*3.2. LCOH with Historical Price Duration Curve*

Comparing the stochastically optimized LCOH to one optimized using historical PDC data is useful for understanding the implications of the distribution tails on cost. The stochastic optimization case outputs the expected LCOH under a wide range of possible synthetic PDC. LCOH optimization using the historical dataset gives an example of the LCOH found on a PDC that is slightly skewed to higher prices.

As with the stochastic case, Figure 9 shows that hydrogen is not dispatched at low hydrogen prices and that there is a range in which a small amount of energy is dispatched for hydrogen production despite the inability to recover the IS capital cost. In this case, when hydrogen prices fall below approximately 80 JPY/m3, the system does not dispatch hydrogen. At 80–98 JPY/m3, a small amount of hydrogen is dispatched. At 98.1 JPY/m3, the ΔNPV equals zero, thus representing the LCOH.

Figure 10 shows the IS unit's utilization rate plotted against the hydrogen price. The utilization rate is zero hours when the hydrogen price is low. At an LCOH of 98.1 JPY/m3, the IS unit produces hydrogen for 637 h. Figure 10 shows the utilization rate of the IS under different hydrogen price conditions.

**Figure 9.** ΔNPV for various hydrogen prices using the historical PDC as input. The red dot represents the breakeven LCOH.

**Figure 10.** Utilization rate of the IS unit plotted against the hydrogen price. As the hydrogen price rises, hydrogen deployment becomes increasingly more economically advantageous than electricity sale, so the number of hydrogen production hours increases. The red dot represents the breakeven LCOH.

Table 5 summarizes the dispatch parameters found at an LCOH of 98.1 JPY/m3 using historical price inputs.

**Table 5.** Dispatch values for the system at a levelized cost of hydrogen of 98.1 JPY/m3.


#### **4. Discussion**

The reported LCOH values should not be relied on as a basis for making investment decisions. Rather, they help us understand the implications of different inputs so that when economic competitiveness is evaluated, the correct breadth of input data can be applied.

The effects of price distribution can be viewed by comparing the stochastic optimization case to the historical PDC case. The hydrogen dispatch is driven by two factors: the hours having the lowest electricity prices and the price of hydrogen. By raising the price of hydrogen, selling hydrogen becomes more profitable during more hours. Lower electricity prices and more incidences of low electricity prices also make hydrogen more economically advantageous than electricity.

The lowest-priced hours of the electricity price distribution are what dictate system profitability, since the capacity is fixed and the hydrogen price varied. The stochastic optimization case uses synthetic price histories in an attempt to produce the expected LCOH. On average, the synthetic histories showed lower electricity prices at the tail than did the historical price distribution. This led to a lower LCOH than in the historical case.

This lowest-priced hour distribution phenomenon is illustrated in Table 6. The lowest 500 h of electricity prices from the year are averaged and compared with the LCOHs for several different synthetic histories. The average electricity price over the year is also provided. The LCOH shares a stronger correlation with the bottom-hour average than with the total yearly price average. By way of comparison, the LCOH at the stochastic mean and historical points are \$0.64/m<sup>3</sup> and \$0.78/m3, respectively at an exchange rate of 106 JPY/USD.


**Table 6.** Impacts of the distribution tail on LCOH.

<sup>1</sup> The historical scenario is the only scenario not produced by sampling the ARMA model.

Synthetic data produced using the ARMA method outputted cheaper bottom-500 h price averages, as well as overall average prices that were lower than the historical averages. This meant that the distribution of PDCs was slightly more favorable to hydrogen dispatch than the historical PDC. As such, the LCOH was lower in the stochastic case than in the historical case.

This analysis demonstrates that careful consideration should be taken when applying PDCs to this type of economic dispatch problem. The breakeven price of hydrogen highly depends on the PDC input. Stochastic optimization helps reduce uncertainty, but care should still be taken to produce PDCs that are meaningful with regard to the chosen timeframe of analysis. For example, using a 2020 PDC to predict the 2030 LCOH would be inappropriate. A projection of 2030 prices would be acceptable, but the best practice would be to use a host of projected possibilities to produce an expected LCOH.

The results from this study also show that lower overall electricity prices and more incidences of low prices would provide greater economic incentives for hydrogen production. This means that NPPs in locations with depressed electricity prices due to factors such as zero- or negative-bid renewable energies, mild climates, or low electricity demand could provide hydrogen at a lower price yet still break even or potentially turn a profit.

Several other pathways exist for reducing the LCOH. Reducing capital expenditure would depress the LCOH. The effects and sizes of potential storage options could be explored in more detail. Additional cashflows generated by the NPP's ability to participate in other areas of the electricity market would lower the ΔNPV and thus the LCOH, as well. Before investment decisions are made, each of these sensitivities should be investigated to better understand their feedback.
