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14th IEEE Madrid PowerTech Conference (IEEE POWERTECH)

作者： Lopez, Juan Camilo Arias, Nataly Banol Rider, Marcos J. State Univ Campinas UNICAMP Sch Elect & Comp Engn FEEC Campinas SP Brazil

ISBN: (纸本)9781665435970

In this paper, a mathematical programming with equilibrium constraints (MPEC) model for the optimal operation of unbalanced three-phase electrical distributed systems is presented. First, the problem is formulated as a non-linear programming (NLP) problem, considering photo-voltaic (PV) generation, dispatchable distributed generation (DG) units, and day-ahead minimization of total active power losses. Then, through a set of efficient linearization techniques, the unbalanced three-phase AC power flow is transformed into a linear programming (LP) model. Finally, through Karush-Kuhn-Tucker (KKT) conditions, the proposed MPEC model is formulated as the combination of the LP primal constraints, the LP dual constraints and complementary constraints. MPEC models are able to optimize without an explicit objective function. Thus, they could be used as inner constraints in bi-level problems, for formulating robust optimization models and in electricity market design for distribution systems. Results show that the proposed MPEC model obtains the same optimal solution of the primal LP problem, without an explicit objective function.

关键词： Complementary constraints Karush-Kuhn-Tucker conditions mathematical programming with equilibrium constraints unbalanced three-phase electrical distributed systems

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Machine Learning for Optimal Inverter Operation in Distribution Grids 55

Machine Learning for Optimal Inverter Operation in Distribut...

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55th Annual Conference on Information Sciences and Systems (CISS)

作者： Singh, Manish K. Gupta, Sarthak Kekatos, Vassilis Virginia Tech Bradley Dept Elect & Comp Engn Blacksburg VA 24061 USA

ISBN: (纸本)9781665412681

Smart inverters have been advocated as a fast-responding voltage control solution in distribution grids with renewables. Nevertheless, finding the optimal inverter setpoints for reactive power in near real time can be computationally and communication-wise taxing. We put forth two deep neural network (DNN)-based approaches to facilitate inverter control. The first approach is a learning-to-optimize scheme, where a DNN is used by the electric utility to predict the optimal power flow (OPF) minimizers once presented with the new grid loading conditions. The novel feature here is that this DNN is trained to match not only the minimizers, but also their sensitivities with respect to the OPF problem parameters. This is a unique feature for the learning-to-optimize setup yielding a dramatic improvement on data efficiency. The second approach targets a decentralized control scheme, where inverter control curves are modeled as DNNs that are jointly trained through an OPF formulation via stochastic primal-dual updates. Thanks to a flexible DNN architecture, the inverters can be partially driven by a utility control signal depending on the available communication specifications. © 2021 IEEE.

关键词： mathematical programming with equilibrium constraints bilevel programming locational marginal prices

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Heterogeneous aggregators competing in a local flexibility market for active distribution system management: A bi-level programming approach

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2022年 136卷 107639-107639页

作者： Evangelopoulos, Vasileios A. Kontopoulos, Theofanis P. Georgilakis, Pavlos S. Natl Tech Univ Athens NTUA Sch Elect & Comp Engn Athens Greece

The emerging role of aggregators in the electric power industry brings forth financial benefits and opportunities for the efficient management of active distribution systems (ADS). Aggregators represent heterogeneous sources of flexibility connected at demand-side, such as flexible loads, small-scale renewable energy sources (RES) and energy storage systems (ESS), and regulate their consumption and/or production in a manner to offer competitive flexibility services. This paper introduces a novel one-leader multi-followers bi-level programming model for the procurement of flexibility services in a local market that is organized for the management of ADS. The upper level problem maximizes the profit of a distribution company, which acts as supplier of electricity to end customers, while considering the network technical constraints that are imposed by the distribution system operator. The lower level problems, in turn, maximize the profit of multiple heterogeneous aggregators acting as flexibility service providers. Two different types of aggregators have been modeled: a) load aggregators, each interacting with a group of flexible end-customers (residential or commercial), and b) RES-ESS aggregators, each managing a group of small-scale RES by exploiting ESS. The model is tested on a modified 33-nodes distribution system to demonstrate the financial benefits that arise, and fruitful findings are extracted with sensitivity analysis.

关键词： Active distribution systems Aggregators Bi-level optimization Demand response Distributed energy resources Flexibility services mathematical programming with equilibrium constraints

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Strategic offering of a flexible producer in day-ahead and intraday power markets

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第3期284卷 1136-1153页

作者： Rintamaki, Tuomas Siddiqui, Afzal S. Salo, Ahti Aalto Univ Sch Sci Dept Math & Syst Anal Syst Anal Lab Espoo Finland UCL Dept Stat Sci London England Stockholm Univ Dept Comp & Syst Sci Stockholm Sweden HEC Montreal Dept Decis Sci Montreal PQ Canada

The increase in intraday electricity market volumes due to intermittent renewable generation may give a strategic producer an opportunity to exert market power. We study offering strategies of a flexible producer in day-ahead and intraday markets using a bi-level model in which the upper level represents the profit-maximization problem of the producer and the lower-level problems clear the day-ahead and intraday markets sequentially. Using a three-node network, we first demonstrate that a flexible producer with perfect forecasts can increase its profit in both markets by coordinating its offer so as to cause transmission grid congestion or lack of competitive generation capacity. Moreover, we show that strategic behavior is possible even when the day-ahead and intraday markets are cleared simultaneously to lower balancing costs. We next assess these market designs in a Nordic test network and offer an explanation for high Nordic intraday prices. Finally, via an annual simulation using the Nordic market data, we verify that strategic offering in day-ahead and intraday markets under imperfect forecasts leads to increased profits vis-a-vis perfect competition but are mitigated through simultaneous market clearing. (C) 2020 Elsevier B.V. All rights reserved.

关键词： OR in energy Day-ahead market Intraday market Strategic offering mathematical programming with equilibrium constraints

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Electricity Market Participation and Investment Planning Frameworks for Energy Storage Systems

Electricity Market Participation and Investment Planning Fra...

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作者： Alharbi, Hisham University of Waterloo

学位级别：博士

The recent trend of increasing share of renewable energy sources (RES) in the generation mix has necessitated new operational and planning studies because of the high degree of uncertainty and variability of these sources. RES such as solar photovoltaic and wind generation are not dispatchable, and when there is excess energy supply during off-peak hours, RES curtailment is required to maintain the demand-supply balance. Furthermore, RES are intermittent resources which have introduced new challenges to the provision of ancillary services that are critical to maintaining the operational reliability of power systems. Energy storage systems (ESS) play a pivotal role in facilitating the integration of RES to mitigate the aforementioned issues. Therefore, there is a growing interest in recent years to examine the potential of ESS in the future electricity grids. This research focuses on developing market participation and investment planning frameworks for ESS considering different ownership structures. First, a novel stochastic planning framework is proposed to determine the optimal battery energy storage system (BESS) capacity and year of installation in an isolated microgrid using a novel representation of the BESS energy diagram. A decomposition-based approach is proposed to solve the problem of stochastic planning of BESS under uncertainty. The optimal decisions minimize the net present value of total expected costs over a multi-year horizon considering optimal BESS operation using a novel matrix representing BESS energy capacity degradation. The proposed approach is solved in two stages as mixed integer linear programming (MILP) problems; the optimal ratings of the BESS are determined in the first stage, while the optimal installation year is determined in the second stage. Extensive studies considering four types of BESS technologies for deterministic, Monte Carlo Simulations, and stochastic cases are presented to demonstrate the effectiveness of the proposed app

关键词： ancillary services battery bi-level optimization electricity markets energy storage investment mathematical programming with equilibrium constraints microgrid mileage planning pumped hydro regulation market stochastic strategic bidding

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Capacity Withholding Constrained by Operational Limits of Generation Under Financial Virtual Divestiture in a Day-Ahead Market

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第1期33卷 771-780页

作者： Ameri, Massoud Rahimiyan, Morteza Latify, Mohammad Amin Shahrood Univ Technol Dept Elect Engn Shahrood *** Iran Isfahan Univ Technol Dept Elect & Comp Engn Esfahan *** Iran

This paper develops an equilibrium-based model for ex ante analysis of capacity withholding under financial virtual divestiture in a day-ahead market, including one dominant producer and a number of small producers considered as a price-taking competitive fringe. We model the offering problem of the dominant producer as a bilevel optimization problem. In the upper-level problem, the dominant producer derives optimal strategy of physical capacity withholding restricted by operational limits of its own generating units and conditions stated in the financial virtual divestiture. In the lower-level problem, market operator clears the day-ahead market on an hourly basis. We recast the bilevel optimization problem as a mathematical programming with equilibrium constraints problem and convert it to a mixed integer linear programming problem. We show how the application of the financial virtual divestiture may mitigate market power in the day-ahead market, through a case study. The numerical results demonstrate that the dominant producer can exploit technological diversification of its own generating units to exercise market power, even in the presence of this market power mitigation policy.

关键词： Financial virtual divestiture market power mathematical programming with equilibrium constraints

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OPTIMAL CONTROL OF A SEMIDISCRETE CAHN-HILLIARD-NAVIER-STOKES SYSTEM WITH NONMATCHED FLUID DENSITIES

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2017年第3期55卷 1954-1989页

作者： Hintermueller, Michael Keil, Tobias Wegner, Donat Humboldt Univ Inst Math Unter Linden 6 D-10099 Berlin Germany Weierstrass Inst Appl Anal & Stochast Mohrenstr 39 D-10117 Berlin Germany

This paper is concerned with the distributed optimal control of a time-discrete Cahn-Hilliard-Navier-Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier-Stokes equation. By proposing a suitable time-discretization, energy estimates are proved, and the existence of solutions to the primal system and of optimal controls is established for the original problem as well as for a family of regularized problems. The latter correspond to Moreau-Yosida-type approximations of the double-obstacle potential. The consistency of these approximations is shown, and first-order optimality conditions for the regularized problems are derived. Through a limit process with respect to the regularization parameter, a stationarity system for the original problem is established. The resulting system corresponds to a function space version of C-stationarity which is a special notion of stationarity for mathematical programs with equilibrium constraints.

关键词： Cahn-Hilliard limiting C-stationarity mathematical programming with equilibrium constraints Navier-Stokes nonmatched densities nonsmooth potentials optimal control semidiscretization in time Yosida regularization

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A bi-level probabilistic transmission planning with intermittent generations based on life cycle cost

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2017年第Sep.期90卷 306-314页

作者： Gan, Lei Li, Gengyin Lin, Jeremy Zhou, Ming North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China PJM Interconnect Audubon PA 19403 USA

With the growing development of intermittent renewable energy sources, such as wind and solar, transmission planners are faced with uncertainly varying generations and resultant probabilistic power flow. A bi-level programming model is proposed to coordinate the process of decision making and reliability assessment. Based on the concept of life cycle cost (LCC), its minimization can be defined as the objective function of a transmission planner. This upper level problem needs to be solved jointly with the lower probabilistic optimal power flow problem of minimizing the load shedding in the system. Hence the bi-level problem is transformed into a mathematical programming with equilibrium constraints (MPEC) with Karush-Kuhn-Tucker conditions. Due to the nonlinearity nature of MPEC, disjunctive inequalities and Generalized Benders Decomposition methods are used to solve this problem. Results of both Garver's 6-bus test system and a realistic 63-bus system are used to illustrate the rationality and validity of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Generalized Benders decomposition Life cycle cost mathematical programming with equilibrium constraints Point estimate Probabilistic optimal power flow Renewable energy Transmission planning

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Robust Strategic Bidding in Auction-Based Markets

Robust Strategic Bidding in Auction-Based Markets

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作者： Bruno Fanzeres dos Santos Pontificia Universidade Catolica do Rio de Janeiro

学位级别：博士

We propose an alternative methodology to devise profit-maximizing stra- tegic bids under uncertainty in markets endowed with a sealed-bid uniform- price auction with multiple divisible products. The optimal strategic bid of a price maker agent largely depends on the knowledge (information) of the rivals' bidding strategy. By recognizing that the bid of rival competitors may devi- ate from the equilibrium and are of difficult probabilistic characterization, we proposed a two-stage robust optimization model with equilibrium constraints to devise an risk-averse strategic bid in the auction. The proposed model is a trilevel optimization problem that can be recast as a particular instance of a bilevel program with equilibrium constraints. Reformulation procedures are proposed to construct a single-level-equivalent formulation suitable for co- lumn and constraint generation (CCG) algorithm. Differently from previously reported works on two-stage robust optimization, our solution methodology does not employ the CCG algorithm to iteratively identify violated scenarios for the uncertain factors, which in this thesis are obtained through continuous variables. In the proposed solution methodology, the CCG is applied to iden- tify a small subset of optimality conditions for the third-level model capable of representing the auction equilibrium constraints at the optimum solution of the master (bidding) problem. A numerical case study based on short-term electricity markets is presented to illustrate the applicability of the proposed robust model. Results show that even for the case where an impression of 1% on the rivals' offer at the Nash equilibrium is observed, the robust solution provides a non-negligible risk reduction in out-of-sample analysis.

关键词： Sealed-Bid Uniform-Price Auction Strategic Bidding mathematical programming with equilibrium constraints Column-and-Contraint Generation Day-Ahead Electricity Markets

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How much is enough? Optimal support payments in a renewable-rich power system

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ENERGY 2016年第Part1期117卷 300-313页

作者： Rintamaki, Tuomas Siddiqui, Afzal S. Salo, Ahti Aalto Univ Sch Sci Dept Math & Syst Anal Syst Anal Lab Helsinki Finland UCL Dept Stat Sci London England Stockholm Univ Dept Comp & Syst Sci S-10691 Stockholm Sweden

The large-scale deployment of intermittent renewable energy sources may cause substantial power imbalance. Together with the transmission grid congestion caused by the remoteness of these sources from load centers, this creates a need for fast-adjusting conventional capacity such as gas-fired plants. However, these plants have become unprofitable because of lower power prices due to the zero marginal costs of renewables. Consequently, policymakers are proposing new measures for mitigating balancing costs and securing supply. In this paper, we take the perspective of the regulator to assess the effectiveness of support payments to flexible generators. Using data on the German power system, we implement a bi-level programming model, which shows that such payments for gas-fired plants in southern Germany reduce balancing costs and can be used as part of policy to integrate renewable energy. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Renewable energy Support payments Day-ahead market Balancing market Congestion management mathematical programming with equilibrium constraints

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