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PESGM 2015--Panel Session

Market-based Approaches for Demand ResponseIntroduction and Overview

Wei Zhang

Assistant Professor

Department of Electrical and Computer Engineering

The Ohio State University

PESGM, Denver, CO

July 28, 2015 1


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Objectives

What is market-based approaches?

transactive control, price-based, incentive-based, pricing, mechanism design,

social welfare maximization, incentive design, contract design, ….

Microeconomics, game theory, stackelberg game, optimization theory,

mechanism design theory, Nash equilibrium, incentive compatibility, efficiency

loss, dominant strategy, individual rationality, dual decomposition ….

Thematically controlled loads, deferrable loads, HVAC, PEV, building, real time

market, ancillary service, frequency regulation …..

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What is market-based approaches?

Identify fundamental challenges instead of focusing on specific formulations or application scenarios.

Objectives

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This talk: technical background for market based demand response

math formulation+ fundamental problems + literature


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Market-based Demand Response

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……

𝒑𝒌

Load 1 Load N

Coordinator

Load 2

𝒓𝒌

𝒑𝒌: coordination signal

𝒓𝒌: information feedback

Load/user:•Understanding load capability• Load dynamics, aggregated flexibility, time constant, ...

• decision making under given market structure• bidding, scheduling,…

•Decision making with given market structure • social welfare optimization, pricing,…

Coordinator:

•Design market rule:• Mechanism design, contract design, …

Wei Zhang (Ohio State)Market-based approaches for demand response

Anuradha Annaswamy (MIT)A Dynamic Market Mechanism for Integration of Renewables and Demand Response

Hamed Mohsenian-Rad (UC Riverside)Enhancing Demand Bids in Wholesale Electricity Markets

Sean Meyn (U. of Florida)From the Sunshine State to the Solar State

Na Li (Harvard)Demand Response Using Supply Function Bidding

Duncan Callaway (UC Berkeley)Dynamic Contracts for Demand Response

Steven Widergren (PNNL)A Transactive Systems Approach to Access Flexibility of End-Use Resources

This Panel


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Mathematical Formulation

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Automation

Device User

Device + Automation+ human: self-interested and often make strategic decisions

Even not strategic: local response strategy can be reverse engineered as the solution to some utility optimization problem

•Valuation function:

𝑉𝑖 𝑎𝑖; 𝜃𝑖

•Utility function:𝑈𝑖 𝑎𝑖 , 𝑝𝑖; 𝜃𝑖 = 𝑉𝑖 𝑎𝑖; 𝜃𝑖 − 𝑝𝑖𝑎𝑖

• Local constraint (LC): 𝑎𝑖 ∈ 𝐴𝑖

Dynamic case:𝑎𝑖 = (𝑎1

𝑖 , … , 𝑎𝐾𝑖 ), 𝑝𝑖 = 𝑝1

𝑖 , … , 𝑝𝐾𝑖

𝑉𝑖 𝑎𝑖; 𝜃𝑖 = 𝑘𝑉𝑘𝑖 𝑎𝑘𝑖 ; 𝜃𝑖

𝑈𝑖 𝑎𝑖 , 𝑝𝑖; 𝜃𝑖 = 𝑘𝑈𝑘𝑖 𝑎𝑘𝑖 , 𝑝𝑘𝑖 ; 𝜃𝑖

𝐴𝑖 = 𝑎𝑖: 𝑥𝑘+1𝑖 = 𝑓 𝑥𝑘

𝑖 , 𝑎𝑘𝑖 , 𝑎𝑘𝑖 ∈ 𝐴𝑘

𝑖 , 𝑥𝑘𝑖 ∈ 𝑋𝑘

𝑖

User 𝒊model


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Mathematical Formulation

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•valuation function:

𝑉𝑖 𝑎𝑖; 𝜃𝑖

•Utility function:𝑈𝑖 𝑎𝑖 , 𝑝𝑖; 𝜃𝑖 = 𝑉𝑖 𝑎𝑖; 𝜃𝑖 − 𝑝𝑖𝑎𝑖

• Local constraint (LC): 𝑎𝑖 ∈ 𝐴𝑖

Dynamic case:𝑎𝑖 = (𝑎1

𝑖 , … , 𝑎𝐾𝑖 ), 𝑝𝑖 = 𝑝1

𝑖 , … , 𝑝𝐾𝑖

𝑉𝑖 𝑎𝑖; 𝜃𝑖 = 𝑘𝑉𝑘𝑖 𝑎𝑘𝑖 ; 𝜃𝑖

𝑈𝑖 𝑎𝑖 , 𝑝𝑖; 𝜃𝑖 = 𝑘𝑈𝑘𝑖 𝑎𝑘𝑖 , 𝑝𝑘𝑖 ; 𝜃𝑖

𝐴𝑖 = 𝑎𝑖: 𝑥𝑘+1𝑖 = 𝑓 𝑥𝑘

𝑖 , 𝑎𝑘𝑖 , 𝑎𝑘𝑖 ∈ 𝐴𝑘

𝑖 , 𝑥𝑘𝑖 ∈ 𝑋𝑘

𝑖

Social Welfare Maximization (SWM)

max𝑎1,…,𝑎𝑁

𝑖𝑉𝑖 𝑎𝑖; 𝜃𝑖 − 𝐶

𝑖

𝑎𝑖

LC: 𝑎𝑖 ∈ 𝐴𝑖

GC: 𝑔 𝑎 ≤ 0

Coordinator

Fundamental nature of the problem depends on

• Information available to coordinator

• Complete vs. incomplete

• Rationality assumption for user

• Strategic vs. non-strategic users

User 𝒊model


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Complete Info with Non-Strategic Users

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𝑖𝑉𝑖 𝑎𝑖; 𝜃𝑖 − 𝐶 𝑎


GC: 𝑔 𝑎 ≤ 0

Coordinator knows all information

Can directly determine 𝑎𝑖 for all users

Centralized optimization/optimal control problem

Many static cases boil down to convex optimization problems

Dynamic load model can be quite challenging (in general)

Infocomplete Incomplete

Coordination Problem

Centralized Optimization

Non-strategic


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Complete Info with Strategic Users

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Stackelberg Game

max𝑝 𝑖𝑉𝑖 𝑎∗

𝑖 ; 𝜃𝑖 − 𝐶 𝑎∗

𝑎∗𝑖 𝑝 = argmax𝑎𝑖∈𝐴𝑖𝑈

𝑖 𝑎𝑖 , 𝑝; 𝜃𝑖

GC: 𝑔 𝑎∗ ≤ 0

Cannot directly control self-interested users

Coordinator first determine price 𝑝, then user optimize its own utility accordingly

Bi-level optimization (Stackelberg game),

DR application: Ratliff2012, Coogan2013, Maharjan2013, Tushar2014, Li2015 ……

Challenging except for static or unconstrained LQ case




Non-strategicStrategic

StackelbergGame





GC: 𝑔 𝑎 ≤ 0


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Elicit user’s local information/decision

User does not strategically determine the information sent to the coordinator to improve its utility

Often use iterative information exchange (Knudsen,2015), (Chen, 2010), (Li, 2011)

Essentially a distributed/decentralized way to solve a centralized optimization problem





GC: 𝑔 𝑎 ≤ 0

Incomplete Info with Non-Strategic Users





StackelbergGame

Non-strategic

Distributed Optimization


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Incomplete Info with Strategic Users

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StackelbergGame

Non-strategic


Mechanism Design

Strategic

Coordinator elicit information from user

Each user strategically determine the information sent to the coordinator

Mechanism design problem:

Social choice: 𝜙 𝜃 = solution to SW

Design market rules (allocation and pricing) so that the game theoretic equilibrium implements the social choice function 𝜙 𝜃

mechanism Γ = (𝑀, 𝑔(⋅))

𝑀: message space (space for user bid 𝑏𝑖)

𝑔:𝑀𝑁 → 𝑎, 𝑝 : maps user bids to market outcome (allocation and payment)

Given mechanism Γ, 𝑈𝑖 𝑏𝑖 , 𝑏−𝑖; 𝜃𝑖 : depends on

other users’ bids , thus inducing a game 𝐺 Γ


𝜙 𝜃 = argmax𝑎1,…,𝑎𝑁



GC: 𝑔 𝑎 ≤ 0


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Mechanism design extensively studied ineconomics, computer science, andvarious engineering fields

Static: Mas-colell95, Nissim2012, Kearns2014,Azevedo2013

Dynamic: Pavan2009, Athey2013, Pavan,2014bergemann2010, Mierendorff2011,

Lead to discriminatory pricing: unit priceis different to different agents.

Discriminatory pricing





GC: 𝑔 𝑎 ≤ 0





StackelbergGame

Non-strategic


Mechanism Design

Strategic


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Uniform-price mechanism design:

Compatible with electricity market

Easier to implement

Challenges:

standard result (e.g., VCG mechanism) is notdirectly applicable

Dominant strategy equilibrium does not exist;Nash equilibrium very hard to analyze

Computationally intractable especially fordynamic case


Uniform-price mechanism





StackelbergGame

Non-strategic


Mechanism Design

Strategic





GC: 𝑔 𝑎 ≤ 0


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Mechanism design with complete analysis

Discriminatory-pricing: Samadi2012

Special static cases: Xu2015

Given mechanism and analyze Nash:

Ma2013, Kohansal2014, Grammatico2015

Forouzandehmehr2014, Gerding2011

Design mechanism but only analyze pricetaker behavior: Li2015_1, Bitar2013

ϵ-Nash based mechanism design: Li2015_2


Uniform-price mechanism





StackelbergGame

Non-strategic


Mechanism Design

Strategic





GC: 𝑔 𝑎 ≤ 0


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Conclusion

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……

𝒑𝒌

Load 1 Load N

Coordinator

Load 2

𝒓𝒌

Four categories of fundamental paradigms

Centralized optimization: complete information & non-strategic users

Stackelberg game: complete information & strategic users

Distributed optimization: incomplete information & non-strategic users

Mechanism design: incomplete information & strategic users

discriminatory pricing

Uniform-price mechanism design





GC: 𝑔 𝑎 ≤ 0


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References

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Author Title Year Journal/Proceedings

Athey, S. and Segal, I. An Efficient Dynamic Mechanism 2013 EconometricaVol. 81(6), pp. 2463-2485

Azevedo, E.M. and Budish, E.B. Strategy-Proofness in the Large 2013 Chicago Booth Research Paper(13-35)

Balandat, M. and Tomlin, C. A dynamic VCG mechanism for random allocation spaces

2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 925-931

Bergemann, D. and Välimäki, J. The Dynamic Pivot Mechanism 2010 EconometricaVol. 78(2), pp. 771-789

Bitar, E. and Xu, Y. On incentive compatibility of deadline differentiated pricing for deferrable demand

2013 IEEE 52nd Annual Conference on Decision and Control (CDC), pp. 5620-5627

Chen, L., Li, N., Jiang, L. and Low, S.

Optimal Demand Response: Problem Formulation and Deterministic Case

2012Vol. 3Power Electronics and Power Systems, pp. 63-85

Chen, L., Li, N., Low, S. and Doyle, J.

Two Market Models for Demand Response in Power Networks

2010 First IEEE International Conference on Smart Grid Communications (SmartGridComm), pp. 397-402

Coogan, S., Ratliff, L., Calderone, D., Tomlin, C. and Sastry, S.

Energy management via pricing in LQ dynamic games

2013 American Control Conference (ACC), 2013, pp. 443-448

Forouzandehmehr, N., Esmalifalak, M., Mohsenian-Rad, H. and Han, Z.

Autonomous Demand Response Using Stochastic Differential Games

2015 IEEE Transactions on Smart GridVol. 6(1), pp. 291-300

Gerding, E.H., Robu, V., Stein, S., Parkes, D.C., Rogers, A. and Jennings, N.R.

Online Mechanism Design for Electric Vehicle Charging

2011 The 10th International Conference on Autonomous Agents and Multiagent Systems -Volume 2, pp. 811-818


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References

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Grammatico, S., Gentile, B., Parise, F. and Lygeros, J.

A mean field control approach for demand side management of large populations of thermostatically controlled loads

2015 European Control Conference

Hansen, J., Knudsen, J., Kiani, A., Annaswamy, A. and Stoustrup, J.

A Dynamic Market Mechanism for Markets with Shiftable Demand Response

2014Vol. 19Proceedings of the 19th IFAC World Congress, pp. 1873-1878

Kearns, M., Pai, M.M., Roth, A. and Ullman, J.

Mechanism Design in Large Games: Incentives and Privacy

2014 American Economic ReviewVol. 104(5), pp. 431-35

Kohansal, M. and Mohsenian-Rad, H.

Price-Maker Economic Bidding in Two-Settlement Pool-Based Markets: The Case of Time-Shiftable Loads

2015 IEEE Transactions on Power SystemsVol. PP(99), pp. 1-11

Kohansal, M. and Mohsenian-Rad, H.

Extended-Time Demand Bids: A New Bidding Framework to Accommodate Time-Shiftable Loads

2015 Proceeding of the IEEE PES General Meeting, Denver, CO

Li, N., Chen, L. and Low, S. Optimal demand response based on utility maximization in power networks

2011 2011 IEEE Power and Energy Society General Meeting, pp. 1-8

Li, S. and Zhang, W. Uniform-Price Mechanism Design for a Large Population of Dynamic Agents

2015 http://arxiv.org/abs/1507.04374

Li, S., Zhang, W., Lian, J. and Kalsi, K.

Market-Based Coordination of Thermostatically Controlled Loads Part I: A Mechanism Design Formulation


Li, S., Zhang, W., Lian, J. and Kalsi, K.

Multi-Stage Pricing for Coordination of Thermostatically Controlled Loads: A Dynamic Stackelberg Game Approach

2015 http://arxiv.org/abs/1507.05011


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References

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Maharjan, S., Zhu, Q., Zhang, Y., Gjessing, S. and Basar, T.

Dependable Demand Response Management in the Smart Grid: A Stackelberg Game Approach


Mierendorff, K. Optimal dynamic mechanism design with Deadlines

2009

Nissim, K., Smorodinsky, R. and Tennenholtz, M.

Approximately Optimal Mechanism Design via Differential Privacy

2012 Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pp. 203-213

Papadaskalopoulos, D. and Strbac, G.

Decentralized Participation of Flexible Demand in Electricity Markets Part I: Market Mechanism

2013 IEEE Transactions on Power SystemsVol. 28(4), pp. 3658-3666

Parise, F., Grammatico, S., Colombino, M. and Lygeros, J.

On Constrained Mean Field Control for Large Populations of Heterogeneous Agents: Decentralized Convergence to Nash Equilibria

2015 European Control Conference

Pavan, A., Segal, I. and Toikka, J. Dynamic Mechanism Design: A MyersonianApproach

2014 EconometricaVol. 82(2), pp. 601-653

Pavan, A., Segal, I.R. and Toikka, J.

Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization and Information Disclosure

2009

Ratliff, L., Coogan, S., Calderone, D. and Sastry, S.

Pricing in linear-quadratic dynamic games 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1798-1805


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References


Samadi, P., Mohsenian-Rad, H., Schober, R. and Wong, V.

Advanced Demand Side Management for the Future Smart Grid Using Mechanism Design


Tushar, W., Zhang, J., Smith, D., Poor, H. and Thiebaux, S.

Prioritizing Consumers in Smart Grid: A Game Theoretic Approach


Xu, Y., Li, N. and Low, S. Demand Response With Capacity Constrained Supply Function Bidding


Mas-Collel, Andreu, Michael D. Whinston, and Jerry R. Green

Microeconomic Theory 1995 New York, NY: Oxford University Press

Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V. Vazirani

Algorithmic Game Theory 2007 Cambridge University Press

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Acknowledgement

Sen Li (Ohio State University)

Lin Zhao (Ohio State University)

Jianming Lian (PNNL)

Karanjit Kalsi (PNNL)

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Comments and questions?

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Thank you!

third level pesgm 2015--panel session market …zhang/mydoc/pesgm15_marketbased...fourth level fifth...

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