A Probabilistic Formulation of Load Margins in Power Systems With Stochastic Generation

Abstract

This paper discusses the impact of uncertain power injections in the grid on the load margin. Two common analyses of voltage stability are those aiming for the closest saddle node bifurcation and those assuming a prefixed direction of load and production increase. In the case of large renewable based generation units or a significant degree of dispersed generation, the loading margin has to be interpreted as a stochastic variable itself. This allows to interpret load margins at different levels of probability of voltage collapse with or without corrective actions undertaken. The probabilistic margin is assessed with a minimum number of samples by use of a stochastic response surface method implementation. The method is illustrated on the IEEE 24-bus and 118-bus system considering stochastic wind generation and dispersed generation.

Analysis of voltage stability uncertainty using stochastic response surface method related to wind farm correlation

“…P Li and Q Li are functions of V i and α i . Equations (3 and 4) represents a pure dynamic system and taking derivative of (3,4) leads to the dynamic quantity _ V i and _ α i [12,13] as:…”

“…The probabilistic analysis was firstly introduced into studying power system small signal stability by Burchett and Heydt in [2]. A series of work later on [3][4][5][6] have further improved the various aspects of the analytical method of power system probabilistic small signal stability. In [7,8], a method of probabilistic analysis was proposed to directly calculate the probabilistic density function of critical eigenvalues of a large scale power system from the probabilistic density function of gird connected multiple sources of wind power generation to investigate the impact of stochastic uncertainty of grid-connected wind generation on power system small-signal stability [9].…”

Active distribution networks planning with integration of demand response

“…In [5], the authors proposed a combined MCS and optimal power flow (OPF) to maximize the social welfare by integrating DR scheme considering different combinations of wind generation and load demand over a year. A stochastic formulation of load margin taking into account the uncertainties related to RES integration into the network is proposed in [6]. In [7], a probabilistic reliability criterion considering uncertainties related to component outage in the expansion planning is proposed.…”

Risk-Averse Preventive Voltage Control of AC/DC Power Systems Including Wind Power Generation

“…One of the main barriers in proper implementation of PVC, is the uncertainties associated with the forecasted system parameters. By increasing penetration of volatile renewable energy resources such as wind power generation, the most important uncertain parameters which directly affect the LM as well as the total costs are wind power generation and demand values [8], [9]. These uncertainties impose technical and economic risks on the system operator [10].…”

“…The uncertainty in the amount of generation provided by the renewable resources is considered by scenario based modelling. LM is considered as a stochastic variable in [9] and the impact of uncertain power injections by wind farms on the LM is investigated. In [11] an approach is proposed to increase wind power penetration by placing new wind generation at the strong buses from the voltage stability viewpoint.…”