Implementing Dynamic Retail Electricity Prices

Implementing Dynamic Retail Electricity Prices Quantify the Benefits of Demand-Side Energy Management Controllers Jingjie Xiao, Andrew L. Liu School of Industrial Engineering, Purdue University West Lafayette, IN 47907 andrewliu@purdue.edu 6 November 2012

Outline Background of Smart Grid, electricity rates and demand response Implement real-time pricing through approximate dynamic programming Numerical results

DOE s Vision of a Smart Grid 1 Enable active participation by consumers 2 Accommodate all generation and storage options 3 Enable new products, services, and markets 4 Provide power quality for the digital economy 5 Optimize asset utilization and operate efficiently 6 Self-heal 7 Operate resiliently against attack and natural disaster

Overview of U.S. Electricity Consumption

Overview of an Electricity System!!! Wholesale( Rates( Retail( Rates(

Lack of Demand Response Utilities Flat Rate Structure Wholesale electricity prices change constantly (e.g. hourly, half-hourly) to reflect the changes of costs of producing electricity at different time Retail prices (what we pay) are flat over a month due to lack of metering infrastructure Variable Costs: - Fuel costs - Non-fuel VOM Per-Unit Fixed Costs: - Power plants - T&D - Metering, billing Electricity Bill ( /KWh)

Issues with Implementing Real-Time Pricing Timeliness (day-ahead vs. hour-ahead), granularity (hour, half-hour, minute)

Issues with Implementing Real-Time Pricing Timeliness (day-ahead vs. hour-ahead), granularity (hour, half-hour, minute) Information overflow (consumers tired of responding after a while)

Issues with Implementing Real-Time Pricing Timeliness (day-ahead vs. hour-ahead), granularity (hour, half-hour, minute) Information overflow (consumers tired of responding after a while) Elusive consumers behavior change

Energy Management Automation Energy management automation through advanced metering infrastructure (AMI) and energy management controllers (EMCs)

RTP via EMCs and 2-Way Communication

Research Questions Modeling Questions to Answer How to make optimal decisions of appliance usage/phev charging under price uncertainty? How to model the dynamics between electricity prices and demand response? More Specific Research Questions to Answer Can RTP + EMCs provide real economic benefits? If yes, how much? Can RTP + EMCs provide any environmental benefits?

Problem Set-Up Who should be the decision makers? ISO/RTO (centralized optimization) consumers (decentralized optimization) utilities/load serving entities (hybrid)

Problem Set-Up Who should be the decision makers? ISO/RTO (centralized optimization) consumers (decentralized optimization) utilities/load serving entities (hybrid) In our work, we start with ISO being the decision maker (utilities may be the most practical decision makers in reality) Power Systems in Consideration EMCs (smart devices) installed on households Consumers specify a time for their PHEVs to be fully charged Renewables (wind plants) in the power system

Make the EMCs Smarter through Dynamic Programming Dynamic Programming { T } To solve min E γ t Ct π (S π t, Xt π (S t)), T = 24 hours (a day). t=0 Bellman equation: V t(s t) = min x t X t { Ct(S t, x t) + γ t E [V t+1(s t+1) S t] }. Modeling Details C t(s t, x t) Cost functions: cost of generating electricity x t Decision variables: energy dispatch (g jt ); # of PHEVs to charge (z t) S t State variables: # of uncharged PHEVs (Y t); system demand; forecast wind power Exogenous information: wind power (W t+1); # of new PHEVs (U t+1) Transition functions: Y t+1 = Y t z t + U t+1 Key: the actions at t (PHEV charging) will affect future states PHEV charging backlog

Implementing Approximate Dynamic Programming (ADP)

Implementing ADP (cont.)

Numerical Results Hourly System Demand under RTP Data source: California electricity system: 107 natural gas power plants PHEV: Chevy Volt: elec. range = 35 miles at elec. usage = 12.9 kwh; 4 hours under Level II; charging time of the day: Agent-Based Simulation

Numerical Results Elec. Prices and Daily Bill under RTP

Numerical Results Elec. Prices and Daily Bill under RTP RTP results in 20% elec. bill reduction for PHEV charging usage;

Numerical Results Elec. Prices and Daily Bill under RTP RTP results in 20% elec. bill reduction for PHEV charging usage; and, 5% elec. bill reduction for the rest of the consumption

Numerical Results System Costs under RTP

Numerical Results System Costs under RTP RTP results in 7% reduction in total system cost

Numerical Results System Emissions under RTP

Numerical Results System Emissions under RTP RTP doubles net reduction in CO2 equivalent emission

Summary and Future Research Summary Presented an ADP-based modeling framework to implement real-time pricing, with AMI, installed smart devices and PHEVs Tested the modeling and algorithm framework using real data from California Demonstrated economic and environmental benefits of real-time pricing Future Research Consider different decision makers (ISO, utilities, individual consumers) and compare efficiency Consider different timelines and granularity of RTP implementation and compare efficiency Consider distributed generation, storage, V2G

Thank you! Acknowledgements: This research is partially supported by National Science Foundation grant CMMI-1234057.

References J. Xiao, A. L. Liu, and J. F. Pekny. Quantify Benefits of in-home Energy Management System under Dynamic Electricity Pricing, working paper. B. Hodge, A. Shukla, S. Huang, G. Reklaitis, V. Venkatasubramanian, and J. Pekny, Multi-Paradigm Modeling of the Effects of PHEV Adoption on Electric Utility Usage Levels and Emissions, Industrial Engineering Chemistry Research, vol. 50, no. 9, pp. 5191 5203, 2011. W. B. Powell, A. George, H. Simao, W. Scott, A. Lamont, and J. Stewart. SMART: A Stochastic Multiscale Model for the Analysis of Energy Resources, Technology, and Policy, INFORMS Journal on Computing, Articles in Advance, pp 1 18, 2011. W. B. Powell. Approximate Dynamic Programming: Solving the Curses of Dimensionality, John Wiley & Sons, Inc, 2nd edition, 2011.

Make the EMCs Smarter through Dynamic Programming Dynamic Programming { T } To solve min E γ t Ct π (S π t, Xt π (S t)), T = 24 hours (a day). t=0 Bellman equation: V t(s t) = min x t X t { Ct(S t, x t) + γ t E [V t+1(s t+1) S t] }. Modeling Details Decision variables (x t): g jt energy dispatch ; z t # of PHEVs to charge State variables (S t) # of uncharged PHEVs (or backlog) Exogenous information: W t+1 wind power; U t+1 # of new PHEVs Transition functions: S t+1 = S t z t + U t+1 Key: the actions at t (PHEV charging) will affect future states PHEV charging backlog Cost functions C t(s t, x t) cost of generating electricity

Solving the DP through ADP Dynamic Programming Bellman equation: V t(s t) = min x t X t { Ct(S t, x t) + γ t E [V t+1(s t+1) S t] }. Difficulties with Solving the Bellman Equation and Solutions Curse of dimensionality (state/decision/random-variable space): Use forward-induction (through sample paths) instead of backward induction How do we calculate the conditional expectation E[V t+1(s t+1) S t]? Use post-decision state variable St x (immediately after decision, before uncertainty arrives). And, Bellman equation around post-decision state becomes V t(s t) = min (C t(s t, x t) + Vt x (St x )) x t X t

Solving the DP through ADP Difficulties with Solving the Bellman Equation and Solutions Curse of dimensionality (state-variable space, decision-variable space, random-variable space): Use forward-induction (through sample paths) instead of backward induction How do we calculate the conditional expectation E[V t+1 (S t+1 ) S t ]? Use post-decision state variable St x = S t z t (immediately after decision x t, before uncertainty arrives) instead of S t+1. And, Bellman equation around post-decision state becomes V t (S t ) = min (C t (S t, x t ) + Vt x (St x )) x t X t If use forward-induction, how to calculate the value function Vt x (St x )? Use value function approximation (e.g. piece-wise linear) K K Vt x (St x ) V t (St x ) = v tk Stk, x Stk x = St x k=1 k=1 v tk the approximation of the slopes

Solving the DP through ADP (cont.) How to determine generation (gjt n) and PHEV charging (zn t ) at n-th iteration? Solve hour-ahead { economic dispatch problem } as an LP ˆV n t (S x t ) = min g jt,z t,s x tk C t ( S n t, g n jt, z n t ) + K k=1 v n 1 tk Stk x, s.t. K k=1 S x tk = S n t z t, J j=1 g jt + Ŵ t = D t + βz t, constraints including power balance - It is a small LP even when we have hundreds of plants. - Wind: E(W t+1 ) = Ŵt (Persistence model for the hour-ahead wind forecast) How to generate the smaple path of wind power and PHEVs that have arrived between time t and t + 1? Take a Monte Carlo sample: Ŵ t+1 and Û t+1

Solving the DP through ADP (cont.) How to update the piecewise linear value functions (i.e. the slopes approximation v n tk)? Use the solution and the Monte Carlo sample and solve a second LP real-time economic dispatch problem to obtain an estimate of ex post electricity price (or LMP) - The real-time power balance constraint: J g jt + Ŵ t+1 = D t + γzt n j=1 - Its dual (λ n t ) an estimate of the marginal electricity cost - Get an estimate of the slope ˆv tk n (i.e. the marginal cost of one more backlog PHEV) using estimate electricity prices - Update the slope approximation v n tk = (1 α n 1 )v n 1 tk + α n 1ˆv tk n, α n 1 the learning stepsize

Numerical Results System Demand under RTP

Numerical Results Deterministic Case Study 0-PHEV Flat Rate RTP RTP, ADP OPT K = 1 Peak demand (MW) 37,249 45,768 39,779 39,727 Relative Increase (%) 22.9% 6.8% 6.7% Fuel cost (M$) 8.47 12.91 11.89 11.97 Relative Increase (%) 52.3% 40.4% 41.3% MTCDE 120,708 179,729 167,846 169,846 Relative Increase (%) 48.9% 39.1% 40.1% RTP, ADP RTP, ADP RTP, ADP K = 5 K = 10 K = 20 Peak demand (MW) 39,727 39,727 39,727 Relative Increase (%) 6.7% 6.7% 6.7% Fuel cost (M$) 11.97 11.98 11.98 Relative Increase (%) 41.3% 41.4% 41.4% MTCDE 169,153 169,216 169,165 Relative Increase (%) 40.1% 40.2% 40.1%