• Energy Research

Dynamic pricing through bilevel programming is widely used for demand response but often assumes perfect knowledge of prosumer behavior, which is unrealistic in practical applications. This paper presents a novel framework that integrates bilevel programming with online learning, specifically Thompson sampling, to overcome this limitation. The approach dynamically sets optimal prices while simultaneously learning prosumer behaviors through observed responses, eliminating the need for extensive pre-existing datasets. Applied to an energy community providing capacity limitation services to a distribution system operator, the framework allows the community manager to infer individual prosumer characteristics, including usage patterns for photovoltaic systems, electric vehicles, home batteries, and heat pumps. Numerical simulations with 25 prosumers, each represented by 10 potential signatures, demonstrate rapid learning with low regret, with most prosumer characteristics learned within five days and full convergence achieved in 100 days.

The system operators usually need to solve large-scale unit commitment problems within limited time frame for computation. This paper provides a pragmatic solution, showing how by learning and predicting the on/off commitment decisions of conventional units, there is a potential for system operators to warm start their solver and speed up their computation significantly. For the prediction, we train linear and kernelized support vector machine classifiers, providing an out-of-sample performance guarantee if properly regularized, converting to distributionally robust classifiers. For the unit commitment problem, we solve a mixed-integer second-order cone problem. Our results based on the IEEE 6- and 118-bus test systems show that the kernelized SVM with proper regularization outperforms other classifiers, reducing the computational time by a factor of 1.7. In addition, if there is a tight computational limit, while the unit commitment problem without warm start is far away from the optimal solution, its warmly-started version can be solved to (near) optimality within the time limit.

The first of this two-paper series proposes a methodology to characterize generation investment equilibria in a pool-based network-constrained electricity market, where the producers behave strategically. To this end, the investment problem of each strategic producer is represented using a bilevel model, whose upper-level problem determines the optimal investment and the supply offering curves to maximize its profit, and whose several lower-level problems represent different market clearing scenarios. This model is transformed into a mathematical program with equilibrium constraint (MPEC) through replacing the lower-level problems by their optimality conditions. The joint consideration of all producer MPECs, one per producer, constitutes an equilibrium problem with equilibrium constraints (EPEC). To identify the solutions of this EPEC, each MPEC problem is replaced by its Karush-Kuhn-Tucker (KKT) conditions, which are in turn linearized. The resulting mixed-integer linear system of equalities and inequalities allows determining the EPEC equilibria through an auxiliary MILP problem.

Abstract Using flexibility from the coordination of power and natural gas systems helps with the integration of variable renewable energy in power systems. To include this flexibility into the operational decision-making problem, we propose a distributionally robust chance-constrained co-optimization of power and natural gas systems considering flexibility from short-term gas storage in pipelines, i.e., linepack. Recourse actions in both systems, based on linear decision rules, allow adjustments to the dispatch and operating set-points during real-time operation when the uncertainty in wind power production is revealed. We convexify the non-linear and non-convex power and gas flow equations using DC power flow approximation and second-order cone relaxation, respectively. Our coordination approach enables a study of the mitigation of short-term uncertainty propagated from the power system to the gas side. We analyze the results of the proposed approach on a case study and evaluate the solution quality via out-of-sample simulations performed ex-ante.

Abstract 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.

Abstract The large penetration of stochastic and non-dispatchable renewable energy sources increases the need for operational flexibility in power systems. Flexibility can be unlocked by aligning the existing interactions and synergies between heat and power systems. However, in the current sequential order of heat and electricity market clearings, the heat market is myopic to its interactions with the electricity market. This paper designs a heat market, aimed at achieving the optimal coordination of heat and power systems while respecting the current market regulations. The proposed electricity-aware heat market yields a soft coordination between heat and power systems by endogenously modeling their interactions in the day-ahead heat market clearing. The proposed market framework requires to solve a hierarchical optimization problem under uncertainty, which can be computationally challenging in large-scale energy systems with many scenarios. To resolve this potential scalability issue, this paper develops an augmented regularized Benders decomposition algorithm. The performance of the proposed market framework is compared against the fully integrated and sequential market frameworks using an ex-post out-of-sample simulation. This comparison reveals that there is a significant room for improvement in the cost-effective operation of the overall energy system. In particular, the proposed electricity-aware heat market framework provides a trade-off between the sequential and fully integrated market frameworks by significantly reducing the inefficiencies in both heat and electricity systems while respecting the current sequence of clearing heat and electricity markets.

Abstract This work addresses a relevant methodology for self-scheduling of a price-taker fuel and emission constrained power producer in day-ahead correlated energy, spinning reserve and fuel markets to achieve a trade-off between the expected profit and the risk versus different risk levels based on Markowitz’s seminal work in the area of portfolio selection. Here, a set of uncertainties including price forecasting errors and available fuel uncertainty are considered. The latter uncertainty arises because of uncertainties in being called for reserve deployment in the spinning reserve market and availability of power plant. To tackle the price forecasting errors, variances of energy, spinning reserve and fuel prices along with their covariances which are due to markets correlation are taken into account using relevant historical data. In order to tackle available fuel uncertainty, a framework for self-scheduling referred to as rolling window is proposed. This risk-constrained self-scheduling framework is therefore formulated and solved as a mixed-integer non-linear programming problem. Furthermore, numerical results for a case study are discussed.

To the best of our knowledge, this paper proposes for the first time a design of a continuous local flexibility market that explicitly considers network constraints. Continuous markets are expected to be the most appropriate design option during the early stages of local flexibility markets, where insufficient liquidity can hinder market development. At the same time, increasingly loaded distribution systems require to explicitly consider network constraints in local flexibility market clearing in order to help resolve rather than aggravate local network problems, such as line congestion and voltage issues. This paper defines the essential design considerations, introduces the local flexibility market clearing algorithm, and -- aiming to establish a starting point for future research -- discusses design options and research challenges that emerge during this procedure which require further investigation. Conference