Abstract
In conventional power system, multiple generators commonly coexist. In the meantime, each of the generators has different characteristics in terms of generation cost. Hence, it is necessary to consider them coordinately and achieve the rational power generation mix. Furthermore, in modern smart grids, the characteristics of the generators become even complex, which requires further considerations of different generation cost factors in order to fulfill the requirements of system optimal operation. In this paper, different types of generation costs are analyzed in detail, including starting cost, minimum power generation cost, marginal cost, etc. At the same time, the simplified optimization model is proposed to accelerate the solving rate and ensure that the solution is a global optimal one. Numerical experiments are conducted to validate the proposed method.
Keywords : Generator mix, marginal cost, generation cost minimization
  1. 1.Introduction
In order to meet the requirements of ever growing electricity demands, the coordinated characteristics of multiple generators should be considered simultaneously so that coordination among various generation units can be achieved and generation costs can be thereby reduced [1]-[4]. Meanwhile, the overall system reliability can be also enhanced by coordinating multiple generators in the same electric grids. Conventional optimization approach and cost analysis are more suitable for studying the characteristics of small-scale power systems. However, for larger-scale power systems with large numbers of synchronous generators (especially for modern smart grids with various generation mix), the legacy approach may not be effective and the corresponding cost optimization could be infeasible. The deployment of microgrids could be a good solution to consolidate the dispersed generations into a single unit with relatively larger generation capacity [5]-[8]. However, microgrids themselves may also induce operational issues regarding power dispatch, electricity transactions, resource allocation, etc. Additional discussions are needed to fully leverage the benefits of microgrids in cost analysis and economic dispatch in modern electric grids.
Economic operation is one of the critical requirements and criteria in the operation and management of modern power systems. Especially for today’s electric grids, the particular requirements can be detailed in the following aspects:
1) The generation costs follow the basic hourly generation cost rate, which determines the particular hourly generation cost of each individual generator;
2) Frequency start-up and shut-down procedures should be avoided, so that the additional cost during the start process can be eliminated, which thereby reduced the overall generation cost;
3) The minimum output power of each generator should be taken into account during the analysis, which is induced by the physical limit of each generator.
4) When the output power of each generator is controlled to be larger than its minimum limit, an additional hourly rate should be considered, which is called marginal cost. Marginal cost is used to represent the overall cost increase induced by the additional power generation of each particular generator.
In order to optimally combine the generation costs from multiple generators (i.e., to minimize the overall system cost), the above cost categories should be comprehensively considered. Hence, the overall cost equation can be derived. Meanwhile, various operational constraints should be considered during the combination of multiple generators, including system topology constraints, maximum power generation constraints, minimum power generation constraints, etc.
For unit commitment and combination of multiple generators, the computational efficiency should be always taken care of. It is necessary to ensure the required computational efficiency and minimize model complexity. In order to solve the above issues, the conventional way of solving the problem is focused on the solving mode, i.e., to improve the original problem solving efficiency and accuracy by altering the solving modes. Particularly, the traditional approaches mainly focus on heuristic methods [9], which is relied on continuously changing the decision variables and gradually approaching the optimal solution. These methods feature lower complexity and less model dependency. However, there could still be some issues regarding convergence. In other words, the algorithm may not converge at the desired and optimal operation points due to the continuous changing and perturbation in the system. In some cases, the optimization problem may lead to sub-optimal other than global optimal due to the inherent issues of heuristic methods.
In this paper, we focus on the improvement of original models, rather than changing the solving methods. In particular, we first adjust the decision variables based on the understanding of physical systems. The purpose of this step is to reduce the numbers of decision variables. Meanwhile, by involving sign signals, the unnecessary procedures or unrealistic unit commitment can be eliminated. Hence, the feasible range is simplified and minimized, and the solving efficiency is thereby enhanced.
Based on the practical and given system model, all the generation costs are listed and analyzed, and the overall cost equation is derived based on the coordination among multiple generation units. After that, in order to minimize the overall generation cost, the optimization model is simplified and the modified model is presented for following analysis. The proposed model can be used to enhance the solving efficiency of the corresponding optimization problem, and the computational efficiency can be enhanced. Meanwhile, it can be guaranteed that the obtained results are the global optimal other than sub-optimal. Finally, the proposed mathematical model is derived in numerical experiment and the proposed optimization problem is thereby analyzed. The related results are given to validate the proposed model and method.