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Dynamic Load
Mask and Parameters
General Parameters
Description  Use this field to add all kinds of information about the component 
Dynamic load status  If 'Enable', the load is ON; if 'Disable', the load is OFF 
Measuring filter status  If “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 positivesequence voltage input. 
External control  

Internal  Use the internal algorithm 
External P and Q  Input pins P_i and Q_i will be used to control P and Q in the load equations 
External P_{0} and Q_{0}  Input 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 frequency 

Load Parameters
V_{min}  Voltage threshold below which the load behaves as a constant impedance (pu) 
U_{0}  Nominal voltage in relation to the base voltage (pu) 
P_{0}  Nominal active power at U0 (MW) 
Q_{0}  Nominal reactive power at U0 (Mvar) 
R_{s}  Series resistance (ohm) 
L_{s}  Series inductance (H) 
R_{p}  Shunt resistance (ohm) 
L_{p}  Shunt inductance (H) 
C_{p}  Shunt capacitance (F) 
n_{p}  Active power variation coefficient as a function of the voltage 
n_{q}  Reactive power variation coefficient as a function of the voltage 
k_{p}  Active power variation coefficient as a function of the frequency 
k_{q}  Reactive power variation coefficient as a function of the frequency 
T_{p1}  Time constant to calculate the active power of the load 
T_{p2}  Time constant to calculate the active power of the load 
T_{q1}  Time constant to calculate the reactive power of the load 
T_{q2}  Time constant to calculate the reactive power of the load 
Ports, Inputs, Outputs and Signals Available for Monitoring
Ports
 Net_1: Network connection (supports only 3phase 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
E(a,b,c)  Output voltage of the dynamic load (V) 
Ed  Direct (D) axis output voltage (pu) 
Eq  Quadrature (Q) axis output voltage (pu) 
Freq  Network frequency (Hz) 
IPROBE(a,b,c)  

I(a,b,c)  Dynamic load current (A) 
P  Total active power of the load (pu) 
P_i  Input control pin active power (W) 
Pcomp  Compensating active power; originating from the internal voltage source (pu) 
Period  Inverse of the frequency (s) 
Q  Total reactive power of the load (pu) 
Q_i  Input control pin reactive power (var) 
Qcomp  Compensating reactive power; originating from the internal voltage source (pu) 
Qdisplay  
VPROBE(a,b,c)  
Vd  Direct (D) axis voltage (pu) 
Vq  Quadrature (Q) axis voltage (pu) 
Vrms  Average value of the positivesequence voltage (pu) 
Description of the Load Model
The singleline 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 positivesequence 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 (RL loads and motor loads). In this document we consider only using R_{p} and C_{p}.
The positivesequence 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:
f_{0}  Nominal frequency (50 Hz or 60 Hz) 
f  Frequency of the fundamental component (near 50 Hz or 60 Hz) 
U_{0}  Reference positivesequence voltage at nominal frequency 
U  Positivesequence voltage at the fundamental frequency f 
V_{min}  Minimum voltage for which np and nq exponents are used (see Note below) 
P_{0}, Q_{0}  Active and reactive powers at reference voltage U_{0} and frequency f_{0} 
P, Q  Active 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, kq  coefficients defining the variations of P and Q as a function of the fundamental frequency 
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:
Load Class  Power Factor  np  nq  kp  kq  

Residential  Summer  0.9  1.2  2.9  0.8  2.2 
Winter  0.99  1.5  3.2  1  1.5  
Commercial  Summer  0.85  0.99  3.5  1.2  1.6 
Winter  0.9  1.3  3.1  1.5  1.1  
Industrial  0.85  0.18  6  2.6  1.6 
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 positivesequence voltage for a dynamic load with the following parameters. Frequency is kept constant at nominal frequency.
 P_{0} = 50 MW
 Q_{0} = 25 Mvar
 V_{0} = 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 HydroQuebec 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 positivesequence 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 f_{0} (R_{0}= 1.47 Ω; X_{0} = 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 1263 PWRS
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