This document provides an overview of load modeling and induction motor modeling. It discusses how load modeling is important for transient stability simulations but challenging due to the diverse and changing nature of loads. Static load models like the ZIP model are commonly used to represent aggregate load behavior. Induction motors make up a large portion of load and can be modeled statically or dynamically, with the dynamic model typically being a third-order model that neglects stator transients. The document provides details on modeling considerations and differences between modeling induction motors versus synchronous machines.

1. 1
Load modeling
Chapter 6
READ CHAPTER 6, 36 pages!
AND HAVE THESE NOTES
WITH YOU AS YOU DO.

2. 2
Introductory comments
Load modeling dictates the manner in which the power consumed
by the load responds during transient conditions when there is
variation in the voltage and/or frequency throughout the network.
Think of the actual devices that consume energy:
air conditioners, water heaters, lights, refrigerators, computers,
televisions and other electronic gadgets, clothes dryers, electric
stoves, and dishwashers for residential use; refrigeration,
ventilation, lighting, heating and cooling, office equipment,
computers, and other electronic devices for commercial use; and
motors, process heating and boiler use, facility
heating/ventilation/cooling, process cooling and refrigeration,
and lighting for industrial use.

3. 3
Introductory comments
It is common that a simulated disturbance at a given operating condition
is stable for one load model and yet unstable for another. As a result,
achieving accurate load representation and modeling is a daunting task
for the following reasons:
(a) the amount and composition of the load continuously changes,
(b) different load types respond to voltage/frequency variations in different ways,
(c) the number of individual devices to be considered is extremely large,
(d) most of the load is located at the distribution level, yet computational cost of
representing distribution systems is inhibiting, and therefore, load is almost
always modeled at the transmission buses in transient stability simulations.
(e) the nature of load has temporal changes, e.g., dominance of incandescent
lighting has given way to compact fluorescent and light-emitting diode (LED)
lighting; variable-frequency motor drives are ubiquitous, plug-in vehicles are
growing, and data centers are a major consumer of electric energy.
(f) distributed energy resources (DERs): what is seen from the transmission bus is
a composition of different types of loads and different types of supply
resources, and these supply resources have their own unique characteristics in
terms of how they respond to variations in voltage and frequency.

4. 4
Static Load Models
POLYNOMIAL (ZIP)
EXPONENTIAL
COMBINED
(6.4)

5. 5
Polynomial load model
The ZIP or polynomial model is a special case of the more general
exponential model, given by a sum of 3 exponential models with
specified subscripts:





































 3
0
2
2
0
1
0
3
0
2
2
0
1
0 q
V
V
q
V
V
q
Q
Q
p
V
V
p
V
V
p
P
P
where the subscript 0 indicates the initial operating conditions.
0
.
1
3
2
1 

 p
p
p
So this model is composed of three components:
• constant impedance component (p1, q1) - lighting
• constant current component (p2, q2) – motor/lighting
• constant power component (p3,, q3) – loads served by LTCs
0
.
1
3
2
1 

 q
q
q
Without no data, it is typical to make values p2 and q2 be the largest.

6. 6
Frequency Dependence
- C. Concordia and S. Ihara, “Load representation in
power system stability studies,” IEEE Trans. Power
App & Sys., Vol. PAS-101, No. 4, April, 1982.
Stability is better with greater (+dP/df) since
frequency decreases indicates gen deficiency, and so
load decrease tends to balance gen deficiency.
Stability is better with greater (-dQ/df) since an
increase in Q with frequency decrease increases
reactive load, depresses voltages, further reduces P;
therefore, this also tends to balance gen deficiency.

7. 7

8. 8
Frequency Dependence
[6] CIGRE Working Group C4.605 (Convenor J. Milanovic) (2014). Modelling and Aggregation of Loads in Flexible Power
Networks (February 2014). CIGRE.
Data can vary widely; consider the following for industrial load
p1=0.189, p2=0.42, p3=0.391, kpf=LP=0.3398,
q1=2, q2=-1, q3=0, kqf =LQ=3.355
(ref [6, p. 125] (sourced from [A]).
[A] Y. Li, H.-D. Chiang, B.-K. Choi, Y.-T. Chen, D.-H. Huang, and M. G. Lauby, “Representative static load
models for transient stability analysis: development and examination,” IET Generation, Transmission &
Distribution, vol. 1, no. 3, p. 422, 2007.

9. 9
Exponential load model
A typical load model for a load at a bus is the exponential model:
where again the subscript 0 indicates the initial operating conditions.
[6] CIGRE Working Group C4.605 (Convenor J. Milanovic) (2014). Modelling and Aggregation of Loads in Flexible Power
Networks (February 2014). CIGRE.
See ref [6. p. 123]
in Ch. 6 of VMAF.
=α =β

10. 10
Illustration
3-phase fault @ bus 7;
clear fault by opening
line 5-7; clearing time=
10.64 cycles

11. 11
Illustration: Fig. 6.1 in VMAF
3-phase fault @ bus 7; clear fault by opening line 5-7; clearing time=10.64 cycles
Further studies indicated that the Critical Clearing Time (CCT) for cases a, b, and c, are
(a) 11.2 cycles (b) 10.64 cycles (c) 9.74 cycles

12. 12
Some comments in “ref frame” notes
It is worthwhile to read what Paul Krause says in his very good text on
electric machinery [] (references within quotes are not included here).
The below quotes are from his chapter 3, titled “Reference-frame
theory.” You would do well to have this book on your bookshelf.
[] P. Krause, O. Wasynczuk, and S. Sudhoff, “Analysis of Electric Machinery,” 1995, IEEE Press.

13. 13

14. 14

15. 15
Induction Motor Loads
• In most developed countries, it is typical that 50% of the load is
comprised of induction motors.
• One can model induction motor load using a static load model (e.g.,
ZIP with frequency dependence);
• It improves fidelity to explicitly model induction motor dynamics, but
the improved fidelity comes with increased states & compute-time.
• Either way (static or dynamic induction motor models), each physical
motor is not modeled (doing so would be intractable); rather, 1 or
possibly 3-4 motors (of different types) are modeled at each bus.
• Most of induction motor load are three-phase motors, but single-phase
motors have become increasingly important recently. We will look at
both of them.
There is a set of notes called “RefFrameTheoryInductionMachines.docx” on the website.
I suggest to review these notes but I will not go over them in class.

16. 16
3-phase Induction Motor Modeling
• Such motors may be squirrel-cage or wound-rotor but dynamics of
these two are similar; we focus on wound-rotor.
• The situation is similar to, but different, from the synchronous mach.
Synchronous Machine Induction Machine
• Stator-stator inductances depend on
rotor position
• DC rotor windings
• d-axis aligned with rotor
• Stator-stator inductances independent
of rotor position
• AC rotor windings
• d-axis offset from rotor a’ axis

17. 17
3-phase Induction Motor Modeling
• Such motors may be squirrel-cage or wound-rotor but dynamics of
these two are similar; we focus on wound-rotor.
• The situation is similar to, but different, from the synchronous mach.
Synchronous Machine Induction Machine
• Stator-stator inductances depend on
rotor position
• Stator-stator inductances independent
of rotor position



















FDQG
abc
RR
Ra
aR
aa
FDQG
abc
i
i
L
L
L
L


Depends on
rotor position
Constant
Depends on
rotor position
Constant
Laa terms are heavily functions of rotor position
in salient pole machines and lightly functions
of rotor position in smooth rotor machines.
Laa terms are not functions of rotor
position in induction machines
because there is no variation with
position of the rotor position.

18. 18
3-phase Induction Motor Modeling
• Such motors may be squirrel-cage or wound-rotor but dynamics of
these two are similar; we focus on wound-rotor.
• The situation is similar to, but different, from the synchronous mach.
Synchronous Machine Induction Machine
• Stator-stator inductances depend on
rotor position
• Stator-stator inductances independent
of rotor position
Salient pole; Round rotor; Induction machine (wound)
This difference is because the rotor of an induction machine is round with
three symmetric windings, in contrast to the synchronous machine which
is salient (or round) with a main field winding construction developed to
direct flux along the polar axis.

19. 19
3-phase Induction Motor Modeling
• Such motors may be squirrel-cage or wound-rotor but dynamics of
these two are similar; we focus on wound-rotor.
• The situation is similar to, but different, from the synchronous mach.
Synchronous Machine Induction Machine
• DC rotor windings • AC rotor windings
Speed of rotation of
magnetic field from rotor
depends on
• speed of rotation of rotor.
Speed of rotation of
magnetic field from rotor
depends on
• speed of rotation of rotor
• speed of rotation relative
to rotor due to AC currents
in rotor windings

20. 20
3-phase Induction Motor Modeling
• Such motors may be squirrel-cage or wound-rotor but dynamics of
these two are similar; we focus on wound-rotor.
• The situation is similar to, but different, from the synchronous mach.
Synchronous Machine Induction Machine
• d-axis aligned with rotor • d-axis aligned with synchronously
rotating reference.
p. 206, VMAF: For stator quantities, this projection is in form the same as it was for the synchronous machine….
However, here, the meaning of the variable θ changes from the angle between the stator a axis and the rotor axis for
the synchronous machine to the angle between the stator a axis and a synchronously rotating frame for the induction
machine. Thus, transformation of stator quantities requires projection of stator current, voltage, and flux linkage
phasors on a fixed (stator a-b-c) reference frame to the synchronously rotating (d-q) reference frame.

21. 21
3-phase Induction Motor Modeling
• Such motors may be squirrel-cage or wound-rotor but dynamics of
these two are similar; we focus on wound-rotor.
• The situation is similar to, but different, from the synchronous mach.
Synchronous Machine Induction Machine
• d-axis aligned with rotor • d-axis offset from rotor a’ axis
Need Park’s on stator quantities, as function of θ Need Park’s on stator quantities, as function of θ
and on rotor quantities, as function of β.
p. 206, VMAF: On the other hand, transformation of rotor quantities requires projection of rotor current, voltage, and
flux linkage phasors on a rotating (rotor a-b-c) reference frame to the synchronously rotating (d-q) reference frame.
The situation for the induction machine is illustrated in Fig. 6.4 (above right), where we define the angle β=θ-θm.

22. 22
3-phase Induction Motor Modeling
• Such motors may be squirrel-cage or wound-rotor but dynamics of
these two are similar; we focus on wound-rotor.
• The situation is similar to, but different, from the synchronous mach.
Synchronous Machine Induction Machine
• d-axis aligned with rotor • d-axis offset from rotor a’ axis
Need Park’s on stator quantities, as
function of θ
Need Park’s on stator quantities, as
function of θ
and on rotor quantities, as function of β.
0
0
abc abc abc abc
FGDQ
FGDQ FGDQ FGDQ
v i
R
v R i


 
   
 
    
   
 
 
 
     
4 4 4 4
0
0 0 0 0
0
0 0 0 0 0
term 4
term 1 term 2 term 3
abc abc abc abc n
FGDQ
FGDQ FGDQ FGDQ
v i
R v
P P P P
v R i
U U U U


 
   
   
       
   
 
   
   
       
         
 
 
     

23. 23
3-phase Induction Motor Modeling
After some work (VMAF pp. 208-214), resulting model is 3rd-order, commonly used:
Commercial software applications implement one or more versions of this model.
• Motor A is used for small (5–15 HP) and large (200–500 HP) compressor motors that
drive constant torque loads such as for commercial cooling and refrigeration units and
central cooling systems in commercial buildings.
• Motor B is used for small (5–25 HP) motors that drive speed-dependent loads such
as ventilation and air handling fans in residential and commercial buildings.
• Motor C is similar to Motor B, except it has lower inertia; it is representative of small
(5–25 HP) motors used with water circulating pumps in central cooling systems.
This model neglects stator transients, see
p. 213 of VMAF: “…the stator electrical
transients are universally neglected in all
components because these transients are
much faster than the rotor transients,
which are of primary interest in stability
studies. Indeed, a similar simplification
is made for all network components, and
so it is essential to do it for induction
machines as well. This is accomplished
by imposing dλds/dt= dλqs/dt=0.”
Is it “essential”? Might it be possible
to retain IM and SM stator transients
but eliminate network transients?

24. 24
Stalled Motor Operation
From p. 216 of VMAF,
“Following a disturbance, when voltage drops, the motor torque reduces to that of A, and because
the load still demands the torque of S, Tm > Te, and the motor decelerates. If voltage recovers to
the nominal value in time (i.e., before the slip exceeds the critical value of sc, typically between 0.5
and 2 s), the operating condition shifts from B to C, and because at C, Tm < Te, the motor
accelerates to point S. If, on the other hand, the low voltage condition persists and the slip exceeds
sc, the motor stalls since Tm > Te, even if the voltage is restored as indicated by the F to G shift.
Under stalled conditions, s = 1, and because the rotor circuit resistance rr/s is minimum under this
condition, the current drawn is very high and further contributes to voltage reduction during stalling.”
Fig. 6.8 in VMAF

25. 25
Single Phase Motors - FIDVR
Single-phase induction motors are the primary device in residential air-
conditioner (RAC) units, which are the main cause of
fault-induced delayed voltage recovery (FIDVR).
FIDVR occurs following faults when undervoltage conditions cause
induction motor stalling within times as short as 3 cycles following the
fault, which subsequently results in large currents that further delay
voltage recovery.
See next four slides. Observe that motor D is a single phase induction
motor.
Lots of good info on FIDVR was provided at a 2015 NERC workshop:
www.nerc.com/comm/PC/System%20Analysis%20and%20Modeling%20Subcommittee%20SAMS%20201/
Workshop%20Presentations%20Fault-Induced%20Delayed%20Voltage%20Recovery%20(FIDVR).pdf

26. 26
Induction motor stalling/tripping
Load SheddingSchemes ZIP Load Aggr.
Large 3- Motor Aggr.
Medium3- MotorAggr.
Small 3- Motor Aggr.
All 1- Motors Aggr.
ExponentialLoad Aggr.
To model this, the industry has recently created the composite
load model. It enables modeling load as a composition of
• ZIP
• Four different types of motors, including single-phase
• Electronic load
• Distributed PV
all at the end of a simple one-segment feeder.
“WECC Composite Load
Model (CMPLDW)
Specifications,” January 27,
2015, available at
www.wecc.biz/Reliability/
WECC%20Composite%20
Load%20Model%20Specifi
cations%2001-27-
2015.docx. Fig. 6.18 in VMAF

27. 27
Induction motor stalling/tripping using the composite load model
cmpldwg 1234 "XXXX" 115.00 "1" : #1 mva=-1.1 /
"Bss" 0 "Rfdr" 0.04 "Xfdr" 0.04 "Fb" 0.75/
"Xxf" 0.08 "TfixHS" 1 "TfixLS" 1 "LTC" 0 "Tmin" 0.9 "Tmax" 1.1 "step" 0.00625 /
"Vmin" 1.025 "Vmax" 1.04 "Tdel" 30 "Ttap" 5 "Rcomp" 0 "Xcomp" 0 /
"Fma" 0.15 "Fmb" 0.15 "Fmc" 0.05 "Fmd" 0.35 "Fel" 0.10 /
"PFel" 1 "Vd1" 0.7 "Vd2" 0.5 "Frcel" 0.8 /
"Pfs" -0.99771 "P1e" 2 "P1c" 0.557361 "P2e" 1 "P2c" 0.442639 "Pfreq" 0 /
"Q1e" 2 "Q1c" -0.5 "Q2e" 1 "Q2c" 1.5 "Qfreq" -1 /
"MtpA" 3 "MtpB" 3 "MtpC" 3 "MtpD" 1 /
"LfmA" 0.75 "RsA" 0.04 "LsA" 1.8 "LpA" 0.12 "LppA" 0.104 /
"TpoA" 0.095 "TppoA" 0.0021 "HA" 0.1 "etrqA" 0 /
"Vtr1A" 0.7 "Ttr1A" 0.02 "Ftr1A" 0.2 "Vrc1A" 1 "Trc1A" 99999 /
"Vtr2A" 0.5 "Ttr2A" 0.02 "Ftr2A" 0.7 "Vrc2A" 0.7 "Trc2A" 0.1 /
"LfmB" 0.75 "RsB" 0.03 "LsB" 1.8 "LpB" 0.19 "LppB" 0.14 /
"TpoB" 0.2 "TppoB" 0.0026 "HB" 0.5 "etrqB" 2 /
"Vtr1B" 0.6 "Ttr1B" 0.02 "Ftr1B" 0.2 "Vrc1B" 0.75 "Trc1B" 0.05 /
"Vtr2B" 0.5 "Ttr2B" 0.02 "Ftr2B" 0.3 "Vrc2B" 0.65 "Trc2B" 0.05 /
"LfmC" 0.75 "RsC" 0.03 "LsC" 1.8 "LpC" 0.19 "LppC" 0.14 /
"TpoC" 0.2 "TppoC" 0.0026 "HC" 0.1 "etrqc" 2 /
"Vtr1C" 0.65 "Ttr1C" 0.02 "Ftr1C" 0.2 "Vrc1C" 1 "Trc1C" 9999 /
"Vtr2C" 0.5 "Ttr2C" 0.02 "Ftr2C" 0.3 "Vrc2C" 0.65 "Trc2C" 0.1 /
"LfmD" 1 "CompPF" 0.98 /
"Vstall" 0.56 "Rstall" 0.1 "Xstall" 0.1 "Tstall" 0.03 /
"Frst" 0.2 "Vrst" 0.95 "Trst" 0.3 /
"fuvr" 0.1 "vtr1" 0.6 "ttr1" 0.02 "vtr2" 1 "ttr2" 9999 /
"Vc1off" 0.5 "Vc2off" 0.4 "Vc1on" 0.6 "Vc2on" 0.5 /
"Tth" 15 "Th1t" 0.7 "Th2t" 1.9 "tv" 0.025 /
“DGtype” 1 “pflgdg” 0 “Pgdg” 0.20 “Pfdg” 1.0 “Imax” 1.1 /
“Vt0” 0.6 “Vt1” 0.8 “Vt2” 1.1 “Vt3” 1.2 “Vrec” 0.5 /
“ft0” 58.0 “ft1” 59.0 “ft2” 61.0 “ft3” 62.0 “frec” 0.0
Percentages of motors A, B,
C, D, Electronic
Motor A data
Motor B data
Motor C data
Motor D data
ZIP data
D-PV data
Motor type: 3-ϕ or 1-ϕ
Note: this is for a “dyd” file which is used by PSLF. I am unsure whether PSSE can read dyd files so may need to convert it to dyr file, but the following gives some clues on this: “Distributed
Energy Resource Modeling Capabilities: Improvements to Simulation Tools”NERC System Planning Impacts from DER Working Group, Informational Webinar, Oct. 28,2021,
www.nerc.com/comm/RSTC/SPIDERWG/2021_10-DER_Simulation_Improvements_Webinar.pdf. Look at each respective user manual for more info on this issue.

28. 28
From p. 216 of VMAF: “Single-phase induction motors are heavily used in low
voltage appliances such as refrigerators, freezers, fans, pumps, dishwashers,
and washing machines. They are also the primary device in residential air-
conditioner (RAC) units, which are the main cause of fault-induced delayed
voltage recovery (FIDVR). FIDVR occurs following faults when undervoltage
conditions cause induction motor stalling within times as short as 3 cycles
following the fault [22], which subsequently results in large currents that further
delay voltage recovery. The nature of the single-phase motor stalling event is
similar to that described in Section 6.3.3 for three-phase motors, however, with
three main differences.
• Torque reduction with declining voltage is worse: First, the tendency for
electric torque to reduce under lower voltage and speed conditions is more
pronounced in single-phase motors; this leads to a lower critical slip (sc in Figure
6.8).
• Stall before trip: Second, stalling in single-phase motors typically occurs at
voltages higher than those necessary for contactor dropout, i.e., single-phase
units stall before tripping. This is consistent with the report in [6] that RAC
contactors open at 40–52% of nominal voltage while they stall at 50–73%.
• But they eventually trip: Third, RACs have thermal overload protection (TOP)
that disconnects the motor if it remains stalled, typically after 10–20 s [6], an
Single phase induction motors relative to three phase induction motors

29. 29
W/O Motor D Stall (Tstall=9999( W Motor D Stall (Tstall=0.033 sec)
Reactive
consumption
of load.
Field current
of nearby
generators
(if excitation limiters
operate to limit field
current, reactive
supply may not
compensate reactive
consumption)
Reactive demand
increases due to
motor stall; then
slowly decreases
as TOPdisconnects
stalled motors
after 10-15s.
Some motors trip
initially; then
reconnect.

30. 30
Illustration (VMAF, pp. 228-229)
3-phase fault @ bus 7;
clear fault by opening
line 5-7; clearing time=
4 cycles
[44] North American Electric Reliability Corporation (2017). Reliability Guideline;
Developing Load Model Composition Data (March 2017). NERC.

31. 31
Illustration (VMAF, p. 230)

32. 32
Illustration (VMAF, p. 231)

33. 33
Illustration (VMAF, p. 232)

34. 34
Illustration: 4 cycle fault
In VMAF, Fig. 6.19 and 6.20 should be exchanged, i.e., Fig. 6.19 is the 9 cycle fault case, and Fig. 6.20 is the 4 cycle fault case.

35. 35
Illustration
3-phase fault @ bus 7;
clear fault by opening
line 5-7; clearing time=
9 cycles

36. 36
Illustration: 9 cycle fault
In VMAF, Fig. 6.19 and 6.20 should be exchanged, i.e., Fig. 6.19 is the 9 cycle fault case, and Fig. 6.20 is the 4 cycle fault case.

37. 37
Data development
Load composition data (data describing the devices comprising the
load) is highly variable in three ways:
1. Cyclic: vary continuously through time but subject to reliable
patterns (time of day, weekday vs weekend, season, temperature);
2. Long-term: load changes over the years as new devices become
popular;
3. Spatial: Load composition varies based on geography (climate
zone), industrial base, and demographics (types of population
groups).
Two approaches:
• Measurement-based: Monitor distribution feeders for transient
events and then use curve-fitting on event data to identify load
model parameters.
• Component-based: identify the devices comprising the load, their
characteristics, and then perform aggregation of their characteristics

38. 38
Component-based
Based on assessment of how
much of each device comprises
the class.
Based on laboratory testing
The percent of motor D to model at bus k is computed as:
The percent of the load at bus k to represent as Motor D residential is: