What Do Prosumer Marginal Utility Functions Look Like? Derivation and Analysis

Abstract

Marginal utility functions (MUFs) encapsulate the prosumer willingness to trade energy with other market agents. In large-scale distributed optimization schemes scalability and convergence are crucial, and the assumption of linear MUFs is common. In this work, instead of assuming the shape and coefficients of those functions, a method is proposed to derive them based on the optimization of a prosumer's energy procurement problem. We formulate a rolling-horizon optimization problem that considers asset characteristics and network tariffs, and we utilize forecasts to capture the effects of uncertainty. We use this formulation to calculate the true prosumer MUF. A test case with real data is used to investigate the shape of these functions. Our results reveal that they present a non-linear shape under certain conditions, they cannot be a priori derived, and their form is sensitive to a variety of factors. This indicates that MUFs should be constructed based on an approach similar to the one proposed in this paper to more accurately capture the prosumer's true willingness to trade. A linearized version of these functions, which is computationally attractive and scalable, can be determined using a least-squares estimator that achieves the best fit to the prosumer's preferences under a linearity constraint.

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“…For example, in an ad hoc P2P energy sharing model, local micro-grids will be combined with potential for energy suppliers using a blockchain-based network (Figure 5). As a result, customers can not only import from another consumer, but they can also opt to purchase electricity from traditional power plants [94]. Because of the blockchain's immutability and distributed existence, this model ensures that all transactions are open to all prosumers and large energy providers, especially governments.…”

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“…P2P transactions do not, however, require a central authority. Energy can be shared directly between consumers, assuming its physical conveyance [ 93 ]. Two adjacent housings can transmit power via a wired connection.…”

A Compensation Mechanism for EV Flexibility Services using Discrete Utility Functions

“…Summarizing, the set of variables from the charging sessions is defined as Y cs = {Z n , λ n,k , λ n,k , y n,k }. Moreover, the discrete utility function in ( 6) can be used to approximate any given nonlinear, nonconvex, or linear and flat function with few large variations, making it suitable to represent prosumers [18].…”

“…For instance, the grid operator can avoid extra costs for grid expansion/reinforcements through flexibility procurement [16], the CPO/aggregator can offer flexibility to the grid operator to improve its local objectives, and the EV owners' discomfort can be levelled in exchange for monetary compensation [17]. Furthermore, prosumers' utility functions can be nonlinear and nonconvex, or linear and flat with few large variations [18], motivating the use of discrete utility functions.…”