TY - JOUR
T1 - A General Sensitivity Analysis Approach for Demand Response Optimizations
AU - Xiang, Ding
AU - Wei, Ermin
N1 - Funding Information:
Manuscript received January 17, 2020; revised June 22, 2020 and September 4, 2020; accepted September 13, 2020. Date of publication September 18, 2020; date of current version March 17, 2021. This work was supported by Leslie and Mac Mcquown. Recommended for acceptance by Dr. J. G. Barajas Ramirez. (Corresponding author: Ding Xiang.) The authors are with the Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208 USA (e-mail: dingxiang2015@u.northwestern.edu; ermin.wei@northwestern.edu).
Publisher Copyright:
© 2013 IEEE.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - In this work, we build upon existing literature on the demand response (DR) market, which consists of price-taking prosumers each with various appliances, an electric utility company and a social welfare optimizing distribution system operator, to design a general sensitivity analysis approach (GSAA) that can quantitatively estimate the potential of each consumer's contribution to the social welfare when given more resource capacity, such as allowing net-selling behavior. GSAA is based on existence of an efficient competitive equilibrium, which we establish in the paper. When prosumers' utility functions are quadratic, GSAA can give closed forms characterization on social welfare improvement based on duality analysis. Furthermore, we extend GSAA to a general convex settings, i.e., utility functions with strong convexity and Lipschitz continuous gradient. Even without knowing the specific forms the utility functions, we can derive upper and lower bounds of the social welfare improvement potential of each prosumer, when extra resource is introduced. For both settings, several applications and numerical examples are provided: including extending AC comfort zone, ability of EV to discharge and net-selling behavior. The estimation results show that GSAA can be used to decide how to allocate potentially limited DR market resources in a more impactful way.
AB - In this work, we build upon existing literature on the demand response (DR) market, which consists of price-taking prosumers each with various appliances, an electric utility company and a social welfare optimizing distribution system operator, to design a general sensitivity analysis approach (GSAA) that can quantitatively estimate the potential of each consumer's contribution to the social welfare when given more resource capacity, such as allowing net-selling behavior. GSAA is based on existence of an efficient competitive equilibrium, which we establish in the paper. When prosumers' utility functions are quadratic, GSAA can give closed forms characterization on social welfare improvement based on duality analysis. Furthermore, we extend GSAA to a general convex settings, i.e., utility functions with strong convexity and Lipschitz continuous gradient. Even without knowing the specific forms the utility functions, we can derive upper and lower bounds of the social welfare improvement potential of each prosumer, when extra resource is introduced. For both settings, several applications and numerical examples are provided: including extending AC comfort zone, ability of EV to discharge and net-selling behavior. The estimation results show that GSAA can be used to decide how to allocate potentially limited DR market resources in a more impactful way.
KW - Demand response
KW - Lipschitz continuous gradient
KW - competitive equilibrium
KW - optimization duality
KW - sensitivity analysis
KW - strong convexity
KW - utility function
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U2 - 10.1109/TNSE.2020.3024786
DO - 10.1109/TNSE.2020.3024786
M3 - Article
AN - SCOPUS:85102979788
SN - 2327-4697
VL - 8
SP - 40
EP - 52
JO - IEEE Transactions on Network Science and Engineering
JF - IEEE Transactions on Network Science and Engineering
IS - 1
M1 - 9200796
ER -