Optimal Power Flow in Distribution Networks Under N – 1 Disruptions: A Multistage Stochastic Programming Approach

Contingency research to find optimal operations and postcontingency recovery plans in distribution networks has gained major attention in recent years. To this end, we consider a multiperiod optimal power flow problem in distribution networks, subject to the N – 1 contingency in which a line or distributed energy resource fails. The contingency can be modeled as a stochastic disruption, an event with random magnitude and timing. Assuming a specific recovery time, we formulate a multistage stochastic convex program and develop a decomposition algorithm based on stochastic dual dynamic programming. Realistic modeling features, such as linearized AC power flow physics, engineering limits, and battery devices with realistic efficiency curves, are incorporated. We present extensive computational tests to show the efficiency of our decomposition algorithm and out-of-samplex performance of our solution compared with its deterministic counterpart. Operational insights on battery utilization, component hardening, and length of recovery phase are obtained by performing analyses from stochastic disruption-aware solutions. Summary of Contribution: Stochastic disruptions are random in time and can significantly alter the operating status of a distribution power network. Most of the previous research focuses on the magnitude aspect with a fixed set of time points in which randomness is observed. Our paper provides a novel multistage stochastic programming model for stochastic disruptions, considering both the uncertainty in timing and magnitude. We propose a computationally efficient cutting-plane method to solve this large-scale model and prove the theoretical convergence of such a decomposition algorithm. We present computational results to substantiate and demonstrate the theoretical convergence and provide operational insights into how making infrastructure investments can hedge against stochastic disruptions via sensitivity analyses.

Stochastic Optimization of Microgrid Operation With Renewable Generation and Energy Storage

The operation of electric energy storages (EES) in power systems where variable renewable energy sources (VRES) and EES must contribute to securing the supply can be considered as an arbitrage against scarcity. The value of using stored energy instantly must be balanced against its potential future value and future risk of scarcity. This paper proposes a multi-stage stochastic programming model for the operation of microgrids with VRES, EES and thermal generation that is divided into a short- and a long-term model. The short-term model utilizes information from forecasts updated every six hours, while the long-term model considers the value of stored energy beyond the forecast horizon. The model is solved using stochastic dual dynamic programming and Markov chains, and the results show that the significance of accounting for short- and long-term uncertainty increases for systems with a high degree of variable renewable generation and EES and decreasing dispatchable generation capacity.<br>

Stochastic Optimization of Microgrid Operation With Renewable Generation and Energy Storage

The operation of electric energy storages (EES) in power systems where variable renewable energy sources (VRES) and EES must contribute to securing the supply can be considered as an arbitrage against scarcity. The value of using stored energy instantly must be balanced against its potential future value and future risk of scarcity. This paper proposes a multi-stage stochastic programming model for the operation of microgrids with VRES, EES and thermal generation that is divided into a short- and a long-term model. The short-term model utilizes information from forecasts updated every six hours, while the long-term model considers the value of stored energy beyond the forecast horizon. The model is solved using stochastic dual dynamic programming and Markov chains, and the results show that the significance of accounting for short- and long-term uncertainty increases for systems with a high degree of variable renewable generation and EES and decreasing dispatchable generation capacity.<br>

Multistage Stochastic Programming for VPP Trading in Continuous Intraday Electricity Markets

<div>The stochastic nature of renewable energy sources has increased the need for intraday trading in electricity markets. Intraday markets provide the possibility to the market participants to modify their market positions based on their updated forecasts. In this paper, we propose a multistage stochastic programming approach to model the trading of a Virtual Power Plant (VPP), comprising thermal, wind and hydro power plants, in the Continuous Intraday (CID) electricity market. The order clearing in the CID market is enabled by the two presented models, namely the Immediate Order Clearing (IOC) and the Partial Order Clearing (POC). We tackle the proposed problem with a modified version of Stochastic Dual Dynamic Programming (SDDP) algorithm. The functionality of our model is demonstrated by performing illustrative and large scale case studies and comparing the performance with a benchmark model.</div>

Multistage Stochastic Programming for VPP Trading in Continuous Intraday Electricity Markets

<div>The stochastic nature of renewable energy sources has increased the need for intraday trading in electricity markets. Intraday markets provide the possibility to the market participants to modify their market positions based on their updated forecasts. In this paper, we propose a multistage stochastic programming approach to model the trading of a Virtual Power Plant (VPP), comprising thermal, wind and hydro power plants, in the Continuous Intraday (CID) electricity market. The order clearing in the CID market is enabled by the two presented models, namely the Immediate Order Clearing (IOC) and the Partial Order Clearing (POC). We tackle the proposed problem with a modified version of Stochastic Dual Dynamic Programming (SDDP) algorithm. The functionality of our model is demonstrated by performing illustrative and large scale case studies and comparing the performance with a benchmark model.</div>

Assessing the Water-Energy-Food nexus on the Jucar river system using hydrometeorological forecasting and stochastic hydro-economic programming

&lt;p&gt;Multipurpose water systems are subject to complex trade-offs among competing water uses, which could eventually have a significant potential for conflict. Hence these interlinkages should be properly identified to estimate the impact of changing allocation rules and avoid the trigger of undesirable outcomes. Concretely, forecast-based water allocation requires to assess the outputs of hydrometeorological forecasting within a sectoral context (e.g. urban, agriculture, energy) and contrast it with the current statu-quo. In this regard, stochastic hydro-economic modelling is an efficient approach to compare multipurpose water allocation rules using a common monetary unit, explicitly considering inflow uncertainty and exploiting the potential of hydrometeorological forecasting systems.&lt;/p&gt;&lt;p&gt;Here, we analyse the economic impacts caused by the implementation of forecast-based allocation rules on the Jucar river system in Spain. The economic revenues are calculated by combining Stochastic Dual Dynamic Programming (SDDP) with Model Predictive Control (MPC) forced with hydrometeorological forecasts. The following forecasting systems have been considered: (1) the current system operating rules forced by historical observations, (2) SMHI&amp;#8217;s pan-European E-HYPE hydrological forecasting system forced with bias-adjusted ECMWF System 4 seasonal meteorological forecasts and post-processed using fuzzy logic to adjust forecasts to the local hydrological conditions, (3) five seasonal meteorological forecasting systems from the Copernicus Climate Change Service (ECMWF SEAS5, UKMO GloSEA5, M&amp;#233;t&amp;#233;oFrance System 6, DWD GCFS and CMCC SPS3), bias-adjusted using linear scaling and further combined with locally-adjusted hydrological models, and (4) an ensemble system based on local observations of past river discharge.&lt;/p&gt;&lt;p&gt;Results show that the forecast-based allocation rules derived from SDDP and MPC improve the revenues obtained by the current policies forced by historical observations (which is the best scenario achievable without modifying the current operation). This indicates that combining stochastic modelling with seasonal forecasts improves water allocation performance without requiring a particular forecasting system. Although the agricultural benefits depend on the forecasting system considered, hydropower&amp;#8217;s increases of economic returns are almost the same regardless of the forecast product. This means that hydropower revenues are mainly driven by the fact that forecast-based policies are adopted instead of using a particular forecasting service. Our results show that both uses (i.e. agriculture and hydropower) can simultaneously benefit from forecast-based operating rules, offering opportunities for collaboration to increase the regional water use efficiency.&lt;/p&gt;&lt;p&gt;&lt;em&gt;Acknowledgements:&lt;/em&gt;&lt;/p&gt;&lt;p&gt;This study has been supported by the ADAPTAMED project (RTI2018-101483-B-I00), funded by the Ministerio de Economia y Competitividad (MINECO) of Spain and with EU FEDER funds, and co-funded by the postdoctoral program of Universitat Polit&amp;#232;cnica de Val&amp;#232;ncia (UPV)&lt;/p&gt;