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stochastic dynamic programming approach to managing power system uncertainty with distributed storage

COMPUTATIONAL MANAGEMENT SCIENCE 2018年第1期15卷 87-110页

作者： Zephyr, Luckny Anderson, C. Lindsay Cornell Univ Dept Biol & Environm Engn Riley Robb Hall Ithaca NY 14853 USA

Wind integration in power grids is challenging because of the uncertain nature of wind speed. Forecasting errors may have costly consequences. Indeed, power might be purchased at highest prices to meet the load, and in case of surplus, power may be wasted. Energy storage may provide some recourse against the uncertainty of wind generation. Because of their sequential nature, in theory, power scheduling problems may be solved via stochastic dynamic programming. However, this scheme is limited to small networks by the so-called curse of dimensionality. This paper analyzes the management of a network composed of conventional power units and wind turbines through approximate dynamic programming, more precisely stochastic dual dynamic programming. A general power network model with ramping constraints on the conventional generators is considered. The approximate method is tested on several networks of different sizes. The numerical experiments also include comparisons with classical dynamic programming on a small network. The results show that the combination of approximation techniques enables to solve the problem in reasonable time.

关键词： Power grid management Energy storage stochastic dynamic programming stochastic dual dynamic programming Approximate dynamic programming Generalized linear programming

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Power System Investment Planningusing stochastic dual dynamicprogramming

Power System Investment Planningusing Stochastic Dual Dynami...

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作者： Newham, Nikki University of Canterbury

学位级别：master

Generation and transmission investment planning in deregulated markets faces new challengesparticularly as deregulation has introduced more uncertainty to the planning problem. Tradi-tional planning techniques and processes cannot be applied to the deregulated planning problemas generation investments are profit driven and competitive. Transmission investments mustfacilitate generation access rather than servicing generation choices. The new investment plan-ning environment requires the development of new planning techniques and processes that canremain flexible as uncertainty within the system is *** optimisation technique of stochastic dual dynamic programming (SDDP) has been success-fully used to optimise continuous stochastic dynamic planning problems such as hydrothermalscheduling. SDDP is extended in this thesis to optimise the stochastic, dynamic, mixed integerpower system investment planning problem. The extensions to SDDP allow for optimisation oflarge integer variables that represent generation and transmission investment options while stillutilising the computational benefits of SDDP. The thesis also details the development of a math-ematical representation of a general power system investment planning problem and applies it toa case study involving investment in New Zealand’s HVDC link. The HVDC link optimisationproblem is successfully solved using the extended SDDP algorithm and the output data of theoptimisation can be used to better understand risk associated with capital investment in *** extended SDDP algorithm offers a new planning and optimisation technique for deregulatedpower systems that provides a flexible optimal solution and informs the planner about investmentrisk associated with uncertainty in the power system

关键词： Power System Planning stochastic dual dynamic programming SDDP Power System Optimisation Benders Decomposition Mixed Integer Optimisation

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Risk-Averse Two-Stage Distributionally Robust Economic Dispatch Model Under Uncertain Renewable Energy

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CSEE Journal of Power and Energy Systems 2024年第4期10卷 1514-1524页

作者： Ce Yang Weiqing Sun Jiannan Yang Dong Han Department of Control Science and Engineering University of Shanghai for Science and TechnologyShanghai 200093China Department of Electrical Engineering University of Shanghai for Science and TechnologyShanghai 200093China School of Economics and Business Administration Chongqing UniversityChongqing 400044China

With the participation of large quantities of renewable energy in power system operations,their volatility and intermittence increases the difficulties and challenges of power system economic *** the uncertainty of renewable energy generation,based on the distributionally robust optimization method,a two-stage economic dispatch model is proposed to minimize the total operation *** this paper,it is assumed that the fluctuating of renewable power generation follows the unknown probability distribution that is restricted in an ambiguity set,which is established by utilizing the first-order moment information of available historical ***,the theory of conditional value-at-risk is introduced to transform the model into a tractable model,which we call robust counterpart *** on the stochastic dual dynamic programming method,an improved iterative algorithm is proposed to solve the robust counterpart ***,the convergence optimum can be obtained by the improved iterative algorithm,which performs a forward pass and backward pass repeatedly in each iterative ***,by comparing with other methods,the results on the modified IEEE 6-bus,118-bus,and 300-bus system show the effectiveness and advantages of the proposed model and method.

关键词： Energy and reserve co-dispatch distributionally robust conditional value-at-risk stochastic dual dynamic programming

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Reliability-Constrained Power System Expansion Planning: A stochastic Risk-Averse Optimization Approach

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第1期36卷 97-106页

作者： da Costa, Luiz Carlos Thome, Fernanda Souza Garcia, Joaquim Dias Pereira, Mario V. F. PSR BR-22250040 Rio De Janeiro Brazil

This work presents a methodology to incorporate reliability constraints in the optimal power systems expansion planning problem. Besides Loss Of Load Probability (LOLP) and Expected Power Not Supplied (EPNS), traditionally used in power systems, this work proposes the use of the risk measures VaR (Value-at-Risk) and CVaR (Conditional Value-at-Risk), widely used in financial markets. The explicit consideration of reliability constraints in the planning problem can be an extremely hard task and, to minimize computational effort, this work applies the Benders decomposition technique splitting the expansion planning problem into an investment problem and two subproblems to evaluate the system's operation cost and the reliability index. The operation subproblem is solved by stochastic dual dynamic programming (SDDP) and the reliability subproblem by Monte Carlo simulation. The proposed methodology is applied to the real problem of optimal expansion planning of the Bolivian power system.

关键词： Power system reliability Reliability Planning Investment Load modeling Generators System expansion planning Benders decomposition Power systems Reliability stochastic programming Risk measures Mixed Integer programming Monte Carlo stochastic dual dynamic programming

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Charge Scheduling of Electric Vehicles in Smart Parking-Lot Under Future Demands Uncertainty

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IEEE TRANSACTIONS ON SMART GRID 2020年第6期11卷 4949-4959页

作者： Fallah-Mehrjardi, Omid Yaghmaee, Mohammad Hossein Leon-Garcia, Alberto Ferdowsi Univ Mashhad Dept Comp Engn Mashhad 91779 Razavi Khorasan Iran Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

In this study, a public parking-lot is assumed to schedule the charging of Electric Vehicles (EVs). Each EV owner upon arriving gives the energy demand as well as departure time to the system and immediately receives feedback;fulfilling or adjusting the request. The system designed in this study decides based on the previously admitted requests and the uncertain future demands in both Admission Control (AC) and Charge Scheduling (CS) mechanisms. We formulate a multi-stage stochastic programming model to minimize the expected total energy costs over the finite time horizon. Next, we approximate the model using a finite scenario tree. However, this model is computationally intractable, even for a moderate number of stages. Therefore, we customize a well-known decomposition procedure, stochastic dual dynamic programming (SDDP), to be matched the time-dependent charging conditions. Since the procedure takes several hours to obtain a high-quality solution, we run it once in the offline mode and employing the results for the online mode. The simulation results indicate that the proposed method outperforms the myopic approach, and obtains a close solution to the theoretical optimal value in terms of total costs and rejected demands.

关键词： stochastic processes Uncertainty Schedules Computational modeling Charging stations Pricing Optimization Electric vehicle admission control parking lot decomposition stochastic dual dynamic programming multi-stage stochastic optimization demand uncertainty

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Generation capacity expansion planning with spatially-resolved electricity demand and increasing variable renewable energy supply: Perspectives from power pooling in West Africa

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APPLIED ENERGY 2024年 364卷

作者： Bissiri, Mounirah Moura, Pedro Perez, Ricardo Cunha Figueiredo, Nuno Carvalho da Silva, Patricia Pereira Univ Coimbra Energy Sustainabil Initiat Rua Luis Reis Santos P-3030788 Coimbra Portugal INESC Inst Syst Engn & Comp Coimbra Portugal Univ Coimbra Inst Syst & Robot Dept Elect & Comp Engn Polo II P-3030290 Coimbra Portugal PSR Energy Consulting & Analyt Rio De Janeiro Brazil Univ Aveiro Dept Mech Engn Campus Santiago P-3810193 Aveiro Portugal Univ Coimbra Fac Econ CeBER Ctr Business & Econ Res Ave Dias Da Silva 165 P-3004512 Coimbra Portugal Univ Coimbra Rua Silvio Lima Polo II P-3030290 Coimbra Portugal

Power pooling has emerged as a regional strategy for accelerating generation capacity expansion in West Africa with the aim of leveraging vast domestic energy resources and promoting investment in regional power infrastructure. As part of their climate action pledges, most West African countries have committed to increasing the shares of variable renewable energy (VRE), particularly solar photovoltaic and wind power, in their generation mix. It, however, appears that approaches to utility-scale capacity expansion planning tend to overlook the inherent temporal intermittency and spatial variability of VRE-based generation. Moreover, despite influencing the techno-economic rationale for grid expansion and off-grid electrification, as well as the trade-offs between high renewable supply areas and grid expansion, the spatial distribution of demand has been overlooked in planning approaches, leading to conservative and weak prospects for the contribution of utility-scale VRE. Such inconsistencies with the region-wide potentials and policy ambitions highlight that it is paramount for West Africa to design its power pooling such that spatial and temporal fluctuations of VRE supply are duly considered in capacity expansion planning while taking advantage of complementarities between VRE supply and national electricity demand profiles. To address this, the present paper applies a long-term generation capacity expansion model, OptGen, soft-linked to a least-cost operation module, the SDDP tool, which is enhanced by geospatial electrification analysis using the OpeN Source Spatial Electrification Tool (OnSSET), to a subset of four member countries of the West African Power Pool - Burkina Faso, Cote d'Ivoire, Ghana, and Mali - for the 2023-2040 time horizon. The results highlight that current frameworks lead to missed opportunities for bridging the supplydemand gap in all countries, not only in terms of VRE generation capacity, but also of cross-border power trade.

关键词： Variable renewable energy Spatial granularity Time granularity stochastic dual dynamic programming Power generation expansion planning West Africa

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A data-driven approach for a class of stochastic dynamic optimization problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2021年第3期80卷 687-729页

作者： Silva, Thuener Valladao, Davi Homem-de-Mello, Tito Pontifical Catholic Univ Rio de Janeiro PUC Rio Dept Ind Engn Rua Marques de Sao Vicente 225 BR-22451900 Rio De Janeiro RJ Brazil Univ Adolfo Ibanez Sch Business Diagonal Torres 2640 Santiago Chile

dynamic stochastic optimization models provide a powerful tool to represent sequential decision-making processes. Typically, these models use statistical predictive methods to capture the structure of the underlying stochastic process without taking into consideration estimation errors and model misspecification. In this context, we propose a data-driven prescriptive analytics framework aiming to integrate the machine learning and dynamic optimization machinery in a consistent and efficient way to build a bridge from data to decisions. The proposed framework tackles a relevant class of dynamic decision problems comprising many important practical applications. The basic building blocks of our proposed framework are: (1) a Hidden Markov Model as a predictive (machine learning) method to represent uncertainty;and (2) a distributionally robust dynamic optimization model as a prescriptive method that takes into account estimation errors associated with the predictive model and allows for control of the risk associated with decisions. Moreover, we present an evaluation framework to assess out-of-sample performance in rolling horizon schemes. A complete case study on dynamic asset allocation illustrates the proposed framework showing superior out-of-sample performance against selected benchmarks. The numerical results show the practical importance and applicability of the proposed framework since it extracts valuable information from data to obtain robustified decisions with an empirical certificate of out-of-sample performance evaluation.

关键词： stochastic programming Distributionally robust dynamic optimization Hidden Markov models Risk constraints stochastic dual dynamic programming

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Assessing the cost of the Hazard-Decision simplification in multistage stochastic hydrothermal scheduling

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APPLIED ENERGY 2020年 280卷 115939-115939页

作者： Street, Alexandre Valladao, Davi Lawson, Andre Velloso, Alexandre Pontifical Catholic Univ Rio de Janeiro PUC Rio Dept Elect Engn Rio De Janeiro Brazil Pontifical Catholic Univ Rio de Janeiro PUC Rio Dept Ind Engn Rio De Janeiro Brazil

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.

关键词： Multistage hydrothermal scheduling stochastic dual dynamic programming Hazard-Decision vs Decision-Hazard Time consistency

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The future of power generation in Brazil: An analysis of alternatives to Amazonian hydropower development

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ENERGY FOR SUSTAINABLE DEVELOPMENT 2017年 41卷 24-35页

作者： de Faria, Felipe A. M. Jaramillo, Paulina Carnegie Mellon Univ Dept Engn & Publ Policy 5000 Forbes Ave Pittsburgh PA 15213 USA

The Brazilian government has plans to build 26 large hydropower plants in the Amazon basin between 2013 and 2028. These plants will have a total installed capacity of 44 GW, 9000 km(2) of reservoir area, and a total cost of US$ 30-70 billion. In this paper we aim to evaluate alternative generation pathways to avoid the adverse social and environmental impacts associated with reservoirs in the Amazon. Specifically we model the Brazilian electricity network under five capacity expansion scenarios. We assumed the government expansion plans as the baseline and created alternative scenarios where wind and natural gas power plants replace large Amazonian hydropower plants. We compared the scenarios using several performance indicators: greenhouse gas emissions, land use, capital and operational costs, wind curtailments, and energy storage in the hydropower reservoirs. The simulations suggest that a more aggressive policy towards wind generation than the baseline has the potential to replace Amazon hydropower providing advantages to the system operation (e.g., higher storage in hydropower reservoirs). However, when installedwind capacity reaches 24% to 28% of the total installed capacity, more thermal generation is required to balance the hydro-wind variability, increasing the operational costs and greenhouse gas emissions compared to the baseline. (C) 2017 International Energy Initiative. Published by Elsevier Inc. All rights reserved.

关键词： stochastic dual dynamic programming Brazilian power system Impact assessment

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Uncertainty dynamics in energy planning models: An autoregressive and Markov chain modeling approach

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 191卷

作者： Guevara, Esnil Babonneau, Frederic Homem-de-Mello, Tito Univ Finis Terrae Fac Econ & Business Ctr Econ & Sustainable Business Providencia Chile KEDGE Business Sch Talence France ORDECSYS Chene Bougeries Switzerland Univ Adolfo Ibanez Sch Business Penalolen Chile

This paper deals with the modeling of stochastic processes in long-term multi -stage energy planning problems when limited information is available about the distributions of such processes. Starting from simple estimates of variation intervals for uncertain parameters, such as energy demands and costs, we model the temporal correlation of these parameters through carefully constructed autoregressive (AR) models that respect intervals defined in each period. We introduce a coefficient for "zigzag"effects in the evolution of uncertain processes, which controls the correlation across periods and also the likelihood of extreme scenarios. preserve the convexity of the stochastic problem, we discretize the AR models associated with the cost parameters involved in the objective function by Markov chains. The resulting formulation is then solved using a stochastic dual dynamic programming (SDDP) algorithm available in the literature that handles finite -state Markov chains. Our numerical experiments, carried out on the Swiss energy system, show a very desirable adaptation strategy of investment decisions to uncertainty scenarios, a behavior that is not observed when the temporal correlation is ignored. Moreover, the solutions lead to better out -of -sample cost performances, especially on extreme scenario realizations, than the non -correlated ones which usually result in overcapacities to protect against high, but unlikely, parameter variations over time.

关键词： Energy planning Uncertainty modeling Temporal correlation Autoregressive processes Markov chains stochastic dual dynamic programming

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