1 2016 IEEE PES General Meeting Panel on Domain-Specific Big Data Analytics Tools in Power Systems Online Learning and Optimization for Smart Power Grid Seung-Jun Kim Department of Computer Sci. and Electrical Engineering University of Maryland, Baltimore County Boston, MA July 19, 2016
2 Outline Background and motivation Online learning and optimization framework Applications A1) Real-time price setting for DR A2) Online optimal power flow A3) Online PMU data analysis Conclusion and future directions
3 Background and motivation Data deluge power system is not an exception Plethora of sensors (smart meters, smart phones, PMUs, ) Networking technologies (high-speed, low latency, IoT,...) Powerful analytics hardware/software Evolving landscape More efficient and cleaner energy (smart grid, renewables, ) Increasing demand (electric vehicle, data centers,...) Resiliency against uncertainty
4 Challenges and opportunities Big data challenges Large volume à compression, sketching High-rate à low-complexity, real-time processing Dirty à cleansing, correction, security Cyber-physical à closing the loop Opportunities From model-based to data-driven (Let the data speak!) Enhanced monitorability Power of statistical analysis/learning
5 Online learning & optimization Online versus batch processing Low latency, real-time Streaming data Low-complexity update Universality, robustness No need of detailed models (rather, law of large numbers) Strong guarantees even under strategic (game) play
6 Online convex optimization framework OCO framework: game between a player and an adversary At each time slot t = 1,2,,T Player chooses p t Adversary chooses c t (. ) Player suffers loss c t (p t ) and receives feedback F t OCO goal: produce {p t } such that regret becomes sublinear with as
7 Application: Real-time pricing for DR Demand response via pricing Indirect load control via pricing/incentivization Privacy preserving; naturally decentralized Real-time pricing based on consumer preference Adjust energy pricing in real-time to shape load Set prices/incentives differently for different customers Load elasticity changes across consumer and time Q: How to learn load elasticity robustly in real time with minimal modeling assumptions?
8 Model Problem formulation : price adjustment for customer k at time slot t : load level at slot t without price adjustment : elasticity of consumer k at slot t : load adjustment of customer k due to price adjustment Aggregate adjusted load Objective: minimize load variance Promote sparsity and fairness Minimize
9 Algorithms Two types of feedback Full feedback: F t = c t (. ) Partial feedback: F t = c t (p t ) (better privacy) Algorithm for full feedback case Composite objective mirror descent (COMID) [Duchi et al. 10] Provably achieves O( T) regret bound η: step size parameter
10 Numerical test for EV charging case 400 Time t EV charging load 300 200 100 150 100 50 10 20 30 40 50 60 70 80 90 100 Consumer k Requested EV charging start/end times 0 0 50 100 150 200 250 300 350 400 450 Iterations t EV charging load Without RTP With RTP Load levels 200 180 160 140 120 100 80 60 40 20 Base load Total load with RTP Total load without RTP 0 0 50 100 150 200 250 300 350 400 450 Iterations t Total load (EV + base load) S.-J. Kim and G. B. Giannakis, An Online Convex Optimization Approach to Real-Time Energy Pricing for Demand Response," IEEE Trans. on Smart Grid, 2016 (to appear)
11 Online optimal power flow OPF is critical for efficient power system operation Min. costs due to generation, losses, consumer disutility, etc. Subject to: KCL, power balancing constraints Challenges Nonconvexity (à Convex relaxation) Uncertainties (e.g. renewable generation) Existing approaches typically need elaborate models of uncertainty or computationally costly
12 A two-stage setup Online OPF formulation In time slot t -1, decide generation levels {Pg,n}, t n 2N g for slot t In time slot t, use the spot market to balance supply & demand X { Cost must capture both generation X and spot market transaction where c t (p t g):= X n2n g f n (P t g,n)+g t (p t g) X X g t (p t g):= min g X t 0,{P t X n(p t s,n) t s,n },{Qt s,n },{Qt g,n } n2n s subject subject to to: V 2 n apple Xnn t apple V 2 n, n 2 N Xnn t + Xn t 0 n 0 Xt nn 0 Xt n 0 n apple V 2 nn 0, (n, n0 ) 2 E tr{x t Ȳ n } Pg,n t + Pl,n t Pr,n t Ps,n t =0, n 2 N tr{x t Ỹ n } Q t g,n + Q t l,n Q t r,n Q t s,n =0,n2 N Q g,n apple Q t g,n apple Q g,n, n 2 N g
t 13 Simulated test results 2 1.8 bus 8 bus 30 8 Solid = online OPF; Dashed = static OPF Generation Spot market Total renewable Renewable generation P r,n 1.6 1.4 1.2 1 0.8 0.6 0.4 Cost 6 4 2 0 0.2-2 spot market renewable 0 100 105 110 115 120 125 130 135 140 145 150 Time slot t Simulated renewable generation 1.6 1.4 100 110 120 130 140 150 Time slot t Total cost = generation + spot market cost Static Online conventional generation IEEE test archive 30-bus case S.-J. Kim, G. B. Giannakis, and K. Y. Lee Online optimal power flow with renewables," in Proc. of the 48 th Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 2014. Average per-time slot cost 1.2 1 0.8 0.6 0.4 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 µ T Average total cost of online & static OPF
14 Online PMU data analysis Phasor measurement unit (PMU) High sampling rate: ~ 1 sample/20 ms Precise synchronization across a wide area using GPS Useful for monitoring dynamics of the power system Challenges with PMU data Large volume of measurements Fast and accurate inference Incomplete measurements Corrupt measurements
15 Method Robust subspace clustering model Data points are assumed to lie in a union of subspaces {S k } Subspaces can capture different modes of grid operation Low rank representation [Liu et al. 13] Postulate data have subspace structures contaminated by sparse outliers Z X + E, X DC X : outlier-corrected component, E : sparse D : dictionary, C : low-rank Our contribution: online algorithm
16 Simulated PMU data Results 23-bus, 6-generator, 7-load test system simulated by PSS/E Line trip at t = 10 and 110 sec; closed back at t = 70 and 170 Measurement Z are voltage magnitudes at all buses 5% of measurement are missing Missing reconstruction (normalized MSE = 4 X 10-5 ) Event detection 5% missing Some transient Y. Lee and S.-J. Kim, ``Online robust subspace clustering for analyzing incomplete synchrophasor measurements, in Proc. IEEE GlobalSIP, Washington, DC, Dec. 2016.
17 Conclusions and future work Online learning framework from machine learning Robust performance guarantees Versatile to various applications Demand response Power system monitoring and management Future directions More sophisticated learning techniques Closing the gap for cyber-physical interaction