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Two-Point Estimate Method for Probabilistic
Optimal Power Flow Computation Including
Wind Farms with Correlated Parameters
Xue Li, Jia Cao, and Dajun Du
Key Laboratory of Power Station Automation Technology
Department of Automation, Shanghai University, 200072 Shanghai, China
Abstract.
This paper is concerned with the probabilistic optimal power
flow (POPF) calculation including wind farms with correlated parame-
ters which contains nodal injections. The two-point estimate method
(2PEM) is employed to solve the POPF. Moreover, the correlation sam-
ples between nodal injections and line parameters are generated by
Cholesky Factorization method. Simulation results show that 2PEM is
feasible and effective to solve the POPF including wind farms with cor-
related parameters, while the 2PEM has higher computation precision
and consume less CPU time than Monte Carlo Simulation.
Keywords:
Probabilistic Optimal Power Flow, Wind Farms, Correlated
Parameters, Cholesky Factorization Method, Point Estimate Method.
1 Introduction
The impacts of wind farms should be studied with the large scale wind power
integrated into the power system due to the characteristics of wind as random-
ness, intermittent, and fluctuation. The probabilistic optimal power flow (POPF)
computation including wind farms can be used to not only assess the economic
impacts in steady state operation of system, but also analyze the basis of various
economic behaviour under the environment of power market.
The existing probabilistic methods applied to power systems can be divided
into three categories: Monte Carlo simulation (MCS) [1], point estimate method
[2] and analytical method [3]-[4]. The probability description of state voltage
and branch power flow can be obtained accurately by MCS [1], however, it
usually consumes large computation effort. The point estimate method [2] is
widely applied to the probability distribution fitting of the optimal power flow
solution, which is based on the deterministic optimal power flow calculation
and can calculate the statistical moment of the quantity of state eciently. The
first order second moment method [3] and Cornish-Fisher series [4] belong to
the analytical method. However, the lectures above mentioned, not considering
the correlation between random variables such as load and generation power,
produce the impractical probabilistic results.
To solve the probabilistic power flow with correlated parameter problem, the
covariance matrix transformation technique [5] is combined into the two-point
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