## 3 The Value of Module Efficiency Depends on System Cost Structure  
The quantitative conclusion in the previous section is only valid for the cost structure shown in Figure 4. The value of module efficiency depends on the percentage of area-proportional non-module costs, and that of the fixed costs insensitive to project area or capacity. With the benchmark system costs in 2018 categorized by function, defined by BloombergNEF [7], we re-group them based on the correlation to area and power. Note that each project has a different cost dependence, and the values shown in Figure 6 are estimated for illustrative analysis purposes. (Prior to this paper, the same authors published one piece eight years ago, also to explore the value of module efficiency, with the benchmark system cost structure derived based on the market at that time [8].) Figure 5: Impact of module efficiency on PV system cost and module price premium. Note: In the left-hand chart, the relative change in terms of percentage refers to the non-module unit cost of the benchmark case as shown in Figure 4. In the right-hand chart, the reference is the module unit cost of the benchmark case in Figure 4.  
Figure 6: 2018 benchmark of PV system capex ($/W\({}_{\text{DC}}\)). Source: BloombergNEF Note: The values presented in the right-hand chart are estimated from BloombergNEF benchmark costs. Module efficiency is 17.7% for the benchmark projects.  
Different electricity generation technologies have diverse patterns for both expenditure and yield over time. A well-recognized metric to quantify the economics of a certain technology is levelized cost of electricity (LCOE), which is \"the cost that, if assigned to every unit of energy produced (or saved) by the system over the analysis period, will equal the total life-cycle cost (TLCC) when discounted back to the base year\" [9]. LCOE can be calculated using the following formula:  
\[LCOE=\frac{TLCC}{\sum_{n=1}^{N}\frac{Q_{n}}{(1+d)^{n}}}=\frac{\sum_{n=0}^{N} \frac{C_{n}}{(1+d)^{n}}}{\sum_{n=1}^{N}\frac{Q_{n}}{(1+d)^{n}}}, \tag{1}\]  
where \(C_{n}\) is the cost for year \(n\), \(Q_{n}\) is the energy output for the year \(n\), \(d\) is the discount rate, and \(N\) is the analysis period. The parameters for all equations in this paper are summarized in Appendix A.  
In this paper, we analyze the impact of module efficiency on system LCOE for three system configurations, as shown in Figure 6: utility with fixed tilt for modules, utility with one-axis tracking, and commercial projects with fixed tilt for modules. Assuming modules of different efficiencies will have the same per-watt yield, and operation cost is a fixed percentage of the system capital expenditure (capex), a PV project's LCOE is proportional to the system unit capex. Applying the capex structure shown in Figure 6, we derive the impact of module efficiency and price on PV LCOE for different applications, in the 'fixed-area' scenario. In Figure 7, negative values on the \(y\)-axis suggest that LCOE in a certain scenario is higher than that in the reference case. For utility PV, when trackers are introduced, the proportion of area-proportional costs is a higher percentage of the total system capex, so module efficiency can impose stronger leverage in reducing system LCOE. This is reflected in the higher position of the dashed lines than the solid lines in the left-hand chart of Figure 7.  
In commercial PV, due to restricted economies of scale, area-proportional and fixed non-module costs are higher than in utility PV. Module efficiency therefore holds more value in commercial PV. For instance, in a tracking utility PV, 20% efficient modules can ask for a price of $0.36/W (the intersection between the dashed green line and the black line in Figure 7a).