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Demand response (DR) has been increasingly growing in significance among the solutions to tackle climate change, by supporting the development of intermittent renewable energy sources in the smart grid. Many models based on mathematical optimization have been developed to address the challenge of supporting residential customers in providing flexibility services to the grid. However, comparing and applying those models is not always straightforward because of particular data handling or specific assumptions. In this work, we take advantage of the common aspects of DR models to build a metamodel, and hence an open source Python library that aims to unify the concepts and the data streaming in and out of the underlying mathematical optimization models. We demonstrate the effectiveness of the metamodel and of the Python library by using it to implement a task scheduler and to optimize the energy consumption for two dwellings. [ABSTRACT FROM AUTHOR]

Semidefinite Programming (SDP) is a powerful technique to compute tight lower bounds for Optimal Power Flow (OPF) problems. Even using clique decomposition techniques, semidefinite relaxations are still computationally demanding. However, there are many different clique decompositions for the same SDP problem and they are not equivalent in terms of computation time. In this paper, we propose a new strategy to compute efficient clique decompositions with a clique merging heuristic. This heuristic is based on two different estimates of the computational burden of an SDP problem: the size of the problem and an estimation of a per-iteration cost for a state-of-the-art interior-point algorithm. We compare our strategy with other algorithms on MATPOWER instances and we show a significant decrease in solver time. [ABSTRACT FROM AUTHOR]

The Time-and-Level-of-Use (TLOU) system is a recently developed approach for electric energy pricing, extending Time-of-Use with an energy capacity that customers can book in advance for a given consumption time. We define a bilevel optimization model for determining the pricing parameters of TLOU, maximizing the supplier revenue while anticipating an optimal reaction of the customer. A solution approach is built, based on the discrete finite set of optimality candidates of the lower-level customer problem. [ABSTRACT FROM AUTHOR]

The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modeled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem, which is highly nonconvex and generally hard to solve. Recently, convex relaxations of the ACOPF problem have attracted a significant interest since they can lead to global optimality. We propose a tight conic relaxation of the ORPD problem and show that a round-off technique applied with this relaxation leads to near-global optimal solutions with very small guaranteed optimality gaps, unlike with the nonconvex continuous relaxation. We report computational results on selected MATPOWER test cases with up to 3375 buses. [ABSTRACT FROM AUTHOR]

Demand-response aggregators are faced with the challenge of how to best manage numerous and heterogeneous distributed energy resources (DERs). This paper proposes a decentralized methodology for optimal coordination of DERs. The proposed approach is based on Dantzig–Wolfe decomposition and column generation, thus allowing to integrate any type of resource whose operation can be formulated within a mixed-integer linear program. We show that the proposed framework offers the same guarantees of optimality as a centralized formulation, with the added benefits of distributed computation, enhanced privacy, and higher robustness to changes in the problem data. The practical efficiency of the algorithm is demonstrated through extensive computational experiments, on a set of instances generated using data from Ontario energy markets. The proposed approach was able to solve all test instances to proven optimality, while achieving significant speed-ups over a centralized formulation solved by state-of-the-art optimization software. [ABSTRACT FROM AUTHOR]

The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite optimization is lower than for second-order cone optimization. We propose a conic relaxation obtained by combining semidefinite optimization with the reformulation-linearization technique, commonly known as RLT. The proposed relaxation is stronger than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. Computational experiments using standard test cases with up to 6515 buses show that the time to solve the new conic relaxation is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks. [ABSTRACT FROM AUTHOR]

Maintenance activities help prevent costly generator breakdowns but because generators under maintenance are typically unavailable, the impact of maintenance schedules is significant and their cost must be accounted for when planning maintenance. In this paper, we address the generator maintenance scheduling problem in hydropower systems. We propose a mixed-integer programing model that considers the time windows of the maintenance activities, as well as the nonlinearities and disjunctions of the hydroelectric production functions. Because the resulting model is hard to solve, we also propose an extended formulation, a set reduction approach that uses logical conditions for excluding unnecessary set elements from the model, and valid inequalities. We performed computational experiments using a variety of instances adapted from a real hydropower system in Canada, and the extended formulation with set reduction achieved the best results in terms of computational time and optimality gap. [ABSTRACT FROM AUTHOR]

This paper presents a system architecture for load management in smart buildings which enables autonomous demand side load management in the smart grid. Being of a layered structure composed of three main modules for admission control, load balancing, and demand response management, this architecture can encapsulate the system functionality, assure the interoperability between various components, allow the integration of different energy sources, and ease maintenance and upgrading. Hence it is capable of handling autonomous energy consumption management for systems with heterogeneous dynamics in multiple time-scales and allows seamless integration of diverse techniques for online operation control, optimal scheduling, and dynamic pricing. The design of a home energy manager based on this architecture is illustrated and the simulation results with Matlab/Simulink confirm the viability and efficiency of the proposed framework. [ABSTRACT FROM PUBLISHER]

This paper examines the polytope of feasible power generation schedules in the unit commitment (UC) problem. We provide computational results comparing formulations for the UC problem commonly found in the literature. We introduce a new class of inequalities, giving a tighter description of feasible operating schedules for generators. Computational results show that these inequalities can significantly reduce overall solution times. [ABSTRACT FROM PUBLISHER]

This paper proposes a two-level framework for the operation of a competitive market for reactive power ancillary services. It is argued that the first-level, i.e., reactive power procurement, be on a seasonal basis while the second-level, i.e., reactive power dispatch, be close to real-time operation. To this effect, a reactive power procurement market model is proposed here taking into consideration system security aspects. This procurement procedure is based on a two-step optimization model. First, the marginal benefits of reactive power supply from each provider with respect to system security are obtained by solving an optimal power flow (OPF) that maximizes system loadability subject to transmission security constraints imposed by voltage limits, thermal limits, and stability limits. Second, the selected set of generators is then determined by solving an OPF-based auction to maximize a societal advantage function comprising generators' offers and their corresponding marginal benefits with respect to system security, considering all transmission system constraints. The proposed procedure yields the selected set of generators and zonal price components, which would form the basis for seasonal contracts between the system operator and the selected reactive power service providers. [ABSTRACT FROM AUTHOR]

An affine supply function equilibrium (SFE) approach is used to discuss voltage constraints and reactive power issues in the modeling of strategic behavior. Generation companies (GenCos) can choose their bid parameters with no restrictions for both energy and spinning reserves. The strategic behavior of generators is formulated as a multi-leader single-follower game. Each GenCo is modeled as a leader, while the central market operator running a cost minimization process is the sole follower. An ac model is considered to represent the transmission system. A three-node system is used to illustrate several cases, and study the implications of the incentives of the strategic players to exploit active and reactive power, and spinning reserves in order to maximize profits. Results for a 14-node system are also presented. [ABSTRACT FROM AUTHOR]

In this paper, oligopolistic competition in a centralized power market is characterized by a multi-leader single-follower game, and formulated as a nonlinear programming (NLP) problem. An ac network is used to represent the transmission system and is modeled using rectangular coordinates. The follower is composed of a set of competitive suppliers, demands, and the system operator, while the leaders are the dominant suppliers. The ac approach allows one to capture the strategic behavior of suppliers regarding not only active but also reactive power. In addition, the impact of voltage and apparent power flow constraints can be analyzed. Different case studies are presented using a three-node system to highlight the features of the formulation. Results on a 14-node system are also presented. [ABSTRACT FROM AUTHOR]