Household Energy System Sizing Technique to Minimise Household Energy Cost and Estimate Optimal System Size

Abstract

The goal of this research is to analytically optimise a Household Energy System (HES), consisting of solar PV generation and energy storage, such that the household’s annual energy cost is minimised for a given capital investment. The household’s annual energy cost is shown to depend only on the amount of energy it is supplied from the grid, called grid sourced energy (GSE). Note if it is assumed that PV generation will first be used to supply the load, then it can be shown that any excess energy the PV system would feed-into the grid is related to the grid sourced energy (GSE). The analytical solution for optimal HES size is derived from two equations: i) a closed-form equation for the GSE in terms of storage capacity for a fixed PV rating, and ii) an estimation equation of the sensitivity of the GSE to variations in PV rating. The relationship between GSE and storage capacity, for a fixed PV rating, is found by identifying that the GSE is a piecewise-linear function of storage capacity, under the given assumptions. A piecewise-linear function can be expressed, in closed form, as a finite series where the series partial sums consists of both a constant term and a variable term (storage capacity). For the relationship between the GSE and storage capacity these constant terms are called the critical capacities and are found using a technique developed in Chapter 2. This technique and the piecewise-linear equation is validated against a conventional numerical approach and the two methods are shown to produce identical results. However the piecewise-linear equation provides a faster computational solution compared to the conventional approach. The critical capacities identified in Chapter 2 also provides analytical insight into the trade-off between storage capacity and annual energy cost for a given PV rating. There currently does not exist a closed-form equation between GSE and PV rating and hence no closed-form equation exists for the sensitivity of GSE to variation in PV ratings. This sensitivity is important since it can be used to find the optimal HES size for a given investment. However by using the GSE to storage capacity equation and the critical capacities, an equation is constructed in Chapter 2 which describes the GSE to PV rating relationship for a discrete set of PV ratings. By using this constructed equation and the sensitivity of GSE to variations in PV rating can be estimated for a given set of assumptions. The GSE to storage capacity relationship and the sensitivity of the GSE to variations in PV rating can be combined to derived an equation which estimates the optimal HES size, for a given investment. The estimation of the optimal HES size is validated against the conventional search based solutions and it is shown that the approximation provides a reasonably accurate but computationally faster solution. The estimation equation can also provide useful insights into the sensitivity of the optimal HES size to variations in the cost parameters.