یک فرمول خطی از AC برنامه ریزی توسعه شبکه انتقال چندساله : یک روش برنامه ریزی خطی عدد صحیح مختلط

This paper presents a method in expansion planning of transmission systems using the AC optimal power flow (AC-OPF). The AC-OPF provides a more accurate picture of power flow in the network compared to the DC optimal power flow (DC-OPF) that is usually considered in the literature for transmission expansion planning (TEP). While the AC-OPF-based TEP is a mixed-integer nonlinear programming problem, this paper transforms it into a mixed-integer linear programming environment. This transformation guarantees achievement of a global optimal solution by the existing algorithms and software. The proposed model has been successfully applied to a simple 3-bus power system, Garver's 6-bus test system, 24-bus IEEE reliability test system (RTS) as well as a realistic power system. Detailed case studies are presented and thoroughly analyzed. Simulations show the effectiveness of the proposed method on the TEP.

Transmission expansion planning (TEP) addresses the problem of augmenting transmission lines of an existing transmission network; the objective is to optimally serve a growing electric load while satisfying a set of economical, technical and reliability constraints [1]. In general, the TEP is considered as making a stochastic decision on when (the time), where (the location), and which types of transmission lines to be installed. In [2] and [3], a classification scheme categorizes the subjects published in this area. A mixed-integer linear programming (MILP) is used in [4], for the TEP problem that considers power losses. We suggest a linearization method for the AC-TEP based on the method in [4]. However, both active and reactive powers are included in our proposed formulation. In [5], a multi-year TEP model is presented using a discrete evolutionary particle swarm optimization approach. Aguado et al. [6], present a novel TEP model that considers a multi-year planning horizon in a competitive electricity market. Both the TEP and generation expansion planning (GEP) problems are analyzed together in [7] and [8]. Also, transmission switching (TS) is investigated in [9] for the TEP showing that the TS could improve the capacity expansion planning model as well as reducing the total planning cost. A meta-heuristic and holistic approach is presented in [10] for the TEP which has been tested on a realistic power system. In [11], a scenario-based multi-objective model is presented for multi-stage TEP where the non-dominated sorting genetic algorithm (NSGA-II) is used to overcome the difficulties in solving the non-convex mixed-integer optimization problem. A multi-objective framework is presented in [12] for the TEP in deregulated environment. Recently, intermittent energy resources have been experiencing a rapid growth in power generation around the world. Therefore, new challenges are introduced to integrate the renewable energy sources (RES) to the power grid. There are many published papers which focus on this newly main issue [13], [14] and [15]. The planner of power system should deal with many uncertainties during the planning process such as load uncertainty, uncertainty in prices, market rules and etc. A multistage TEP problem including available transfer capability (ATC) is modeled in [16] that takes load uncertainty into account by considering several scenarios generated by Monte Carlo simulation. In [17], the TEP is studied by considering the load uncertainty using benders decomposition. Since this paper is focused on transforming a mixed-integer nonlinear programming (MINLP) problem into a MILP, uncertainties have not been considered in this paper. However, the presented model can easily be extended for taking uncertainties into account. The surveyed literatures use the DC-OPF for solving the TEP problem which is not completely suitable due to ignoring reactive power. However, there have been some published papers which use the AC-OPF to solve the TEP problem [18], [19], [20] and [21]. This paper proposes an approach for transmission planning based on the AC-OPF, providing a more accurate picture of both active and reactive power flows in the expanded power network in the future planning horizon. The novelty of this paper is the introduction of a MILP formulation using the AC-OPF approach so as to solve the expansion planning problem of transmission grid. In brief, an AC-OPF-based TEP is formulated, and linearized around the operating point in order to derive a MILP problem. Solving a MILP problem is a mature technology, where the MILP solvers can be embedded in many tools and applications. Moreover, some numerical examples are presented in which simulations are discussed accordingly. The whole linearization process provided in subsection “B” of section “II” that converts the non-linear AC approach to a MIP problem is novel and has not been previously presented. This paper contributes to the TEP by approximating the sine and cosine functions in power flow equations by their Taylor's series; then, the quadratic function is modeled using piecewise linear functions. Moreover, the inequality constraints for apparent powers of existing and candidate lines are transformed into a set of linear constraints. Numerical results confirm the contribution of the proposed method in comparison with the conventional solutions. Since the proposed optimization problem for solving the TEP is linear, the global optimal solution can be obtained easily by the available software. In addition, outcomes obtained by the proposed method are more accurate (due to taking reactive power into account) than those of the available conventional methods (due to ignoring reactive power by using the DC-OPF for solving the TEP). It should be emphasized that the ISO (independent system operator) is responsible for transmission expansion planning; the ISO aims at minimizing the investment cost plus the total payment to the generating companies.

In this paper a new expansion planning model was formulated and applied to several power systems. The presented method uses the AC-OPF for solving the TEP problem in order to get a more accurate and real picture of both active and reactive power flow in the network. The AC-OPF–based TEP is an MINLP that is transformed into an MILP by the proposed method. A new linearization method is presented to transform the nonlinear AC model to a linear one. The formulated problem then can be solved by the available commercial MILP software. Moreover, due to the linearity of the proposed formulated problem, the global optimal solution is guaranteed to be found by many existing algorithms and software which are reliable and efficient. The main difficulties and disadvantages of the presented methodology are to deal with the dimensionality and the mathematical computation burden of the problem, in particular when the size of the power system gets larger. This requires sufficient memory and high-speed processors to solve the MIP problem. With increasing system size, the execution time of the problem will increase as well. However, this depends considerably on the number of binary variables rather than the number of blocks or segment used in piecewise linearization approach. As a solution for this case, in order to reduce the search space the method can be applied to the high-voltage transmission lines initially, and then the planning can be conducted for lower voltage level transmission lines.