This thesis discusses how losses can be equitably allocated to photovoltaic inverters in a residential system. One possible strategy discussed here is to optimize the active-power injections to equitably allocate losses to these inverters in distribution networks based on their kVA ratings. To achieve this, we first obtain closed form approximation of nonlinear power-flow solution. A circuit-theoretic method called power tracing then uses this power-flow solution to determine a set of loss coefficients to allocate losses to the inverters present in the network. Finally, these loss coefficients are used in an equitable-loss allocation method to allocate losses fairly in the distribution network. To discuss the benefits of our method, the losses allocated to the inverters by this method are compared with the losses that are allocated by power tracing which uses a power-flow solution obtained from a nonlinear power-flow method.