In this paper, we model strategic interaction of multiple producers in hydrodominated power systems under uncertainty as an equilibrium problem with equilibrium constraints (EPEC), reformulated as a stochastic mixed-integer linear program with disjunctive constraints. We model strategic hydropower producers who can affect the market price by submitting strategic bids in quantity, price, and ramp rate. The bids are submitted to the system operator who minimizes the dispatch cost. We take into account the hydrospecific constraints and uncertainty in the system. Solving the problem results in finding Nash equilibria. We discuss two types of Nash equilibria under uncertainty: Bayesian and robust Nash equilibria. Large EPEC instances can be solved using a decomposition method-Modified Benders Decomposition Approach. This method eliminates the problem of tuning the disjunctive parameter and reduces the memory requirements, resulting in improved computation time.

This paper proposes a mathematical model for transmission investment game where there are several transmission planners (TPs). The model is developed assuming a simultaneous-move game between TPs. Each TP maximizes the total surplus (producers', consumers', and transmission surplus) minus the investment cost of its region given the investment decisions of rival TPs. The transmission investment risk is also considered using the probability-of-shortfall measure. We assume one market operator who dispatches the generators in all TP's regions. The risk-constrained Nash equilibria model is formulated as amixed-integer linear program (MILP). To solve the proposed MILP, a solution algorithm is proposed that combines the standard branch-and bound algorithm (BB) with a proposed modified benders decomposition algorithm (MBD). The proposed BB-MBD algorithm is also parallelized to improve the computation performance. To improve the coordination between TPs, a supporting budget mechanism is also mathematically modeled in the MILP. The numerical results are carried out using the 9-bus 3-area and the IEEE Three Area RTS-96 networks. The computational performance of proposed BB-MBD is compared with standard BB algorithm.

This paper proposes a probabilistic pricing which achieves efficient operation of and investment in ramp-service providers in power systems with a large amount of wind or solar generation. The proposed pricing differs from the existing literature in that it focuses exclusively on the efficient dispatch of electrical energy with no exogenous consideration of the need for reserves or balancing services. The proposed optimal dispatch task determines both the efficient level of any preventive actions taken before a contingency event occurs and the efficient response of the power system - i.e., corrective actions - once an event occurs. We show analytically that the efficient dispatch outcome can be achieved in a decentralized market mechanism provided the market participants are profit-maximizers and price-takers. We show how the total economic benefit of an investment can be decomposed into two components (a) the normal dispatch cost benefit and (b) the economic value of the investment in contributing ramp service to the power system. In order to study different aspects of the probabilistic pricing, the IEEE 30-node example system is deliberately modified. The results show the efficiency of the proposed pricing and the use of the investment model to assess the economic value of ramp-service providers.

This paper proposes a stochastic bilevel program for strategic bidding of a hydropower producer. The price, quantity and ramp-rate bids are considered. The uncertainty of wind power generation, variation of inflows for the hydropower producer, and demand variability are modeled through the moment-matching scenario generation technique. Using discretization the stochastic bilevel program is reformulated as a stochastic mixed-integer linear program (MILP) with disjunctive constraints. We propose a modified Benders decomposition algorithm (MBDA), which fully exploits the disjunctive structure of reformatted MILP model. More importantly, the MBDA does not require optimal tuning of disjunctive parameters and it can be efficiently parallelized. Through an illustrative 5-node example, we identify possible strategies (specific to a hydropower producer) for maximizing profit, which in turn leads to market insights. We also use the IEEE 24-node, 118-node, and 300-node case studies to show how our parallelized MBDA outperforms the standard benders decomposition algorithm. The parallelized MBDA is also compared to the state-of-the-art CPLEX solver.

This paper proposes a mathematical model for strategic generation expansion planning problem. The model is developed based on the the simultaneous-move game between Gencos. Gencos investment decisions are passed to the dispatch center which decides about the production level in operating scenarios considered. Using Karush-Kuhn-Tucker conditions (KKTs) and disjunctive linearization, the model is formulated as a mixed-integer linear program (MILP). The concepts of worst Nash equilibrium (WNE) and best Nash equilibrium (BNE) are introduced to handle multiple NE problem. The impact of uncertainty (scenarios) on equilibria band, i.e., the difference between WNE and BNE is discussed. The developed model is simulated on illustrative 2-node and 3-node example systems and also on IEEE-RTS96 test system.

The issue of applying high performance computing (HPC) techniques to computation-intensive probabilistic optimal power flow has not been well discussed in literature. In this paper, the probabilistic convex AC OPF based on second order cone programming (P-SOCPF) is formulated. The application of P-SOCPF is demonstrated by accounting uncertainties of loads. To estimate the distributions of nodal prices calculated from PSOCPF, two point estimation method (2PEM) is deployed. By comparing with Monte Carlo (MC) method, the accuracy of 2PEM is proved numerically. The computation efficiency of 2PEM outperforms MC significantly. In the context of large scale estimation, we propose to apply high performance computing (HPC) to P-SOCPF. The HPC accelerated P-SOCPF is implemented in GAMS grid computing environment. A flexible parallel management algorithm is designed to assign execution threads to different CPUs and then collect completed solutions. Numerical results from IEEE 118-bus and modified 1354pegase case network demonstrate that grid computing is effective means to speed up large scale P-SOCPF computation. The speed up of P-SOCPF computation is approximately equal to the number of cores in the computation node.

Transmission charges aim to recover the cost of transmission network investments and provide efficient locational signals to new generators. In this paper, we investigate the effect of these charges on the development of new generation capacities in the system. Generation expansion planning is decided by strategic generation planners (SGPs) trying to maximize their profits, while transmission line investments are planned by a central planner and regulatory body aimed at minimizing the overall operation and network investment costs of the system. Regulatory transmission charges (RTCs) are calculated according to the marginal responsibility of generation investment on transmission network investment costs. An iterative algorithm is proposed to model the interaction taking place between the central planner and SGPs. The developed methodology is applied to a 2-node illustrative example and the IEEE-RTS96, and effects of RTCs on investment decisions of SGPs are analyzed.

Distribution locational marginal pricing (DLMP) is critical market mechanism to boost services from distributed energy resources (DER). This paper propose to design zonal pricing in distribution network according to the concept of pricing equivalence (PE). The rules of the zonal pricing are derived. We prove that equivalent load shift from demand response can be achieved by zonal pricing if pricing equivalence is deployed. Convex AC optimal power flow (OPF) is used to calculate zonal prices. The benefits of convex AC OPF are more accurate energy pricing and global optimization target. The responsive load with passive load controllers are modeled and solved in GAMS platform. Different zonal pricing approaches (PE, reference node and average of nodal prices) are compared. IEEE 14-bus network and two IEEE 13-node networks are connected to be an illustrative test case offering numerical results. The results show that zonal pricing designed according to PE can achieve the same load shift effects and quite close consumer payments as nodal pricing. PE outperform other zonal pricing approaches prominently in congested network situations.