Algebraic Analysis of Electric Load and Electricity Pricing

This paper presents a perspective of functional analysis to analyze electric load and electricity pricing in the $L_2$ space and its isomorphic vector space, which also yields the general algebraic model of load and pricing associated with time course. It clarifies law of interaction between payment and load associated with time course and necessity of pricing to sufficiently convey information on how load results in supply cost. It describes classic paradigm of modeling in a general algebraic form and formally proves the ineffectiveness of classic integral-based pricing in modeling. It consequently introduces to: describe electricity supply cost by a mapping defined on an isomorphic space of the original space of load constituted by orthonormal basis that quantifies the dynamism of load, named the space of dynamism; a pricing model defined on the space of dynamism that sufficiently conveys the information; a further derived computational model of pricing based on the Fourier series; simple examples to demonstrate use of the proposed pricing and its effectiveness in distinguishing loads and reflecting supply cost associated with time course, which theoretically completes the incentive to reshape loads.