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ABSTRACT
The increasing complexity of the transmission expansion planning problem in the restructured industry makes simulation the only viable means to evaluate and compare the performances of different plans. Ordinal optimization is an approach suitable for solving the simulation-based multiyear transmission expansion planning problem. It uses crude models and rough estimates to derive a small set of plans for which simulations are necessary and worthwhile to find good enough solutions. In the end, reasonable solutions are obtained with drastically reduced computational burden.


TRANSMISSION EXPANSION PLANNING (TEP): aims at strengthening an existing transmission network to serve power producers and customers in an optimal way. Due to the large-scale nature of a transmission system and its inherent complexities, TEP has always been a complex problem. It has been formulated as a large-scale mixed-integer nonlinear optimization problem. Various optimization techniques have been used to solve the problem, such as linear programming, dynamic programming, nonlinear programming, and mixed-integer programming. At the same time, various divide-and-conquer strategies such as Benders decomposition, hierarchical decomposition, and branch-and-bound algorithm have also been applied to solve large-scale TEP problems.
Industry restructuring in recent years has resulted in the separation of generation and transmission systems and the introduction of competitive electricity markets. A comprehensive methodology, called the Transmission Economic Assessment Methodology (TEAM), was developed by the California ISO and London Economics to evaluate the economic benefits of transmission expansion.
The economic impacts of alternative transmission enhancement schemes are different for different market participants. The participants of an electricity market include independent power producers, large customers, transmission network owners, and the independent system operator. The interests of different parties vary a great deal. Furthermore, other factors, such as uncertainties in generation patterns, transmission congestions, and regulatory policy changes, need to be considered in the evaluation. Transmission expansion planning in the restructured industry has become much more complicated than before . No simple mathematical model can capture all the major factors in the transmission expansion planning. Computer simulation, in particular Monte Carlo simulation, has become the only viable approach for assessing alternative plans for transmission expansion.

If, on the other hand, analytical approaches can be used to complement the simulation-based search methods so that the search for optimum performance can be narrowed down to a set of good enough solutions, then the computational requirements may be manageable. Ordinal Optimization (OO) is a method that provides a theoretical foundation for such an approach.
In Section II, a TEP problem is described. Ordinal optimization theory is introduced in Section III. In Section IV, ordinal optimization theory is applied to solve the TEP problem. In Section V, numerical examples are given to illustrate the approach. Conclusions are drawn in Section VI.


II. TRANSMISSION EXPANSION PLANNING PROBLEM
We assume that there is an entity, which may be the transmission company, the independent system operator (ISO), or the regional transmission organization (RTO), who is responsible for planning the expansion of the transmission network (i.e., when and where to install new lines, capacities and types, etc.). The economic effects of TEP on various market players are different. Transmission owners are concerned about their investment returns; generation companies are about congestion rents affecting their profits; the system operator is about congestion revenues; and the consumers are about electricity prices after network enhancement. On the other hand, societal outage costs may very well be reduced after adding line capacities in the network. The magnitudes of the economic effects on generators, consumers, the system operator, and the society depend on system operating conditions that change from moment to moment. The benefit of an expansion scheme to an individual participant may take several years to realize. To simulate the effects of multiple years of an expansion plan on market players, an hourly-based dispatch model is more or less necessary for the whole expansion time horizon.
Industry restructuring is an ongoing process in many parts of the world. Its initial focus has been on the competitive market for generation. Transmission systems remain largely regulated, and the rules and regulations for transmission expansion are mostly unsettled. The obligations and responsibilities of the participants are not fully defined, except that some general characteristics can be detected. The TEP has become an optimization problem whose variables are strongly stochastic and lumpy (discrete), with multiple participants having different objectives. Traditional optimization formulations and techniques are no longer appropriate. In this paper, we propose the application of ordinal optimization to the TEP problem. The development of OO is motivated by the complexities of large-scale, stochastic, discrete-event nonlinear dynamic systems, such as manufacturing systems, whose performance can only be evaluated by way of computer simulations.
Because the TEP problem is not fully standardized and specified, we will not attempt to give a definitive algorithmic solution to the problem. Instead, our goal is to demonstrate that the OO approach is viable. Therefore, our formulation of the TEP problem and its solution algorithm are for illustration purposes only. For that purpose and for the ease of exposition and understanding, the classical TEP formulation which has been commonly used in the past decades is used in this paper. The OO approach can be adopted by the planners to a formulation that incorporates the issues and considerations relevant to individual systems and to the development of models and performance indexes that the OO approach requires.


III. ORDINAL OPTIMIZATION
The ordinal optimization theory developed by Ho et al is for solving simulation-based complex optimization problems. It has recently been applied to many areas in power systems such as optimal power flow (OPF) with discrete control and bidding strategies of power suppliers in markets. In this paper, the theory is applied to solve the multiyear transmission expansion planning problem.

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