# A New Multi-Objective Unit Commitment Model
## 1 Introduction
However, researchers have addressed that issue by search of the entire Pareto-optimal front, such as weighted sum [16], \(\epsilon\)-constraint [17] and simultaneously optimization [18; 19; 20], which are time-consuming. In [21], the lexicographic optimization along with augmented \(\epsilon\)-constraint technique are proposed to generate the Pareto optimal solutions, then a Fuzzy-based decision making procedure is implemented to select the most desired solution. [PERSON] [22] combines the non-dominated sorting genetic algorithm-II (NSGA-II) and a local search algorithm to look for the Pareto-optimal solutions. [PERSON] [23] analyses how emission caps and emission market prices can influence generation decisions and the resulting generation scheduling. In [12], the objectives of MOUC are decomposed into several scalar optimization subproblems and optimizing the subproblems simultaneously by using the information from its several neighboring subproblems only. The UC problem is a nonlinear, mixed-integer, combinatorial, high-dimensional, and highly constrained optimization problem and non-deterministic polynomial-time hard (NP hard) problem [12], which could not be solved in a feasible time when solving a large system or require trade-off between speed and result of the calculation. One of the most effective methods is to decompose the UC problem to sets of subproblems. These subproblems are usually independent to each other and could be solved in parallel; besides, subproblems could be solved locally, which protects the data privacy of generating companies. Some decomposition techniques have been applied to solve UC problem, such as Benders [24], Lagrangian [25] and Dantzig-Wolfe [26]. In [27], a two level decomposition framework is presented, the lower level solve the local problem to optimize the local cost, while the upper level use the coordinators obtained in lower level to update the prices by subgradient method [28]. Under some weak assumptions, this method could converge in a finite number of iterations, but it will cost a whole lot of time. In this work, we present a novel MOUC model and a decomposition coordination method for solving MOUC problem. Instead of generating the Pareto optimal solutions and then looking for a solution among them. In the MOUC model, we look for the best solution directly by minimizing the distance to the Utopian point, which could find the optimal solution more efficiently. The MOUC model is then solved in a decomposition-coordination approach. The whole system is decomposed into subsystems by their geographic region or each subsystem is an independent system operator (ISO). The MOUC problem is also decomposed into a set of subproblems, where each subproblem is independent of each other, corresponding to one subsystem. During iteration, subproblems are solved in parallel and multi-objective margin price in each subsystem is updated. A system-level operator fine-tunes tie-line power flow between subsystems according to the multi-objective margin price and get an improved solution during each iteration. The proposed decomposition coordination method do not need the subsystem to upload their units parameters, hence the privacy of subsystems could be protected. This work is organized as follows: Section 2 presents the MOUC model. Section 3 explains the proposed decomposition coordination algorithm. Section 4 presents the test cases and obtained result. Finally, Section 5 concludes the manuscript and discusses future work.