Abstract
The backbone of a conventional electrical power generation system relies on hydro-thermal coordination. Due to its intrinsic complex, large-scale and constrained nature, the feasibility of a direct approach is reduced. With this limitation in mind, decomposition methods, particularly Lagrangian relaxation, constitutes a consolidated choice to “simplify” the problem. Thus, translating a relaxed problem approach indirectly leads to solutions of the primal problem. In turn, the dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. However, this class of methods presents a set of sensitive aspects that often require time-consuming tuning tasks or to rely on the dispatchers’ own expertise and experience. Hence, to tackle these shortcomings, a novel Lagrangian multiplier update adaptative algorithm is proposed, with the aim of automatically adjust the step-size used to update Lagrange multipliers, therefore avoiding the need to pre-select a set of parameters. A results comparison is made against two traditionally employed step-size update heuristics, using a real hydrothermal scenario derived from the Portuguese power system. The proposed adaptive algorithm managed to obtain improved performances in terms of the dual problem, thereby reducing the duality gap with the optimal primal problem.
Highlights
The objective of short-term hydro-thermal coordination is to optimize electricity generation [1], meaning to find an optimal generation dispatch, or close to ideal, for all the thermal and hydro units available in a system. This ensures the total operation cost is minimized within horizons ranging from one day to one week (168 h), taking into account the entire system and its individual constraints [2,3,4,5] and with a planning period, typically set from hour to hour [5]. This crucial process is responsible for scheduling the start-up and shutdown of thermal units, in coordination with hydro plants, to ensure the continuity of electricity supply with appropriate levels of spinning reserve, while minimizing the operating costs [6]
This scheduling constitutes a unit commitment (UC) problem, where the dispatch policy of the thermal units is made in such a way that the total cost is minimal over a pre-defined time-horizon
As we saw earlier, obtaining the Lagrange dual function optimal value goes hand-in-hand with the Lagrange multiplies choice/update method, i.e., at the outset, this choice determines how close we are to the solution of the dual problem and, how close we are from reaching the primal problem best solution
Summary
The objective of short-term hydro-thermal coordination is to optimize electricity generation [1], meaning to find an optimal generation dispatch, or close to ideal, for all the thermal and hydro units available in a system. This ensures the total operation cost is minimized within horizons ranging from one day to one week (168 h), taking into account the entire system and its individual constraints [2,3,4,5] and with a planning period (discrete time-step), typically set from hour to hour [5] In other words, this crucial process is responsible for scheduling the start-up and shutdown of thermal units (binary level decisions), in coordination with hydro plants, to ensure the continuity of electricity supply with appropriate levels of spinning reserve, while minimizing the operating costs [6]. We are primarily speaking about the load balance constraint, i.e., ensuring that our electric energy demand
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