Hydro-thermal power flow scheduling accounting for head variations

El-Hawary, M.E.; Ravindranath, K.

doi:10.1109/59.207338

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…If the on/off states of adjustable generators are given, DOPF model contains only continuous variables and can be modelled as a large-scale non-linear programming (NLP) model. Various types of power plants, such as thermal, hydro [15], wind farm [16], can be considered in detail with comprehensive characteristics, like valve-point effects [17], water head variation [18], and so on. Uncertainty was also included and solved by stochastic dual dynamic programming using a linearised OPF model [19,20].…”

Section: Introductionmentioning

confidence: 99%

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

Qin

Hou

et al. 2014

IET Generation, Transmission & Distribution

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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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Section: Introductionmentioning

confidence: 99%

“…Two major methodologies have been employed to solve large-scale DOPF problems. One is to find sub-optimal solution by dividing the model into optimal network sub-problem and feasible generation sub-problem, as in [15,18]. The other is to exactly optimise the Lagrangian function.…”

Section: Introductionmentioning

confidence: 99%