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This paper presents a new decentralized optimization-based approach for an aggregator involved in residential demand response programs. The proposed approach relies on an existing two-phase optimization framework, whereby prosumers optimize first their self-generation and household consumption, which are subsequently coordinated by the aggregator via incentives through the solution of a mixed-integer linear program. As a distinctive aspect, the notion of fairness in the distribution of incentives among prosumers is incorporated through new nonlinear constraints based on the Shapley Value while respecting standard demand response requirements. A mathematical approximation, which is proven to be exact under certain practical assumptions, is proposed to accommodate the new constraints into the linear model. Furthermore, a novel solution methodology, which combines the divide-and-conquer principle and Dantzig–Wolfe decomposition, is devised to tackle the resulting problem in a distributed fashion. For validation purposes, the behavior of the linear approximations is examined by comparing the results with those attained with their nonlinear counterparts. Moreover, scenarios for prosumers featuring different flexibility levels are generated to assess the practicality of the assumptions adopted. Simulations also show the scalability of the proposed tool by considering cases with up to 10,000 prosumers with computing times within an hour if distributed computing is implemented. Furthermore, as compared to classical Shapley Value approaches, a similar distribution of incentives is attained by the new solution methodology with relative less and acceptable computational effort. Finally, the impact of the new constraints on Peak-to-Average Ratio is quantified, obtaining an increment of up to 13.2% with respect to cases disregarding fairness. • Fair allocation of incentives is integrated in residential demand response. • The notion of Shapley Value is used to quantify prosumers' contribution. • Practical assumptions are adopted to obtain linear expressions for incentives. • Prosumers privacy is preserved using a new optimization-based solution approach. • Experimental results with real-world data show the superiority of our approach. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of price multiplicity in network-constrained pool-based electricity markets under marginal pricing. This problem consists in the existence of multiple vectors of locational marginal prices for the same optimal market-clearing dispatch solution. As a consequence, delicate conflicts of interest may arise among market participants. Price multiplicity may take place even in auction designs based on convex formulations for the market-clearing procedure. An effective duality-based solution approach is proposed in this paper to handle the issue of price multiplicity. Once the optimal market-clearing dispatch is known, we propose the subsequent solution of a simple pricing problem in order to determine the vector of locational marginal prices. Unlike previously reported methodologies, the proposed approach presents two salient features: 1) it is based on sound mathematical programming, and 2) it is computationally inexpensive since it relies on the solution of a linear program. Numerical results are provided to illustrate the performance of the proposed tool. [ABSTRACT FROM PUBLISHER]

This paper presents a risk-based approach for the transmission network expansion problem under deliberate outages. Malicious attacks expose network planners to a new challenge: how to expand and reinforce the transmission network so that the vulnerability against intentional attacks is mitigated while meeting budgetary limits. Within this framework network planners face the nonrandom uncertainty of deliberate outages. Unlike in previous approaches, the risk associated with this uncertainty is explicitly addressed in the proposed model. Risk characterization is implemented through the minimax weighted regret paradigm. The resulting mixed-integer nonlinear programming formulation is transformed into an equivalent mixed-integer linear programming problem for which efficient commercial solvers are available. Numerical results illustrate the performance of the proposed methodology. The risk-based expansion plans are compared with those achieved by a previously reported risk-neutral model. An out-of-sample assessment is carried out to show the advantages of the risk-based model over the risk-neutral approach. In addition, the tradeoff between risk mitigation and cost minimization is analyzed. [ABSTRACT FROM AUTHOR]

Abstract: The reasons why the transmission network is a potentially attractive target for deliberate outages are twofold: (i) its crucial importance as a critical infrastructure for the society welfare, and (ii) its high level of vulnerability due to the current operation close to its static and dynamic limits. This new context where destructive agents come into play has been recognized by several agencies in Europe and North America, and various initiatives have been launched worldwide in order to assess and mitigate the vulnerability of transmission. Within this framework, this paper proposes the reinforcement and expansion of the transmission network as a way of mitigating the impact of increasingly plausible deliberate outages. The network planner selects the new lines to be built accounting not only for economic issues, as traditionally done, but also for the vulnerability of the transmission network against a set of credible intentional outages. The resulting vulnerability- and economic-constrained transmission expansion planning problem is formulated as a mixed-integer linear program. A number of case studies numerically illustrate the tradeoff between economic- and vulnerability-related issues and its impact on the expansion plans. In addition, we compare the results with those achieved by a traditional expansion planning model based on cost minimization. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Presents a mixed-integer linearized power approach to the solution of the long-term power transmission expansion planning problem. Formulation of the transmission expansion problem; Linear approximation of the transmission static expansion problem; Case studies; Conclusions.

This paper proposes a two-phase optimization framework for users that are involved in demand response programs. In a first phase, responsive users optimize their own household consumption, characterizing not only their appliances and equipment but also their comfort preferences. Subsequently, the aggregator exploits in a second phase this preliminary non-coordinated solution by implementing a coordination strategy for the aggregated loads while preserving users' privacy. The second phase relies on the solution of a bilevel program in which the aggregator's profit is maximized in the upper level while ensuring that the aggregated residential users do not incur any economic or comfort losses by participating in the demand response program. The lower level models the users' reaction to the aggregator's requests. As major complicating aspects, the resulting bilevel problem features nonlinear terms and lower-level binary variables. This challenging problem is addressed by a mixed-integer linear single-level reformulation and the application of an exact solution technique based on Dantzig–Wolfe decomposition. Simulations with up to 10,000 residential users illustrate the advantages of the proposed two-phase framework in terms of users' privacy, computational efficiency, and scalability. • Residential demand response is examined from an aggregator's perspective. • A two-phase framework to coordinate users' consumption is proposed. • Bilevel optimization reformulated as mixed-integer linear single-level. • An exact distributed approach is devised preserving users' privacy at no extra costs. • Real-life instances with up to 10,000 users are successfully solved. [ABSTRACT FROM AUTHOR]

In the restructured power industry, bulk energy storage may play a crucial role to provide the flexibility required by system operators to cater for the unprecedented levels of uncertainty. Within the context of co-optimized electricity markets for energy and reserves under wind uncertainty, this paper addresses the incorporation of bulk energy storage units in day-ahead network-constrained energy and reserve scheduling. A novel two-stage robust optimization approach is presented whereby the nonconvex and time-coupled operation of storage devices is precisely modeled while accounting for the anticipativity of the two-stage setting. The resulting robust counterpart is cast as a mixed-integer trilevel program with lower-level binary variables. In order to address the nonconvexity of the recourse problem, this paper proposes the application of an exact nested column-and-constraint generation algorithm. Numerical results illustrate the effective performance of the proposed approach. [ABSTRACT FROM AUTHOR]

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]

This paper presents an alternative day-ahead auction based on consumer payment minimization for pool-based electricity markets. This auction is an instance of price-based market clearing wherein market-clearing prices are explicitly modeled as decision variables of the optimization. The auction design includes network constraints, inter-temporal constraints associated with generation scheduling, and marginal pricing. Hence, consumer payment is expressed in terms of locational marginal prices. The proposed solution approach is based on bilevel programming. In the upper-level optimization, generation is scheduled with the goal of minimizing the total consumer payment while taking into account that locational marginal prices are determined by a multiperiod optimal power flow in the lower level. In this bilevel programming setting, locational marginal prices are the Lagrange multipliers or dual variables associated with the nodal power balance equations of the lower-level problem. The resulting mixed-integer linear bilevel program is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation relies on the application of results from duality theory of linear programming and integer algebra. The proposed methodology has been successfully applied to several test systems including the IEEE 118-bus system. Numerical results have been compared with those obtained from declared social welfare maximization. [ABSTRACT FROM AUTHOR]

Highlights: [•] We examine the consumer payment minimization problem by mixed-integer linear programming. [•] Quadratic and piecewise linear supply offers, and inter-temporal constraints are modeled. [•] As a salient feature, no heuristic manipulation or control parameter tuning are required. [•] Optimal or high-quality near-optimal solutions are attained in moderate computing times. [•] Inter-temporal constraints enlarge payment reductions with slight cost increases. [ABSTRACT FROM AUTHOR]

Market clearing in restructured power systems is mostly implemented through an offer-based setting with the goal of maximizing social welfare. This approach leads to sound results from an economic viewpoint when generation offers reflect true production costs. However, offers may significantly differ from actual costs in practice, thus yielding undesired distortion. Under a marginal pricing scheme, this paper presents a general bilevel programming framework for alternative market-clearing procedures dependent on market-clearing prices rather than on offers. The resulting nonlinear mixed-integer bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. The bilevel formulation is investigated through a particular instance of price-based market clearing driven by consumer payment minimization. This problem has recently received considerable attention due to the open challenges posed from both modeling and computational perspectives. Numerical results are provided to illustrate the performance of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper addresses the vulnerability analysis of the electric grid under terrorist threat. This problem is formulated as a mixed-integer nonlinear bilevel program. In the upper-level optimization, the terrorist agent maximizes the damage caused in the power system, which is measured in terms of the level of system load shed. On the other hand, in the lower-level optimization, the system operator minimizes the damage by means of an optimal operation of the power system. The distinctive modeling feature introduced in this paper is that, among the different corrective actions available, the system operator has the capability to modify the network topology. Due to its nonconvexity and nonlinearity, the resulting bilevel programming problem cannot be equivalently transformed into a standard one-level optimization problem. Therefore, this paper proposes a new approach based on Benders decomposition within a restart framework. Some numerical results obtained by the proposed algorithm are provided and compared with those published, based on the IEEE Reliability Test System. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Recently, several authors have reported specific criteria to support the widely accepted use of a convex operational model for bulk energy storage in the formulation of power system operation and planning problems involving binary variables. Using two counterexamples, we show that this modeling simplification may give rise to impractical solutions featuring simultaneous charging and discharging, even though the recently published criteria are satisfied. Thus, both counterexamples invalidate those criteria and demonstrate that the customarily used convex model may be unsuitable for the precise incorporation of bulk storage in such instances of mixed-integer programming. [ABSTRACT FROM AUTHOR]

Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, the solution of practical large-scale instances remains a challenge. In order to address this issue, this paper presents an alternative column-and-constraint generation algorithm wherein the max–min problem associated with the second stage is solved by a block coordinate descent method. As a major salient feature, the proposed approach does not rely on the transformation of the second-stage problem to a single-level equivalent. As a consequence, bilinear terms involving dual variables or Lagrange multipliers do not arise, thereby precluding the use of computationally expensive big-M-based linearization schemes. Thus, not only is the computational effort reduced, but also the typically overlooked case-dependent, nontrivial, and time-consuming tuning of bounding parameters for dual variables or Lagrange multipliers is avoided. The practical applicability of the proposed methodology is confirmed by numerical testing on several benchmarks including a case based on the Polish 2383-bus system, which is well beyond the capability of the robust methods available in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes a flow-based approach for the transmission tariff allocation problem based on the notions of long-run marginal cost (LRMC) and nodal exchange factors (NEFs). A worst-case power flow, expressed in terms of NEFs, is formulated to characterize the system state. Additionally, the NEFs optimal values are determined considering a specific criterion to compute tariffs. The resulting problem is formulated as a bilevel program. The upper level is a worst-case power flow that maximizes line flows taking into account the transmission tariffs computed in the lower level. The criterion considered in the lower level aims to minimize the variation range of transmission tariffs, which is particularly desirable to provide incentives for renewable sources installed far away from load centers. The resulting bilevel problem may have multiple solutions. Here, the uniqueness in tariffs is preserved by solving an alternative problem once both the generation dispatch and the variation range of transmission tariffs are known. Numerical results are provided for a 6-bus system and the IEEE 118-bus system. [ABSTRACT FROM AUTHOR]