1302 IEEE Transactions on Power Systems. Vol. 10. No. 3, August 1995

Standard Load Models for

Power Flow and Dynamic Performance Simulation

IEEE Task Force on Load Representation for Dynamic Performance*

System Dynamic Performance Subcommittee Power System Engineering Committee

Abstract - We recommend standard load models for power flow and dynamic simulation programs. The goal of this paper is to promote better load modeling and advanced load modeling, and to facilitate data exchange among users of various production-grade simulation programs. Flexibility of modeling is an important consideration.

For transient stability, longer-term dynamics, and small-disturbance stability programs, we recom- mend the structure of multiple load types connected to a load bus. Load types are static including dis- charge lighting, induction motors, synchronous motors, and transformer saturation. For each load type, multiple models may be connected to the bus. For longer-term dynamics programs, a model for LTC transformers is also recommended.

Keywords - load modeling, power flow program, tran- sient stability, voltage stability, long term dynamics, induction motors

1 .O Introduction

Nowadays, procedures are in place for exchange of power flow and dynamic simulation data among individual utilities, power pools, and reliability councils. These data exchange activities are greatly facilitated by IEEE committee work to standardize (or at least clearly define) models for generation and SVC equipment [1-51. The IEEE committee recom- mended models are developed by specialists from

*W. W. Price, chairman. Contributors to paper were C, W. Taylor (writer/editor), W. W. Price, G. J. Rog- ers, K. Srinivasan, C. Concordia, M. K. Pal, K. C. Bess, P. Kundur, B. L. Agrawal, J. F. Luini, E. Vaa- hedi, and B. K. Johnson.

utilities, manufacturers, and consultants. The rec- ommended models are implemented in large-scale, production-grade computer simulation programs used by utilities.

There are over ten large-scale production-grade dynamic programs in use by utilities, and many more power flow programs. Individual utilities often use more than one program. Compatible models and data sets are essential. A recent paper by the IEEE Task Force on Load Rep- resentation for Dynamic Performance [61 highlights the importance of load modeling in power system simulation studies. The paper describes different approaches and modeling practices used by electric utilities. In particular, the paper describes several alternative model structures. No recommendations, however, are made regarding standard models for industry use.

Currently, there are no standard models for system loads. Emerging utility challenges related to voltage stability (also termed load stability) have placed increased emphasis on better load models, and on standard load models. Partly in response to voltage stability simulation needs, several transient stabil- ity and longer-term dynamics programs are now integrated.

As power systems are designed and operated with less stability margin, the importance of good models and good data increases. Industry standard models facilitate the validation and certification of simula- tion software. Purpose of paper. This paper is a follow-up to the previous Task Force paper [SI, and recommends standard load models for power flow, transient sta- bility, and longer-term dynamic simulation. The goal of this paper is two-fold: 9L SM 579-3 PWRS A paper recommended and approved . . .

b j the IEEE Power s y s i e i Engineering Committee of the . IEEE Power Engineering Society for presentation a t the IEEE/PES 1991 Summer Meeting, San Francisco, CA,

to promote better load modeling, and advanced load modeling, in widely used simulation pro- -

July 24 - 28, 1994. Manuscript submitted December 20, 1993; made avai lable f o r pr int ing May 3, 1994.

grams; and 6 to facilitate data exchange among users of vari-

ous production-grade simulation programs.

0885-8950/95/$04.00 0 1994 IEEE

1303

This paper is being coordinated with the work of the necessary. In some cases, voltage sensitive loads, IEEE Power Systems Analytical Data Task Force. along with voltagdoad controls are represented

(i.e.,load tap changer transformers or distribution voltage regulators). Generally, system frequency is assumed to be at rated value, although off-nominal frequency effects could be represented.

what are loads' as represented in large- scale computer simulations, represent the aggrega- tion of hundreds or thousands of individual compo- nent devices such as motors, lighting, and electrical appliances. Except for detailed voltage stability Most power flow programs can model voltage sensi- analysis, the aggregated load is usually the load as tive loads as combinations of constant power and seen from bulk power delivery points, comprising constant impedance loads. This, however, may several megawatts to tens of megawatts. In addition require additional data preparation work: to load components, the aggregated load model ficomme&tions. power flows represent snap- approximates the effects of subtransmission and dis- tribution system lines, cables, reactive power com-

regulators, and even relatively small synchronous or induction generators.

shots in time along the power system,s dynamic tra- jectory. For the first, say, 30-60 seconds following a

voltage sensitive like transient stability program load models. Therefore we recommend the load mod-

pensation, LTc transformers, distribution disturbance (lhe or generator outage), the loads are

Characteristics of good load models. In recom- mending load models, desirable characteristics include correspondence to physical loads and flexi- bility. As an example of a load model without physi- cal correspondence, consider the following static model employed in several widely-used transient stability programs:

" 1 - P = [PI(&) v 2 + P - + P 3 (l+L,,Af) PO VO

els be compatible with static models and data sets of companion dynamic simulation programs. Power flow programs should, optionally, be able to read load model data from dynamic program data files. Recommended models for dynamic simulation pro- grams are presented below. For time frames of sev- eral minutes following a disturbance, loads are often considered constant power because of the action of LTC transformers and other load restoring equip- ment.

This is the 'ZIP' (constant impedance, constant cur- rent, constant power) model multiplied by a linear- ized frequency dependence term. A similar equation is used for reactive power. Since, for example, the resistive portion of physical loads is not frequency dependent, the model is not physically based.

In voltage stability studies, consideration should be given to including equivalents for subtransmissiod distribution feeder impedances and reactive power compensation [9,271. If the load is modeled at the high-side bus of bulk power delivery transformers, the bulk power delivery transformer reactance (typi-

The above model is also limited in its flexibility. For example, field tests often show the reactive portion of the load to be very voltage sensitive (e.g., AQ/AV is 4-7 per unitlper unit) C71. This high voltage sensitiv- ity may be due to distribution transformers operat- ing in saturation. I t is difficult to model such a high (and nonlinear) voltage dependency over the voltage range of interest with the above model.

Better load models are required for relatively new problems such as voltage stability. With present-day and near future computer capabilities in mind, there is more reason than ever to increase model flexibility and fidelity.

2.0 Power Flow Program Models

Due to voltage stability challenges, there is strong current interest in improved load models for power flow simulation. Although constant (voltage insensi- tive) loads are usually assumed for base cases, volt- age sensitive loads need to be modeled for snapshots in time shortly following a disturbance. Expanded representation of subtransmission networks may be

cally about 10%) and the distribution transformer reactance (typically 2-3%) is neglected. Representa- tion of the additional impedance is especially impor- tant if much of the load is motors, or if the load is controlled to be constant power. For the area that is prone to voltage instability, representation of addi- tional busses is required. (These considerations also apply to dynamic simulation.)

3.0 Models for Dynamic Programs

We recommend models that can be used in transient stability, longer-term stability, and small-disturbance stability programs. For small-disturbance stability, the models may be linearized by the small- disturbance stability program.

Dynamic programs receive initial bus load (Po + j Q o ) and voltage magnitude (V,) from compan- ion power flow programs.

3.1

Most dynamic programs allow multiple generators, multiple motor loads, and a single static load model

Multiple loads on a bus concept

-- I

1304

to be connected to a bus. We recommend generaliza- tion of this capability to allow multiple loads of vari- ous types on a bus.

Each individual load type (static, induction motor, synchronous motor, and transformer saturation) may have multiple representation. For example, a bus load may consist of one or more static models, one or more induction motors, and a synchronous motor.

Small synchronous or induction generators embed- ded in the load area may also be connected to the bus.

Each load type may have load shedding or discon- nection logic.

3.2

In large-scale transient stability simulations, loads are typically modeled as purely static (algebraic) functions of voltage and frequency. As described in the Task Force paper [61, both polynomial ('ZIP) and exponential models are used. These models are con- tinuous over the entire voltage range, except for pro- gram logic that may convert static load to impedances at voltages below 0.3-0.7 per unit.

Normally, only one static model is required per bus.

The load powers are functions of bus voltage and frequency. (Usually, the per unit voltage variation is much larger than the per unit frequency variation.) The active part of motor load is generally repre- sented as voltage insensitive, with frequency sensi- tivity depending on the mechanical load characteris- tic. (It's better to represent the frequency dependence of the load directly rather than grossly approximating the effect as a generator damping term.)

As discussed below, static models for dynamic load components should be used cautiously. Representa- tion of loads by exponential models with exponent values less than 1.0 (or by equivalent polynomial models) in a dynamic simulation is questionable [Ell.

Recommendations. As discussed in the introduc- tion, the model should be sufficiently flexible t o allow several forms of representation. Reference 6 describes several good candidate models.

In the following equations, Po and Qo are the initial active and reactive load powers from the power flow base case; they may be termed the nominal load powers meaning the load power at initial voltage and frequency [231. P and Q are the consumed load pow- ers as a function of voltage and frequency. In longer- term dynamic simulations, Po and Qo could be func- tions of time; see 93.10.

Static model for dynamic simulation

In order to standardize on a single static model, we recommend the following model consisting of ZIP terms plus two voltage/f?equency dependent terms:

v 2 V = K (-) + K . - + K , P P h C P O pz vo P' vo

Kpz = 1- (Kpi +K, +Kpl +K*)

where P,, is the fraction of the bus load repre- sented by the static model.

Q = K (-) v 2 + K . - + K q c V Q h c Q o qz Vo qVo

( 3 )

where Qhc is the fraction of the bus load repre- sented by the static model.

A further feature of the recommended static model applies to the voltage/frequency dependent (fourth and fifth) terms in equations 1 and 3. The nominal load power is linearly reduced to zero starting at a specified threshold voltage (Val, Va2); the power is zero for voltage below a second threshold voltage (vbl, vb2). Nominal load power is ramped up for volt- age recovery. See Figure 1. Referring to $3.3, this models the extinction and re-ignition of discharge lighting. This feature could also be used to model some loads with electronic power supplies.

Data to be exchanged for each static model are listed in Table 1. Note that K and K are computed rather than entered. Tabfe 2 provilfzes data descrip- tion.

Discussion. The model provides the flexibility to model various types of loads. For instance, the fre- quency dependent terms could be used for static rep- resentation of two types of motors. Alternatively, the frequency dependent terms could be used to repre- sent a motor and also fluorescent lighting. In soft- ware such as EPRI's LOADSYN program [13,321, the flexibility facilitates accurate aggregation of the estimated load composition.

1305

P Q

Fig. 1. Characteristic of discharge lighting or other discontinuous load as a function of voltage.

Referring to Equations 3 and 4, there is obviously a problem if the load is unity power factor at initial voltage and frequency, but not unity power factor at other voltages and frequencies. This can be avoided by separating the load and reactive power compen- sation. A dynamic program could automatically cor- rect for unity power factor initial conditions by assuming the load is, say, 0.99 power factor lagging, with reactive power compensation applied to match the initial conditions. See Appendix A for fbrther dis- cussion.

On a global rather than individual bus basis, most programs have provisions to convert all static load to constant impedance at very low voltage (0.3-0.7 per unit). This helps solution iterations to converge, and is consistent with the physical fact that near nomi- nal load cannot be consumed at abnormally low volt- age.

3.3 Discharge lighting

Discharge lighting may represent up to 20% of com- mercial load [61.

Various types of discharge lighting (fluorescent, mer- cury vapor, sodium vapor) are essentially static, but extinguish during low voltage. Upon voltage recov- ery, they will re-ignite after a short time delay. Although the extinction and re-ignition may have a hysteresis characteristic, a single-valued power volt- age relation is normally used for modeling numerous individual lamps in transient stability programs. An exponential model is used above a certain voltage such as 0.8 per unit. Below a certain voltage such as 0.7 per unit, all lamps are extinguished with power set to zero. Between the two voltages, the nominal power is ramped to zero 115,161. The re-ignition delay is ignored.

Referring to the static model ($3.2) and Figure 1, dis- charge lighting can be represented by the voltage/ frequency dependent terms using the load ramp down parameters.

3.4 Dynamic induction motor models

About 57% of the US. electricity consumption goes to power motors, mostly integral horsepower three- phase induction motors I101 . Over a decade ago, Undrill and Laskowski presented very strong argu- ments for representing major blocks of induction motor load by dynamic models including both iner- tial and rotor flux dynamics [U. With today’s com- puter capabilities and numerical techniques, there is little reason to represent large motor equivalents with static models.

Lack of dynamic motor models are suspected to be a major source of discrepancies between field mea- surements and large-scale simulation results. Motors that have difficulty reaccelerating following faults affect voltage recovery of important busses. Inertia effects are important in studies involving fie- quency excursions. Rotor flux transients affect damping of oscillations 1111. Taylor showed that motor dynamics, including rotor flux dynamics, is important in undervoltage load shedding program design [121. Compared to a static constant power load, dynamic motor models improve numerical performance of simulation programs. Particularly for explicit inte- gration methods, however, the time step must be small enough.

In the absence of specific data, typical data sets for aggregated motors are available from the EPRI LOADSYN project 113,141, and other sources [15,161. Use of typical motor data sets is better than using static models 1111. Table 1 provides data extracted from the LOADSYN reports.

Because of significantly different characteristics, it may be desirable to model equivalents for both small and large motors 113-161. For small motors, repre- sentation of inertia dynamics only, without rotor flux dynamics, may be sufficient 1211.

An important input parameter is the machine load- ing in per unit of motor MVArating. This determines the motor load factor defined as MW loadinghated MVA. Surveys in the US. have shown that motors purchased individually (not part of an appliance) are typically oversized [lo]. This practice, while uneco- nomical, improves system dynamic performance.

An alternative to routine representation of motors is sensitivity studies for each new situation to be simu- lated. The sensitivity studies involve simulation

* Although large motors dominate energy use, peak load condtions could be dominated by smaller three-phase and single-phase air condi- tioning motors. See reference 20.

1306

with and without dynamic motor models.

Recommendations. Reference 11 and 22 provide equations for modeling induction motors.

Models representing three-phase motors with a sin- gle rotor circuit in each axis are generally appropri- ate for aggregated motors in large-scale simulations (third order model with slip and d, q axis internal voltage or flux as state variables).

For data exchange, however, we recommend the flex- ibility to represent both simpler models and more detailed models. The simpler model is an option to represent slip dynamics only, and uses the same equivalent circuit data. More detailed models are recommended for representation of double cage and deep-bar rotor types of motors, and for representa- tion of saturation of leakage inductances and magne- tizing inductance. More detailed models may be required for representation of large industrial motors including power plant auxiliaries, especially if motor starting or stalling (i.e., high current) is involved 130,313.

The basic recommended model, with rotor dynamics included, automatically tracks changes in system frequency. In the simple model with only inertial (slip) dynamics, this automatic tracking is lost, and for use in simulations where the frequency changes significantly, the motor terminal bus frequency should be used to compute slip to modify the steady- state equivalent circuit.

Based on references 22 and 30-31, Figures 2-4 show equivalent circuits for single-cage, deep-bar, and double-cage motors. Parameters are defined in Table 2 except for D, and Dr which are saturation coeffi- cients that are computed internally from saturation current 122,301. Figure 5 shows a general purpose saturation model that is used with Figures 2-4 to represent magnetizing inductance saturation.

The motor's fraction of initial bus active load is an input parameter. The corresponding initial reactive power load is computed during model initialization. Differences between motor reactive power and bus initial reactive power (portions of Q,) unused by other load types) are resolved by adding shunt reac- tive power compensation.

In order to facilitate flexibility and compatibility of programs, the recommended mechanical torque model is:

C = 1- ( A + B + D ) (7)

Motor starter ac contactors or undervoltage protec-

Fig. 2. Single-cage induction motor steady-state equivalent circuit.

Fig. 3. Deep-bar induction motor steady-state equiv- alent circuit.

Fig. 4. Double cage induction motor steady-state equivalent circuit.

tion may trip motors at low voltage. We recommend provision to trip a percentage, Ptfip, of motor load for low voltage, VI, lasting a specified time, TI. Table 1 lists mandatory and optional data exchange parameters. Table 2 provides data description. Table 3 provides typical data for use in large-scale simula- tions [13,141.

Induction generators are often embedded in load areas. Except for mechanical loaaprime mover data, the same induction machine models and data sets should be used for induction generators.

There is current research in modeling single-phase induction motors and variable speed drives in dynamic programs. These models are outside the scope of this paper.

3.5 Dynamic synchronous motor models

Synchronous motors sometimes need to be repre- sented. The most obvious need is for pumped storage plants. Synchronous machine models are available in all programs. The only requirement is the mechanical load torque model.

1307

Recommendations. The recommended load torque model is the same as the induction motor load torque model given by Equations 6 and 7.

Similar to synchronous generators, the fraction of initial active and reactive bus load are input param- eters.

3.6 Transformer saturation

Distribution transformers, which may be considered part of the load, normally operate with significant magnetizing induction saturation. Many field tests show large voltage sensitivity of reactive power load following voltage changes. For small changes, reac- tive power may change as the third to seventh power of voltage.

To more correctly represent reactive power demand as seen from the bulk power network, i t may be desirable to have compatible transformer saturation models in both stability and power flow programs.

Transformer saturation will limit fundamental fre- quency temporary overvoltages. Accurate evaluation of potentially damaging temporary overvoltages, however, require evaluation by electromagnetic transients programs.

Recommendations. Figure 5 shows the recom- mended model. This model is also used to represent induction motor magnetizing inductance saturation (83.4). The transformer exciting current as a func- tion of voltage is represented by a piecewise linear characteristic.

Table 1 lists data exchange parameters and Table 2 provides data description.

Q,

- Slope of region 1 Slope of region 2 2 VI--- *= Slope of region 1 Slope ofregion 3

G - -

1 b Excitation current

Fig. 5. Saturation function for induction motors and transformers.

3.7 Load tap changing transformers

This is actually a network rather than a load model.

For longer-term dynamics, load restoration by LTC transformers and distribution voltage regulators may need to be modeled. Tap changing regulates load-side voltage, and thereby voltage sensitive load.

Loads with voltage controlled by tap changers require LTC transformer representation in the power flow case. Additional buses may be required compared to traditional representation.

Modeling for longer-term voltage stability analysis usually requires expanded representation of sub- transmission, and equivalents for distribution 1231. Figure 6 shows a typical situation involving a bulk power delivery LTC transformer.

High Distribution voltage equivalent,

bus 2 = %lo%

I limits XE 10%

Ldad

Fig. 6. LTC transformer and distribution equivalent for voltage stability simulation.

Recommendations. Figure 7 shows the recom- mended model. Provision is made for line drop com- pensation. North American practice is to start tap changing after an initial time delay, Td,,, of 30-120 seconds. Tapping then continues until the voltage is within a bandwidth. The mechanism delay, T,, between tap steps is typically 5-10 seconds. If desired, intentional time delay, Tdl, between tap steps can be modeled.

Typical North American data is +lo% voltage tap limits, 5/8% voltage tap steps (+16 steps), and 2-4 volts bandwidth based on 120 volts. Reference 23 provides additional information, including European practices (a limitation of the recommended model is that inverse-time relay control of tap changing is not included).

Note that the model is discontinuous, involving both pure time delays and deadbands. This has implica- tions for small-disturbance analysis.

Table 1 lists data exchange parameters and Table 2 provides data description.

3.8 Models for load shedding

Underfrequency or undervoltage load shedding mod- els are required for some dynamic and quasi- dynamic simulations. The simplest assumption is to

1308

8 I-

Qa , $3 '8 a t

-A---

i i i h h h VI A A

II e 6

0 3 rl

O d d I

II 9

' r l

II I

1309

Table 1 : Load Model Types and Data Exchange Parameters

Synchronous motor Discharge lighting Transformer saturation

See text See static model 10, Vi, V2, GI, Gq

I - - - - I LTC transformer I Rc, x c , DB, E, Tam Tal 9 Ttn I I

- - -- -- I I

a. Bus nameds) and kV identification not included.

trip each part of the load according to its proportion of the total load. Sometimes it may be desirable to trip specific components (static load, motor load, etc.).

Most underfrequency relays have no intentional time delay, but have operating times of 6-9 cycles. Several steps of underfrequency load shedding may need to be represented at a single bulk power deliv- ery bus.

Undervoltage relays normally trip load after signifi- cant time delay [121. An inverse time delay (volt- second integrating) relay may be used.

Circuit breaker operating times are usually 5-15 cycles.

In some installations, underfrequency or undervolt- age relays trip lines with tapped load, rather than tripping load directly [121. Models are provided in several existing programs. Automatic load restoration following recovery of fre- quency or voltage is also applied by some utilities. This may be important in preventing overfrequency as a result of overshedding [291.

Recommendations. To limit the scope and length of this report, we do not recommend specific models and data exchange parameters. Industry activity to define standard relay models for dynamic programs would be valuable.

3.9 Dynamic constant energy load models and generic dynamic load models

For simulation of wintertime voltage stability situa- tions, thermostatically-controlled conductance (heat- ing) load is important. Other loads such as water heating, industrial heating, and cooking are either automatically or manually controlled to deliver con- stant energy.

In most cases, we are interested in the composite

response of a large number of individual loads. For low voltage, constant energy loads cause loss of load diversity. Individual loads stay on longer. The low voltage period may start after tap changer controls reach boost limits. Time constants may be as short as several minutes [17,18,251. First order (single time constant) models have been proposed to model aggregated constant energy loads 117,273. More com- plex physically-based models have been imple- mented in a longer-term dynamics program [221. The loads are assumed to be unity power factor and only active power dynamics are modeled.

In highly detailed studies, several constant energy load models with different time constants could be used at a bus. For example, older homes, highly insulated homes, and other constant energy loads (water heating, cooking, industrial heating) could be represented with Werent time constants.

Thermostatically-controlled air conditioner loads are essentially constant power load (load restoration by induction motor action). Therefore thermostatic con- trol usually need not be modeled.

Recently, several generic first-order dynamic models have been proposed for longer-term voltage stability simulation [18,23,25,26,281. These models approxi- mate both active and reactive power dynamics of aggregated loads. Depending on the time constant, load restoration dynamics by induction motors, load tap changers, or constant energy mechanisms can be approximated.

Because of limited experience with these models, and because data exchange between different pro- grams is unlikely to be needed in the near future, we do not recommend standard models in this paper.

3.10 Load changes as a function of time

For longer-term dynamics, facility to ramp or other- wise change the load as a function of time is

1310

Table 2: Dynamic Data Description

K D 1

npv2

Induction motor p

Fraction of total active or reactive nominal (initial) load.

Per unit of active load that is constant current. Per unit of active load that is constant. Per unit of active load that is voltage and frequency sensitive (term 1). Per unit of active load that is voltage and frequency sensitive (term 2).

Frequency sensitivity (term 1). Voltage sensitivity exponent (term 2). Frequency sensitivity (term 2). Per unit voltage at which load starts to be ramped to zero (Figure 1). Per unit voltage at which load is set to zero (Figure 1).

Dynamic order of model: 1,3, or 5. Motor rated MVA. MVA and Pfmct determines motor load factor. Motor rated voltage; may be different than power flow bus rated voltage.

1

I Motor and motor load inertia in MW-s/MVA.

a. Only data for active load is described; reactive load data is similar-see equations 1-4. b. Tap range and tap step size is assumed to available from the companion power flow program data.

131 1

Table 3: Typical Induction Motor Data [13,14Ia

7 I 0.064 I 0.091 I 2.23 I 0.059 I 0.071 I 0.2 10 1 0 I 0.34 - I 0.8 a. Data is suitable for large-scale simulations where motors do not stall

Type 1: Small industrial motor. Type 2: Large industrial motor. Type 3: Water pump. Type 4: Power plant auxiliary. Type 5: Weighted aggregate of residential motors. Type 6: Weighted aggregate of residential and industrial motors. Type 7: Weighted aggregate of motors dominated by air conditioning.

required. For example, morning load pickup may be critical in voltage stability analysis. The load changes may be different for different load classes (residential, commercial, industrial). This can be done by changing the Po and Qo of individual bus- ses or load types. It may also be desirable to change load on a zone or area basis.

This is a desired feature of longer-term dynamics programs [231. Implementation details and data exchange are outside the scope of this paper.

4.0 Example Based on Load Composition

Typical data values were summarized as part of the EPRI LOADSYN computer program development [131. This data is now available in a textbook C271. There are also many other sources of data. In some cases, the data may be the aggregate response of load components as determined by system measure- ments.

As an example, assume a load delivery point consists of 30% heating (space heating, cooking, water heater, clothes dryer, etc.), 20% fluorescent lighting, and 50% small industrial motors with load factor of 0.6. The total load is forecasted to be Po +jQo = 1O+j2 MW. Using the LOADSYN data values, the standard load model data is as follows.

All static model. Based on equations 1-5, the data is:

Pfrac = Qfrac = 1.0 Kpi = Kpc = Kqi = Kqc = 0

K - 0.2, npvl = 1.0, npfl = 1.0, nqvl = 3.0, nqfl = -2.8, PI-

Val = 0.8, vbl= 0.7 (fluorescent lighting)

Kp2 = 0.5, npv2 = 0.1, npn = 1.9, ngv2 = 0.5, nqn = 1.2 (small induction motor)

The power factor of heating is 1.0, the power factor of fluorescent lighting is 0.9 (Q = Ptang = 0.969 MVAr), and the power factor of the small induction motor is 0.83 (Q = Ptan4 = 1.344 MVAr). As a frac- tion of Qo, Kql = 0.4845 and Kq2 = 0.672 (additional input data). Using equation 5, qz = -0.1516 is com- puted internally (capacitive shunt compensation to resolve the mismatch between the load component power factors and the forecasted reactive power). Kpz is computed to be 0.3.

Static and dynamic model. Data for the static portion of the load is: Pfrac = Qfrac = 0.5, Kpi = Kpc = Kp2 = Kqi = Kqc = Kqz = 0

Kpl = 0.4, Kql =0.969, npvl = 1.0, n fl = 1.0, nqvl = 3.0, nqfl = -2.8, va1 = 0.8, vbl= 0.7 duorescent light- ing) Computed internally, Kpz = 0.6, Kqz = 0.031.

Data for the dynamic (motor) portion of the load is:

Pfrac = 0.5, Order = 3, MVA = 8.33, R, = 0.31, X, = 0.10, R, = 0.018, X, = 0.18, X, = 3.2, X, = Xr = 0, H = 0.7, A = 1.0, B = 0

The initial motor reactive power is computed based on the terminal voltage, active power, and equiva- lent circuit parameters. Shunt compensation is internally added to resolve mismatch with the fore- casted reactive power; the shunt compensation is

I

1312

combined with the Kqz term.

With more complex load mixtures, a computer pro- gram such as LOADSYN can be used for aggregation and for computing data for the models.

5.0 Summary

We recommend standard load models for power flow and dynamic simulation programs. Static models are suitable for power flow simulations, and for dynamic simulations at locations where results are not sensi- tive to load modeling. We recommend induction motor models for use at locations where results are sensitive to load modeling. We also recommend mod- els for longer-term dynamic simulations. Table 1 summarizes the data to be exchanged for the several types of models and Table 2 provides data descrip- tion.

6.0 Referencedselected Bibliography

1. IEEE Standard 1110-1991, ZEEE Guide f ir Synchro- nous Generator Modeling Practices in Stability Analy- ses, 1991.

2. IEEE Standard P421.5-1992, IEEE Recommended Practice for Excitation System Models for Power Sys- tem Stability Studies, 1992.

3. IEEE Committee Report, ”T)ynamic Models for Fossil Fired Steam Units in Power System Studies,” IEEE Zkansactions on Power Systems, Vol. 6, No. 2, pp. 753- 761, May 1991.

4. IEEE Committee Report, “Hydraulic Turbine and Tur- bine Control Models for System Dynamic Studies,” IEEE hnsactwns on Power Systems, Vol. 7, No. 1, pp. 167-179, February 1992.

5. IEEE Committee Report, “Static Var Compensator Models for Power Flow and Dynamic Performance Simulation,” paper 93 WM 173-5 PWRS, IEEEPES 1993 winter meeting.

6. IEEE Committee Report, “Load Representation for Dynamic Performance Studies,” IEEE lFansactions on Power Systems, Vol. 8, No. 2, pp. 472-482, May 1993.

7. CIGRE Task Force 38-02-05, “Load Modelling and Dynamics,” Electra, pp. 124-142, May 1990.

8. M. K. Pal, discussion of “An Investigation of Voltage Instability Problem,” by N. Yorino et al., IEEE Duns- actions on Power Systems, Vol. 7, No. 2, pp. 600-611, May 1992.

9. K. Walve, “Modeling of Power System Components at Severe Disturbances,” paper 38-18, Proceedings of CIGRE, 1986.

10. S. Nadel, M. Shepard, S. Greenberg, G. Katz, A. T. de Almeida, Energy-Efficient Motor Systems: A Handbook on Technology, Programs, and Policy Opportunities, American Council for an Energy-Efficient Economy, Washington, D.C., 1991.

11. J. M. Undrill and T. F. Laskowski, “Model Selection and Data Assembly for Power System Simulation,” IEEE fiansactions on Power Apparatus and Systems, Vol. PAS-101, No. 9, pp. 33334341, September 1982.

12. C. W. Thylor, “Concepts of Undervoltage Load Shed- ding for Voltage Stability, ZEEE hnsactwns on Power Delivery, Vol. 7, No. 2, pp. 480488, April 1982.

13. General Electric Company, Load Modeling f i r Power Flow and Dansient Stability Computer Studies, EPRI Final Report EL-5003, January 1987. (Four volumes; describes LOADSYN computer program. Volume 2 is a load modeling reference manual.)

14. F. Nozari, M. D. Kankam, and W. W. Price, “Aggrega- tion of Induction Motors for Transient Stability Load Modeling,” ZEEE hnsactions on Power Systems, Vol. 2, No. 4, pp. 10961103, November 1987.

15. H. K. Clark, T. F. Laskowski, k Wey Fo, and D. C. 0. Alves, “Voltage Control in a Large Industrialized Load Area Supplied by Remote Generation,” paper A 78 558-9, IEEEPES 1978 Summer Meeting.

16. H. K. Clark and T. F. Laskowski, “’kansient Stability Sensitivity to Detailed Load Models: a Parametric Study,” paper A 78 559-7, IEEEPES Summer Meet- ing, Los Angeles, July 1621, 1978.

17. Klaus-Martin G d , ”Dynamic Simulation of Voltage Collapse Processes in EHV Power Systems,” Proceed- ings: Bulk Power System Voltage Phenomena-Voltage Stability and Security, EPRI EL-6183, Section 6.3, January 1989.

18. D. Karlsson, K. Lindbn, I. Segerqvist, and B. Stenborg, “T’emporary Load-Voltage Characteristics for Voltage Stability StudienField and Laboratory Measure- ments,” CIGR& paper 38-204,1992.

19. M. S. Calovic, ”Modeling and Analysis of Under-Load Tap Changing Transformer Control Systems,” ZEEE Dansactions on Power Apparatus and Systems, Vol.

20. B. R. Williams, W. R. Schmus, and D. C. Dawson, “I‘ransmission Voltage Recovery Delayed by Stalled Air-conditioner Compressors,” IEEE Dansactions on Power Systems, Vol. 7, No. 3, pp. 1173-1181, August 1992.

21. S. Ahmed-Zaid, M. Web, and W. W. Price, “First- Order Induction Machine Models Near Voltage Col- lapse,* International Workshop on Bulk Power System Voltage Phenomena: Voltage Stability and Security, Deep Creek Lake, Maryland, pp. 403-410,4-7 August 1991.

22. P. Kundur, Power System Stability and Control, McGraw-Hill, 1994.

23. CIGRG Task Force 38-02-10, Modelling of Voltage Col- lapse Including Dynamic Phenomena, CIGRE Bro- chure No. 75,1993.

24. W. W. Price, D. B. mapper, N. W. Miller,A. Kurita, and H. Okubo, “A Multi-Faceted Approach to Power Sys- tem Voltage Stability Analysis,” CZGRk, paper 38-205, 1992.

25. D. Karlsson, and D. J. Hill, “Modelling and Identifica- tion of NonLinear Dynamic Loads in Power Systems,” IEEEPES paper 93 WM 171-9 PWRS.

26. W. Xu and Y. Mansour, “Voltage Stability Analysis Using Generic Dynamic Load Models,” IEEWES paper 93 WM 185-9 PWRS.

27. C. W. Taylor, Power System Voltage Stability, McGraw- Hill, 1993.

28. D. J. Hill, “Nonlinear Dynamic Load Models with Recovery for Voltage Stability Studies,” IEEE %ns-

PAS-103, NO. 7, pp. 1909-1915, July 1984.

1313

actions on Power Systems, Vol. 8, No. 1, February 1993.

29. C. W. Taylor, F. R. Nassief, and R. L. Cresap, “North- west Power Pool Transient Stability and Load Shed- ding Controls for Generation-Load Imbalances,” IEEE Dansactions on Power Apparatus and Systems, Vol.

30. G. J. Rogers and D. Shirmohammadi, “Induction Machine Modelling for Electromagnetic Transient Program,” IEEE lhnsactions on Energy Conversion, Vol. EC- 2, No. 4, pp. 622-628, December 1987.

31. G. J. Rogers and D. S . Benaragama, “An Induction Motor Model with Deep-Bar Effect and Leakage Inductance Saturation,” Archiv fur Ekkhtechnik, Vol. 60, pp. 193-201,1978.

32. W. W. Price, K. A Wirgau, A. Murdoch, J. V. Mitsche, E. Vaahedi, and M. A El-Kady, “Load Modeling for Power Flow and Transient Stability Computer Stud- ies,” IEEE lhnsactions on Power Systems, Vol. 3, No. 1, pp. 180-187, February 1988.

PAS-100, pp. 3486-3495, July 1981.

i

Appendix A: Base Values for Load Data

Equations 1 and 3 contain base values for active and reactive power, and voltage. In the computer world, the base values are from a solved power flow.

The base values used in developing model parame- ters from field tests could have different meanings. For instance, base power could be transformer or load MVA rating. Most commonly, however, the base values are the initial values of active and reactive power.

A particular problem occurs if the initial measured reactive power is very small. Then computing per unit reactive power, Q/Qo, becomes erratic. (The meaning of exponents nqvl and nm in Equation 3 if obtained by tests is AQ/AV per unitlper unit.)

In providing data from field tests, the instrumenta- tion and the methods used for obtaining parameters should be clearly described.

Because prevailing practice and nearly all data sets are based on use of Po in computing per unit active power and Qo in computing per unit reactive power, we recommend this convention in equations 1 and 3. S6me experts, however, recommend either use of So (apparent power) as the base for both active and reactive power, or use of Po as the base for reactive power. This avoids difficulties when reactive power is small or zero.