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This paper provides a stochastic programming approach to optimally reinforce and expand the transmission network so that the impact of deliberate attacks is mitigated. The network planner selects the new lines to be built accounting for the vulnerability of the transmission network against a set of credible intentional outages. The vulnerability of the transmission network is measured in terms of the expected load shed. An instance of the previously reported terrorist threat problem is solved to generate the set of credible deliberate attacks. The proposed model is formulated as a mixed-integer linear program for which efficient solvers are available. Results from a case study based on the IEEE Two Area Reliability Test System are provided and analyzed. Index Terms--Deliberate outages, mixed-integer linear programming, stochastic programming, transmission expansion planning, vulnerability.

The concept of electrothermal coordination (ETC) in power system operation introduced in Part I proposes to exploit thermal inertia to coordinate line temperature dynamics with existing power system controls, thus increasing power transfer capability and enhancing system security and economic performance. In this Part II, the characteristics of ETC and its benefits in operational functions such as augmenting power transfer capability, emergency control, congestion management, and system loadability are numerically analyzed through a number of case studies. This paper also examines some practical issues concerning the deployment of ETC. Index Terms--Congestion management, emergency control, heat balance equation, line thermal rating, load shedding, power transfer capability, temperature dynamics.

The concept of electrothermal coordination (ETC) in power system operation is proposed. ETC exploits thermal inertia to coordinate line temperature dynamics with existing system controls, thus increasing power transfer capability and enhancing system security and economic performance. This Part I begins with the theoretical basis of ETC and follows with an algorithm suitable for large-scale implementation in electricity markets, emphasizing that ETC can be readily integrated into existing software. The characteristics of ETC and its benefits in system operation are analyzed numerically in Part II through several case studies in power transfer capability, emergency load-shedding, congestion management, and system loadability. Index Terms--Day-ahead energy market clearing, electrothermal coordination, heat balance equation, line temperature dynamics, static and dynamic line thermal ratings.

This paper provides a procedure for the allocation of the cost of transmission losses that is based on deriving a radial network that is fully equivalent to the original one. This equivalence materializes in that voltage magnitudes and angles, and active and reactive power injections are identical for both networks. Once this radial equivalent network is available, the allocation of the cost of transmission losses to generators and demands can be performed in a straightforward manner. This equivalent network is derived solving a simple quadratic optimization problem whose solution can be obtained efficiently. A realistic case study including two load scenarios is analyzed. Results using the proposed technique are compared with those obtained using alternative allocation procedures. Index Terms--Allocation of the cost of losses, quadratic programming, radial equivalent networks, transmission losses.

This paper presents a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem. In general, this problem is large-scale, mixed-integer, nonlinear, and nonconvex. We derive a mixed-integer linear formulation that considers losses and guarantees convergence to optimality using existing optimization software. The proposed model is applied to Garver's 6-bus system, the IEEE Reliability Test System, and a realistic Brazilian system. Simulation results show the accuracy as well as the efficiency of the proposed solution technique. Index Terms--Linearized power flow, mixed-integer linear programming, power loss modeling, transmission expansion planning.

This paper presents the numerical analysis of the bilevel programming approach for revenue- and network-constrained market clearing developed in its companion paper. The impact of minimum revenue conditions and minimum declared profits on generation and consumption levels as well as on locational marginal prices for energy is examined in detail through three case studies. First, the results from an illustrative example including minimum revenue conditions are comprehensively analyzed. The second case study is based on the IEEE Reliability Test System and considers minimum declared profits. In the third case study, a modified version of the IEEE 118-bus system is tested while accounting for minimum revenue conditions. In addition, the computational behavior of the proposed approach is illustrated with several case studies including the IEEE 300-bus system. Numerical results show the effectiveness of the proposed approach to handle revenue constraints as well as its superiority over the heuristic currently implemented in the Iberian electricity market. Moreover, simulations reveal that, unlike previous works in the literature, generation revenue constraints can be precisely incorporated in day-ahead market clearing while explicitly considering the standard economic-dispatch-based marginal pricing scheme and without requiring price uplifts. [ABSTRACT FROM AUTHOR]

The first of this two-paper series addresses a practical day-ahead auction model, where generation revenue constraints are explicitly incorporated in the problem formulation, as routinely done in several national electricity markets across Europe. The revenue-constrained market-clearing procedure includes the effect of the transmission network, inter-temporal constraints associated with generation scheduling, demand-side bidding, and marginal pricing. This auction design is an instance of price-based market clearing which features two major complicating factors. First, locational marginal prices become decision variables of the optimization process. In addition, producer revenues are formulated as bilinear and highly nonconvex products of power outputs and market-clearing prices. The resulting problem is formulated as a mixed-integer nonlinear bilevel program with bilinear terms for which available solution techniques rely on heuristics, approximations, or modeling simplifications. This paper presents a novel and exact methodology whereby the original problem is recast as an equivalent single-level mixed-integer linear program. As a consequence, finite convergence to optimality is guaranteed and the use of standard commercial software is allowed. The proposed transformation is based on duality theory of linear programming, Karush-Kuhn-Tucker optimality conditions, and integer algebra results. In the second part of this two-paper series, numerical results from several case studies illustrate the effective performance of the proposed solution approach. [ABSTRACT FROM AUTHOR]