the Powergui and select Machine Initialization. Specify the desired active power and reactive powers for the dynamic load (50 MW, 25 Mvar):

Active Power = 50e6; Reactive Power = 25e6

Then press the Compute and Apply button. Once the load flow has been solved the three phase-to-phase voltages of the dynamic load (0.9844 pu) as well as its line currents are displayed. The phase angle of the phase-to-neutral load voltage Uan is also displayed (−1.41 degrees). This angle corresponds to the angle of the positive-sequence voltage. If you now open the Three-Phase Dynamic Load dialog box, notice that the values of Po, Qo, and Vo have been updated.

Start the simulation and observe load voltage, P&Q powers, and current on Scope1. Observe that simulation starts in steady state. At t = 0.2 s, when voltage modulation is initiated, P and Q start to increase (trace 2), but, as np and nq are set to 1, the load current (trace 3) stays constant. When voltage falls below 0.7 pu the load behaves as a constant impedance. Therefore load current follows this voltage variation.

Observe on Scope2 variations of instantaneous voltages and currents. Also, notice that computed P and Q displayed on Scope3 are the same as P and Q internal signals returned by the Dynamic Load measurement output.

The signals displayed on the Scope1 block are shown below.