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The establishment of a single European day-ahead market has accomplished the integration of the regional day-ahead markets. However, reserve provision and activation remain an exclusive responsibility of regional operators. This limited spatial coordination and the separated structure hinder the efficient utilization of flexible generation and transmission, since their capacities have to be ex-ante allocated between energy and reserves. To promote reserve exchange, recent work proposed a preemptive model that withdraws a portion of the inter-area transmission capacity available from day-ahead energy for reserves by minimizing the expected system cost. This decision-support tool, formulated as a stochastic bilevel program, respects the current architecture but does not suggest area-specific costs that guarantee sufficient benefits for areas to accept the solution. To this end, we formulate a preemptive model in a framework that allows application of game theory methods to obtain a stable benefit allocation, i.e., an outcome immune to coalitional deviations ensuring willingness of areas to coordinate. We show that benefit allocation mechanisms can be formulated either at the day-ahead or the real-time stages, in order to distribute the expected or the scenario-specific benefits, respectively. For both games, the proposed benefits achieve minimal stability violation, while allowing for a tractable computation with limited queries to the bilevel program. Our case studies, based on an illustrative and a more realistic test case, compare our method with well-studied benefit allocations, namely, the Shapley value and nucleolus, and analyze the factors that drive these allocations (e.g., flexibility, network structure, wind correlations). We show that our method performs better in stability and tractability., Omega (United Kingdom), 113

The interdependence between electricity and natural gas systems has lately increased due to the wide deployment of gas-fired power plants (GFPPs). Moreover, weather-driven renewables introduce uncertainty in the operation of the integrated energy system, increasing the need for operational flexibility. Recently proposed stochastic dispatch models optimally use the available flexibility and minimize the total expected system cost. However, these models are incompatible with the current sequential market design. We propose a novel method to optimally define the available natural gas volume for power production scheduling, anticipating the real-time flexibility needs. This volume-based model is formulated as a stochastic bilevel program that aims to enhance the inter-temporal coordination of scheduling and balancing operations, while remaining compatible with the sequential clearing of day-ahead and real-time markets. The proposed model accounts for the inherent flexibility of the natural gas system via the proper modeling of linepack capabilities and reduces the total expected system cost by the optimal definition of natural gas volume availability for GFPPs at the forward phase. The volume-based coordination model is compared with a price-based coordination alternative, which was recently proposed. In the latter one, the natural gas price perceived by GFPPs is similarly adjusted to enhance the temporal coordination of scheduling and balancing stages. This comparison enables us to highlight the main properties and differences between the two coordination mechanisms.

In this paper, the Unit Commitment (UC) problem in a power network with low levels of rotational inertia is studied. Frequency-related constraints, namely the limitation on Rate-of-Change-of-Frequency (RoCoF), frequency nadir and steady-state frequency error, are derived from a uniform system frequency response model that incorporates dynamics and controls of both synchronous generators and grid-forming inverters. These constraints are then included into a stochastic UC formulation that accounts for wind power and equipment contingency uncertainties using a scenario-tree approach. In contrast to the linear RoCoF and steady-state frequency error constraints, the nadir constraint is highly nonlinear. To preserve the mixed-integer linear formulation of the stochastic UC model, we propose a computationally efficient approach that allows to recast the nadir constraint by introducing appropriate bounds on relevant decision variables of the UC model. This method is shown to be generally more accurate and computationally more efficient for medium-sized networks than a piece-wise linearization method adapted from the literature. Simulation results for a modified IEEE RTS-96 system revealed that the inclusion of inertia-related constraints significantly influences the UC decisions and increases total costs, as more synchronous machines are forced to be online to provide inertial response.

Considering the sequential clearing of energy and reserves in Europe, enabling inter-area reserve exchange requires optimally allocating inter-area transmission capacities between these two markets. To achieve this, we provide a market-based allocation framework and derive payments with desirable properties. The proposed min-max least core selecting payments achieve individual rationality, budget balance, and approximate incentive compatibility and coalitional stability. The results extend the works on private discrete items to a network of continuous public choices., Operations Research Letters, 49 (4), ISSN:0167-6377, ISSN:1872-7468

Wind power producers participating in today's electricity markets face significant variability in revenue streams, with potential high losses mostly due to wind's limited predictability and the intermittent nature of the generated electricity. In order to further expand wind power generation despite such challenges, it is important to maximize its market value and move decisively towards economically sustainable and financially viable asset management. In this paper, we introduce a decision-making framework based on stochastic optimization that allows wind power producers to hedge their position in the market by trading physically settled options in futures markets in conjunction with their participation in the short-term electricity markets. The proposed framework relies on a series of two-stage stochastic optimization models that identify a combined trading strategy for wind power producers actively participating in both financial and day-ahead electricity markets. The proposed models take into consideration penalties from potential deviations between day-ahead market offers and real-time operation and incorporates different preferences of risk aversion, enabling a trade-off between the expected profit and its variability. Empirical analysis based on data from the Nordic region illustrates high efficiency of the stochastic model and reveals increased revenues for both risk neutral and risk averse wind producers opting for combined strategies.

Energy storage systems are bound to play a critical role in the transition towards a decarbonized power sector with high shares of variable renewables. However, an open question is whether all storage capacity that is needed will be profitable under the current market paradigm. In this paper, we assess how the profitability of energy storage systems is affected by the increasing penetration of variable renewables. Moreover, we discuss the potentially detrimental effects of strategic storage capacity withholding on system costs, renewable penetration and the profitability of all technologies.

The increasing shares of stochastic renewables bring higher uncertainty in power system operation and underline the need for optimal utilization of flexibility. However, the European market structure that separates energy and reserve capacity trading is prone to inefficient utilization of flexible assets, such as the HVDC interconnections, since their capacity has to be ex-ante allocated between these services. Stochastic programming models that co-optimize day-ahead energy schedules with reserve procurement and dispatch, provide endogenously the optimal transmission allocation in terms of minimum expected system cost. However, this perfect temporal coordination of trading floors cannot be attained in practice under the existing market design. To this end, we propose a decision-support tool that enables an implicit temporal coupling of the different trading floors using as control parameters the inter-regional transmission capacity allocation between energy and reserves and the area reserve requirements. The proposed method is formulated as a stochastic bilevel program and cast as mixed-integer linear programming problem, which can be efficiently solved using a Benders decomposition approach that improves computational tractability. This model bears the anticipativity features of a transmission allocation model based on a pure stochastic programming formulation, while being compatible with the current market structure. Our analysis shows that the proposed mechanism reduces the expected system cost and thus can facilitate the large-scale integration of intermittent renewables.

The trading of electricity and natural gas, according to the current organizational framework, takes place in independent and sequentially cleared trading floors. This setup leads to imperfect coordination between the two energy systems and it also separates the day-ahead scheduling from the real-time balancing decisions. Acknowledging these market inefficiencies, we propose defining standardized contracts in the form of swing options that allow for a flexible demand pattern according to a predetermined price. In this paper, swing option contracts are parameterized and priced on the gas system side and can be concluded by the power generators to hedge against gas price uncertainty. We perform the contract pricing using a stochastic bilevel optimization model that anticipates the reaction of both systems with respect to contract definition. Our analysis shows that if these contracts are properly priced and valuated by the gas and electricity system, respectively, they can improve intersystem, as well as inter-temporal, coordination and thus reduce the expected system cost.

On the path towards power systems with high renewable penetrations and ultimately carbon-neutral, more and more synchronous generation is being displaced by variable renewable generation that does not currently provide system inertia nor reactive power support. This could create serious issues of power system stability in the near future, and countries with high renewable penetrations such as Ireland are already facing these challenges. Therefore, this paper aims at answering the questions of whether and how explicitly including inertia and reactive power constraints in generation expansion planning would affect the optimal capacity mix of the power system of the future. Towards this end, we propose the novel Low-carbon Expansion Generation Optimization model, which explicitly accounts for: unit commitment constraints, Rate of Change of Frequency inertia requirements and virtual inertia provision, and, a second-order cone programming approximation of the AC power flow, accounting for reactive power constraints. An illustrative case study underlines that disregarding inertia and reactive power constraints in generation expansion planning can result in additional system cost, system infeasibilities, a distortion of optimal resource allocation and inability to reach established policy goals.

The increasing use of gas-fired power plants requires a more thorough consideration of the interdependencies between power and gas systems. Ideally, these systems should be dispatched in a fully coordinated manner. However, they are generally operated as separate entities and it may not be possible to share complete information regarding the internal variables and constraints of each network. To overcome this limitation, we propose an inter-system flexibility set as a proxy to provide information about the power system to the gas network, so that actions taken in the gas network, such as load shedding, retain feasibility in the power system.

Compared to Seasonal Line Rating (SLR), Dynamic Line Rating (DLR) allows for higher power flows on overhead transmission lines, depending on the actual weather conditions. Nevertheless, the potential of DLR has to be traded off against the additional uncertainty associated with varying ratings. This paper proposes a DC-Optimal Power Flow (DCOPF) algorithm that accounts for DLR uncertainty by means of Chance-Constraints (CC). The goal is to determine the optimal day-ahead dispatch taking the cost of reserve procurement into account. The key contribution of this paper consists in considering both non-parametric predictive distributions of DLR and the combined wind power uncertainty in the optimization problem. Our results highlight the benefits of DLR in wind-dominated power systems, assuming typical risk aversion levels in the line rating estimation.

In order to enable large-scale penetration of renew-abies with variable generation, new sources of flexibility have to be exploited in the power systems. Allowing asymmetric block offers (including response and rebound blocks) in balancing markets can facilitate the participation of flexibility aggregators and unlock load-shifting flexibility from, e.g., thermostatic loads. In this paper, we formulate an optimal offering strategy for a risk-averse flexibility aggregator participating in such a market. Using a price-taker approach, load flexibility characteristics and balancing market price forecast scenarios are used to find optimal load-shifting offers under uncertainty. The problem is formulated as a stochastic mixed-integer linear program and can be solved with reasonable computational time. This work is taking place in the framework of the real-life demonstration project EcoGrid 2.0, which includes the operation of a balancing market on the island of Bornholm, Denmark. In this context, aggregators will participate in the market by applying the offering strategy optimization tool presented in this paper.

This paper deals with the problem of clearing sequential electricity markets under uncertainty. We consider the European approach, where reserves are traded separately from energy to meet exogenous reserve requirements. Recently pro- posed stochastic dispatch models that co-optimize these services provide the most efficient solution in terms of expected operating costs by computing reserve needs endogenously. However, these models are incompatible with existing market designs. This paper proposes a new method to compute reserve requirements that bring the outcome of sequential markets closer to the stochastic energy and reserves co-optimization in terms of cost efficiency. Our method is based on a stochastic bilevel program that implicitly improves the inter-temporal coordination of energy and reserve markets, but remains compatible with the European market design. We use two standard IEEE reliability test cases to illustrate the benefit of intelligently setting operating reserves in single and multiple reserve control zones.

Energy storage systems (ESS) are considered as a promising solution to improve power system flexibility and facilitate the integration of renewables in electricity markets. This paper investigates the impact of strategic offering by an ESS operator in the day-ahead and balancing market. The offering strategy of a price-maker ESS operator is formulated as a bilevel model, where the upper-level problem represents the profit maximization of the ESS operator and the lower-level problem simulates the market-clearing outcome. This methodological framework can be used either to assess market efficiency distortion or as a trading strategy from the perspective of the ESS operator. Our analysis shows that adopting strategic behavior may improve ESS expected profit but reduces social welfare, especially for high ESS energy-to-power ratios.

The trend towards electrification of the heating sector in many cases leads to the replacement of fossil-fueled heating systems with electric heat pumps. This may result to significantly higher consumption and potentially violations of thedistribution grid operational limits. We propose a day-ahead optimization strategy to assess the cost of imposing capacity limitations in the total consumption of individual buildings, as well as aggregations of buildings. We show that such capacity limitations lead to an increase for the buildings operational costs, which can be interpreted as the value of these limitations. Based on such calculations, the aggregator can value capacity-limitation services to the distribution system operator. Moreover, the value of aggregation is also highlighted, since it leads to lower costs than imposing the same total capacity limitation on individual buildings.

The establishment of the single European day-ahead market has accomplished a crucial step towards the spatial integration of the European power system. However, this new arrangement does not consider any intra-regional coordination of day-ahead and balancing markets and thus may become counterproductive or inefficient under uncertain supply, e.g., from weather-driven renewable power generation. In the absence of a specific target model for the common balancing market in Europe, we introduce a framework to compare different coordination schemes and market organizations. The proposed models are formulated as stochastic equilibrium problems and compared against an optimal market setup. The simulation results reveal significant efficiency loss in case of partial coordination and diversity of market structure among regional power systems.

The large scale integration of stochastic renewable energy introduces significant challenges for power system operators and disputes the efficiency of the current market design. Recent research embeds the uncertain nature of renewable sources by modelling electricity markets as a two-stage stochastic problem, co-optimizing day-ahead and real-time dispatch. In this framework, we introduce a bilevel model to derive the optimal bid of a strategic wind power producer acting as price-maker both in day-ahead and real-time stages. The proposed model is a Mathematical Program with Equilibrium Constraints (MPEC) that is reformulated as a single-level Mixed-Integer Linear Program (MILP), which can be readily solved. Our analysis shows that adopting strategic behaviour may improve producer's expected profit as the share of wind power increases. However, this incentive diminishes in power systems where available flexible capacity is high enough to ensure an efficient market operation.

Large scale integration of fluctuating and non-dispatchable generation and variable transmission patterns induce high uncertainty in power system operation. In turn, transmission system operators (TSOs) need explicit information about available flexibility to maintain a desired reliability level at a reasonable cost. In this paper, locational flexibility is defined and a unified framework to compare it against forecast uncertainty is introduced. Both metrics are expressed in terms of ramping rate, power and energy and consider the network constraints. This framework is integrated into the operational practice of the TSO using a robust reserve procurement strategy which guarantees optimal system response in the worst-case realization of the uncertainty. The proposed procurement model is applied on an illustrative three-node system and a case study focuses on the available locational flexibility in a larger power system.

In view of the predictability and stochasticity of wind power generation, transmission system operators (TSOs) can benefit from predictive dispatch of slow and manual control reserves in order to maintain reactive reserve levels for unpredictable events. While scenario-based approaches for stochastic optimization are well suited for this problem, it appears that TSOs are hesitant in adopting this method into their practice of predictive dispatch. Differences in the formulation of constraints and cost functions, the timing and reserve product constraints influence the dispatch result significantly and yield varying results with different practical implications. To support adoption, there is a need to study relevant parameters and trade-offs to be considered in introducing such methods to operation practice, enabling also the investigation of alternate reserve product constraints, e.g., to enable reserve contribution from storage-constrained units. This paper introduces a framework for comparison of operational strategies for system balancing, proposes criteria for performance assessment and exemplifies a systematic evaluation of several operation strategies.

The large scale integration of wind generation in existing power systems requires novel operational strategies and market clearing mechanisms to account for the variable nature of this energy source. An efficient method to cope with this uncertainty is stochastic optimization which however requires high-quality forecasts in the form of scenarios. The main goal of this work is to release a public dataset of wind power forecasts to be used as a reference for future research. To that extent, we provide a complete framework to describe wind power uncertainty in terms of single-valued and probabilistic predictions as well as scenarios representing the spatio-temporal dependence structure of forecast errors. The applicability of the proposed framework is demonstrated with a small-scale stochastic unit commitment model.

The deployment of large shares of stochastic renewable energy, e.g., wind power, may bring important economic and environmental benefits to the power system. Nonetheless, their efficient integration depends on the ability of the power system to cope with their inherent variability and the uncertainty arising from their partial predictability. Considering that the existing setup of the European electricity markets promotes the spatial coordination of neighbouring power systems only on the day-ahead market stage, regional system operators have to rely mainly on their internal balancing resources in order to guarantee system security. However, as power systems are forced to operate closer to their technical limits, where flexible generation resources become scarce, the conventional market paradigm may not be able to respond effectively on the wide range of uncertainty. The operational flexibility of the power system depends both on the technical parameters of its components, i.e., generators and transmission infrastructure, as well as on the operational practices that make optimal use of the available assets. This work focuses on alternative market designs that enable sharing of cross-border balancing resources between adjacent power systems through High Voltage Direct Current (HVDC) interconnections which provide increased controllability. In this context, we formulate a stochastic market-clearing algorithm that attains full spatio-temporal integration of reserve capacity, day-ahead and balancing markets. Against this benchmark we compare two deterministic market designs with varying degrees of coordination between the reserve capacity and energy services, both followed by a real-time mechanism. Our study reveals the inefficiency of deterministic approaches as the shares of wind power increase. Nevertheless, enforcing a tighter coordination between the reserves and energy trading floors may improve considerably the expected system cost compared to a sequential market design. Aiming to provide some insights for improvement of the sequential market-clearing, we analyse the effect of explicit transmission allocation between energy and reserves for different HVDC capacities and identify the market dynamics that dictate the optimal ratio.