Solving long time‐horizon dynamic optimal power flow of large‐scale power grids with direct solution method

Abstract

Dynamic optimal power flow (DOPF) is an extension of optimal power flow for the optimal generation dispatch in a given time-horizon. The dynamic constraints bring tremendous numerical difficulties in solving this model. With particular attention to handle dynamic constraints, an efficient method has been presented for directly solving the large-scale DOPF Karush-Kuhn-Tucker (KKT) system arising from the primal-dual interior point method. First, the reduced KKT system is derived, showing that dynamic constraints lead to non-zeros in off-diagonal parts in the coefficient of KKT system. Then, the efficiency of the algorithm is improved by two measures: (i) to utilise the Cholesky factorisation algorithm, a constant diagonal perturbation is introduced in the positive-indefinite KKT coefficient and (ii) efficient reordering algorithms are identified and integrated in the sparse direct solver to improve the efficiency. Case studies on the IEEE 118-bus system over 24-96 time intervals are presented. These case studies show that the proposed method has a significant speed-up than decomposed interior point methods. The proposed method has also been successfully applied in Chinese realistic large-scale power grids. Two realistic case studies are reported. Both realistic cases have over 100 000 decision variables. NomenclatureF DOPF objective function f t generation cost at the tth time interval N t number of time intervals K number of blocks of dynamic constraints N d number of dynamic constraints N ineq number of inequality constraints in each time interval N eq number of equality constraints in each time interval N g number of generators N number of variables in each time interval L Lagrangian function μ barrier parameter ε convergence criteria a, b, c arrays of generation cost coefficients of all generators P gt , Q gt arrays of active and reactive power generation of generators at the tth time interval P lt , Q lt arrays of active and reactive load demands at the tth time interval V t ,V t arrays of complex bus voltage and its conjugation of all buses at the tth time interval Y conjugation of nodal admittance matrix S bt array of apparent power of branches at the tth time interval P g , P g , Q g , Q g arrays of lower and upper bound of active output of generators, lower and upper bound of reactive output of generators S b , S b arrays of lower and upper bound of apparent power of branches V , V arrays of lower and upper bound of all buses' voltages R, R arrays of lower and upper bound of generators' ramping rates C, C arrays of lower and upper bound of generators' generation contracts x t array of variables at the tth time interval x array of variables of the whole time-horizon www.ietdl.org & The Institution of Engineering and Technology 2014 h t , g tArrays of equality constraints and inequality constraints at the tth time interval g, g arrays of lower and upper bound of inequality constraints g d , g d arrays of lower and upper bound of dynamic constraints l t , u t arrays of lower and upper slack variables of ineq...

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