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Moving towards regional Supergrids, an increasing number of interconnections are formed by High Voltage Direct Current (HVDC) lines. Currently, in most regions, HVDC losses are not considered in market operations, resulting in additional costs for Transmission System Operators (TSOs). Nordic TSOs have proposed the introduction of HVDC loss factors in the market clearing algorithm, to account for the cost of losses and avoid HVDC flows between zones with zero price difference. In this paper, we introduce a rigorous framework to assess the introduction of loss factors, in particular HVDC loss factors, in nodal and zonal pricing markets. First, we focus on the identification of an appropriate loss factor. We propose and compare three different models: constant, linear, and piecewise linear. Second, we introduce formulations to include losses in market clearing algorithms. Carrying numerical tests for a whole year, we find that accounting only for HVDC or AC losses may lead to lower social welfare for a non-negligible amount of time. To counter this, this paper introduces a framework for including both AC and HVDC losses in a zonal or nodal pricing environment. We show both theoretically and through simulations that such a framework is guaranteed to increase social welfare. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-stage model of zonal electricity markets with day-ahead market clearing, and real-time re-dispatch and balancing that accounts for transmission line switching at both stages. We show how the day-ahead problem with switching can be formulated as an adaptive robust optimization problem with mixed integer recourse, and present a new algorithm for solving the adversarial max-min problem that obeys the structure of an interdiction game. We apply the model on a realistic instance of the Central Western European system, and comment on the impacts of both proactive, and reactive transmission switching on the operating costs of the system. Part I presents day-ahead models of a short-term zonal electricity market with switching, and describes our algorithmic approach for solving these models efficiently. Part II describes variants of the real-time model, and presents the results of our case study on the Central Western European market. [ABSTRACT FROM AUTHOR]

Determining contingency aware dispatch decisions by solving a security-constrained optimal power flow (SCOPF) is challenging for real-world power systems, as the high problem dimensionality often leads to impractical computational requirements. This problem becomes more severe when the SCOPF has to be solved not only for a single instance, but for multiple periods, e.g. in the context of electricity market analyses. This paper proposes an algorithm that identifies the minimal set of constraints that exactly define the space of feasible nodal injections for a given network and contingency scenarios. By internalizing the technical limits of the nodal injections and enforcing a minimal worst-case impact of contingencies to line flows, computational effort can be further improved. The case study applies and analyzes the methods on the IEEE 118 and A&M 2000 bus systems, as well as the German and European transmission systems. In all tested cases the proposed algorithm identifies at least 95% of the network and security constraints as redundant, leading to significant SCOPF solve time reductions. Scalability and practical implementation are explicitly discussed. The code and input data of the case study is published supplementary to the paper under an open-source license. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology for the conversion of balancing energy offers, submitted during the integrated scheduling process (ISP) of European central-dispatch systems, into replacement reserve (RR) standard products. The aim is to allow the integration of the balancing market of central-dispatch systems, where generating unit operating constraints and real-time dispatch lie in the responsibility of the TSO, with the pan-European balancing market mainly characterized by self-dispatch arrangements and portfolio-based market participation. To respect the diversified clearing rules of both systems, we propose a break-down of the one-shot RR clearing problem into four distinct steps: (a) a local RR quantity maximization process, where the maximum quantity of upward and downward RR balancing energy offered by each balancing service provider (BSP) is defined by the TSO subject to detailed unit operating limitations, (b) a local mandatory activation process, driven by binding unit constraints determined in the previous step, (c) a local conversion process, during which the ISP offers are converted into RR standard products, and (d) the purely economic RR clearing to obtain the activated volumes. Four different modeling approaches are constructed, the attained solution of which is compared with the one-shot techno-economic clearing benchmark currently applied in central-dispatch systems. The comparison indicates that the break-down process results coincide with the one-shot benchmark results, achieving identical social welfare and final unit dispatch, while additionally allowing less-costly Europe-wide cross-border activations of RR. [ABSTRACT FROM AUTHOR]

The concept of adjustable combinatorial products within the scope of the day-ahead electricity market is introduced in this paper. These adjustable products comprise simple and linked profile block offers/bids, with a variable energy quantity profile during the block periods. In the proposed formulation, these blocks can be partially cleared, namely, the indivisibility of the classical profile blocks that are present in European markets is relaxed. This flexibility allows the elimination of paradoxically accepted and rejected blocks and, thus, the elimination of iterative heuristic procedures for their handling. Such modeling is not possible as a mixed-integer linear programming problem, due to the inherent indivisibility denoted by the use of binary variables. Additionally, advanced profile bids are formulated for demand entities, called “joint demand profile block bids” in this paper, which involve not only inter-temporal relations, but also spatial relations with each other. This two-dimensional relation between demand profile blocks is novel and is deemed feasible with the model presented here. These advanced profile orders are incorporated in a day-ahead market problem, formulating a mixed complementarity problem model, which is solved using commercial solvers. The model is validated using the IEEE RTS-96 system; nevertheless, its scalability to large real-world power systems is straightforward. [ABSTRACT FROM PUBLISHER]

A novel model for the clearing of European day-ahead electricity markets, with all associated types of orders, namely simple hourly orders, block orders, complex orders and PUN (“Prezzo Unico Nazionale”) orders is presented in this paper. An iterative algorithm is employed for the market clearing, bearing an inner iteration process for the handling of Paradoxically Accepted block and MIC orders, and an outer iteration process for the handling of PUN orders. During the iterative process a Master Problem and a PUN subproblem are sequentially solved and coordinated, for the efficient handling of all order clearing conditions and market and/or system constraints. The clearing conditions of each order type are explicitly incorporated in the PUN subproblem, formulating a Mixed Complementarity Problem bearing both primal and dual decision variables. The PUN subproblem concerns the sequential clearing of 24 hourly subproblems, employing a special technique for handling the possible inefficiencies due to the myopic nature of the hourly subproblem solutions, leading to enhanced behavior in terms of social surplus with respect to the state-of-the-art day-ahead market clearing solver. The model and the algorithmic process are evaluated in a west-European test case, demonstrating minimal computational requirements and proving its excellent escalation capabilities. [ABSTRACT FROM AUTHOR]

The first of this two-paper series addresses a practical day-ahead auction model, where generation revenue constraints are explicitly incorporated in the problem formulation, as routinely done in several national electricity markets across Europe. The revenue-constrained market-clearing procedure includes the effect of the transmission network, inter-temporal constraints associated with generation scheduling, demand-side bidding, and marginal pricing. This auction design is an instance of price-based market clearing which features two major complicating factors. First, locational marginal prices become decision variables of the optimization process. In addition, producer revenues are formulated as bilinear and highly nonconvex products of power outputs and market-clearing prices. The resulting problem is formulated as a mixed-integer nonlinear bilevel program with bilinear terms for which available solution techniques rely on heuristics, approximations, or modeling simplifications. This paper presents a novel and exact methodology whereby the original problem is recast as an equivalent single-level mixed-integer linear program. As a consequence, finite convergence to optimality is guaranteed and the use of standard commercial software is allowed. The proposed transformation is based on duality theory of linear programming, Karush-Kuhn-Tucker optimality conditions, and integer algebra results. In the second part of this two-paper series, numerical results from several case studies illustrate the effective performance of the proposed solution approach. [ABSTRACT FROM AUTHOR]

In this paper we present a regression based model for day-ahead electricity spot prices. We estimate the considered linear regression model by the lasso estimation method. The lasso approach allows for many possible parameters in the model, but also shrinks and sparsifies the parameters automatically to avoid overfitting. Thus, it is able to capture the autoregressive intraday dependency structure of the electricity price well. We discuss in detail the estimation results which provide insights to the intraday behavior of electricity prices. We perform an out-of-sample forecasting study for several European electricity markets. The results illustrate well that the efficient lasso based estimation technique can exhibit advantages from two popular model approaches. [ABSTRACT FROM PUBLISHER]

With Europe dedicated to limiting climate change and greenhouse gas emissions, large shares of Renewable Energy Sources (RES) are being integrated in the national grids, phasing out conventional generation. The new challenges arising from the energy transition will require a better coordination between neighboring system operators to maintain system security. To this end, this paper studies the benefit of exchanging primary frequency reserves between asynchronous areas using the Supplementary Power Control (SPC) functionality of High-Voltage Direct-Current (HVDC) lines. First, we focus on the derivation of frequency metrics for asynchronous AC systems coupled by HVDC interconnectors. We compare two different control schemes for HVDC converters, which allow for unilateral or bilateral exchanges of reserves between neighboring systems. Second, we formulate frequency constraints and include them in a unit commitment problem to ensure the N-1 security criterion. A data-driven approach is proposed to better represent the frequency nadir constraint by means of cutting hyperplanes. Our results suggest that the exchange of primary reserves through HVDC can reduce up to 10% the cost of reserve procurement while maintaining the system N-1 secure. [ABSTRACT FROM AUTHOR]

Securing profits from energy, reserve capacity and balancing markets is critical to ensure the profitability of battery energy systems (BES). However, the intimate connection between offers on these trading floors combined with the limited energy storage capacity of BES renders its scheduling very complex. In this paper, we develop a bilevel optimization problem for strategic participation of a BES in the day-ahead energy-reserve and balancing markets, improving the state-of-the-art by (i) considering the conditional-value-at-risk; (ii) ensuring the real-time feasibility of the obtained day-ahead schedule; (iii) addressing the operational underperformance risk stemming from inaccurate battery modeling. In a case study, we illustrate how the proposed model allows risk-averse BES owners to hedge their day-ahead position without jeopardizing their expected profit, while ensuring the feasibility of their day-ahead schedule. [ABSTRACT FROM AUTHOR]

This paper addresses the bidding problem faced by a virtual power plant (VPP) in a joint market of energy and spinning reserve service. The proposed bidding strategy is a non-equilibrium model based on the deterministic price-based unit commitment (PBUC) which takes the supply-demand balancing constraint and security constraints of VPP itself into account. The presented model creates a single operating profile from a composite of the parameters characterizing each distributed energy resources (DER), which is a component of VPP, and incorporates network constraints into its description of the capabilities of the portfolio. The presented model is a nonlinear mixed-integer programming with inter-temporal constraints and solved by genetic algorithm (GA). [ABSTRACT FROM PUBLISHER]

Transitioning from fossil fuel dominated power systems to high penetrations of intermittent renewable generation is affecting classical electricity market designs. Here, a method is proposed to model and assess the absence of co-optimization of energy and reserve that prevails in the European system. Co-optimization is formulated through an optimization problem (COM), and its absence as an equilibrium problem (EQM) built on Karush-Kuhn-Tucker conditions of agents’ optimization and market clearing equations. EQM cannot be reformulated as a single optimization problem. Market distortions are identified by comparing the complementarity conditions of both models. These are then discussed on system with Feed in Premium to wind generation. Parameters in the models allow to represent different market configurations regarding: available wind generation, Feed in Premium to wind, generators’ risk aversion, and required reserve from wind generation. [ABSTRACT FROM AUTHOR]

The integration of the spot electricity markets in Europe shall lead to multi-area power exchanges that will substitute the local markets. In such scheme, market prices are affected by physical (e.g., network) constraints, yet they should sometimes follow regulatory policy rules, which do not necessarily reflect or depend on physical characteristics. In some cases, complex pricing rules should be implemented, which impose price discrimination for supply and demand entities within the same area. The methodology presented in this paper enables the balancing of supply and demand in a multi-area market considering energy and reserve bids, under complex pricing rules, which mix energy and reserve prices. A demand bid corresponds to the whole cost a demand entity is willing to pay for its participation in the energy market, including the cost for the procurement of the necessary reserves. The approach attains price integration of energy and reserves markets, simultaneous settlement of energy and reserves, and significant decrease of the payments through the uplift accounts. The main principle is the formulation of a mixed complementarity problem for the system equilibrium conditions, in which supply and demand are associated to explicitly or implicitly defined prices, which may be different even in the same zone. [ABSTRACT FROM PUBLISHER]

Increasing numbers of very small generators are being connected to electricity distribution systems around the world. Examples include photovoltaics (PV) and gas-fired domestic-scale combined heat and power (micro-CHP) systems, with electrical outputs in the region of 1 to 2 kW. These generators are normally installed within consumers' premises and connected to the domestic electricity supply network (230 V single-phase in Europe, 120 V in North America). There is a growing need to understand and quantify the technical impact that high penetrations of such generators may have on the operation of distribution systems. This paper presents an approach to analyzing this impact together with results indicating that considerable penetrations of micro-generation can be accommodated in a typical distribution system. [ABSTRACT FROM AUTHOR]

This paper presents a robust controller designed to address both local and interarea oscillations. It is an extension of the "desensitized four-loop regulator" (DFLR) that has been developed by Electricité de France. The suggested controller is a second-order state-space regulator which will be called the "extended DFLR" (EDFLR). As the DFLR, the EDFLR can be converted to an AVR+PSS structure. The performance of the EDFLR has been extensively tested using modal analysis and time-domain simulations of a large-scale model of the European power system. [ABSTRACT FROM AUTHOR]

Efficient operation of electricity markets necessitates a penalty mechanism to penalize market participants who do not fulfill their market obligations. However, the traditional penalty mechanisms that have been successfully implemented in wholesale electricity markets may result in unintended consequences in transactive markets where the participants have uncertain supply or demand. In this regard, this letter investigates main challenges of applying traditional penalty mechanisms in transactive energy markets. Some efficient strategies are also proposed to operate the transactive markets in such a way that guarantees its security as well as liquidity. [ABSTRACT FROM AUTHOR]

Network constraints play a key role in the price finding mechanism for European Power Markets, but historical data is very sparse and usually insufficient for many quantitative applications. We reconstruct the constraints data, known as the Power Transmission Distribution Factors (PTDFs) and Remaining Available Margins (RAMs), by first recovering the underlying time dependent signals known as the Generation Shift Keys (GSKs) and Phase Angles (PAs), and the electricity grid characteristics, via a mathematical optimisation problem. This is solved by exploiting marginal convexity in certain subspaces via alternating minimisation. The GSKs and PAs are then mapped to the PTDFs and RAMs, using the grid structure. Our reconstruction achieves in-sample relative errors of 22.3% and 15.9% for the PTDFs and RAMs respectively, while the out-of-sample ones are 25.4% and 18.1% respectively. We further show that our model outperforms the naive approach, and that the reconstructed GSKs and PAs recover specific structure. [ABSTRACT FROM AUTHOR]

Convex hull pricing is a well-documented method for coping with the non-existence of uniform clearing prices in electricity markets with non-convex costs and constraints. We revisit primal and dual methods for computing convex hull prices, and discuss the positioning of existing approximation methods in this taxonomy. We propose a dual decomposition algorithm known as the Level Method and we adapt the basic algorithm to the specificities of convex hull pricing. We benchmark its performance against a column generation algorithm that has recently been proposed in the literature. We provide empirical evidence about the favorable performance of our algorithm on large test instances based on PJM and Central Europe. [ABSTRACT FROM AUTHOR]

We propose a chance-constrained formulation for the problem of dimensioning frequency restoration reserves on a power transmission network. We cast our problem as a two-stage stochastic mixed integer linear program, and propose a heuristic algorithm for solving the problem. Our model accounts for the simultaneous sizing of both upward and downward reserves, and uncertainty driven by imbalances, contingencies and available transmission capacity. Our core methodology is further adapted in order to minimize inter-zonal flows and in order to split reserve requirements between automatic and manual frequency restoration reserves. We apply our methodology to the problem of sizing reserves in the four load frequency control areas of the Swedish power system. We demonstrate the benefits of our method in terms of decreasing reserve requirements in the absence of reserve sharing, we analyze the spatial allocation of reserves, and we perform various sensitivity analyses. [ABSTRACT FROM AUTHOR]

The single imbalance pricing is an emerging mechanism in European electricity markets where all positive and negative imbalances are settled at a unique price. This real-time scheme thereby stimulates market participants to deviate from their schedule to restore the power system balance. However, exploiting this market opportunity is very risky due to the extreme volatility of the real-time power system conditions. In order to address this issue, we implement a new tailored deep-learning model, named encoder-decoder, to generate improved probabilistic forecasts of the imbalance signal, by efficiently capturing its complex spatio-temporal dynamics. The predicted distributions are then used to quantify and optimize the risk associated with the real-time participation of market players, acting as price-makers, in the imbalance settlement. This leads to an integrated forecast-driven strategy, modeled as a robust bi-level optimization. Results show that our probabilistic forecaster achieves better performance than other state of the art tools, and that the subsequent risk-aware robust dispatch tool allows finding a tradeoff between conservative and risk-seeking policies, leading to improved economic benefits. Moreover, we show that the model is computationally efficient and can thus be incorporated in the very-short-term dispatch of market players with flexible resources. [ABSTRACT FROM AUTHOR]

The rise of distributed energy resources (DERs) can enhance the efficiency of system operations by providing flexibility services to the different agents involved, but they also pose a major resource allocation problem. This study considers three different agents procuring DER services: distribution system operators (DSOs) for local congestion management, transmission system operators (TSOs) for system-wide reserve deployment, and retailers for hedging against network usage tariffs based upon peak-load pricing. A variety of market mechanisms are identified to co-ordinate these needs, and three schemes are developed in detail. These are separate markets for each agent, co-ordinated Shapley value allocations for TSO and DSO, and a co-ordinated mechanism including retailers. These designs are evaluated on a realistic distribution network in Britain for two operational days. The results show a more efficient dispatch from the TSO–DSO co-ordinated procurement over independent sequential procurements. However, the inclusion of retailers in the joint dispatch is surprisingly less attractive due to the lack of improvement in social welfare and the undesirable impacts on the DSO. [ABSTRACT FROM AUTHOR]