Demand Side Management in A Day-Ahead Wholesale Market: A Comparison of Industrial & Social Welfare Approaches

The intermittent nature of renewable energy has been discussed in the context of the operational challenges that it brings to electrical grid reliability. Demand Side Management (DSM) with its ability to allow customers to adjust electricity consumption in response to market signals has often been recognized as an efficient way to mitigate the variable effects of renewable energy as well as to increase system efficiency and reduce system costs. However, the academic & industrial literature have taken divergent approaches to DSM implementation. While the popular approach among academia adopts a social welfare maximization formulation, the industrial practice compensates customers according to their load reduction from a predefined electricity consumption baseline that would have occurred without DSM. This paper rigorously compares these two different approaches in a day-ahead wholesale market context analytically and in a test case using the same system configuration and mathematical formalism. The comparison of the two models showed that a proper reconciliation of the two models might make them mitigate the stochastic netload in fundamentally the same way, but only under very specific conditions which are rarely met in practice. While the social welfare model uses a stochastic net load composed of two terms, the industrial DSM model uses a stochastic net load composed of three terms including the additional baseline term. DSM participants are likely to manipulate the baseline in order to receive greater financial compensation. An artificially inflated baseline is shown to result in a different resources dispatch, high system costs, and unachievable social welfare, and likely requires more control activity in subsequent layers of enterprise control. NOMENCLATURE GC subscript for dispatchable (controllable) generators (e.g. thermal plants) GS subscript for stochastic generators (e.g. wind, solar photo-voltaic) DC subscript for dispatchable (controllable) demand units (i.e. participating in DSM) DS subscript for stochastic demand units (i.e. conventional load) i index of dispatchable generators j index of dispatchable demand unit k index of stochastic generators l index of stochastic demand unit t index of unit commitment time intervals NGC Number of dispatchable generators NDC Number of dispatchable demand units NGS Number of stochastic generators NDS Number of stochastic demand units T Number of unit commitment time intervals W social welfare PGCit dispatched power generation at the ith dispachable generator in the tth time interval Bo Jiang is with the Mechanical Engineering at the Massachusetts Institute of Technology, Cambridge, MA, USA. [email protected] Amro M. Farid is an Associate Professor of Engineering with the Thayer School of Engineering at Dartmouth, Hanover, NH, USA. He is also a Research Affiliate with the MIT Mechanical Engineering Department. [email protected], [email protected] Kamal Youcef-Toumi is a Professor of Mechanical Engineering at the Massachusetts Institute of Technology, Cambridge, MA, USA. [email protected] APPLIED ENERGY 156(1):642-654, 2015. (AUTHOR PREPRINT) (DOI) 2 PDCjt dispatched power consumption at the jth dispatchable demand unit in the tth time interval P̂DCjt forecasted power consumption of the jth dispatchable demand unit in the tth time interval P̃DCjt baseline power consumption of the jth dispatchable demand unit in the tth time interval P̂GSkt forecasted power generation at the kth stochastic generator in the tth time interval P̂DSlt forecasted power consumption of the lth stochastic demand unit in the tth time interval PGCi min. capacity of the ith dispatchable generator PDCj min. capacity of the jth dispatchable demand unit RGCi min. ramping capability of the ith dispatchable generator RDCj min. ramping capability of the jth dispatchable demand unit PGCi max. capacity of the ith dispatchable generator PDCj max. capacity of the jth dispatchable demand unit RGCi max. ramping capability of the ith dispatchable generator RDCj max. ramping capability of the jth dispatchable demand unit CGCi cost of the ith dispatchable generator SGCi startup cost of the ith dispatchable generator DGCi shutdown cost of the ith dispatchable generator RGCit running cost of the ith dispatchable generator in the tth time interval AGCi quadratic cost function coefficient of the ith dispatchable generator BGCi linear cost function coefficient of the ith dispatchable generator ζGCj cost function constant of the ith dispatchable generator UDCj demand utility of the jth dispatchable demand unit SDCj startup utility of the jth dispatchable demand unit DDCj shutdown utility of the jth dispatchable demand unit RDCjt running utility of the jth dispatchable demand unit in the tth time interval ADCj quadratic utility function coefficient of the jth dispatchable demand unit BDCj linear utility function coefficient of the jth dispatchable demand unit ζDCj utility function constant of the jth dispatchable demand unit CDCj cost of the jth virtual generator SDCj startup cost of the jth virtual generator DDCj shutdown cost of the jth virtual generator RDCjt running cost of the jth virtual generator in the tth time interval ADCj quadratic cost function coefficient of the jth virtual generation BDCj linear cost function coefficient of the jth virtual generation ξj cost function constant of the jth virtual generation wGCit binary variable for the state of the ith dispatchable generator in the tth time interval uGCit binary variable for the startup state of the ith dispatchable generator in the tth time interval vGCit binary variable for the shutdown state of the ith generator in the tth time interval wDCjt binary variable for the state of the ith dispatchable demand unit in the tth time interval uDCjt binary variable for the startup state of the jth dispatchable demand unit in the tth time interval vDCjt binary variable for the shutdown state of the jth dispatchable demand unit in the tth time interval ωDCjt binary variable for the state of the jth virtual generation in the tth time interval μDCjt binary variable for the startup state of the jth virtual generation at the beginning of the tth time interval νDCjt binary variable for the shutdown state of the jth virtual generation at the beginning of the tth time interval