Mask and Parameters

General Parameters

Load Parameters

Ports, Inputs, Outputs and Signals Available for Monitoring

Ports

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

Inputs

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

Outputs

• None

Sensors

Description of the Load Model

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

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 (R_s and L_s) 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 R_p and C_p 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 L_p that can be used instead of C_p. The R_p//L_p 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 R_p and C_p.

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:

where:

Note: 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:

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
• V_min = 0.7 pu

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.

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 E_m behind a series impedance R_m and L_m. 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 k_m 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 R_m and L_m 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 L_m ~ 0.25 pu based on the motor load power (k_m*Pi) and R_m=X_m/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).

Example

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.

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 R_s, L_s, R_p and C_p 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 (f_max= 240 Hz).
• The impedance magnitude at resonance frequency (Z_max = 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 Z_max at resonance is practically equal to the resistance R_p, the computation of X_s and X_p is first performed by neglecting the resistance R_s. Under these conditions, one can show that the inductive reactance X_s of the series branch and the capacitive reactance X_p 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:

• X_s = 3.88 Ω
• R_p1 = 15.2 Ω
• X_p = 62.1 Ω

Once X_s and X_p are known, the resistance R_s is computed as follows:

Thus:

• R_s = 0.459 Ω
• X_s = 3.88 Ω

Note that the new X_s 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 R_p (R_p1) must be corrected to take into account the resistive losses introduced by R_s at resonance:

From this equation:

• R_p = 15.6 Ω

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

• Series branch:
  • R_s = 0.459 Ω
  • X_s = 3.90 Ω (L_s = 0.0103 H)
• Shunt branch:
  • R_p = 15.6 Ω
  • X_p = 62.1 Ω (C_p = 42.7 μF)

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

• Series branch:
  • R_s = 0.488 Ω
  • X_s = 3.90 Ω (L_s = 0.0103 H)
• Shunt branch:
  • R_p = 15.6 Ω
  • X_p = 62.5 Ω (C_p = 42.4 μF)

References

[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