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This paper presents a perspective of functional analysis to analyze electricload and electricity pricing in the $L_2$ space and its isomorphic vectorspace, which also yields the general algebraic model of load and pricingassociated with time course. It clarifies law of interaction between paymentand load associated with time course and necessity of pricing to sufficientlyconvey information on how load results in supply cost. It describes classicparadigm of modeling in a general algebraic form and formally proves theineffectiveness of classic integral-based pricing in modeling. It consequentlyintroduces to: describe electricity supply cost by a mapping defined on anisomorphic space of the original space of load constituted by orthonormal basisthat quantifies the dynamism of load, named the space of dynamism; a pricingmodel defined on the space of dynamism that sufficiently conveys theinformation; a further derived computational model of pricing based on theFourier series; simple examples to demonstrate use of the proposed pricing andits effectiveness in distinguishing loads and reflecting supply cost associatedwith time course, which theoretically completes the incentive to reshape loads.

Algebraic Analysis of Electric Load and Electricity Pricing