To solve the unitcommitment (UC) problems with efficient mixed-integer linear programming solvers, the quadratic cost functions (QCFs) of thermal units are always approximated to piecewise linear (PWL) functions. Thi...
详细信息
To solve the unitcommitment (UC) problems with efficient mixed-integer linear programming solvers, the quadratic cost functions (QCFs) of thermal units are always approximated to piecewise linear (PWL) functions. This study examines the accuracies of different approximation methods for piecewise linearizing the QCFs of units in UC problems. We use five piecewise linearization methods-evenly spaced PWL interpolation, evenly spaced PWL tangent, evenly spaced PWL-e(max)/2 shifted interpolation, tighter PWL interpolation, and evenly spaced PWL least-squares fit-to approximate the QCFs of units. The authors first perform a series of reproductivity studies to verify the program. Then, numerical tests are conducted using different methods on the systems with 10, 100, and 800 units. The results show that different approximation methods lead to considerable differences in operating costs and the tighter PWL interpolation, compared with the other methods, is preferred in terms of approximation accuracy.
Inspired by the neighbourhood cooperation, a new discrete optimisation algorithm is proposed. The so-called binary neighbourhood field optimisation (BNFO), utilises the attractive field of the superior neighbour and t...
详细信息
Inspired by the neighbourhood cooperation, a new discrete optimisation algorithm is proposed. The so-called binary neighbourhood field optimisation (BNFO), utilises the attractive field of the superior neighbour and the repulsive field of the inferior neighbour. As a kind of local search, BNFO is able to deliver promising results efficiently within acceptable computational time. BNFO is applied to solve the unitcommitment problem (UCP), whose objective is to minimise the operation cost of the generation units over the scheduling horizon. After numerical tests on several benchmark UCP cases, the obtained costs are less expensive compared with conventional Lagrangian relaxation, genetic algorithm, evolutionary programming, particle swarm optimisation and differential evolutionary. BNFO can converge to promising results with less computation times, especially for the large-scale UCPs.
A new adjustable robust optimisation formulation to solve unitcommitment (UC) problems under uncertainty is proposed. Unlike the stochastic programming or chance-constrained approaches, the robust formulation does no...
详细信息
A new adjustable robust optimisation formulation to solve unitcommitment (UC) problems under uncertainty is proposed. Unlike the stochastic programming or chance-constrained approaches, the robust formulation does not require information on the exact probability distributions. This method protects power systems against all possible scenarios within a deterministic uncertainty set. The degree of conservatism can be conveniently controlled by the parameters of the uncertainty set. The formulation is divided into two stages, where here-and-now UC decisions are determined in the first stage, and the second stage makes wait-and-see dispatch decisions. The second-stage problems are reformulated into the equivalent form, so that a practical cutting-plane algorithm can be used to solve the proposed two-stage problems in an iterative manner. Numerical studies show that the robust formulation offers more consistent performance than the stochastic method when the underlying distribution of demand or generating unit reliability varies.
We consider the optimal scheduling of hydropower plants in a hydrothermal interconnected system. This problem, of outmost importance for large-scale power systems with a high proportion of hydraulic generation, requir...
详细信息
We consider the optimal scheduling of hydropower plants in a hydrothermal interconnected system. This problem, of outmost importance for large-scale power systems with a high proportion of hydraulic generation, requires a detailed description of the so-called hydro unit production function. In our model, we relate the amount of generated hydropower to nonlinear tailrace levels;we also take into account hydraulic losses, turbine-generator efficiencies, as well as multiple 0-1 states associated with forbidden operation zones. Forbidden zones are crucial to avoid nasty phenomena such as mechanical vibrations in the turbine, cavitation, and low efficiency levels. The minimization of operating costs subject to such detailed constraints results in a large-scale mixed-integer nonlinear programming problem. By means of Lagrangian Relaxation, the original problem is split into a sequence of smaller and easy-to-solve subproblems, coordinated by a dual master program. In order to deal better with the combinatorial aspect introduced by the forbidden zones, we derive three different decomposition strategies, applicable to various configurations of hydro plants (with few or many units, which can be identical or different). We use a Sequential Quadratic Programming algorithm to solve nonlinear subproblems. We assess our approach on a real-life hydroelectric configuration extracted from the south sub region of the Brazilian hydrothermal power system.
暂无评论