Managing Price Uncertainty in Prosumer-Centric Energy Trading: A Prospect-Theoretic Stackelberg Game Approach

Abstract

In this paper, the problem of energy trading between smart grid prosumers, who can simultaneously consume and produce energy, and a grid power company is studied. The problem is formulated as a single-leader, multiple-follower Stackelberg game between the power company and multiple prosumers. In this game, the power company acts as a leader who determines the pricing strategy that maximizes its profits, while the prosumers act as followers who react by choosing the amount of energy to buy or sell so as to optimize their current and future profits. The proposed game accounts for each prosumer's subjective decision when faced with the uncertainty of profits, induced by the random future price. In particular, the framing effect, from the framework of prospect theory (PT), is used to account for each prosumer's valuation of its gains and losses with respect to an individual utility reference point. The reference point changes between prosumers and stems from their past experience and future aspirations of profits. The followers' noncooperative game is shown to admit a unique pure-strategy Nash equilibrium (NE) under classical game theory (CGT) which is obtained using a fully distributed algorithm. The results are extended to account for the case of PT using algorithmic solutions that can achieve an NE under certain conditions. Simulation results show that the total grid load varies significantly with the prosumers' reference point and their loss-aversion level. In addition, it is shown that the power company's profits considerably decrease when it fails to account for the prosumers' subjective perceptions under PT.

A Self-Governed Online Energy Management and Trading for Smart Micro/Nano-Grids

“…In [9], energy trading between smart grid prosumers and a grid power company was studied. The problem was formulated as a single-leader, multiple-follower Stackelberg game between the power company and multiple prosumers.…”

“…whereP rer k (h) is the actual renewable generated power. It is clear from (9) that the least-conservative decision, ∆ k (τ ) = 0 (i.e., offering P rer k (h) = P max k,rer (h)), can impose the most possible penalty to prosumer k.…”

Leader–Follower Network Aggregative Game With Stochastic Agents’ Communication and Activeness

“…Now, using Assumptions 5, we can write (22) as follows − α k n e k n Ψ k n ≤ −α k C n e k n ||∇x k n || 2 + α k κL||∇x k n ||(||∇y k || + m∈Nn w nm ||∇x k m ||).…”

“…However, in many applications, there is a high-level agent (leader) who aims to optimize its own objective function which also depends on the strategies of other agents at a lower level (followers). Several researches have investigated leader-follower games [17]- [19] and it has been extensively utilized in many engineering fields such as wireless sensor networks [20], supply chain management [21], and smart grid [22]. If the leader has complete information about the followers' cost functions, then the concept of Stackelberg equilibrium can be applied directly [18].…”

Stackelberg Game Approach on Modeling of Supply Demand Behavior Considering BEV Uncertainty

“…Therefore, by limiting the hours that the battery is being charged or discharged, we reduce the detrimental effect of constant battery usage. In (14) the sequence of charging/discharging should be in a way that by the time that the BEV owner decides to leaves the house, the SOC should be 100%.…”