This paper proposes to speed up solving large-scale second-order cone ac optimal power flow (SOC-ACOPF) problem by decomposition and parallelization. First, we use spectral factorization to partition large power network to multiple subnetworks connected by tie-lines. Then a modified Benders decomposition algorithm (M-BDA) is proposed to solve the SOC-ACOPF problem iteratively. Taking the total power output of each subnetwork as the complicating variable, we formulate the SOC-ACOPF problem of tie-lines as the master problem and the SOC-ACOPF problems of the subnetworks as the subproblems in the proposed M-BDA. The feasibility and optimality (preserving the original optimal solution of the SOC-ACOPF model) of the proposed M-BDA are analytically and numerically proved. A GAMS grid computing framework is designed to compute the formulated subproblems of M-BDA in parallel. The numerical results show that the proposed M-BDA can solve large-scale SOC-ACOPF problem efficiently. Accelerated M-BDA by parallel computing converges within few iterations. The computational efficiency (reducing computation CPU time and computer RAM requirement) can be improved by increasing the number of partitioned subnetworks.

Electricity markets employ different congestion management methods to handle the limited transmission capacity of the power system. This paper compares production efficiency and other aspects of nodal and zonal pricing. We consider two types of zonal pricing: zonal pricing with Available Transmission Capacity (ATC) and zonal pricing with Flow-Based Market Coupling (FBMC). We develop a mathematical model to study the imperfect competition under zonal pricing with FBMC. Zonal pricing with FBMC is employed in two stages, a dayahead market stage and a re-dispatch stage. We show that the optimality conditions and market clearing conditions can be reformulated as a mixed integer linear program (MILP), which is straightforward to implement. Zonal pricing with ATC and nodal pricing is used as our benchmarks. The imperfect competition under zonal pricing with ATC and nodal pricing are also formulated as MILP models. All MILP models are demonstrated on 6-node and the modified IEEE 24-node systems. Our numerical results show that the zonal pricing with ATC results in large production inefficiencies due to the inc-dec game. Improving the representation of the transmission network as in the zonal pricing with FBMC mitigates the inc-dec game.

Optimal power flow (OPF) is the fundamental mathematical model to optimize power system operations. Based on conic relaxation, Taylor series expansion and McCormick envelope, we propose three convex OPF models to improve the performance of the second-order cone alternating current OPF (SOC-ACOPF) model. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods. A heuristic algorithm to recover feasible ACOPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The proposed SOC-ACOPF models are examined through IEEE case studies under various load scenarios and power network congestions. The quality of solutions from the proposed SOC-ACOPF models is evaluated using MATPOWER (local optimality) and LINDOGLOBAL (global optimality). We also compare numerically the proposed SOC-ACOPF models with other two convex ACOPF models in the literature. The numerical results show robust performance of the proposed SOC-ACOPF models and the feasible solution recovery algorithm.

This paper investigates joint investment planning of transmission lines and energy storage. Energy storage can be seen as a complement to transmission infrastructure and can be used for transmission deferral. On the other hand, under certain conditions, when the expected profit of both sectors depends on congestion in the system, transmission and energy storage can be seen as competitors. The transmission sector is in this study assumed to be a natural monopoly and operation and planning of transmission lines is performed by an independent company whereas the energy storage owner company operates and invests under competitive market rules. Three main questions are addressed in this paper. First of all, will additional energy storage capacity contribute to the growth of social welfare? Second, how will incentive regulation of the transmission network affect the need for energy storage? Third, how will the choice of incentive regulation affect the value of energy storage. This paper first provides an overview of incentive regulation which can be applied to transmission investments. Then case studies based on a 6-node power system network and the IEEE 118-node system are proposed in order to answer the aforementioned questions. The results of the case studies show that energy storage investments complement transmission expansion and contribute to higher social welfare values. The benefits from energy storage investments are significantly higher under two investigated incentive regulations as compared to the case without incentive regulation. Thus, the transmission investment planning process should consider energy storage options.

We address the challenges of power flow computation and network operator coordination to implement distribution locational marginal pricing (DLMP) in this paper. Compared with other dynamic pricing schemes, DLMP can give clearer economic signals regarding distributed energy resources (DERs) investment, demand side response, congestion management and network reinforcement. Without neglecting the power loss of distribution network, the second-order cone AC optimal power flow (SOPF) model is used here to calculate DLMP. A distributed economic dispatch mechanism based on the modified Benders decomposition and distributed generation cost (DGC) is proposed to reduce the dispatch complexity in facing high penetration of DERs. The key contribution is that we take the tie-line power flow as the complicating variable to formulate the modified Benders decomposition algorithm. The concept of DGC is proposed to reallocate the global dispatch cost to economically incentivize the regional network operators for coordination. The distributed economic dispatch mechanism is implemented in GAMS grid computing platform. Numerical results show that SOPF can give accurate power flow and DLMP results. The fast convergence of the proposed distributed dispatch is guaranteed by the convexity of the SOPF model and efficient grid computing technique.

This paper proposes a max-affine power flow (MAPF) model to solve the power flow (PF) problem based on linear approximation. Both active and reactive power loss variables in the original power flow equations are approximated by multiple sets of affine functions. The derivations of the proposed MAPF model are based on the branch flow equations which have been validated in the literature. The problem of solving PF equations is then equivalently reformulated in an linear optimization model. The proposed MAPF model works by minimizing the approximation error in the objective function of the formulated optimization model while satisfying all the power flow equations serving as the constraints of the formulated optimization model. Since the proposed MAPF model is linear, it is advantageous in that the accuracy of the approximation is controllable by the number of affine functions. The fast convergence and accuracy of the proposed MAPF model are proved by numerical results for various IEEE test cases. A comparison with DC power flow (DCPF) results using AC power flow (ACPF) as the benchmark shows that the accuracy of MAPF is better especially in power distribution networks where power loss is un-neglectable due to larger resistance to reactance (R/X) ratio of the power lines. The proposed MAPF model is applicable for both radial and mesh power networks.

The informationally simple approach to incentive regulation applies mechanisms that translate the regulator's objective function into the firm's profit-maximizing objective. These mechanisms come in two forms, one based on subsidies/taxes, the other based on constraints/price caps. In spite of a number of improvements and a good empirical track record simple approaches so far remain imperfect. The current paper comes up with a new proposal, called H-R-G-V, which blends the two traditions and is shown in simulations to apply well to electricity transmission pricing and investment. In particular, it induces immediately optimal pricing/investment but is not based on subsidies. In the transmission application, the H-R-G-V approach is based on a bilevel optimization with the transmission company (Transco) at the top and the independent system operator (ISO) at the bottom level. We show that H-R-G-V, while not perfect, marks an improvement over the other simple mechanisms and a convergence of the two traditions. We suggest ways to deal with remaining practical issues of demand and cost functions changing over time. 

This paper considers hypothetical options for the transformation of the Bolivian power generation system to one that emits less carbon dioxide. Specifically, it evaluates the influence of the weighted average cost of capital (WACC) on marginal abatement cost curves (MACC) when applying carbon taxation to the power sector. The study is illustrated with a bottom-up least-cost optimization model. Projections of key parameters influence the shape of MACCs and the underlying technology configurations. These are reported. Results from our study (and the set of assumptions on which they are based) are country-specific. Nonetheless, the methodology can be replicated to other case studies to provide insights into the role carbon taxes and lowering finance costs might play in reducing emissions.

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.

We address a generalization of change point detection with the purpose of detecting the change locations and the levels of clusters of a piece- wise constant signal. Our approach is to model it as a nonparametric penalized least square model selection on a family of models indexed over the collection of partitions of the design points and propose a computationally efficient algorithm to approximately solve it. Statistically, minimizing such a penalized criterion yields an approximation to the maximum a-posteriori probability (MAP) estimator. The criterion is then ana-lyzed and an oracle inequality is derived using a Gaussian concentration inequality. The oracle inequality is used to derive on one hand conditions for consistency and on the other hand an adaptive upper bound on the expected square risk of the estimator, which statistically motivates our approximation. Finally, we apply our algorithm to simulated data to experimentally validate the statistical guarantees and illustrate its behavior.