Dynamic decentralized voltage control for power distribution networks

Voltage regulation in power distribution networks has been increasingly challenged by the integration of volatile and intermittent distributed energy resources (DERs). These resources can also provide limited reactive power support that can be used to optimize the network-wide voltage. A decentralized voltage control scheme based on the gradient-projection (GP) method is adopted to minimize a voltage mismatch error objective under limited reactive power. Coupled with the power network flow, the local voltage directly provides the instantaneous gradient information. This paper aims to quantify the performance of this decentralized GP-based voltage control under dynamic system operating conditions modeled by an autoregressive process. Our analysis offers the tracking error bound on the instantaneous solution to the transient optimizer. Under stochastic processes that have bounded iterative changes, the results can be extended to general constrained dynamic optimization problems with smooth strongly convex objective functions. Numerical tests using a 21-bus network have been performed to validate our analytical results.

[1]  Georgios B. Giannakis,et al.  Distributed Optimal Power Flow for Smart Microgrids , 2012, IEEE Transactions on Smart Grid.

[2]  Seth Blumsack,et al.  Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure , 2011, IEEE Systems Journal.

[3]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[4]  Qing Ling,et al.  Decentralized dynamic optimization through the alternating direction method of multipliers , 2013, SPAWC.

[5]  Michael Chertkov,et al.  Optimal Distributed Control of Reactive Power Via the Alternating Direction Method of Multipliers , 2013, IEEE Transactions on Energy Conversion.

[6]  Gang Wang,et al.  Stochastic Reactive Power Management in Microgrids With Renewables , 2015 .

[7]  IEEE Statistical Signal Processing Workshop, SSP 2012, Ann Arbor, MI, USA, August 5-8, 2012 , 2012, Symposium on Software Performance.

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

[9]  Christoforos N. Hadjicostis,et al.  A Two-Stage Distributed Architecture for Voltage Control in Power Distribution Systems , 2013, IEEE Transactions on Power Systems.

[10]  D. West.  Introduction to Graph Theory , 1995 .

[11]  L.A.F. Ferreira,et al.  Distributed Reactive Power Generation Control for Voltage Rise Mitigation in Distribution Networks , 2008, IEEE Transactions on Power Systems.

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

[13]  Gonzalo Mateos,et al.  Stochastic Approximation vis-a-vis Online Learning for Big Data Analytics [Lecture Notes] , 2014, IEEE Signal Processing Magazine.

[14]  Ali H. Sayed,et al.  Adaptive Penalty-Based Distributed Stochastic Convex Optimization , 2013, IEEE Transactions on Signal Processing.

[15]  Steven H. Low,et al.  Optimal inverter VAR control in distribution systems with high PV penetration , 2011, 2012 IEEE Power and Energy Society General Meeting.

[16]  Hao Jan Liu,et al.  Fast Local Voltage Control Under Limited Reactive Power: Optimality and Stability Analysis , 2015, IEEE Transactions on Power Systems.

[17]  Lijun Chen,et al.  Equilibrium and dynamics of local voltage control in distribution systems , 2013, 52nd IEEE Conference on Decision and Control.

[18]  Tong Zhang,et al.  Accelerating Stochastic Gradient Descent using Predictive Variance Reduction , 2013, NIPS.

[19]  A. Yu. Popkov,et al.  Gradient Methods for Nonstationary Unconstrained Optimization Problems , 2005 .

[20]  Léon Bottou,et al.  Large-Scale Machine Learning with Stochastic Gradient Descent , 2010, COMPSTAT.