![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.](https://image.slidesharecdn.com/loadmodeling1-230703145709-e756b196/85/LoadModeling-1-ppt-8-320.jpg)
![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](https://image.slidesharecdn.com/loadmodeling1-230703145709-e756b196/85/LoadModeling-1-ppt-9-320.jpg)
![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.](https://image.slidesharecdn.com/loadmodeling1-230703145709-e756b196/85/LoadModeling-1-ppt-12-320.jpg)
![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](https://image.slidesharecdn.com/loadmodeling1-230703145709-e756b196/85/LoadModeling-1-ppt-28-320.jpg)
![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.](https://image.slidesharecdn.com/loadmodeling1-230703145709-e756b196/85/LoadModeling-1-ppt-30-320.jpg)
LoadModeling (1).ppt
- 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: