Abstract
This paper proposes a probabilistic power flow (PPF) method considering continuous and discrete variables (continuous and discrete power flow, CDPF) for power systems. The proposed method—based on the cumulant method (CM) and multiple deterministic power flow (MDPF) calculations—can deal with continuous variables such as wind power generation (WPG) and loads, and discrete variables such as fuel cell generation (FCG). In this paper, continuous variables follow a normal distribution (loads) or a non-normal distribution (WPG), and discrete variables follow a binomial distribution (FCG). Through testing on IEEE 14-bus and IEEE 118-bus power systems, the proposed method (CDPF) has better accuracy compared with the CM, and higher efficiency compared with the Monte Carlo simulation method (MCSM).
Highlights
Probabilistic power flow (PPF) was first proposed by Borkowska in 1974 [1], and is an effective probabilistic analysis method for the exploration of the influence of stochastic factors on power systems [2]
The Monte Carlo simulation method (MCSM) is an outstanding representation, and it is regarded as a standard to evaluate the accuracy and efficiency of other PPF methods
The active output power of multiple fuel cell generation (FCG) is usually assumed to follow a binomial distribution, listed as follows: PFCG,i = Cni (1 − sd)i sdn−i xi = s · i where n is the total number of FCGs, i is the number of FCGs which are in the operational status, sd is the probability value of a single FCG in the shutdown status, s is the rated power of a single
Summary
Probabilistic power flow (PPF) was first proposed by Borkowska in 1974 [1], and is an effective probabilistic analysis method for the exploration of the influence of stochastic factors on power systems [2]. To obtain the probability distributions of power flow responses accurately and reduce errors from PEM, cumulant method (CM) is presented, which is an analytical method. Probability distributions of power flow responses cannot be obtained accurately, because the von Mises method handles discrete variables with an approximate approach. Cai et al [29] applied MCSM to calculate the cumulants of random input variables with complex probability distributions, but this method cannot diminish errors in CM. In order to solve PPF problems with continuous and discrete variables accurately, this paper presents a novel PPF method considering continuous and discrete variables (CDPF). Probability distributions of power flow responses can be calculated accurately and efficiently by the convolution of continuous and discrete variables of power flow responses. This paper proposes a novel PPF method (CDPF) that can accurately solve PPF problems with continuous and discrete variables simultaneously. The main framework of this paper is organized as follows: Section 2 introduces probability distributions of WPGs, FCGs, and loads which are used in this paper; Section 3 describes the CDPF method in detail; Section 4 shows case studies and analysis results; and Section 5 draws conclusions
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