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The power and natural-gas industries have narrowed the time differences between daily power market clearing and natural-gas market clearing. This facilitates the gas-power coordination in day-ahead scheduling. However, using natural-gas-fired power units to balance the variability of renewable energy production may cause fluctuations in natural-gas demand, which result in risks to the natural-gas system in actual operation. As such, gas-power coordination at all time is highly desirable. We analyze the coordinated operation of power and natural-gas systems at the scheduling stage and in actual operation. We assume that the two systems are operated independently, but with information interchange. We use a Lagrangian decomposition approach to identify an operational equilibrium involving the two systems. Numerical results on two test systems verify the value of gas-power coordination in actual operation. [ABSTRACT FROM AUTHOR]

A supply-function equilibrium model fits well current electricity market practice, but entails the solution of an equilibrium problem composed of bi-level problems, which is computationally very demanding. To ease such computational burden, we propose a computationally efficient single-level equilibrium model that identifies equilibria similar to those obtained by equilibrium models of bi-level problem. In our model, producers/consumers offer/bid both energy and prices. We use a simple example and a case study to illustrate and characterize the performance of the proposed single-level equilibrium model. [ABSTRACT FROM AUTHOR]

The interdependency of electric power and natural gas systems requires co-ordinated operational planning. We propose a unit commitment model that integrates a second-order-cone relaxation of a non-convex nonlinear natural-gas flow model that considers pipeline line pack. The model is enhanced by using convex envelopes of bilinear terms, which tighten the relaxation. By fixing the binary variables at their optimal values and linearizing the natural gas-flow-balance equations around the solution that is obtained, we obtain electricity and natural gas locational marginal prices as the dual variables of electricity- and natural gas-flow-balance equations, respectively. The interdependence between these sets of prices is discussed. Numerical results from two test systems validate the solution-quality and computational-efficiency benefits of the proposed modeling methodology. [ABSTRACT FROM AUTHOR]

Increasing use of natural gas for electricity production places added strains on pipeline systems that are used for transporting fuel. Pipeline constraints require power system operators to account for natural gas-supply restrictions in their operational processes. This paper proposes separate optimization models for clearing day-ahead wholesale markets for scheduling power and natural gas systems. We then develop a market-based mechanism that allows for efficient co-ordination of the two systems. Importantly, the co-ordination mechanism only requires the exchange of fuel-price, -supply, and -demand information between the two markets. This can be contrasted with other co-ordination mechanisms that require operations of the two systems by a single entity. Thus, we provide a computationally tractable co-ordination mechanism that does not require the exchange of proprietary information between natural gas and electricity system operators. We demonstrate the effectiveness and scalability of the technique using a numerical example. [ABSTRACT FROM AUTHOR]

The work reported in this paper aims at developing an algorithm for identifying the worst contingencies to be used in a security-constrained optimal power flow problem. A bilevel max-min optimization model is proposed to find the worst contingency scenario while solving an ac optimal power flow problem and considering corrective actions. The objective is to minimize the total cost including generation and load shedding cost while satisfying all relevant constraints. The upper-level problem allows representing contingencies using binary variables. We formulate a second-order cone problem in the lower-level to represent the ac power flow equations. Duality is used to merge the upper- and lower-level problems into a single-level one. The resulting mixed-integer second-order conic problem can be efficiently solved. Three case studies are presented as applications of this novel technique. [ABSTRACT FROM AUTHOR]

This paper focuses on the estimation of the rotor speeds of synchronous machines by means of phasor measurement units. This estimation is aimed at online monitoring of electromechanical transients and transient stability analysis. The proposed technique is based on the concept of frequency divider formula recently published by the first two authors in these Transactions. The dynamic state estimation is formally stated as a convex optimization problem and a thorough discussion of the sensitivity analysis of the optimal solution is provided. The case study considers a dynamic 1479-bus model of the all-island Irish system and discusses the effect of bad data, noise, and latency on the proposed estimation technique. [ABSTRACT FROM AUTHOR]

The second part of this two-paper series presents the extended formulation for the lifted multiyear multistage robust transmission expansion planning model introduced in the first part. The proposed planning approach is successfully tested on the Garver 6-bus and on a 118-bus+118-bus test system with different input settings. [ABSTRACT FROM AUTHOR]

Distribution expansion planning (DEP) is used to determine the best expansion plan of a distribution system. Considering the uncertainties of loads and of power productions of wind distributed energy resources (DERs) and incorporating AC power flow equations make the DEP problem increasingly challenging. In this context, this paper presents a new adaptive robust distribution expansion planning model to identify the timing of feeder reinforcements in addition to the location, capacity, and installation time of dispatchable and wind DERs. The proposed approach characterizes the uncertain nature of loads and power productions of wind DERs through polyhedral uncertainty sets and the robustness of the solution can be controlled by means of a budget of uncertainty. Since AC power flow equations rather than DC ones are considered, the proposed model is a nonlinear and non-convex min–max–min optimization problem, which cannot be solved directly by commercial optimization packages. Hence, a tri-level decomposition algorithm using both primal and dual cutting planes is introduced to solve the problem. Additionally, to attain a smoother optimization problem, the non-convex AC power flow equations are convexified. The working of the proposed model is illustrated using 33-bus and 123-bus distribution networks. [ABSTRACT FROM AUTHOR]

We propose a multistage multiscale linear stochastic model to optimize electricity generation, storage, and transmission investments over a long planning horizon. The multiscale structure captures “large-scale” uncertainties, such as investment and fuel-cost changes and long-run demand-growth rates, and “small-scale” uncertainties, such as hour-to-hour demand and renewable-availability uncertainty. The model also includes a detailed treatment of operating periods so that the effect of dispatch decisions on long-term investments are captured. The proposed model can be large in size. The progressive hedging algorithm is applied to decompose the model by scenario, greatly reducing computation times. We also derive bounds on the optimal objective-function value, to assess solution quality. We use a case study based on the state of Texas to demonstrate the model and show the benefits of its detailed representation of the operating periods in making investment decisions. [ABSTRACT FROM PUBLISHER]

This paper proposes a pricing scheme for the day-ahead market in power systems with a large percentage of renewable stochastic production. To clear the day-ahead market, instead of a simplistic deterministic model, we use a two-stage stochastic programming model that embodies a prognosis of future operating conditions. Non-convexities due to start-up costs and the on/off status of generators and their minimum power outputs are properly taken into account. Our goal is to obtain uniform day-ahead clearing prices that deviate in the least possible manner from marginal prices and that allow producers to recover their costs without uplifts. The proposed methodology is illustrated using a simple example and a realistic case study. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive robust network-constrained AC unit commitment (AC-UC) model. This model is formulated as a min–max–min optimization problem, which allows representing the uncertain nature of wind power productions in terms of bounded intervals. A tri-level decomposition algorithm using primal and dual cutting planes is introduced to solve this AC-UC problem and to find a robust commitment schedule withstanding the worst realizations of uncertain wind power. To reduce the computation burden and to obtain a tractable formulation, the AC power flow equations are convexified using a Signomial transformation. The proposed AC-UC model is illustrated using the IEEE 24-bus reliability test system. Simulation results demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Distribution microgrids are being challenged by reverse power flows and voltage fluctuations due to renewable generation, demand response, and electric vehicles. Advances in photovoltaic (PV) inverters offer new opportunities for reactive power management provided PV owners have the right investment incentives. In this context, reactive power compensation is considered here as an ancillary service. Accounting for the increasing time-variability of distributed generation and demand, a stochastic reactive power compensation scheme is developed. Given uncertain active power injections, an online reactive control scheme is devised. This scheme is distribution-free and relies solely on power injection data. Reactive injections are updated using the Lagrange multipliers of a second-order cone program. Numerical tests on an industrial 47-bus microgrid and the residential IEEE 123-bus feeder corroborate the reactive power management efficiency of the novel stochastic scheme over its deterministic alternative, as well as its capability to track variations in solar generation and household demand. [ABSTRACT FROM PUBLISHER]

The smart grid technology enables an increasing level of responsiveness on the demand side, facilitating demand serving entities—large consumers and retailers—to procure their electricity needs under the best conditions. Such entities generally exhibit a proactive role in the pool, seeking to procure their energy needs at minimum cost. Within this framework, we propose a mathematical model to help large consumers to derive bidding strategies to alter pool prices to their own benefit. Representing the uncertainty involved, we develop a stochastic complementarity model to derive bidding curves, and show the advantages of such bidding scheme with respect to non-strategic ones. [ABSTRACT FROM PUBLISHER]

This paper proposes a decentralized methodology to optimally schedule generating units while simultaneously determining the geographical allocation of the required reserve. We consider an interconnected multi-area power system with cross-border trading in the presence of wind power uncertainty. The multi-area market-clearing model is represented as a two-stage stochastic programming model. The proposed decentralized procedure relies on an augmented Lagrangian algorithm that requires no central operator intervention but just moderate interchanges of information among neighboring regions. The methodology proposed is illustrated using an example and a realistic case study. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of identifying the optimal investment of a strategic wind power investor that participates in both the day-ahead (DA) and the balancing markets. This investor owns a number of wind power units that jointly with the newly built ones allow it to have a dominant position and to exercise market power in the DA market, behaving as a deviator in the balancing market in which the investor buys/sells its production deviations. The model is formulated as a stochastic complementarity model that can be recast as a mixed-integer linear programming (MILP) model. A static approach is proposed focusing on a future target year, whose uncertainties pertaining to demands, wind power productions, and balancing market prices are precisely described. The proposed model is illustrated using a simple example and two case studies. [ABSTRACT FROM PUBLISHER]

As a result of subsidies and technological maturity, renewable electricity producers have grown in some jurisdictions to clearly dominant positions in the market. Under this context, we propose an offering strategy for a wind power producer with market power that participates in the day-ahead market as a price-maker, and in the balancing market as a deviator. Uncertainty pertaining to wind power production and balancing market price is represented through a set of correlated scenarios. The proposed model is a stochastic mathematical program with equilibrium constraints (MPEC) that can be recast as a tractable mixed-integer linear programming (MILP) problem, which is solvable using available optimization software. Results from an illustrative example and two case studies show the effectiveness of the proposed model. [ABSTRACT FROM PUBLISHER]

The first of this two-paper series proposes a methodology to characterize generation investment equilibria in a pool-based network-constrained electricity market, where the producers behave strategically. To this end, the investment problem of each strategic producer is represented using a bilevel model, whose upper-level problem determines the optimal investment and the supply offering curves to maximize its profit, and whose several lower-level problems represent different market clearing scenarios. This model is transformed into a mathematical program with equilibrium constraint (MPEC) through replacing the lower-level problems by their optimality conditions. The joint consideration of all producer MPECs, one per producer, constitutes an equilibrium problem with equilibrium constraints (EPEC). To identify the solutions of this EPEC, each MPEC problem is replaced by its Karush-Kuhn-Tucker (KKT) conditions, which are in turn linearized. The resulting mixed-integer linear system of equalities and inequalities allows determining the EPEC equilibria through an auxiliary MILP problem. [ABSTRACT FROM PUBLISHER]

This paper proposes an alternative formulation for the problem of dispatching generation units in a predominantly hydro system considering a medium-term horizon. Hydro-power dispatch is expressed as a equilibrium problem with equilibrium constraints (EPEC) and its solutions are compared to the solutions of a classical optimal hydro dispatch problem. A stochastic formulation is used to represent uncertainties in water inflows. Results are presented for realistic test systems with interconnected reservoirs. [ABSTRACT FROM PUBLISHER]

This paper considers the yearly maintenance scheduling of generating units within a market environment. Each producer schedules its units' maintenance periods to maximize its revenue using a bilevel approach. The upper-level problem of this bilevel model seeks maximum revenue and contains unit scheduling constraints, while the lower-level problems represent the market clearing process under different operating conditions. This single producer maintenance problem can be recast as a mathematical program with equilibrium constraints (MPEC). Since the MPECs of all producers have to be considered simultaneously and the market clearing process is common to all of them, the proposed formulation for maintenance scheduling is an equilibrium problem with equilibrium constraints (EPEC) corresponding to a multiple-leader-common-follower game. The solution of this EPEC is a set of equilibria, in which none of the producers is able to increase its revenue unilaterally by changing the maintenance periods of its generating units. [ABSTRACT FROM PUBLISHER]

Investment in wind power facilities involves a high level of uncertainty. To properly model such uncertainty, we consider a large number of scenarios and formulate this investment problem as a mathematical program with equilibrium constraints. The target of this problem is to maximize the profit from wind power investment in a target year, and it is subject to complementarity constraints describing a large number of market clearing conditions. Since the profit as a function of the investment variables has as sufficiently convex envelope, the considered problem can be solved by Benders decomposition. Thus, we propose, describe, and analyze a Benders decomposition algorithm to efficiently tackle the wind power investment problem. [ABSTRACT FROM PUBLISHER]

We address the generation investment problem faced by a strategic power producer and consider a detailed description of the uncertain parameters involved, namely, rival producer investment and market offering, and demand growth. To identify optimal investment decisions, we consider a target year and propose a bilevel model whose upper-level problem determines investment and offering decisions to maximize expected profit, and whose many lower-level problems represent market clearing conditions per demand block and scenario. Since the producer total expected profit is sufficiently convex with respect to investment decisions, a Benders' decomposition approach is proposed that results in a tractable formulation even if hundred of scenarios are used to describe uncertain parameters. Extensive numerical simulations based on realistic case studies show the good performance of the proposed decomposition approach. [ABSTRACT FROM PUBLISHER]

This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed. [ABSTRACT FROM PUBLISHER]