A Multiperiod Optimal Power Flow to Improve Power

A Multiperiod Optimal Power Flow to Improve Power System Voltage Stability Using Demand Response Mengqi Yao University of Michigan 5/21/2019 The research was funded under NSF Grant #ECCS-1549670 11 th Seminar for Next Generation - Mengqi Yao 1

Background • Influences of fluctuating renewables on the power system Ø Introduce more variability in operating points Ø Reduce system inertia Ø Decrease the controllability of active power injections • Objective: Developing methods to coordinate flexible loads to improve electric power transmission system stability Demand response Power system stability 11 th Seminar for Next Generation - Mengqi Yao 2

Power System Stability • Definition: The ability to operate normally after a disturbance [Kundur et al. 2004] • Categories: Frequency stability, Voltage stability, Rotor angle stability the ability of a power system to maintain steady frequency after a significant imbalance between generation and load the ability of a power system to maintain acceptable voltages at all buses in common conditions and after disturbances 11 th Seminar for Next Generation - Mengqi Yao the ability of a power system to maintain synchronism when subjected to small disturbances. 3

Demand Response • Flexible loads: air conditioners, washing machines, dryers, etc. • What did we use DR for in the past? q Bring benefits to the electricity market, reduce costs [Borenstein 2002; Borenstein et al. 2002; Albadi et al. 2008] q Improve power system frequency stability Time shifting load to help balance supply and demand [Short et al. 2007; Callaway 2009; Zhang et al. 2013; Mathieu et al. 2013] • Our purpose: Using DR to improve voltage stability 11 th Seminar for Next Generation - Mengqi Yao 4

Our DR Strategy • Past work: Demand response based on load shedding [Berizzi et al. 1996; Feng et al. 1998; Huang et al. 2010; Yu et al. 2016] • Impair the comfort of consumers • Require change in system-wide generation • Our work: Demand response based on spatially shifting load, without load shedding, in order to improve voltage stability and not affect system frequency. 11 th Seminar for Next Generation - Mengqi Yao 5

Voltage Stability Margins 11 th Seminar for Next Generation - Mengqi Yao 6

Problem Description Stability margin improvement period Disturbance Energy payback period Spatio-temporal DR Problem 11 th Seminar for Next Generation - Mengqi Yao 7

Contributions • Our contributions: • We formulate a multiperiod OPF that uses spatio-temporal load shifting to improve voltage stability while considering the generation cost in the energy payback period; • We develop a computationally-tractable iterative linear programming solution algorithm usingular value sensitivities and benchmark it against the iterative nonlinear programming algorithm in literature; • We compare the cost and performance of spatio-temporal load shifting to that of generator actions and load shedding. 11 th Seminar for Next Generation - Mengqi Yao 8

Optimization Formulation SSV in period 1 cost in period 2 Computes the SSV in each period Total loading is constant Energy payback Constant power load model Maintain the SSV in period 2 AC power flow equations Engineering limits 11 th Seminar for Next Generation - Mengqi Yao 9

Solution Approaches • Interior point method [Kodsi et al. 2007] • Require the Hessian of • Semidefinite programming [Lavaei et al. 2007; Molzahn et al. 2016] AC power flow equations need to be relaxed; solution of relaxed problem may not be feasible 11 th Seminar for Next Generation - Mengqi Yao 10

Solution Approaches • Iterative nonlinear programming [Avalos et al. 2008] • Singular value decomposition • Around a given operating point, the approximate SSV is • Symbolic matrix multiplication is complex for large systems; nonlinear programming problem solved in each iteration may not be scalable 11 th Seminar for Next Generation - Mengqi Yao 11

Singular Value Sensitivities [Tiranuchit and Thomas 1988] 11 th Seminar for Next Generation - Mengqi Yao 12

Iterative Linear Programming Algorithm 1. Linearize the objective function and constraints at the operating point; the decision variable is now the change in system states. 2. Solve the linear program to obtain the optimal change in system states; compute the new system states. 11 th Seminar for Next Generation - Mengqi Yao Ensure the accuracy of the linearization 13

Iterative Linear Programming Algorithm 3. Solve the AC power flow equation to compute the new operating point. 4. Iterations are terminated when the absolute value of the objective function of the linear program is less than a threshold. 11 th Seminar for Next Generation - Mengqi Yao 14

Results: 9 -bus system 11 th Seminar for Next Generation - Mengqi Yao 15

Results: 118 -bus system 11 th Seminar for Next Generation - Mengqi Yao 16

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Computation Time Eigenvalue Sensitivities [Smed 1993] 11 th Seminar for Next Generation - Mengqi Yao 18

DR vs Generation actions Base case is to choose only DR load real power consumption in Period 1 Generator real power production/voltage magnitudes fixed, except slack bus 11 th Seminar for Next Generation - Mengqi Yao 19

DR vs Generation actions Case 1: slack bus manages change in losses Case 2: Loads manage change in losses 11 th Seminar for Next Generation - Mengqi Yao 20

DR vs Generation actions DR vs Generation Redispatch with ramp rates 11 th Seminar for Next Generation - Mengqi Yao 21

DR vs Generation actions Benefit of Voltage Control 11 th Seminar for Next Generation - Mengqi Yao 22

DR vs Generation actions Just loads vs everything (Optimistic) 11 th Seminar for Next Generation - Mengqi Yao 23

DR vs Generation actions Just Loads vs. Everything (Bounded) 11 th Seminar for Next Generation - Mengqi Yao 24

Cost of Different Strategies 11 th Seminar for Next Generation - Mengqi Yao 25

Comparison to Load Shedding P 5(MW) P 7(MW) P 9(MW) 90 100 125 Our DR strategy 147. 93 134. 32 29. 84 Load shedding 90 76. 89 92. 8 Initial the load would need to drop 17% to achieve the same SSV we obtain by spatial load shifting without any net load shedding 11 th Seminar for Next Generation - Mengqi Yao 26

Note on Different Stability Margin Distance to closest SNB SSV • Advantages • Captures any change in power directions • It can (easily) be included in optimization formulations • Captures any change in power directions • Gives direct information on the stability margin in the system parameter space. • Disadvantages • Only provides implicit information on the distance to the solvability boundary • May not be well behaved • Its numeric value is system dependent • There are multiple locally closest SNBs and it is difficult to determine the globally closest SNB. 11 th Seminar for Next Generation - Mengqi Yao 27

• M. Yao, D. K. Molzahn, and J. L. Mathieu. An Optimal Power Flow Approach to Improve Power System Voltage Stability Using Demand Response. In IEEE Transactions on Control of Network Systems (2019). Conference papers: 1. M. Yao, J. L. Mathieu, and D. K. Molzahn. Using Demand Response to Improve Power System Voltage Stability Margins. In IEEE Power. Tech, Manchester, United Kingdom. 2017. 2. M. Yao, D. K. Molzahn, and J. L. Mathieu. The Impact of Load Models in an Algorithm for Improving Voltage Stability via Demand Response. In Allerton. 2017. 3. K. Kasra, M. Yao, S. Roy, and J. L. Mathieu. Using Demand Response to Shape the Fast Dynamics of the Bulk Power Network. In IREP. 2017. 4. M. Yao, I. A. Hiskens, and J. L. Mathieu. Improving Power System Voltage Stability by Using Demand Response to Maximize the Distance to the Closest Saddle Node Bifurcation. In CDC. 2018. 11 th Seminar for Next Generation - Mengqi Yao 28

Future Work • Gain a better understanding of why the loading patterns change in the way they do. • Develop a formulation that incorporates both the voltage stability metrics and the small signal stability metrics and determines how different metrics impact the control of resources. 11 th Seminar for Next Generation - Mengqi Yao 29

Thank you for your time! Any questions? 11 th Seminar for Next Generation - Mengqi Yao 30