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...