## 1 Introduction  
Distributed generation (DG) using photovoltaic (PV) technology has become attractive in the past decades primarily because of the dramatic technological development that has led to cost savings. As such, the US Department of Energy (DOE) estimates that solar power will provide 40% of the nations' electricity by 2035 [1] and serve as a cost-effective option for decarbonizing the US electric grid. Net energy metering (NEM), where the timing of solar energy delivery and electricity use from the grid is tracked using a bi-directional meter, allows the accumulation of energy credits when PV production is higher than the use and valued at the same price that utility providers charge (net-to-compensate). Such sales to the grid are usually limited to the amount of electricity consumed over an annual billing cycle. As such, NEM has been consistently recognized as a foundational policy to support DG growth but occurs at a cost to utilities in terms of lost marketing margin. It also leads to a larger number of smaller-scale installations that may not be as scale-efficient as fewer larger installations. More than four-fifths of US states have employed NEMpricing to encourage adoption in their electricity sectors [2], thereby paving the road to allow renewable resources to be a real and growing part of the US rural energy landscape. Utilities lose their marketing margin, resulting from retail electricity sales bought at cost with solar vs. at a lower wholesale cost; however, some have argued that this lost revenue will lead to cost-shifting to non-solar customers [3]. Some states and utilities are thus engaged in efforts to reform distributed solar compensation rules to better align with the value that such systems generate [4]. The future of NEM is under debate across the US as the DG of solar power has gained electricity market share [5]. In contrast with NEM, a buy-all, sell-all arrangement offers a standard sell rate to a customer for all the PV electricity they generate. Unlike NEM, a \"buy-all, sell-all\" customer continues to be billed for all the electricity that they consume at the applicable retail rate, independent of electricity generated by their PV system. The PV system exports all electricity directly to the utility grid, and the distributed system owner is compensated at a predetermined and typically fixed sell rate either through utility bill credits or in cash. The sell rates can be set at a fixed long-term contract price or dynamic rates, including Time-of-use pricing schemes. As an example, Indiana allowed utilities to pay solar customers at much lower DG rates after solar reached 1.5% of electricity market penetration [6]. A third metering and billing arrangement is net energy billing (NEB), also called \"instantaneous netting\". With NEB, a DG system owner can consume electricity generated by their DG system in real time and export any generation in excess of on-site consumption to the utility grid. When DG production is insufficient to meet the farm's electricity needs, the farmer buys from the utility at retail rates. Under NEB, the banking of kilowatt-hours (kWh) within a billing cycle to offset future consumption is not allowed. In fact, credits are not granted in kWh terms at all. Rather, all net energy exports are metered and credited at a predetermined sell rate the moment that they are supplied to the grid. A PV system owner's meter(s) must thus at least record either real-time net electricity consumption using a smart meter or can be designed using two separate meters, one for DG sales to the utility and one for electricity grid use. Using either setup, electricity supplied to the grid and used from the grid are measured in real time and billed/credited separately at the end of the billing cycle. The predetermined sell rates are called avoided costs and typically reflect the cost to an electric utility for purchasing electricity at wholesale prices or what it costs them to generate electricity on their own.