Calculation of the static voltage stability margin (SVSM) of a power system with high wind-power penetration requires consideration of the uncertain fluctuation of wind farms' (WFs') output. Using interval numbers to describe the uncertain WF output fluctuation and based on the interval optimisation theory, a new SVSM interval calculation method is proposed. The method establishes two bi-level optimal power flow (OPF) models to calculate the SVSM interval, including a min-min model for the upper bound and a max-min model for the lower bound. Through the dual theory of convex programming, the max-min model is transformed into a max-max model, which is solved by transforming it into a one-layer optimisation model. Using correlation angles to describe the correlation of different WF output intervals and using linear transformation to decorrelate them into independent intervals, two bi-level OPF models of calculating the SVSM interval considering different WFs' correlation are established. Take the IEEE-39 bus system and an actual 964-bus provincial power grid as examples, compared with the Monte-Carlo method and the continuous power flow and affine interval integrated method, the results indicate the proposed method obtains more accurate SVSM interval and has better calculation efficiency.
The static voltage stability margin (SVSM) of a power system considering the uncertain fluctuation range of wind farm (WF) output can be described as an interval value called the SVSM interval. A multi-objective optimal control model for SVS of a power system considering the interval uncertainty of WF output is proposed. The objective functions of the model are to increase the central value and reduce the fluctuation range of the SVSM interval, and the decision variables are the active power output and terminal voltage of generators and the switching capacity of shunt capacitors. Thus, it is a multi-layer optimization model. A parametric approximation (PA) method is used to obtain the approximate functional relationship between the optimal objective function values and the decision variables of the inner-layer and mid-layer optimization models and convert the optimization model into a single-layer bi-objective optimization model. A method for obtaining the continuous Pareto frontier of the bi-objective optimization model is proposed based on the normalized normal constraint and PA methods, and the compromise optimal solution calculated from the continuous Pareto frontier is used as the optimal control scheme. Two methods for improving the calculation efficiency of the PA method are also proposed. Finally, results from experimentation on the IEEE 39-bus system and an actual provincial power grid demonstrate the effectiveness of the proposed method.
Due to the absence of historical data and the errors of measurement instruments, there may be uncertainties in the distribution parameters of the random variables describing the uncertain fluctuations of node power including renewable energy station output and load power in the combined cooling heating and power (CCHP) campus microgrid. In this paper, intervals are used to describe the uncertainties of distribution parameters of the random variables, and an interval probabilistic energy flow (IPEF) calculation model of the CCHP campus microgrid is established. Introducing the interval arithmetic (IA) into the cumulant method, an IA-based IPEF algorithm is proposed to obtain the analytical expressions of probability density function or cumulative distribution function intervals of the state variables. Moreover, affine arithmetic (AA) is introduced to address the interval extension problem in the calculation, and an AA&IA-based IPEF algorithm is proposed. By constructing the correlation transformation matrixes, the correlation among different node power is considered in the IPEF calculation. A case study on a CCHP campus microgrid demonstrates that the results of the AA&IA-based IPEF algorithm are more accurate than those of the IA-based IPEF algorithm by using the results of the double-layer Monte Carlo method as a reference. Moreover, the proposed algorithms are more efficient than the double-layer Monte Carlo method. INDEX TERMS CCHP campus micro-grid, interval probabilistic energy flow calculation, higher-order uncertainty, cumulant method, interval arithmetic, affine arithmetic, correlation NOMENCLATURE A. ACRONYMS
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