Energy Storage Planning in Active Distribution Grids: A Chance-Constrained Optimization With Non-Parametric Probability Functions

By considering the specific characteristics of random variables in active distribution grids, such as their statistical dependencies and often irregularly-shaped probability distributions, we propose a non-parametric chance-constrained optimization approach to operate and plan energy storage units in power distribution girds. In particular, we develop new closed-form stochastic models for the key operational parameters in the system. Our approach is analytical and allows formulating tractable optimization problems. Yet, it does not involve any restricting assumption on the distribution of random parameters, hence, it results in accurate modeling of uncertainties. Different case studies are presented to compare the proposed approach with the conventional deterministic and parametric stochastic approaches, where the latter is based on approximating random variables with Gaussian probability distributions.

[1]  Pu Li,et al.  Chance constrained optimal power flow with non-Gaussian distributed uncertain wind power generation , 2013, 2013 12th International Conference on Environment and Electrical Engineering.

[2]  M. Brucoli,et al.  A new decomposition method for optimal operation of transmission/generation and subtransmission/distribution systems , 1993 .

[3]  P. Bastard,et al.  Impact of energy storage costs on economical performance in a distribution substation , 2005, IEEE Transactions on Power Systems.

[4]  Xu Yang,et al.  Integrated Planning for Transition to Low-Carbon Distribution System With Renewable Energy Generation and Demand Response , 2014, IEEE Transactions on Power Systems.

[5]  Vinod Khadkikar,et al.  Planning active distribution networks considering multi-DG configurations , 2014, 2014 IEEE PES General Meeting | Conference & Exposition.

[6]  S. M. Jovanović,et al.  Decoupled and decomposed power flow solution method , 1987 .

[7]  Felix F. Wu,et al.  Network Reconfiguration in Distribution Systems for Loss Reduction and Load Balancing , 1989, IEEE Power Engineering Review.

[8]  M. E. Baran,et al.  Optimal capacitor placement on radial distribution systems , 1989 .

[9]  Julio Romero Aguero,et al.  Integration of pevs and PV-DG in power distribution systems using distributed energy storage — Dynamic analyses , 2013, 2013 IEEE PES Innovative Smart Grid Technologies Conference (ISGT).

[10]  Vincenzo Marano,et al.  A stochastic dynamic programming model for co-optimization of distributed energy storage , 2013, Energy Systems.

[11]  Fushuan Wen,et al.  A chance constrained programming approach to transmission system expansion planning , 2005 .

[12]  Gintaras V. Reklaitis,et al.  Quantifying System-Level Benefits from Distributed Solar and Energy Storage , 2012 .

[13]  D. Evans,et al.  Algorithms for computing the distributions of sums of discrete random variables , 2004, Math. Comput. Model..

[14]  G. Baiocchi,et al.  Modeling of financial incentives for investments in energy storage systems that promote the large-scale integration of wind energy , 2013 .

[15]  G.A.N. Mbamalu,et al.  Stochastic optimal load flow using a combined quasi-Newton and conjugate gradient technique , 1989 .

[16]  Michael Chertkov,et al.  Options for Control of Reactive Power by Distributed Photovoltaic Generators , 2010, Proceedings of the IEEE.

[17]  A. Schellenberg,et al.  Enhancements to the Cumulant Method for Probabilistic Optimal Power Flow Studies , 2009, IEEE Transactions on Power Systems.

[18]  Johan Driesen,et al.  Techno-Economical And Life Expectancy Modeling Of Battery Energy Storage Systems , 2011 .

[19]  Pavlos S. Georgilakis,et al.  Optimal distributed generation placement under uncertainties based on point estimate method embedded genetic algorithm , 2014 .

[20]  Hamed Mohsenian Rad,et al.  Optimal Residential Load Control With Price Prediction in Real-Time Electricity Pricing Environments , 2010, IEEE Transactions on Smart Grid.

[21]  András Prékopa.  Static Stochastic Programming Models , 1995 .

[22]  C. Moo,et al.  Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries , 2009 .

[23]  Pu Li,et al.  Advances and applications of chance-constrained approaches to systems optimisation under uncertainty , 2013, Int. J. Syst. Sci..

[24]  Hamed Mohsenian Rad,et al.  Developing a Test Data Set for Electric Vehicle Applications in Smart Grid Research , 2014, 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall).

[25]  Christos Thrampoulidis,et al.  Optimal Placement of Distributed Energy Storage in Power Networks , 2013, IEEE Transactions on Automatic Control.

[26]  G. Joos,et al.  A Stochastic Optimization Approach to Rating of Energy Storage Systems in Wind-Diesel Isolated Grids , 2009, IEEE Transactions on Power Systems.

[27]  Na Li,et al.  An optimization-based demand response in radial distribution networks , 2012, 2012 IEEE Globecom Workshops.

[28]  Mario Paolone,et al.  Optimal Allocation of Dispersed Energy Storage Systems in Active Distribution Networks for Energy Balance and Grid Support , 2014, IEEE Transactions on Power Systems.

[29]  F. Pilo,et al.  Optimal integration of energy storage in distribution networks , 2009, 2009 IEEE Bucharest PowerTech.

[30]  Steven H. Low,et al.  Branch Flow Model: Relaxations and Convexification—Part II , 2012 .

[31]  Alexander Shapiro,et al.  Convex Approximations of Chance Constrained Programs , 2006, SIAM J. Optim..

[32]  J. Apt,et al.  Economics of electric energy storage for energy arbitrage and regulation in New York , 2007 .

[33]  B. Jansen,et al.  Sensitivity analysis in linear programming: just be careful! , 1997 .

[34]  Atena Darvishi,et al.  Optimized Fuzzy Control Algorithm in Integration of Energy Storage in Distribution Grids , 2011 .

[35]  Zhipeng Liu,et al.  Optimal Siting and Sizing of Distributed Generators in Distribution Systems Considering Uncertainties , 2011, IEEE Transactions on Power Delivery.

[36]  Raja Ayyanar,et al.  Probabilistic Power Flow Analysis With Generation Dispatch Including Photovoltaic Resources , 2013, IEEE Transactions on Power Systems.

[37]  Ratnesh K. Sharma,et al.  A joint bidding and operation strategy for battery storage in multi-temporal energy markets , 2015, 2015 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT).

[38]  P Frías,et al.  Assessment of the Impact of Plug-in Electric Vehicles on Distribution Networks , 2011, IEEE Transactions on Power Systems.

[39]  Alfred Stein,et al.  Modelling, interpolation and stochastic simulation in space and time of global solar radiation. , 2000 .

[40]  Canbing Li,et al.  Chance-Constrained Optimization-Based Unbalanced Optimal Power Flow for Radial Distribution Networks , 2013, IEEE Transactions on Power Delivery.

[41]  Ming Ding,et al.  Three-Phase Probabilistic Power Flow in Distribution System with Grid-Connected Photovoltaic Systems , 2012, 2012 Asia-Pacific Power and Energy Engineering Conference.

[42]  Jesse Martin Gantz,et al.  Optimal implementation of energy storage systems in power distribution networks. , 2012 .

[43]  Ufuk Topcu,et al.  Risk-mitigated optimal power flow for wind powered grids , 2012, 2012 American Control Conference (ACC).

[44]  Carmen L. T. Borges,et al.  A non parametric stochastic model for river inflows based on kernel density estimation , 2014, 2014 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS).

[45]  Robin Jenkins,et al.  Power Factor Control for Grid-Tied Photovoltaic Solar Farms , 2015 .

[46]  A. Leon-Garcia,et al.  Probability, statistics, and random processes for electrical engineering , 2008 .

[47]  Saahil Shenoy,et al.  Stochastic optimization of power market forecast using non-parametric regression models , 2015, 2015 IEEE Power & Energy Society General Meeting.

[48]  Ali Nourai,et al.  Installation of the first Distributed Energy Storage System (DESS) at American Electric Power (AEP). , 2007 .

[49]  J. Aguado,et al.  Cumulant-based probabilistic optimal power flow (P-OPF) with Gaussian and gamma distributions , 2005, IEEE Transactions on Power Systems.

[50]  Minxiao Han,et al.  Configuration of energy storage system for distribution network with high penetration of PV , 2011 .

[51]  Steven H. Low,et al.  Branch Flow Model: Relaxations and Convexification—Part I , 2012, IEEE Transactions on Power Systems.

[52]  Stephen P. Boyd,et al.  Non-parametric regression modeling for stochastic optimization of power grid load forecast , 2015, 2015 American Control Conference (ACC).

[53]  Michael Chertkov,et al.  Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty , 2012, SIAM Rev..