Distributed Power Management under Limited Communication Na Li - PowerPoint PPT Presentation

Distributed Power Management under Limited Communication Na Li Harvard University Rutgers, 08/22/2017

Acknowledgment : Harvard Univ : Guannan Qu, Chinwendu Enyioha, Vahid Tarokh KTH : Sindri Magnusson, Carlo Fishchione Caltech: Steven Low NREL: Changhong Zhao Univ. of Colorado, Boulder: Lijun Chen

A Vision of Future(IoT)? All devices are connectedand coordinated to ➢ Maximize social welfare ➢ Satisfy operation constraints

Distributed Optimization Devices communicate, compute decisions, & communicate, … until reach an efficient point ( Iterative , two-way comm)

Sensing, Communication, Computation Intelligent Power Systems Sources: Gigaom

Communication Challenges Lack reliability ▪ Unaccepted delays ▪ Package Vulnerable to malicious attacks ▪ drop Leak privacy ▪ Limited bandwidth ▪ (e.g. Power Line Comm.) High deployment cost ▪ … ▪ How about reducing communication needs?

Reduce communication in power management Extract information from physical measurements (Feedback) ▪ • Load frequency control • Power allocation in buildings/data centers Recover information from local computation ▪ • Quantized dual gradient for power allocation

This talk: Limited communication in power systems Extra information from physical measurements (Feedback) ▪ • Load frequency control • Power allocation in buildings/data centers Recover information from local computation ▪ • Quantized dual gradient for power allocation

Power Systems Blue: Transmission Sub- Transmission Lines Green: Distribution transmission 765, 500, 345, 230, 138 kV Black: Generation 26kV, 69kV Primary Substation distribution Step-Down 13kV, 4kV Transformer Secondary Transmission Customer Transformer Generating distribution 138kV or 230kV station 120kV, 240kV Supply = Demand Storage EV DR appliances Source: Graphic courtesy of North American Electric Reliability Corportion(NERC)

Optimal Load Control ➢ Balance total generation and load ➢ Keep frequency deviation small ➢ Minimize aggregate load disutility j   P     i   ij 2   1 min C d D l l 2 i i m   P  i l L i ( ) i disutility Freq deviation     over d d d , ,  l l l i   D  l i d         l i i m s. t. P = d D P P i l i i ij ki    i: control area l L i ( ) j i : j k k : i Power balance at each i /aggregated bus Distributed Optimization (e.g. ADMM) Applies. But…

j But… P i ij m P i   D  l i d  l i i Hard to get the real-time disturbance information ▪ Heavily relies on iterative communication ▪ Can loads response in real-time and closed-loop? ➢ Network physical dynamics help!

j Physical dynamics: Swing Dynamics P i ij i : Aggregated bus/control area/balance authority m P i   D  d l i i  l i Mechanical freq-sensitive Inertia power flow power load freq-insensitive frequency loads Variables denote the deviations from their reference (steady state) values

j Network dynamics P i ij m P DC approximation of power flow i   D  d l i i  l i • Lossless (resistance=0) • Fixed voltage magnitudes V i • Small deviation of angles

j P System Model Recap i ij m P i   D  d l i i Load Control  l i ?         2   1 min C d D l l 2 i i    i l L i ( )     over d d d , ,  l l l i        m s. t. P = d D P P i l i i ij ki    l L i ( ) j i : j k k : i

Load frequency control System Dynamics Dual Dynamics Load   d       l ' 1 d t ( ) C ( ) t for l L i ( )   Control l l i d l Converge to the optimal solution ( Primal-Dual Gradient Flow )       Optimal    2  1 min C d D l l 2 i i    Load i l L i ( )     over d d d , , Control  l l l i          m s. t. P = c d D P P i l l i i ij ki    l L i ( ) j i : j k k : i Primal-Dual Gradient Flow: Arrow etc 1958, Feijer and Paganini 2010, Zhao, Low etc 2013, You, Chen etc 2014, Cherukuri, Mallada, Cortes, 2015, etc

Load frequency control frequency load control frequency load control frequency load control ➢ Frequency: a locally measurable signal (“price” of imbalance) ➢ Completely decentralized; no explicit communication necessary

Simulations Dynamic simulation of IEEE 68-bus system (New England) • Power System Toolbox (RPI) • Detailed generation model • Exciter model, power system stabilizer model • Nonzero resistance lines Sample rate 250ms Step increase of loads on bus 1, 7, 27

Simulations 59.964 Hz ERCOT threshold for freq control

Simulations

j Recap P i ij m P i   D  d l i i  l i Network Dynamics Optimization         2   1 min C d D l l 2 i i    i l L i ( )     over d d d , ,  l l l i        m s. t. P = d D P P i l i i ij ki    l L i ( ) j i : j k k : i

This Idea Extends to General Systems Network Dynamics: How to design distributed, closed-loop controller u?        Optimization: min f x g u i i i i x u , i i i i     s. t. A x B u C w 0 ij j i i i i j i : ~ j  h x u ( , ) 0 i i i • [Li, Chen, Zhao, 2015]: Economic Automatic Generation Control • [Zhang, Antonois, Li, 2016]: Sufficient and Necessary Conditions • [Zhang, Malkawi, Li, 2016]: Thermal Control for HVAC

This talk: limited communication Extract information from physical measurements (Feedback) ▪ • Load frequency control • Decentralized voltage control (distribution network) (Qu, Li, Dahleh, 2014) • Power allocation in buildings/data center Recover information from local computation ▪ • Quantized dual gradient for power allocation

This talk: limited communication Extract information from physical measurements (Feedback) ▪ • Load frequency control • Decentralized voltage control (distribution network) (Qu, Li, Dahleh, 2014) • Power allocation in buildings/data center Recover information from local computation ▪ • Quantized dual gradient for power allocation

This talk: limited communication Extract information from physical measurements (Feedback) ▪ • Load frequency control • Decentralized voltage control (distribution network) (Qu, Li, Dahleh, 2014) • Power allocation in buildings/data center Recover information from local computation ▪ • Quantized dual gradient for power allocation

Power management within buildings Control center coordinates power consumption of appliances ➢ Maximize utility, minimize cost ➢ Satisfy operation constraints, e.g. power capacity constraints Control Center

Distributed Coordination under Two-way Comm. Step 1 : Appliances to center: Power request Iterate Step 2 : Center to appliances: Coordination signal Assume perfect, reliable, and ubiquitous communication resources Control Center

Reduce Communication Needs Q 1: Is it possible to use only one-way comm.? Q 2: How many bits are needed? Control Center

Not just for the buildings/grids Data Center Communication cost is much higher than computation [Bolsens I., 2002] Multi-core Processor

Power allocation problem Control center p (t) q 1 (t) … User N: User 1: User 2:

A distributed algorithm: Dual gradient descent Control center p (t) q 1 (t) User 2 User 1 … User N

A distributed algorithm: One-way comm. Control center Q (t) p (t) q 1 (t) User 2 User 1 User N … Replace this with true measurement of total power consump. Q(t).

What’s the problem here? Control center p (t) User 2 User 1 User N … It might violates hard physical constraint Theorem: If the step size and initial setting are chosen properly, the constraint will hold all the time. “Distributed resource allocation using one - way communication”, Magnusson, Enyioha, Li, Fischione, Tarokh, 2016

This Talk Extract information from physical measurements (Feedback) ▪ • Load frequency control • Power allocation in buildings/data center Recover information from local computation ▪ • Quantized dual gradient for power allocation

This Talk Extract information from physical measurements (Feedback) ▪ • Load frequency control • Power allocation in buildings/data center Recover information from local computation ▪ • Quantized dual gradient for power allocation

Recall: Dual Gradient with One-way Comm. Control center p (t) User 2 User 1 User N …

Further reduce comm. Control center Just send one bit to p (t) indicate the sign s(k)=0 or 1 User 2 User 1 User N …

Dual Gradient with One-bit One-way Comm. Control center s (k) User 2 User 1 User N … This is quantized (normalized) gradient descent of dual function Normalized Gradient Descent [Shor 1985]: