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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]

In this paper, we present BilevelJuMP.jl, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the JuMP algebraic syntax. Because of the generality and flexibility that our library inherits from JuMP's syntax, our package allows users to model bilevel optimization problems with conic constraints in the lower level and all constraints supported by JuMP in the upper level including conic, quadratic, and nonlinear constraints. Moreover, the models defined with the syntax from BilevelJuMP.jl can be solved by multiple techniques that are based on reformulations as mathematical programs with equilibrium constraints (MPEC). Manipulations on the original problem data are possible due to MathOptInterface.jl's structures and Dualization.jl features. Hence, the proposed package allows quick modeling, deployment, and thereby experimenting with bilevel models based on off-the-shelf mixed-integer linear programming and nonlinear solvers. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The authors were partially supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The work of A. Street was also partially supported by Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). The work was partially funded by the project P&D ANEEL PD-00403-0050/2020 sponsored by ENGIE BRASIL ENERGIA S.A. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0135) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0135). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

• A standardized nomenclature for electricity market design comparison. • An international benchmark based on physical characteristics and market mechanisms. • Short- and long-term markets aspects are considered in the comparisons. • Recommendations for the Brazilian electricity market based on selected benchmarks. • Transitioning from centralized and bid-based markets is discussed. The Brazilian power-market design features were based on the system's physical and economic characteristics in the '90s. However, some of the approximations and assumptions adopted for the regulatory framework are no longer valid. Failing to adapt the regulatory framework to the current system and economic reality may provide poor market signals, possibly threatening the sustainability and supply adequacy of the long-run system. Despite the national consensus on the need for modernization, there are still many concerns about which changes should be carried out. The vast literature and international experience in the subject notwithstanding, each system's par- ticularities challenge any simplistic attempt to match the Brazilian case with previously reported experiences. Thus, this work aims to 1) define a general market design nomenclature and clas- sify relevant market structures, 2) draw a systematized panorama of the physical characteristics that have influenced the selection of different market designs and mechanisms, and 3) compare the Brazilian market design, to the international experience. Based on that, we contribute with an updated and standardized panorama of a few relevant market designs and structures. Addi- tionally, we raise awareness and discuss the lessons from the international experience applicable to support and foster the Brazilian market modernization agenda. [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]

Electricity grid operators and planners need to deal with both the rapidly increasing integration of renewables and an unprecedented level of uncertainty that originates from unknown generation outputs, changing commercial and regulatory frameworks aimed to foster low-carbon technologies, the evolving availability of market information on feasibility and costs of various technologies, etc. In this context, there is a significant risk of locking-in to inefficient investment planning solutions determined by current deterministic engineering practices that neither capture uncertainty nor represent the actual operation of the planned infrastructure under high penetration of renewables. We therefore present an alternative optimization framework to plan electricity grids that deals with uncertain scenarios and represents increased operational details. The presented framework is able to model the effects of an array of flexible, smart grid technologies that can efficiently displace the need for conventional solutions. We then argue, and demonstrate via the proposed framework and an illustrative example, that proper modelling of uncertainty and operational constraints in planning is key to valuing operationally flexible solutions leading to optimal investment in a smart grid context. Finally, we review the most used practices in power system planning under uncertainty, highlight the challenges of incorporating operational aspects and advocate the need for new and computationally effective optimization tools to properly value the benefits of flexible, smart grid solutions in planning. Such tools are essential to accelerate the development of a low-carbon energy system and investment in the most appropriate portfolio of renewable energy sources and complementary enabling smart technologies. [ABSTRACT FROM AUTHOR]

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]

Investment decisions in renewable energy sources such as small hydro, wind power, biomass and solar are frequently made in the context of enormous uncertainty surrounding both intermittent generation and the highly volatile electricity spot prices that are used for clearing of trades. This paper presents a new portfolio-based approach for selecting long-term investments in small-scale renewable energy projects and matching contracts for the sale of the resulting electricity. Using this approach, we have formulated a stochastic optimisation model that maximises a holding company's risk-averse measure of value. Using an illustrative example representative of investment decisions within the Brazilian electricity system, we investigate the sensitivity of the optimised portfolio composition and commercialisation strategy to contract prices in the free contracting environment and to the decision maker's attitude towards risk. The numerical results demonstrate it is possible to reduce significantly financial risks, such as the price-quantity risk, not only by exploiting the complementarity of the considered renewable sources generation profiles, but also by selecting the optimal mix of commercialisation contracts from different markets. We find that the multi-market strategy generally results in appreciably higher optimal value than single-market strategies and can be applied to a wide range of renewable generators and contracts. [ABSTRACT FROM AUTHOR]

This paper proposes a new methodological framework to support the decision of Brazilian distribution companies (DISCOs) when defining maximum demand contracts with the transmission system. The contract must be established one year ahead, and several uncertainties associated to loads, distributed generation (DG) and internal grid contingency events, should be considered. The optimal contracting decision should take into account the risk profile of DISCO's stakeholders and the interest of final consumers. To tackle these topics, an engineering-based approach is proposed in which a chain of four methods composes the final solution approach. To ensure realistic and tractable solutions, load and DG time series are decomposed into low and high frequencies to address the challenge of deriving long-term probabilistic forecasts for high-dimensional time series in high frequency. The proposed methodology considers exogenous long-term trend drivers (such as economic and climatic indices) in the probabilistic forecasts of loads and DG, as well as corrective actions to respond against contingencies in the power flow simulation. Results for a Brazilian DISCO show that the proposed probabilistic forecasts are adherent and tractable. Our case study corroborates the effectiveness of our approach to support DISCOs' decision and adjust their contracts based on pre-specified risk levels. • Four integrated methods to define long-term DSO-TSO demand contracts in Brazil. • A new method for simulating high-dimensional hourly load and DG time series in a long-term horizon. • A new array of quantile regressions to estimate and simulate conditional dynamic load curves. • A risk-averse optimization model to define the optimal demand contracting strategy of a distribution company. [ABSTRACT FROM AUTHOR]

• A new time series model to generate probabilistic forecasts for renewable generation time series. • A regularized multi-quantile-regression model is used to define a non-parametric conditional distribution function (CDF). • A Lipschitz regularization of the first derivative of coefficients is proposed to impose coefficient smoothness in the quantile dimension. • The proposed regularization induces a coupling effect among quantiles, creating the concept of a single non-parametric CDF model. • Results show an improved out-of-sample performance against relevant benchmarks. Modern decision-making processes require uncertainty-aware models, especially those relying on non-symmetric costs and risk-averse profiles. The objective of this work is to propose a dynamic model for the conditional non-parametric distribution function (CDF) to generate probabilistic forecasts for a renewable generation time series. To do that, we propose an adaptive non-parametric time-series model driven by a regularized multiple-quantile-regression (MQR) framework. In our approach, all regression models are jointly estimated through a single linear optimization problem that finds the global-optimal parameters in polynomial time. An innovative feature of our work is the consideration of a Lipschitz regularization of the first derivative of coefficients in the quantile space, which imposes coefficient smoothness. The proposed regularization induces a coupling effect among quantiles creating a single non-parametric CDF model with improved out-of-sample performance. A case study with realistic wind-power generation data from the Brazilian system shows: 1) the regularization model is capable to improve the performance of MQR probabilistic forecasts, and 2) our MQR model outperforms five relevant benchmarks: two based on the MQR framework, and three based on parametric models, namely, SARIMA, and GAS with Beta and Weibull CDF. [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]

This paper presents a nonparametric approach based on adjustable robust optimization to consider correlated nodal demand uncertainty in a joint energy and reserve scheduling model with security constraints. In this model, up- and down-spinning reserves provided by generators are endogenously defined as a result of the optimization problem. Adjustable robust optimization is used to characterize the worst-case load variation under a given user-defined uncertainty set. This paper differs from recent previous work in two respects: (i) nonparametric correlations between nodal demands are accounted for in the uncertainty set and (ii) based on the binary expansion linearization approach, a mixed-integer linear model is provided for the optimization related to the worst-case demand. The resulting problem is formulated as a trilevel program and solved by means of Benders decomposition. Empirical results suggest that the effect of nodal correlations can be effectively captured by the robust scheduling model. [ABSTRACT FROM AUTHOR]

• addresses the challenges of using the DC and AC TEP models • aims to improve the understanding of the AC and DC TEP models and their impact on the planning • develops a new and more reliable method based on the approximated AC and on the exact DC TEP solutions • uses the F&I boundary characteristics to improve the final solution plan In the last years, a lot of effort was placed into approximated or relaxed models and heuristic and metaheuristic algorithms to solve complex problems, mainly with non-linear and non-convex natures, in a reasonable time. On one hand, approximated/relaxed mathematical models often provide convergence guarantees and allow the problem to be solved to global optimality. On the other hand, there is no guarantee that the optimal solution of the modified problem is even feasible in the original one. In contrast with that, the metaheuristic algorithms lack mathematical proof for optimality, but as the obtained solutions can be tested against the original problem, the feasibility can be ensured. In this sense, this work brings a new method combining exact solutions from a Mixed-Integer-Linear-Problem (MILP) Transmission Expansion Planning (TEP) model and stochastic solutions from metaheuristic algorithms to solve the non-linear and non-convex TEP problem. We identify the issues that came up with the linear approximations and metaheuristics procedures and we introduce a MILP-Based Heuristic (MBH) algorithm to overcome these issues. We demonstrate our method on a single-stage TEP with the RTS 24 nodes and on a multi-stage TEP with the IEEE 118 nodes test system. The AC TEP solution was obtained using Evolutionary Computation, while the DC TEP solution was obtained using a commercial solver. From the simulations results, the novel MBH method was able to reduce in 42% and in 85% the investment cost from an evolutionary computation solution for the single-stage and multi-stage TEP, respectively. [ABSTRACT FROM AUTHOR]

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]

Highlights: [•] We model a post-contingency transmission response in electrical systems operation. [•] We measure the benefits in grid security, operational costs and reserve levels. [•] We compare the results among three different system operation methodologies. [•] Results show that transmission switchings occur in some specific critical lines. [•] A wide range of contingencies is covered even with limited transmission reactions. [ABSTRACT FROM AUTHOR]

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]

The consideration of a flexible network topology has been previously shown to produce significant benefits to power system operation. In this paper, we study the effects of considering smart transmission switching actions to unlock flexible generation resources from the network. More specifically, we consider a smart network capable of performing both preventive and real-time corrective topology changes in response to the occurrence of contingencies. The proposed economic dispatch model ensures the co-optimization of energy and reserves with pre- and post-contingency transmission switching actions, thus producing the optimal policy with transmission flexibility. An exact decomposition methodology based on the nested column-and-constraint generation algorithm is devised to address the challenging mixed-integer program arising from the proposed formulation. Numerical simulations show that the incorporation of corrective transmission switching in the optimization process offers significant benefits to system reliability and substantial cost savings. • We consider a smart network capable of preventive and corrective topology changes. • Co-optimizing corrective switching allows improving security in economic dispatch. • The co-optimization of corrective switching allows unlocking reserve capabilities. • An exact and computationally efficient nested decomposition method is applied. [ABSTRACT FROM AUTHOR]

Hydropower is one of the world's primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is crucial for driving the sustainable use of this scarce resource. Nevertheless, traditional computational tools use stochastic dual dynamic programming under the Hazard-Decision (HD) modeling simplification, where dispatch decisions are determined assuming perfect information about the current inflows. In practice, however, some dispatch decisions are made before water inflows are observed, i.e., under a Decision-Hazard (DH) scheme. This inconsistency generates an optimistic assessment of the opportunity cost of the water, inducing a sub-optimal use of energy resources. Thus, our objectives are: (i) to raise awareness of the HD issue bridging research and implementation with a clear recommendation to system operators and regulators; (ii) to incorporate the DH scheme into the long-term hydrothermal scheduling problem; (iii) to assess the economic impacts and other market distortions due to the actual energy usage policy based on the HD simplification. For a representative case-study with realistic data from the Brazilian power system, results show that the HD simplification introduces a regret cost of 12%. Furthermore, we show that incorporating the DH scheme into the hydrothermal planning model, the energy supply cost can be reduced up to 5.3%. We also show that spot-price distortions and expensive thermal generation could be mitigated in the DH scheme. • SDDP applied to hydrothermal dispatch relies on Hazard-Decision (HD) approximation. • The applied HD approximation implies in one-step-ahead anticipative process. • Proposed Decision-Hazard (DH) model considers here-and-now decisions in each stage. • Numerical simulations based on the Brazilian case reveals an overcost of 12% due to HD. • Incorporating the DH model, simulations show a reduced overcost up to 5.3%. [ABSTRACT FROM AUTHOR]

• We design a methodology to find specific Nash equilibrium in electricity markets. • We devise an efficient column-and-constraint generation method to solve the EPEC. • We benchmark the proposed solution method with the state-of-the-art methodology. • The proposed algorithm is 20 times faster than current state-of-the-art on average. Equilibrium analysis is crucial in electricity market designs, with Nash equilibrium recognized as the most powerful one. Its most prominent hindrance, however, is an efficient methodology to compute an equilibrium point in large-scale systems. In this work, a Column-and-Constraint Generation (CCG) algorithm is proposed to tackle this challenge. More precisely, the master problem finds a candidate for Nash equilibrium and the oracle identifies whether this candidate point is indeed an equilibrium. A set of numerical experiments was conducted, comparing its computational performance with the solution of an Equilibrium Problem with Equilibrium Constraint (EPEC). We identify that the proposed algorithm overcomes the benchmark in the magnitude of 20 times on average and more than 30 times in the most demanding instances. Furthermore, the scalability of the EPEC formulation is challenged even for medium-scale instances, whilst the proposed algorithm was able to handle all tested instances in a reasonable computational time. [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]

Real-time operation of electric power systems under high penetration of renewable energy generation has to incorporate strategies for managing the uncertainty associated with this type of power sources. In the case of the unit commitment problem, models based on robust optimization have been widely used for the day-ahead computation of power dispatch and reserves schedule. Typical approaches use uncertainty sets with fixed levels of conservativeness, without considering the real-time performance of the solutions. This paper proposes a solution scheme for the adaptive robust unit commitment problem using online adjusted data-driven uncertainty sets. Conservativeness parameters of the uncertainty sets are dynamically calculated as a function of previous operating results and incoming data via reinforcement learning, resulting in an online learning-optimization framework. The paper also develops an experimental framework to simulate real-time operation under the proposed methodology. Out-of-sample experiments illustrate the effectiveness of the proposed scheme against well-known benchmarks with fixed robustness levels. Results show improvements in power generation costs, voltage violations, and use of reserves. Two systems of different sizes are analyzed, illustrating the scalability of the proposed approach. • Q-learning algorithms for data-driven robust uncertainty sets adaptation. • Uncertainty sets dynamical adaptation based on real-time system indicators. • Novel framework for real-time power systems operation simulation. • Results comparison against two-stage robust and stochastic optimization approaches. • Statistically significant lower generation costs and use of system reserves. [ABSTRACT FROM AUTHOR]

Highlights: [•] The new approach to allocate transmission cost. [•] The approach is based on LRMC method and the min–max optimization technique. [•] The approach reduces the dispersion of the tariffs maintaining the locational signal. [•] An iterative method to set tariffs based on a linear programming optimization model. [Copyright &y& Elsevier]

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]

The behavior of a photovoltaic (PV) module may be captured via its current–voltage ( $I$–$V$ ) characteristic. The single-diode model is able to adequately fit this characteristic while featuring limited parameterization difficulty, and is thus widely adopted to represent the performance of a PV module. However, the identification of the model's parameters is a complex task due to the nonconvex nature of the underlying optimization problem. In this paper, an efficient method for the parameter extraction of the single-diode PV model from experimental $I$ –$V$ curves is developed. This method features two advantages with respect to the existing procedures. On the one hand, it is able to find high-quality solutions at a reduced computational complexity. On the other hand, it does not rely on any preliminary data selection and it can thus be fully automated without user intervention. Numerical results obtained for case studies common in the literature and a large-scale repository show its performance. A computer program implementing the proposed methodology is available upon request via an e-mail to all interested researchers. [ABSTRACT FROM AUTHOR]