  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.
