the LILCO Southold feeder load to a voltage variation from 0.95 to. 1.10 per unit. The program was also usedto simulate the response of the Southold load to a ...
Summary
Previous studies and experience have shown that load models can have a significant effect on the results of stability simulations. Past practice has been to assume load models which produce the most conservative (pessimistic) results. The planning and operations decisions made from these studies are often costly and unnec¬ essarily conservative. The work reported in this paper was perfomed under EPRI contract RP849-5. The EPRI RP849 project series has the goal of developing a systematic procedure for building load models suitable for transient stability studies from knowledge of the characteristics of the end use components. This paper describes work which was performed to extend the component models and model building procedure developed in earlier RP849 projects so that the real and reactive power response under both steady state and transient conditions is better modeled. The scope of the work performed so far has been limited to residential loads and this has allowed the feasibility of the procedure to be demonstrated. Further research is required to extend the procedure to handle commercial and industrial loads. Physical models were developed for residential load components including refrigerators, freezers, furnace fans, washing machines, dryers, electric heat, water heaters, ranges, incandescent lights, distribution transformers, and capacitors. Small induction motor load components are modeled using equivalent circuits. This approach provides a model which is ap¬ plicable over a wide voltage and frequency range for both steady state and dynamic conditions. A computer program was written to simulate the response of the distribution system load to an arbitrary variation in supply voltage. The program includes models for induction motors, distribution transformers, incandescent lights, resistive load and shunt capa¬ citors. It can simulate the steady state and dynamic response of the real and reactive power in a distribution feeder load to arbitrary voltage variations over the range 0-120%. The composition of the load broken down by components was obtained using appliance saturation statistics and diversity factors which reflect seasonal and time of day effects. The program was used to simulate the steady state response of the LILCO Southold feeder load to a voltage variation from 0.95 to 1.10 per unit. The program was also used to simulate the response of the Southold load to a circuit breaker trip followed by a reclosure after 0.8 seconds. The results of the steady state simulations are compared with the field test results in Figs. 1 and 2.
X-X-X CALCULATED ?. ?. * MEASURED
BASE VOLTAGE 7.62 KV
SOUTHOLD FEEDER STEAUr STATE SIMULATION TEST PERFORMED JA« IB 197? 21 :
Fig. 2. Comparison of Measured and Simulated Reactive Power for Steady State Test. January 1982, p.
136
A Generalized Methodology for
Modeling System Components in Power System Dynamics Simulation
M. H. Dwarakanath, Senior Member IEEE, B. Dembart, A. M. Erisman, Member IEEE, K. Hemmaplardh, Member IEEE, and J. W. Manke Boeing Computer Services Company, Energy Technology Applications Division Tukwila, WA A generalized methodology for modeling various system com¬ ponents in power system dynamics simulation studies is presented
SOUTHOLD FEEDER STEAD* STATE SIMULATION TEST PERFORMED JAM IB 197? 21¡48
VOLTAGE PER UNIT
Fig. 28
1.
Comparison
1.17
1.20
of Measured and Simulated Real Power For Steady State Test
in this paper. The salient features of the method are: . It permits the modeling of control systems of varied degrees of complexity with no change to software whatsoever. . It permits the order of the model to be modified with very minimal input from the user. . It provides an orderly procedure for computing initial conditions for the control system, utilizing a sparse matrix technique. . It provides an orderly procedure for computing the dynamics of the control systems using either the explicit or implicit inte¬ gration method. . It lends itself for implementation on an array processor. The salient features of the method are described in detail with the aid of a simple exciter control system and a fairly complex fossil-fuel steam turbine model. The capability of the method to model control systems of varied degrees of complexity with no change to software will result in a substantial savings of the software enhancement efforts. Fur¬ thermore, this feature provides a viable analysis tool for a power system engineer to analyze the effects of nonlinearities and models of varied degrees of complexity. In addition it allows the modi¬ fication of models with very minimal input data. Computation of initial conditions for the various control systems to satisfy the steady state conditions imposed by the solution of nonlinear algebraic equations of the transmission network is an important aspect in power system dynamics analysis. This is ac¬ complished by an orderly procedure with the aid of an ordering scheme derived from the application of sparse matrix techniques.
PER JAN
Even though the generalized modeling methodology apparently increases the dimensionality of the problem, the computation of the dynamics is performed without incurring any penalty for the higher dimension. This is accomplished by using the invariance property of the first order linearization and the application of sparse matrix techniques. By this procedure it is assured that the number of equations to be solved by iterative process is consistent with the order of the control system. Implementation of this generalized methodology concept in an array processor should contribute in the long run to the de¬ velopment of a power system training simulator. The potential future applications of the generalized modeling
The network Zeq is a combination of resistance-capacitance (R-C) units and has a frequency response that matches that of the line characteristic impedance ZCM (Fig. 2(a)). The current sources lkh and lmh represent the weighted history of the voltage and current waves traveling along the line. These sources are derived from the simulation of the system propagation function A fa) in the fre¬ quency domain by means of a rational function approximation (Fig. 2(b). In the time domain this rational function corresponds to a sum of exponential terms. This allows the evaluation of the convolution integrals that are necessary to determine lkh and lmh to be performed
recursively [2]. Numerical Techniques methodology are: . Its application to modeling of power plants The numerical techniques for the synthesis of Zfa) and the . Study of model order reduction simulation of A fa) are based on an asymptotic tracing of the . Design of power system training simulator corresponding magnitude functions, from their initital to their final . Exchanging of power system data among various organiza¬ asymptotic values. This results in a uniformly accurate represen¬ tions. tation over the entire frequency band, from the de condition to, for instance, 106 Hz. The order of the approximations is automatically defined by the breaking points of the asymptotes. This process January 1982, p. 147 overcomes the limitations of previous rational function approxi¬ mations where, due to the difficulty of pre-establishing the form of the approximating functions, the characteristic impedance has been assumed constant and the propagation function has been simulated of Accurate with only three exponentials [2] (resulting in loss of accuracy over an extended frequency range). The approximation of Zfa) in Fig. 2 (a) Transmission Lines in resulted in 8 R-C blocks, and the simulation of A fa) in Fig. 2 (b) resulted in 13 exponential terms. Transient
Modeling FrequencyDependent Electromagnetic
Simulations
J. R. Marti, Member IEEE University of British Columbia, Department of Electrical Engineering, Vancouver, B.C., Canada
Electromagnetic Transient Simulations The experience over the last ten years in the digital simulation of electromagnetic transients in power systems has proven the ad¬ vantages of time domain formulations [1] for a large class of system conditions. It has also been recognized, however, that not to account for the frequency dependence of the parameters of system com¬ ponents such as transmission lines with ground return can greatly affect the results of the simulations. Different formulations have been suggested in order to develop circuit models that without restricting the generality of time domain formulations can incorporate the effect of the frequency depend¬ ence of the parameters. The improvement obtained with these models as compared to constant-parameter representations has been quite encouraging. However, these models have encountered in their application a series of numerical instability and inaccuracy problems, and their use has required many particular considera¬
10 JO* NT* FREQUENCY IHZI
10"
\(f
Iff
IO*
JO'
(a)
tions.
New Formulation The formulation presented in this paper avoids the numerical problems encountered in previous formulations and leads to much more accurate models without the need for particular considera¬ tions on the part of the users. The general form of the new models is shown in Fig. 1.
¡k(0
Fig.
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m
lunn imwii iirnw i nun iiimiiDmi hhmt rTmn nun limn nmn
IO* IO1 IO"'
I
IO
10*
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FREQUENCT IHZI
10*
IO*
IO*
IO'
l(f
(b)
Vm(t)
1. New frequency-dependent line models at nodes k and m.
PER JAN
02H
¡m(t)
n Zeq lkhQj(T)lmhzeq jn
VU
20.4-f
Fig. 2.
Simulation of Zfa) and A fa). Curves (I): Exact parameters. Curves (II): New Model parameters.
29
