Allocating Sensors and Actuators via Optimal Estimation and Control

We consider the problem of planning the location and size of sensors and actuators to achieve optimal dynamic performance. Using basic results from control and convex optimization, we formulate mixed-integer semidefinite programs for the actuator placement and sizing to obtain the linear quadratic regulator with the lowest cost, and the sensor placement to obtain the Kalman filter with the lowest error. The two formulations are nearly identical due to the duality of optimal linear control and estimation. We also pose similar problems in terms of observability and controllability, which result in smaller mixed-integer semidefinite programs. Since the mixed-integer semidefinite programing is not yet a mature technology, we also use greedy heuristics in conjunction with continuous semidefinite programming. The approach is demonstrated on two modern applications from power systems: the placement and sizing of energy storage for regulation and the placement of phasor measurement units for estimation.

[1]  Joshua A. Taylor.  Convex Optimization of Power Systems , 2015 .

[2]  I. Kamwa,et al.  Dynamic State Estimation in Power System by Applying the Extended Kalman Filter With Unknown Inputs to Phasor Measurements , 2011, IEEE Transactions on Power Systems.

[3]  D. Chmielewski,et al.  On the theory of optimal sensor placement , 2002 .

[4]  Kai Sun,et al.  Optimal PMU placement for power system dynamic state estimation by using empirical observability Gramian , 2015, 2015 IEEE Power & Energy Society General Meeting.

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

[6]  Greg Welch,et al.  Optimal PMU placement evaluation for power system dynamic state estimation , 2010, 2010 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe).

[7]  M.C. De Oliveira,et al.  Linear output feedback controller design with joint selection of sensors and actuators , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[8]  Youyi Wang,et al.  Robust decentralized nonlinear controller design for multimachine power systems , 1997, Autom..

[9]  A.G. Phadke,et al.  Synchronized phasor measurements in power systems , 1993, IEEE Computer Applications in Power.

[10]  P. Kundur,et al.  Power system stability and control , 1994 .

[11]  Soummya Kar,et al.  A structured systems approach for optimal actuator-sensor placement in linear time-invariant systems , 2013, 2013 American Control Conference.

[12]  I. Grossmann.  Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques , 2002 .

[13]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[14]  Alper Atamtürk,et al.  Lifting for conic mixed-integer programming , 2011, Math. Program..

[15]  Vijay Vittal,et al.  PMU Based State Estimation by Integrating Correlation , 2014, IEEE Transactions on Power Systems.

[16]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[17]  James B. Rawlings,et al.  Tutorial overview of model predictive control , 2000 .

[18]  Dennice F. Gayme,et al.  Grid-scale energy storage applications in renewable energy integration: A survey , 2014 .

[19]  Alexander Olshevsky,et al.  Minimal Controllability Problems , 2013, IEEE Transactions on Control of Network Systems.

[20]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[21]  Cynthia A. Phillips,et al.  Sensor Placement in Municipal Water Networks , 2003 .

[22]  Qi Qi,et al.  Wireless sensor networks in intelligent transportation systems , 2009 .

[23]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[24]  J. Willems.  Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[25]  Andreas Krause,et al.  Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies , 2008, J. Mach. Learn. Res..

[26]  Johanna L. Mathieu,et al.  Modeling, identification, and optimal control of batteries for power system applications , 2014, 2014 Power Systems Computation Conference.