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This paper exploits the decomposition structure of the large-scale hydrothermal generation expansion planning problem with an integrated modified Benders Decomposition and Progressive Hedging approach. We consider detailed and realistic data from the Brazilian power system to represent hourly chronological constraints based on typical days per month and year. Also, we represent the multistage stochastic nature of the optimal hydrothermal operational policy through co-optimized linear decision rules for individual reservoirs. Therefore, we ensure investment decisions compatible with a nonanticipative (implementable) operational policy. To solve the large-scale optimization problem, we propose an improved Benders Decomposition method with multiple instances of the master problem, each of which strengthened by primal cuts and new Benders cuts generated by each master’s trial solution. Additionally, our new approach allows using Progressive Hedging penalization terms for accelerating the convergence of the method. We show that our method is 60% faster than the benchmark. Finally, the consideration of a nonanticipative operational policy can save 7.64% of the total cost (16.18% of the investment costs) and significantly improve spot price profiles. [ABSTRACT FROM AUTHOR]

This paper addresses the incorporation of transmission switching in the contingency-constrained unit commitment problem within the context of co-optimized electricity markets for energy and reserves. The proposed generation scheduling model differs from existing formulations due to the joint consideration of four major complicating factors. First, transmission switching actions are considered both in the pre- and post-contingency states, thereby requiring binary post-contingency variables. Secondly, generation scheduling and transmission switching actions are co-optimized. In addition, the time-coupled operation of generating units is precisely characterized. Finally, practical features of modern power systems, such as uncertain nodal net injections and the operation of energy storage, are also considered. The proposed model is cast as a challenging mixed-integer program for which the off-the-shelf software customarily used for simpler models may lead to intractability even for moderately-sized instances. In order to circumvent this computational issue, this paper presents an enhanced and novel application of an exact nested column-and-constraint generation algorithm featuring the inclusion of valid constraints to improve the overall computational performance. Numerical simulations based on the IEEE 118- and 300-bus systems demonstrate the effective performance of the proposed approach as well as its economic and operational advantages over existing models disregarding post-contingency transmission switching. [ABSTRACT FROM AUTHOR]

One of the most used methods for long-term hydrothermal operation planning is the stochastic dual dynamic programming (SDDP). Using this method, the immediate and future water opportunity cost can be balanced and an economic-dispatch policy can be defined for multiple reservoirs under inflow uncertainty. In this framework, equipment outages and reserve deliverability are generally disregarded, despite their strong impact on the operative plan. However, recent advances in robust optimization have shown how to endogenously account for security criteria in scheduling models with reduced computational burden. Within this framework, reserve deliverability is ensured across the network via the co-optimization of energy and reserves (ancillary services). In this paper, we propose a new multistage model for planning hydrothermal coordination that co-optimizes the nominal energy dispatch and individual up and down reserve allocations. The main goal of this paper is to address a general $n-K$ security criterion, such that, for each inflow scenario, the system is capable of withstanding the loss of up to $K$ components, i.e., generation or transmission assets. The proposed methodology uses the column-and-constraint generation algorithm to efficiently incorporate a compound umbrella set of contingencies in the SDDP algorithm. Results for the Brazilian power system data corroborate the effectiveness of the proposed model. [ABSTRACT FROM PUBLISHER]

The current state-of-the-art method used for medium- and long-term planning studies of hydrothermal power system operation is the stochastic dual dynamic programming (SDDP) algorithm. The computational savings provided by this method notwithstanding, it still relies on major system simplifications to achieve acceptable performances in practical applications. In contrast with its actual implementation, simplifications in the planning stage may induce time-inconsistent policies, and consequently, a suboptimality gap. In this paper, we extend the concept of time inconsistency to measure the effects of modeling simplifications in the SDDP framework for hydrothermal operation planning. Case studies involving simplifications in transmission lines modeling and in security criteria indicate that these source of time inconsistency may result in unexpected reservoir depletion and spikes in energy market spot prices. [ABSTRACT FROM PUBLISHER]

This work proposes a dynamic model to devise the optimal risk-averse investment policy in a portfolio of complementary renewable sources for a generation company in the Brazilian power system. The proposed method merges a static energy-contracting model, based on a hybrid robust-and-stochastic optimization approach, with a mean reverting binomial lattice model for real-option valuation. The proposed merge extends previous works by providing support to risk-averse investment decisions in complementary renewable sources dynamically distributed over time. The most important results of the model are: how much capacity to invest or build from each renewable source, how much to sell from the energy portfolio in bilateral contracts, and the optimal timing to invest. Unlike previous reported works, our model takes into account three classes of uncertainties simultaneously: renewable production of candidate sources and prices in the spot and contract markets. A case study with realistic data from the Brazilian power system is presented to illustrate the value of our model. [ABSTRACT FROM AUTHOR]

Portfolios of renewable electricity sources are interesting risk-management mechanisms for trading in electricity contract markets. When formed by players belonging to different companies, their stability relies on the way the benefit generated by the optimal portfolio is allocated. The challenge of finding a fair and efficient allocation can be mathematically formulated in terms of finding the Core of a cooperative game, which in turn is stated as an optimization problem with a set of constraints that exponentially grows with the number of participants, quickly becoming computationally intractable. Moreover, the right-hand-side of each constraint relies on a given coalition value, which in our case is obtained by a two-stage stochastic optimization model. This paper presents an efficient methodology based on mixed —linear programming and Benders decomposition to find the Nucleolus share of large-scale renewable portfolios. Case studies are presented with data from the Brazilian power system. [ABSTRACT FROM PUBLISHER]

We present a new methodology to support an energy trading company (ETC) to devise contracting strategies under an optimal risk-averse renewable portfolio. The uncertainty in the generation of renewable energy sources is accounted for by exogenously simulated scenarios, as is customary in stochastic programming. However, we recognize that spot prices largely depend on unpredictable market conditions, making it difficult to capture its underlying stochastic process, which challenges the use of fundamental approaches for forecasting. Under such framework, industry practices make use of stress tests to validate portfolios. We then adapt the robust optimization approach to perform an endogenous stress test for the spot prices as a function of the buy-and-sell portfolio of contracts and renewable energy generation scenarios. The optimal contracting strategy is built through a bilevel optimization model that uses a hybrid approach, mixing stochastic and robust optimization. The proposed model is flexible to represent the traditional stochastic programming approach and to express the ETC's uncertainty aversion in the case where the price distribution cannot be precisely estimated. The effectiveness of the model is illustrated with examples from the Brazilian market, where the proposed approach is contrasted to its stochastic counterpart and both are benchmarked against observed market variables. [ABSTRACT FROM PUBLISHER]

This paper presents a novel approach for the transmission network expansion planning under generalized joint generation and transmission n-K security criteria. The proposed methodology identifies the optimal expansion plan while modeling the power system operation under both normal and contingency states. An adjustable robust optimization approach is presented to circumvent the tractability issues associated with conventional contingency-constrained methods relying on explicitly modeling the whole contingency set. The adjustable robust model is formulated as a trilevel programming problem. The upper-level problem aims at minimizing the investment, operation, and system power imbalance costs. The middle-level problem identifies, for a given expansion plan, the contingency state leading to maximum power imbalance if any. Finally, the lower-level problem models the operator's best reaction for a given contingency and investment plan by minimizing the system power imbalance. The resulting trilevel program is solved by a primal-dual algorithm based on Benders decomposition combined with a column-and-constraint generation procedure. The proposed approach is finitely convergent to the optimal solution and provides a measure of the distance to the optimum. Simulation results show the superiority of the proposed methodology over conventional contingency-constrained models. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach for energy and reserve scheduling in electricity markets subject to transmission flow limits. Security is imposed by guaranteeing power balance under each contingency state including both generation and transmission assets. The model is general enough to embody a joint generation and transmission n-K security criterion and its variants. An adjustable robust optimization approach is presented to circumvent the tractability issues associated with conventional contingency-constrained methods relying on explicitly modeling the whole contingency set. The adjustable robust model is formulated as a trilevel programming problem. The upper-level problem aims at minimizing total costs of energy and reserves while ensuring that the system is able to withstand each contingency. The middle-level problem identifies, for a given pre-contingency schedule, the contingency state leading to maximum power imbalance if any. Finally, the lower-level problem models the operator's best reaction for a given contingency by minimizing the system power imbalance. The proposed trilevel problem is solved by a Benders decomposition approach. For computation purposes, a tighter formulation for the master problem is presented. Our approach is finitely convergent to the optimal solution and provides a measure of the distance to the optimum. Simulation results show the superiority of the proposed methodology over conventional contingency-constrained models. [ABSTRACT FROM PUBLISHER]

The objective of this work is threefold. We firstly present an optimization model for a price-taker hydrothermal generation company (Genco) to devise bidding strategies in multi-item iterative auctions of long-term contracts. The bidding model calculates a bidder's best-response function, which takes into account the key issues on the auctioned contracts, such as its time horizon, the risk factors that affect the future contract outcomes, interdependence between auctioned products, and the agents' risk profile. The risk profile of the Gencos are represented as piecewise linear utility functions and a practical specification approach is proposed. We finally present a simulator of a uniform-pricing and iterative multi-item contract auction, where the set of auction rules is implemented and the optimization model developed is used to determine the Gencos's best responses at each auction round. The simulator enables auctioneers and generators to estimate the auction's competitive equilibrium price and to study the auction dynamics. A real multiproduct descending clock auction is simulated for the Brazilian power system under the proposed bidding scheme. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions. [ABSTRACT FROM PUBLISHER]

Renewable sources have recently emerged as a generation option for many countries in order to promote clean energy development. In the case of Brazil, small hydro plants and cogeneration from sugarcane waste (bagasse) have been attractive alternatives during the past years, with hundreds of MW installed since 2004. Despite their advantages, both alternatives are hindered by seasonal yet complementary availability. This forces producers to discount (or price) the risks faced when selling firm energy contracts and may ultimately lead to projects being commercially unattractive. We propose a stochastic optimization model that defines the optimal composition of a portfolio based on these two renewable sources in order to maximize the revenue of an energy trading company. At the same time, this model mitigates hydrological and fuel unavailability risks, thus allowing the participation of both sources in the forward market environment in a competitive manner. A case study is presented, based on data from the Brazilian system. [ABSTRACT FROM AUTHOR]

The worldwide development of the natural gas industry resulted in an integration process between electrical and gas sectors in several countries. In Brazil, this process has been taking place in a consistent manner, especially on account of the increase in gas consumption for industrial use and of the installation of thermoelectric plants. Due to the predominance of hydro plants in electric power generation, thermoelectric energy production is basically dependent on hydrology and, as a result, presents a wide annual variability. Consequently, the investment applied to gas production and transportation infrastructure may become under-utilized during a large part of the time; thus, it is important to find mechanisms apt to improve its utilization. In this respect, the present work investigates the creation of a flexible market for gas, where contracts for flexible gas supply would be offered to industrial users, who would receive the gas assigned to thermal power plants when the latter are not dispatched, and would resort to an alternate fuel when these plants are dispatched. The attractiveness of such a contract would depend, of course, on its price. The purpose of this work is to develop a stochastic model for pricing flexible gas supply contracts, taking into account the uncertainty associated to the supply-dependent on the dispatch of the thermal power plants, which have the priority of use of the gas-and the risk profile of potential consumers. [ABSTRACT FROM AUTHOR]

We present a distributionally robust optimization (DRO) approach for the transmission expansion planning problem, considering both long- and short-term uncertainties on the system demand and non-dispatchable renewable generation. On the long-term level, as is customary in industry applications, we address the deep uncertainties arising from social and economic transformations, political and environmental issues, and technology disruptions by using long-term scenarios devised by experts. In this setting, many exogenous long-term scenarios containing partial information about the random parameters, namely, the average and the support set, can be considered. For each long-term scenario, a conditional ambiguity set models the incomplete knowledge about the probability distribution of the uncertain parameters in the short-term operation. Consequently, the mathematical problem is formulated as a DRO model with multiple conditional ambiguity sets. The resulting infinite-dimensional problem is recast as an exact, although very large, finite mixed-integer linear programming problem. To circumvent scalability issues, we propose a new enhanced-column-and-constraint-generation (ECCG) decomposition approach with an additional Dantzig–Wolfe procedure. In comparison to existing methods, ECCG leads to a better representation of the recourse function and, consequently, tighter bounds. Numerical experiments based on the benchmark IEEE 118-bus system are reported to corroborate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

The development of medium-/long-term studies for power-system operation and planning under the uncertainty of renewable generation is a key challenge faced by power-system agents worldwide. There is a vast literature on stochastic optimization models devoted to addressing the relevant issues on both operation and planning applications. Notwithstanding, few papers focus on addressing the gaps within the subject of joint scenario generation despite the high sensibility of stochastic optimization models with regard to their input scenarios. Characterizing wind power generation (WPG) stochastic processes to devise time- and spatial-dependent scenarios, based on simulation procedures, for time horizons of one to a few years is a difficult task. Multiple regimes and non-Gaussian distributions are two of the main issues that significantly change the risk described through generated scenarios. In this paper, a new methodology to simulate long-term joint scenarios for multivariate WPG time series is presented. The proposed framework, known as generalized auto regressive score models, is derived based on a new class of time-series model with time-varying parameters and an arbitrary non-Gaussian distribution. Our case study shows, based on real data from the Brazilian power system, that the proposed methodology is capable of producing scenarios with coherent temporal and spatial dependence that are needed in power system studies. [ABSTRACT FROM AUTHOR]

The current renewable-driven generation expansion wave, pushed by high renewable targets, is not accompanied by the same movement in the transmission expansion planning (TEP) side. In this context, new techniques are needed to balance the cost of relying in expensive reserve resources and the cost of building new lines to ensure least-cost reserve deliverability and foster new renewable projects. The situation is worsened in the presence of contingencies, where the interaction between the optimal reserve siting and deployment, the amount of renewable curtailment, the construction of new lines, and the selection of candidate renewable sites to be developed became even more complex. This paper presents a two-stage min-max-min model for co-optimizing the expansion of the transmission system and renewable generation capacity to meet renewable targets under high security standards and renewable uncertainty. In order to account for realistic reserve needs and its interaction with the expansion plan, correlations between renewables injection as well as generation and transmission (GT) outages are accounted for in a robust fashion. In order to ensure security within a flexible framework, the concept of compound GT $n-K$ security criteria is presented. Three case studies are proposed to illustrate the applicability of the proposed model. A case study with realistic data from the Chilean system is presented and solutions obtained with different levels of security are tested against a set of 10 000 simulated scenarios of renewable injections and system component outages. [ABSTRACT FROM AUTHOR]

The benefits of new transmission investment significantly depend on deployment patterns of renewable electricity generation that are characterized by severe uncertainty. In this context, this paper presents a novel methodology to solve the transmission expansion planning problem under generation expansion uncertainty in a min–max regret fashion, when considering flexible network options and $n-1$ security criterion. To do so, we propose a five-level mixed integer linear programming (MILP) based model that comprises: (i) the optimal network investment plan (including phase shifters), (ii) the realization of generation expansion, (iii) the co-optimization of energy and reserves given transmission and generation expansions, (iv) the realization of system outages, and (v) the decision on optimal post-contingency corrective control. In order to solve the five-level model, we present a cutting plane algorithm that ultimately identifies the optimal min–max regret flexible transmission plan in a finite number of steps. The numerical studies carried out demonstrate: (a) the significant benefits associated with flexible network investment options to hedge transmission expansion plans against generation expansion uncertainty and system outages, (b) strategic planning-under-uncertainty uncovers the full benefit of flexible options which may remain undetected under deterministic, perfect information methods, and (c) the computational scalability of the proposed approach. [ABSTRACT FROM PUBLISHER]