Research on stochastic power-flow study methods. Final report
- ed.
A general algorithm to determine the effects of uncertainty in bus load and generation on the output of conventional power flow analysis is presented. The use of statistical moments is presented and developed as a means for representing the stochastic process. Statistical moments are used to describe the uncertainties, and facilitate the calculations of single and multivarlate probability density functions of input and output variables. The transformation of the uncertainty through the power flow equations is made by the expansion of the node equations in a multivariate Taylor series about an expected operating point. The series is truncated after the second order terms. Since the power flow equations are nonlinear, the expected values of output quantities is in general not the solution to the conventional load flow problem using expected values of input quantities. The second order transformation offers a correction vector and allows the consideration of larger uncertainties which have caused significant error in the current linear transformation algorithms. Voltage controlled busses are included with consideration of upper and lower limits. The finite reactive power available at generation sites, and fixed ranges of transformer tap movement may have a significant effect on voltage and line power flow statistics. A method is given which considers limitation constraints in the evaluation of all output quantities. The bus voltages, line power flows, transformer taps, and generator reactive power requirements are described by their statistical moments. Their values are expressed in terms of the probability that they are above or below specified limits, and their expected values given that they do fall outside the limits. Thus the algorithm supplies information about severity of overload as well as probability of occurrence. An example is given for an eleven bus system, evaluating each quantity separately. The results are compared with Monte Carlo simulation.
- Research Organization:
- Purdue Univ., Lafayette, IN (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AS02-77ET29102
- OSTI ID:
- 6576841
- Report Number(s):
- DOE/ET/29102--1
- Country of Publication:
- United States
- Language:
- English
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EHV & UHV-- (-1989)
24 POWER TRANSMISSION AND DISTRIBUTION
ENERGY SYSTEMS
INTERCONNECTED POWER SYSTEMS
LOAD ANALYSIS
MATHEMATICAL MODELS
MATHEMATICS
MONTE CARLO METHOD
OPERATION
OUTAGES
POWER DEMAND
POWER GENERATION
POWER SYSTEMS
POWER TRANSMISSION
PROBABILITY
RELIABILITY
STATISTICS
STOCHASTIC PROCESSES
SYSTEMS ANALYSIS