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We consider the operation of a power system with high renewable penetration and minimal network bottlenecks and provide a technique to determine the appropriate level of reserve to enforce. Within a daily scheduling framework, we model the production uncertainty of renewable units via scenarios and include security constraints per scenario to ensure an uneventful operation in case of failure of key thermal units. The rarely constraining network is modeled via areas with limited capacity at their interfaces. The considered decision-making framework results in a two-stage stochastic programming problem whose first stage decides on the commitment of thermal units and whose second stage reproduces, per scenario, the operation of the system with and without the failure of key thermal units. The optimal unit scheduling obtained from the proposed model implicitly identifies a generating reserve pattern that we compare with common rules used in industry for reserve identification, such as 20% or 30% of the demand. We use the Illinois 200-bus system to illustrate and computationally characterize the methodology proposed. • An economically efficient yet secure reserve determination procedure. • Renewable uncertainty is modeled via scenarios. • Security regarding unit failures is ensured via security constraints. • The resulting optimization model is tractable and does not need decomposition. • The reserve determined is superior to setting a percentage of the load as reserve. [ABSTRACT FROM AUTHOR]

In this paper, the coordinated investment in transmission and storage systems under uncertainty is addressed from the perspective of a central planner. The problem is formulated with the objective of achieving an effective expansion of both transmission and storage that minimizes the investment cost, while achieving an effective operation of a power system with high penetration of renewable power. The problem is stated within an adaptive robust optimization framework that incorporates stochastic modeling. Future available generation capacity and peak load in the target year (long-term uncertainty) are modeled using a robust set, while daily operating conditions (short-term uncertainty) are represented with a scenario set. The expansion tradeoff between transmission and storage systems is analyzed using the IEEE RTS 24-bus and IEEE 118-bus networks. [ABSTRACT FROM AUTHOR]

This two-paper series introduces a new multistage robust approach for solving the transmission expansion planning (TEP) problem under the uncertainty of loads and wind power productions. The proposed multistage robust TEP model is formulated using mixed binary and linear decision rules, which aims at finding a solution withstanding any realization of the uncertain parameters belonging to a set-based uncertainty model. The robustness of the optimal expansion plan can be adjusted by the budget of uncertainty. The first part of this two-paper series presents the extended and compact formulations for a deterministic TEP problem. Then, the compact formulation of the TEP problem under the uncertainty of loads and wind power productions is introduced as a multistage robust optimization problem, which is reformulated using mixed binary and linear decision rules. The extended formulation of these decision rules, as functions of uncertain parameters, is presented in this part as well. [ABSTRACT FROM AUTHOR]

This paper addresses the transmission expansion planning problem under long- and short-term uncertainty. Long-term uncertainty pertains to changes across years (demand growth and future increase in production capacity), whereas short-term uncertainty pertains to changes within a year (demand and wind/solar power production variability, and equipment availability). This expansion problem is formulated as an adaptive robust optimization problem that provides protection against long-term uncertainty while carefully representing short-term uncertainty via scenarios. The problem is solved via a tailored implementation of the primal Benders’ decomposition algorithm that focuses on an efficient solution of the subproblem. The effectiveness of the proposed algorithm to identify robust expansion plans and its computational efficiency are illustrated through a realistic case study. [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 presents a novel model for two-stage adaptive robust transmission expansion planning (AR-TEP) problem considering the uncertainty of future load demand and future wind power production. Linear decision rules (LDRs) are utilized to reformulate the AR-TEP model as a tractable mixed-integer linear programming problem, which can be directly solved by off-the-shelf optimization packages. The proposed LDR-based AR-TEP model is illustrated using the Garver 6-bus test system, the IEEE 24-bus reliability test system, and a 236-bus test system under different conditions and compared with a decomposition-based AR-TEP model that uses primal cutting planes. Also, the robustness of the expansion plans obtained from these two AR-TEP models is evaluated by carrying out an ex-post out-of-sample analysis for different values of the budget of uncertainty. Simulation results demonstrate the effectiveness of the proposed LDR-based AR-TEP model. [ABSTRACT FROM PUBLISHER]

This paper analyzes the impacts of flexible demands on day-ahead market outcomes in a system with significant wind power production. We use a two-stage stochastic market-clearing model, where the first stage represents the day-ahead market and the second stage represents the real-time operation. On one hand, flexibility of demands is beneficial to the system as a whole since such flexibility reduces the operation cost, but on the other hand, shifts in demands from peak periods to off-peak periods may influence prices in such a way that demands may not be willing to provide flexibility. Specifically, we investigate the impacts of different degree of demand flexibility on day-ahead prices. A number of scenarios modeling the uncertainty associated with wind production at the operation stage, and nonconvexities due to start-up costs of generators and their minimum power outputs are taken into account. [ABSTRACT FROM AUTHOR]

We propose a two-stage mixed-integer linear stochastic optimization model to analyze the scheduling of electricity-production units under natural gas-supply uncertainty due to pipeline congestion and natural gas-price variability. The first stage of this stochastic optimization model represents the day-ahead scheduling (i .e., unit commitment) stage, while the second stage represents actual real-time operations through a number of scenarios. We use this model to analyze the effect on unit commitment and dispatch of two types of natural gas-supply conditions. First, we analyze a case involving low-cost natural gas supply with natural gas-transmission issues related to potential gas-pipeline congestion. We then examine a case involving higher-cost natural gas, which is used solely to attain feasibility with fast-ramping events. The first case mimics situations in the ISO New England system, in which relatively low-cost natural gas supply is uncertain in cold-weather conditions due to natural gas-transmission bottlenecks. The second case is reminiscent of situations in the California ISO system, in which relatively expensive but flexible natural gas-fired units need to be used to handle rapid changes in net demand in the early mornings and late afternoons. [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]

This paper presents a tri-level reliability-constrained robust power system expansion planning (SEP) framework modeling the uncertainty of electricity demand, wind power generation, and availability of units and lines. In the proposed tri-level SEP model, electricity demand and wind power generation being continuous uncertain variables are modeled by bounded intervals and availability of units and lines being discrete uncertain variables are modeled by probability distributions. Simulation results on the Garver 6-bus, the IEEE 24-bus, and the IEEE 73-bus test systems confirm the effectiveness of the proposed tri-level framework to cope with multi-fold planning uncertainties. [ABSTRACT FROM AUTHOR]

Given the significant amount of installed generation-capacity based on wind power, and also due to current economic downturn, the subsidies and incentives that have been widely used by wind-power producers to recover their investment costs have decreased and are even expected to disappear in the near future. In these conditions, wind-power producers need to develop offering strategies to make their investments profitable counting solely on the market. This paper proposes a multi-stage risk-constrained stochastic complementarity model to derive the optimal offering strategy of a wind-power producer that participates in both the day-ahead and the balancing markets. Uncertainties concerning wind-power productions, market prices, demands' bids, and rivals' offers are efficiently modeled using a set of scenarios. The conditional-value-at-risk metric is used to model the profit risk associated with the offering decisions. The proposed model is recast as a tractable mixed-integer linear programming program solvable using available branch-and-cut algorithms. Results of a case study are reported and discussed to show the effectiveness and applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper proposes an efficient solution approach based on Benders’ decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders’ approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

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 an optimal power flow (OPF) model with flexible AC transmission system (FACTS) devices to minimize wind power spillage. The uncertain wind power production is modeled through a set of scenarios. Once the balancing market is cleared, and the final values of active power productions and consumptions are assigned, the proposed model is used by the system operator to determine optimal reactive power outputs of generating units, voltage magnitude and angles of buses, deployed reserves, and optimal setting of FACTS devices. This system operator tool is formulated as a two-stage stochastic programming model, whose first-stage describes decisions prior to uncertainty realization, and whose second-stage represents the operating conditions involving wind scenarios. Numerical results from a case study based on the IEEE RTS demonstrate the usefulness of the proposed tool. [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]

We consider a cluster of interconnected price-responsive demands (e.g., an industrial compound or a university campus) that can be supplied through the main grid and a stochastic distributed energy resource (DER), e.g., a wind plant. Additionally, the cluster of demands owns an energy storage facility. An energy management system (EMS) coordinates the price-responsive demands within the cluster and provides the interface for energy trading between the demands and the suppliers, main grid and DER. The DER and the cluster of demands have a contractual agreement based on a take-or-pay contract. Within this context, we propose an energy management algorithm that allows the cluster of demands to buy, store, and sell energy at suitable times. This algorithm results in maximum utility for the demands. The uncertainty related to both the production level of the DER and the price of the energy obtained from/sold to the main grid is modeled using robust optimization (RO) techniques. Smart grid (SG) technology is used to realize 2-way communication between the EMS and the main grid, and between the EMS and the DER. Communication takes place on an hourly basis. A realistic case study is used to demonstrate the advantages of both the coordination provided by the EMS through the proposed algorithm and the use of SG technology. [ABSTRACT FROM AUTHOR]

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]

When deciding on wind power investments, three major issues arise: the production variability and uncertainty of wind facilities, the eventual future decline in wind power investment costs, and the significant financial risk involved in such investment decisions. Recognizing the above important issues, this paper proposes a risk-constrained multi-stage stochastic programming model to make optimal investment decisions on wind power facilities along a multi-stage horizon. The proposed model is illustrated using a clarifying example and a case study. [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]