[Show abstract][Hide abstract] ABSTRACT: As compared to short-term forecasting (e.g., 1 day), it is often challenging to accurately forecast the volume of precipitation in a medium-term horizon (e.g., 1 week). As a result, fluctuations in water inflow can trigger generation shortage and electricity price spikes in a power system with major or predominant hydro resources. In this paper, we study a two-stage robust scheduling approach for a hydrothermal power system. We consider water inflow uncertainty and employ a vector autoregressive (VAR) model to represent its seasonality and accordingly construct an uncertainty set in the robust optimization approach. We design a Benders' decomposition algorithm to solve this problem. Results are presented for the proposed approach on a real-world case study.
Full-text · Article · Jan 2016 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: This paper explores the effects of allowing large, price-responsive consumers to provide reserves in a power system with significant penetration of wind energy. A bilevel optimization model represents the utility maximization problem of a large consumer, subject to a stochastic day-ahead co-optimization of energy and reserves that a system operator would solve to clear the market while considering wind power uncertainty. An examination of the market outcomes from both an illustrative and a large-scale study using this model allows analysis of a) the effects of the type of behavior of the large consumer (i.e. strategic vs competitive), b) limits on the amount of reserves it is allowed to provide, and c) variability and accuracy of characterization of wind power uncertainty.
Full-text · Article · Oct 2015 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: Distribution grids are critically challenged by the variability of renewable
energy sources. Slow response times and long energy management periods cannot
efficiently integrate intermittent renewable generation and demand. Yet
stochasticity can be judiciously coupled with system flexibilities to improve
efficiency of the grid operation. Voltage magnitudes for instance can
transiently exceed regulation limits, while smart inverters can be overloaded
over short time intervals. To implement such a mode of operation, an ergodic
energy management framework is developed here. Considering a distribution grid
with distributed energy sources and a feed-in tariff program, active power
curtailment and reactive power compensation are formulated as a stochastic
optimization problem. Tighter operational constraints are enforced in an
average sense, while looser margins are satisfied at all times. Stochastic dual
subgradient solvers are developed based on exact and approximate grid models of
varying complexity. Numerical tests on a real-world 56-bus distribution grid
relying on both grid models corroborate the advantages of the novel schemes
over its deterministic alternative.
[Show abstract][Hide abstract] ABSTRACT: To a large extent, electricity markets worldwide still rely on deterministic procedures for clearing energy and reserve auctions. However, increasing shares of the production mix consist of renewable sources whose nature is stochastic and non-dispatchable, as their output is uncertain and cannot be controlled by the operators of the production units. Stochastic programming models allow the joint determination of the day-ahead energy and reserve dispatch accounting for the uncertainty in the output from these sources. However, the size of these models gets quickly out of hand as a large number of scenarios are needed to properly represent the uncertainty. In this work, we take an alternative approach and cast the problem as an adaptive robust optimization problem. The resulting day-ahead energy and reserve schedules yield the minimum system cost, accounting for the cost of the redispatch decisions at the balancing (real-time) stage, in the worst-case realization of the stochastic production within a specified uncertainty set. We propose a novel reformulation of the problem that allows considering general polyhedral uncertainty sets. In a case-study, we show that, in comparison to a risk-averse stochastic programming model, the robust optimization approach progressively trades off optimality in expectation with improved performance in terms of risk. These differences, however, gradually taper off as the level of risk-aversion increases for the stochastic programming approach. Computational studies show that the robust optimization model scales well with the size of the power system, which is promising in view of real-world applications of this approach.
No preview · Article · Jun 2015 · European Journal of Operational Research
[Show abstract][Hide abstract] ABSTRACT: 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 non-linear and generally intractable, into a mixed-integer linear master problem and a set of non-linear, 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.
No preview · Article · May 2015 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: 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.
No preview · Article · Apr 2015 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: The work reported in this paper addresses the problem of transmission expansion planning under uncertainty in an electric energy system. We consider different sources of uncertainty, including future demand growth and the availability of generation facilities, which are characterized for different regions within the electric energy system. An adaptive robust optimization model is used to derive the investment decisions that minimizes the system’s total costs by anticipating the worst case realization of the uncertain parameters within an uncertainty set. The proposed formulation materializes on a mixed-integer three-level optimization problem whose lower-level problem can be replaced by its KKT optimality conditions. The resulting mixed-integer bilevel model is efficiently solved by decomposition using a cutting plane algorithm. A realistic case study is used to illustrate the working of the proposed technique, and to analyze the relationship between the optimal transmission investment plans, the investment budget and the level of supply security at the different regions of the network.
No preview · Article · Apr 2015 · European Journal of Operational Research
[Show abstract][Hide abstract] ABSTRACT: 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.
No preview · Article · Apr 2015 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: This paper addresses the optimization under uncertainty of the self-scheduling, forward contracting, and pool involvement of an electricity producer operating a mixed power generation station, which combines thermal, hydro and wind sources, and uses a two stage adaptive robust optimization approach. In this problem the wind power production and the electricity pool price are considered to be uncertain, and are described by uncertainty convex sets. To solve this problem, two variants of a constraint generation algorithm are proposed, and their application and characteristics discussed. Both algorithms are used to solve two case studies based on two producers, each operating equivalent generation units, differing only in the thermal units’ characteristics. Their market strategies are investigated for three different scenarios, corresponding to as many instances of electricity price forecasts. The effect of the producers’ approach, whether conservative or more risk prone, is also investigated by solving each instance for multiple values of the so-called budget parameter. It was possible to conclude that this parameter influences markedly the producers’ strategy, in terms of scheduling, profit, forward contracting, and pool involvement. These findings are presented and analyzed in detail, and an attempted rationale is proposed to explain the less intuitive outcomes. Regarding the computational results, these show that for some instances, the two variants of the algorithms have a similar performance, while for a particular subset of them one variant has a clear superiority.
No preview · Article · Jan 2015 · European Journal of Operational Research
[Show abstract][Hide abstract] ABSTRACT: Renewable energy sources are here to stay for a number of important reasons, including global warming and the depletion of fossil fuels. We explore in this paper how a thermal-dominated electric energy system can be transformed into a renewable-dominated one. This study relies on a stochastic programming model that allows representing the uncertain parameters plaguing such long-term planning exercise. Being the final year of our analysis 2050, we represent the transition from today to 2050 by allowing investment in both production and transmission facilities, with the target of achieving a renewable-dominated minimum-cost system. The methodology developed is illustrated using a realistic large-scale case study. Finally, policy conclusions are drawn.
No preview · Article · Jan 2015 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: This article provides an overview of the European Union (EU) electricity and natural gas sectors by focusing on the specific case of mainland Spain. The integration of renewable production has created a strong link between the operations of the electricity and natural gas systems. This calls for a coordinated gas and electricity operation and for the coordinated long-term planning of both electricity and natural gas facilities.
No preview · Article · Nov 2014 · IEEE Power and Energy Magazine
[Show abstract][Hide abstract] ABSTRACT: 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. Such scheme is distribution-free and relies
solely on power injection data. Reactive injections are updated using the
Lagrange multipliers of the second-order cone program obtained via a convex
relaxation. Numerical tests on an industrial 47-bus test 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
Full-text · Article · Sep 2014 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: 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.
No preview · Article · Sep 2014 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: 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.
No preview · Article · Jul 2014 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: This paper presents an analysis and systemization of automatic generation control (AGC) in distribution networks (DNs) with high penetration of distributed resources, including electric vehicles (EVs). A methodology is developed that allows designing the AGC service at the distribution level, and an optimization model is proposed to assess the potential of AGC provision from EVs according to an objective of optimal economic management. A realistic case study is considered to analyze the proposed approach, and to illustrate both the potential of the methodology and the effectiveness of the optimization model. Results show that the proposed methodology represents a flexible tool that any system operator could use for the operational planning and the management of ancillary services such as AGC with EVs.
No preview · Article · Jun 2014 · Electric Power Systems Research
[Show abstract][Hide abstract] ABSTRACT: 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.
No preview · Article · May 2014 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: This paper analyzes the operation of a fully renewable electric energy system from the viewpoint of the system operator. The generation system is dominated by concentrating solar power plants (CSP) with storage, and includes wind and biomass power plants and pumped-storage facilities. The transmission network is represented using a dc approximation, the demand is considered elastic and the uncertainty of renewable production is modeled via scenarios. To carry out the analysis, we use a two-stage stochastic programming model that represents the day-ahead market (first stage) and the actual operation of the system (second stage). This model is recast as a mixed-integer linear programming problem solvable using branch-and-cut techniques. The proposed model is applied to a realistic case study based on the IEEE 118-node system and solar/wind data from Texas, US. The impact on operation and operation cost of the system flexibility and of the operation and maintenance costs of renewable energies are analyzed. Finally, we study the operation of the system throughout the four seasons of the year.
[Show abstract][Hide abstract] ABSTRACT: 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.
No preview · Article · Mar 2014 · IEEE Transactions on Power Systems
[Show abstract][Hide abstract] ABSTRACT: This addition to the ISOR series addresses the analytics of the operations of electric energy systems with increasing penetration of stochastic renewable production facilities, such as wind- and solar-based generation units.
As stochastic renewable production units become ubiquitous throughout electric energy systems, an increasing level of flexible backup provided by non-stochastic units and other system agents is needed if supply security and quality are to be maintained.
Within the context above, this book provides up-to-date analytical tools to address challenging operational problems such as:
• The modeling and forecasting of stochastic renewable power production.
• The characterization of the impact of renewable production on market outcomes.
• The clearing of electricity markets with high penetration of stochastic renewable units.
• The development of mechanisms to counteract the variability and unpredictability of stochastic renewable units so that supply security is not at risk.
• The trading of the electric energy produced by stochastic renewable producers.
• The association of a number of electricity production facilities, stochastic and others, to increase their competitive edge in the electricity market.
• The development of procedures to enable demand response and to facilitate the integration of stochastic renewable units.
This book is written in a modular and tutorial manner and includes many illustrative examples to facilitate its comprehension. It is intended for advanced undergraduate and graduate students in the fields of electric energy systems, applied mathematics and economics. Practitioners in the electric energy sector will benefit as well from the concepts and techniques explained in this book.
[Show abstract][Hide abstract] ABSTRACT: New generation algorithms focus on hybrid miscellaneous of exact and heuristic methods. Combining meta-heuristics and exact methods based on mathematical models appears to be a very promising alternative in solving many combinatorial optimization problems. ...
No preview · Article · Jan 2014 · Computers & Operations Research