  This two-part paper considers the day-ahead operational planning problem of a
radial distribution network hosting Distributed Energy Resources (DERs)
including Solar Photovoltaic (PV) and storage-like loads such as Electric
Vehicles (EVs). We estimate dynamic Distribution nodal Location Marginal Costs
(DLMCs) of real and reactive power and employ them to co-optimize distribution
network and DER schedules. In Part I, we develop a novel AC Optimal Power Flow
(OPF) model encompassing transformer degradation as a short-run network
variable cost, and we decompose real/reactive power DLMCs into additive
marginal cost components related to (i) the costs of real/reactive power
transactions at the T&D interface/substation, (ii) real/reactive power marginal
losses, (iii) voltage and (iv) ampacity congestion, and (v) a new transformer
degradation marginal cost component. Our detailed transformer degradation model
captures the impact of incremental transformer loading during a specific time
period, not only on its Loss of Life (LoL) during that period, but also during
subsequent time periods. To deal with this phenomenon, we develop methods that
internalize the marginal LoL occurring beyond the daily horizon into the DLMCs
evaluated within this horizon. In Part II, we use real distribution feeders to
exemplify the use of DLMCs as financial incentives that convey sufficient
information to optimize Distribution Network, and DER (PV and EV) operation.
