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Dynamic Load

Dynamic Load


The purpose of the dynamic load is to model a portion of a power system including a combination of loads (motor loads, constant impedance RLC loads), distribution lines, transformers and generators, as a simple equivalent representing the dynamic behavior of this subnetwork. As HYPERSIM is used to model both the low frequency electromechanical oscillations (typically 0.01 Hz to 2 Hz) imposed by the power system dynamics and the high frequency electromagnetic transients resulting from faults and switchings (typically a few kHz), the load model must fulfill the following requirements:

  • The load must represent the variations of load active power P and reactive power Q as function of variable positive-sequence voltage V and fundamental frequency.

  • The load impedance must represent the subnetwork impedance as function of frequency for an acceptable frequency range. The network impedance will determine the frequency content of transient voltages and currents, especially for switchings and faults occurring in the vicinity of the dynamic load. The critical parameters are, the impedance at fundamental frequency, the position of impedance poles (parallel resonances) and zeros (series resonances) as well as damping (amplitude of poles).

Table of Contents

Mask and Parameters

General Parameters

DescriptionUse this field to add all kinds of information about the component
Dynamic load statusIf 'Enable', the load is ON; if 'Disable', the load is OFF
Measuring filter statusIf “Enable”, the measuring filter is ON, and if “Disable”, the filter is OFF; The measurement filter is a second order Butterworth filter applied on the Vd and Vq voltage components extracted from the positive-sequence voltage input.
External control
InternalUse the internal algorithm
External P and QInput pins P_i and Q_i will be used to control P and Q in the load equations
External P0 and Q0Input pins P_i and Q_i will be used to control P0 and Q0 in the load equations
Base power (total)Base value pour PU conversion (MVA)
Base voltage (rmsLL) 
  • Base value pour PU conversion (kV)
Base frequency 
  • Base value pour PU conversion (Hz)

Load Parameters

VminVoltage threshold below which the load behaves as a constant impedance (pu)
U0Nominal voltage in relation to the base voltage (pu)
P0Nominal active power at U0 (MW)
Q0Nominal reactive power at U0 (Mvar)
RsSeries resistance (ohm)
LsSeries inductance (H)
RpShunt resistance (ohm)
LpShunt inductance (H)
CpShunt capacitance (F)
npActive power variation coefficient as a function of the voltage
nqReactive power variation coefficient as a function of the voltage
kpActive power variation coefficient as a function of the frequency
kqReactive power variation coefficient as a function of the frequency
Tp1Time constant to calculate the active power of the load
Tp2Time constant to calculate the active power of the load
Tq1Time constant to calculate the reactive power of the load
Tq2Time constant to calculate the reactive power of the load

Ports, Inputs, Outputs and Signals Available for Monitoring


  • Net_1: Network connection (supports only 3-phase connections)


  • P_i: Controls P or P0 when external control is activated
  • Q_i: Controls Q or Q0 when external control is activated


  • None


E(a,b,c)Output voltage of the dynamic load (V)
EdDirect (D) axis output voltage (pu)
EqQuadrature (Q) axis output voltage (pu)
FreqNetwork frequency (Hz)


I(a,b,c)Dynamic load current (A)
PTotal active power of the load (pu)
P_iInput control pin active power (W)
PcompCompensating active power; originating from the internal voltage source (pu)
PeriodInverse of the frequency (s)
QTotal reactive power of the load (pu)
Q_iInput control pin reactive power (var)
QcompCompensating reactive power; originating from the internal voltage source (pu)
VdDirect (D) axis voltage (pu)
VqQuadrature (Q) axis voltage (pu)
VrmsAverage value of the positive-sequence voltage (pu)

Description of the Load Model

The single-line diagram of the dynamic load model is the following:

Dynamic Load Diagram

In the network, the dynamic load acts as a load that absorbs an active power and a reactive power as a function of the voltage and frequency levels.

The series impedance (Rs and Ls) together with the internal voltage E model the motor part of the load and the system series impedance due to lines and leakage reactances of transformers. The shunt impedances Rp and Cp represent the resistive load as well as line capacitances and capacitor banks.

The dynamic load topology shown above allows modeling the first pole of the positive-sequence impedance versus frequency curve. The HYPERSIM dynamic load model also includes a parallel shunt inductance Lp that can be used instead of Cp. The Rp//Lp shunt topology is rarely used. It would allow fitting a combination of circuits presenting no shunt resonance (R-L loads and motor loads). In this document we consider only using Rp and Cp.

The positive-sequence voltage V is measured at the load terminals and the internal voltage E magnitude and phase angle δ with respect to voltage V are automatically varied in the load model so that the net power P and Q entering the load terminals follow the variation laws given below. Also, the voltage dependency of load characteristics is traditionally represented by an exponential model.

If the voltage at the load terminals U > Vmin:

and if the voltage at the load terminals U < Vmin:


f0Nominal frequency (50 Hz or 60 Hz)
fFrequency of the fundamental component (near 50 Hz or 60 Hz)
U0Reference positive-sequence voltage at nominal frequency
UPositive-sequence voltage at the fundamental frequency f
VminMinimum voltage for which np and nq exponents are used (see Note below)
P0, Q0Active and reactive powers at reference voltage U0 and frequency f0
P, QActive and reactive powers at voltage V and frequency f
np, nq

exponents defining the variation law of P and Q as a function of the voltage (see Note below)

depend on the nature of the loads which are lumped in the dynamic load

can represent respectively a constant power, constant current, or constant impedance load with the value 0, 1, or 2

kp, kqcoefficients defining the variations of P and Q as a function of the fundamental frequency

: The P, Q variations follow the above equations as long as voltage is above a minimum value Vmin. When voltage falls below Vmin, the load varies as a constant impedance (np=2 and nq=2). The variation laws then respect the following parabolic law:

Exponents np and nq depend on the nature of loads which are lumped in the dynamic load. In particular, np and nq= 0, 1, 2 represent respectively constant power, constant current and constant impedance loads. According to reference [1] np usually ranges between 0.5 and 1.8, whereas nq is typically between 1.5 and 6. Reference [2] also gives examples for residential and commercial loads.

The following table taken from reference [1] summarizes typical load characteristics of different load classes in North America:

Load ClassPower Factornpnqkpkq

Hint: In the absence of information on the load composition, the most commonly accepted load model is to represent active power as constant current (np=1) and reactive power as constant impedance (nq=2).

Example: The following figure shows variations of active power and reactive power as a function of positive-sequence voltage for a dynamic load with the following parameters. Frequency is kept constant at nominal frequency.

  • P0 = 50 MW
  • Q0 = 25 Mvar
  • V0 = 0.96 pu
  • Vmin = 0.7 pu

P and Q as a function of positive-sequence voltage

Determination of Load Parameters

General Considerations

In order to determine the four parameters Rs, Ls, Rp and Cp, the load impedance Z(f) as a function of the frequency must be known. It is quite rare that utilities have field measurements available, the only practical method is therefore to perform a detailed simulation of the system to be reduced, including resistive loads, motor loads, lines, transformers, etc. This can be a complex task requiring extensive modeling of the distribution network and some parts of the high voltage network to be reduced. The load global value is usually known from a load flow program but the detailed nature of the load is not necessarily known. Some approximations can then be used.

Below is an example where we assume a 25 kV distribution network connected to a 161 kV transmission network.

Dynamic Load Diagram

From the load flow calculations output, the active and reactive powers Pi and Qi flowing into each individual feeder or group of feeders (25 kV) is known. The load is assumed to have a resistive part R which contributes to damping the transients, and a motor part which practically does not contribute to damping. This motor load is modeled as a voltage source Ebehind a series impedance Rm and Lm. If capacitor banks are used for power factor correction at low voltage level (600 V and below) they should be lumped on the distribution level (25 kV). The sharing factor km between the resistive load and motor load varies widely according to the country, the season and the nature of the load (residential, commercial...). For example, for the HYPERSIM model of the Hydro-Quebec system, the following typical load sharing has been used for determining dynamic load models:

  • Winter: 70% resistive; 30% motor (km=0.3)
  • Summer: 50% resistive; 50% motor (km=0.5)

The series impedance Rm and Lm represent the motor impedance (leakage reactance of induction motors, or subtransient reactance of synchronous motors and generators) in series with distribution transformers. A reasonable approximation of motor and associated transformer impedance could be Lm ~ 0.25 pu based on the motor load power (km*Pi) and Rm=Xm/8 (0.03 pu).

Once the complete system including all individual loads has been modeled, its impedance is measured by performing a frequency scan for the desired frequency range (typically 0 to 2 kHz).


Let us assume that the load flow program gives the following values:

  • V = 25 kV
  • P = 80 MW
  • Q = 15 Mvar

The net active and reactive powers to be programmed in the HYPERSIM load are therefore +80 MW and +15 Mvar. The 80 MW active power is the total power absorbed by a mix of motor and resistive loads as well as line and transformer losses. The 15 Mvar reactive power is the net reactive power consumed by the subnetwork (let’s say +25 Mvar absorbed by motors and series inductances - 10 Mvar generated by power factor correction capacitor banks). The positive-sequence magnitude and phase of Z(f) are as shown on the following figure.

Positive-sequence magnitude and phase of Z(f)

This impedance curve corresponds to a sharing of 40 MW resistive loads and 40 MW motor loads. The magnitude curve shows a resonance at 240 Hz. This parallel resonance is mainly due to the interaction of the distributed 10 Mvar capacitor banks used for power factor correction as well as motor and transformer inductances. From 0 Hz to 240 Hz, the system is inductive. At resonance, the impedance is resistive (15.2 Ω). The R value corresponds approximately to the resistive load (P = 25e3^2/15.2 = 41.1 MW). Above 240 Hz, the system is capacitive.

The four parameters of the dynamic load Rs, Ls, Rp and Cp can be determined from the following four parameters selected on the impedance curve:

  • The resistance and reactance at fundamental frequency f0 (R0= 1.47 Ω; X0 = 3.64 Ω)
  • The resonance frequency (fmax= 240 Hz).
  • The impedance magnitude at resonance frequency (Zmax = 15.2 Ω).

Solving this problem is not trivial. The easiest way to get the exact solution is to use an iterative solution. However, the iteration process can usually be simplified by using the five equations given below. Because the impedance magnitude Zmax at resonance is practically equal to the resistance Rp, the computation of Xs and Xp is first performed by neglecting the resistance Rs. Under these conditions, one can show that the inductive reactance Xs of the series branch and the capacitive reactance Xp of the shunt branch are given by:

Series branch Ls:

Shunt branch (Rp/Cp):

Thus in this example, with:

  • f0= 60 Hz
  • fmax=240 Hz
  • R0= 1.47 Ω
  • X0= 3.64 Ω
  • Zmax= 15.2 Ω

One can obtain the following values:

  • Xs = 3.88 Ω
  • Rp1 = 15.2 Ω
  • Xp = 62.1 Ω

Once Xs and Xp are known, the resistance Rs is computed as follows:


  • Rs = 0.459 Ω
  • Xs = 3.88 Ω

Note that the new Xs value remained the same as the one computed by the equation a little further above, indicating that the computation process has converged.

Finally, the initial value of Rp (Rp1) must be corrected to take into account the resistive losses introduced by Rs at resonance:

From this equation:

  • Rp = 15.6 Ω

If we summarize, the four parameters computed with the above equations are:

  • Series branch:
    • Rs = 0.459 Ω
    • Xs = 3.90 Ω (Ls = 0.0103 H)
  • Shunt branch:
    • Rp = 15.6 Ω
    • Xp = 62.1 Ω (Cp = 42.7 μF)

Those values are very close to the exact values found from an iterative solution:

  • Series branch:
    • Rs = 0.488 Ω
    • Xs = 3.90 Ω (Ls = 0.0103 H)
  • Shunt branch:
    • Rp = 15.6 Ω
    • Xp = 62.5 Ω (Cp = 42.4 μF)


[1] Power System Stability and Control; by P. Kundur, Mc Graw Hill book, 1993
[2] Load Representation For Dynamic Performance Analysis; by IEEE task force on Load Representation for Dynamic Performance, IEEE paper 1992 WM 126-3 PWRS

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