*2.3. HTTR-GT/H2 Dispatch Dynamics*

After sampling the FARMA to produce a synthetic dataset, the model dispatches either electricity or hydrogen depending on the electricity price at each time step. When the electricity price exceeds the cost of producing electricity, electricity is produced and sold. When the electricity price falls below the cost of producing electricity, hydrogen is produced and sold. In this manner, the model chooses the most economically advantageous commodity to produce and sell during each hour.

The dispatch algorithm assumes that the HTTR-GT/H2 operates in one of two modes, as put forth by Yan et al. [13]. These modes are the electricity and hydrogen mode in Table 2. The dispatch algorithm decides between dispatching electricity in accordance with electricity operation mode or dispatching hydrogen in accordance with hydrogen mode. The system is assumed to be flexible enough to switch back and forth between modes within the 30-min time steps allotted. Note that these configurations are based on proposed test designs for the HTTR-GT/H2, which may not necessarily utilize the HTTR's entire 30-MWt heat for hydrogen/electricity production.

**Table 2.** HTTR-GT/H2 operational modes (data reproduced from [13]).


The IS cycle design developed by JAEA is sized to provide 29.5 Nm3/h of hydrogen, as per the design in [13].

The amount of hydrogen delivered during each hour (*mH*<sup>2</sup> ) is represented in Equation (3). When the price of electricity (*Pelec* ) falls below the electricity production cost (*Celec*), the system dispatches hydrogen in accordance with the previously defined operation modes. When electricity price is higher than the cost of producing electricity, hydrogen is not produced; instead, the power is used to make electricity.

$$m\_{H\_2} = \begin{cases} \; 29.5 \frac{\text{Nm}^3}{\text{h}}, & P\_{elec} < C\_{elec} \\ \; 0 \; \frac{\text{Nm}^3}{\text{h}}, & P\_{elec} \ge C\_{elec} \end{cases} \tag{3a}$$

$$\mathcal{e} = \begin{cases} \begin{array}{c} 0.3 \text{ MW}, \ P\_{\text{elec}} < \text{C}\_{\text{elec}}\\ 0.6 \text{ MW}, \ P\_{\text{elec}} \ge \text{C}\_{\text{elec}} \end{array} \end{cases} \tag{3b}$$

#### *2.4. Cash Flow Analysis*

Once the dispatch is complete, the model collects economic data to produce a system net present value (NPV). These cash flows include the capital cost, operating and maintenance costs of the IS cycle, and an assumed hydrogen storage cost. Revenue comes from the sale of hydrogen and electricity.

The NPVs in this report represent a differential NPV, shown in Equation (4). NPVref is the NPV of the HTTR-GT/H2 when only electricity is sold and no hydrogen process has been built. NPVref serves as a baseline against which NPVcogen is compared. When ΔNPV is positive, the cogeneration system is more profitable than only selling electricity. When ΔNPV is negative, the system would be more profitable focusing on electricity and not building the IS unit. Thus, when ΔNPV is 0, the profitability of the cogeneration system equals that of only generating electricity. This is the breakeven point, at which the hydrogen price represents the LCOH for this system.

$$
\Delta \text{NPV} = \text{NPV}\_{\text{Cogen}} - \text{NPV}\_{\text{ref}} \tag{4}
$$

Using ΔNPV means that only cash flows that differ between reference and cogeneration cases need to be tracked. Expenditures such as fixed HTTR costs and capital investments associated with the nuclear reactor can be disregarded, as they are equivalent in both the reference case and cogeneration cases. The limitation of this method is that ΔNPV only reflects the nuclear-IS profitability relative to the reference case rather than determining its absolute profitability. More information on the economics of the HTTR-GT/H2 are required before an analysis of total system profitability can be conducted.

Equation (5) gives the mathematical basis for disregarding equivalent cash flows that appear in both the reference and cogeneration NPVs.

$$\text{NPV}\_{\text{ref}} = \text{CF}\_{\text{c-sales}} - \text{CF}\_{\text{muc}, \text{FOM}} - \text{CF}\_{\text{muc}, \text{marginal}} - \text{CF}\_{\text{muc}, \text{CAPEX}} \tag{5a}$$

$$\begin{array}{cc} \text{NPV}\_{\text{Cogen}} = & \text{CF}\_{\text{H}\_{2}\text{-ads}, \text{cs}} + \text{CF}\_{\text{c-sales, cogen}} - \text{CF}\_{\text{muc, FOM}} - \text{CF}\_{\text{muc, marginal}}\\ & - \text{CF}\_{\text{muc, CAPEX}} - \text{CF}\_{\text{IS, CAPEX}} - \text{CF}\_{\text{IS, FOM}} - \text{CF}\_{\text{IS, marginal}} \end{array} \tag{5b}$$

$$\Delta \text{NPV} = \left( \text{CF}\_{\text{H}\_2-\text{sales}} + \text{CF}\_{\text{c-sales, oçen}} - \text{CF}\_{\text{IS,CAPEX}} - \text{CF}\_{\text{IS,FMM}} - \text{CF}\_{\text{IS,mrayinal}} \right) - \text{CF}\_{\text{c-sales}} \tag{5c}$$

The NPVs are calculated by summing the discounted cash flows associated with each case. Equation (6) details the NPV calculation. For this analysis, the discount rate, *r*, is 8%.

$$\text{NPV} = \sum\_{yr=0}^{lifetime} \frac{CF\_{total,yr}}{(1+r)^{yr}} \tag{6}$$

The cash flows accounted for in the cogeneration case are (1) cost of electricity generation from HTTR-GT/H2, (2) IS capital and operating cost, (3) hydrogen storage, (4) revenue from electricity sale, and (5) revenue from hydrogen sale. Only the cost of electricity generation and revenue from electricity sale are tabulated in the reference case. The simulation is run for 1 year and used for every year of the project's 30-year lifetime.

The output for this model is the breakeven cost of hydrogen. Hydrogen prices exceeding the LCOH would make building the nuclear-IS system and strategically dispatching hydrogen more profitable than just selling electricity. Prices below the LCOH mean that the system would lose money relative to only selling electricity. The model allows for

investigating the uncertainty that certain model inputs (e.g., electricity price data) impose on the LCOH.

To find the LCOH, the hydrogen price was varied, and the point at which ΔNPV equaled zero was found. This can either be achieved via optimization or by sweeping the solution space on a grid and locating the zero point. For this analysis, the grid sweep was used since the only variable being perturbed was the hydrogen price.

#### *2.5. Economic Parameters*

The cost of hydrogen production from the nuclear-IS system is given in Table 3, as estimated by JAEA in [18]. The capital cost is driven by the capacity of the IS cycle. For example, the provided capital cost of 3.4 JPY/m3 was multiplied by the IS cycle capacity of 29.5 m3/h and the 8760 h in the year. The loss of chemicals during operation of the IS was treated as a variable operating cost.

**Table 3.** Cost breakdown of hydrogen production by nuclear-IS system. Note that, for this analysis, the capital cost is taken on a capacity basis (i.e., Nm3 of capacity). The table uses data from [18].


The dispatch model also assumes a hydrogen storage cost for a tank sized to hold 4 h of production from the IS cycle. Storage flexing and hydrogen overproduction is not included in this analysis. The storage acts as a simple addition to the capital cost. A price of \$600/kg was used [5], equivalent to 5326.5 JPY/Nm3 at an exchange rate of 106 JPY = 1 USD.

#### **3. Results**

Two scenarios were run: dispatch using synthetic price histories and dispatch using the historical PDC. For the synthetic case, each dispatch instance was run with 100 synthetically generated electricity price time histories to produce a more stochastic optimization. The historical case used the 2018 historical electricity prices as inputs. The outer loop varied hydrogen prices from 0 to 120 JPY/Nm3.

A sample 8 h dispatch window is shown in Figure 6. The amount of revenue that the system would generate during each hour is calculated for hydrogen and electricity sales while operating in hydrogen production mode and electricity production mode, respectively, as shown in Figure 6a. Hydrogen or electricity is then produced, depending on which opportunity cost is greater (see Figure 6b).

**Figure 6.** *Cont.*

**Figure 6.** Example of dispatch logic over an 8 h period. (**a**) The opportunity cost for producing hydrogen or electricity. (**b**) Hydrogen or electricity modes dispatched in accordance with higher opportunity cost. This strategy ensures that electricity is sold only when profitable.

#### *3.1. Stochastic Optimization of LCOH*

The stochastic optimization case performed economic dispatch on 100 different synthetic price time histories generated by sampling the trained electricity-price FARMA. The individual economic parameters were gathered for each of these runs, and the model returned the expected ΔNPV.

Figure 7 shows the relationship between hydrogen price and ΔNPV. Breakeven LCOH occurs at 67.5 JPY/m3, when the ΔNPV is zero. Hydrogen prices were evaluated in increments of 10 JPY/m3 (from 20 to 120 JPY/m3), with higher resolution around the breakeven price of hydrogen.

**Figure 7.** ΔNPV for various hydrogen prices using the synthetic PDC as inputs. The red dot represents the breakeven LCOH.

Hydrogen prices above and below the LCOH offer insight into the system dynamics. With the IS cycle dispatched while hydrogen prices are less than the LCOH, too few hydrogen-producing hours exist to recover the capital expenditure incurred from building the IS unit. With hydrogen prices greater than the LCOH, hydrogen sale becomes economically advantageous in ample time, ultimately recovering—even exceeding—the capital cost.

Figure 8 shows the number of hours per year during which the IS cycle dispatches hydrogen. At 40 JPY/m<sup>3</sup> or less, the hydrogen price is so low that the IS unit is never economically advantageous to dispatch. An LCOH of 67.5 JPY/m<sup>3</sup> equates to 431 expected hours of hydrogen production per year. Price increases result in boosting the number of hours in which hydrogen production is economically advantageous. At a high enough hydrogen price, the system would choose to dispatch hydrogen exclusively.

**Figure 8.** Utilization rate of the IS unit, plotted against the hydrogen price in the stochastic optimization scenario. As the hydrogen price rises, hydrogen deployment becomes increasingly more economically advantageous than electricity sale. Thus, the number of hydrogen production hours increases. The red dot represents the breakeven LCOH.

Table 4 summarizes the expected parameters for dispatch at the LCOH of 67.5 JPY/m<sup>3</sup> using synthetic price inputs.

**Table 4.** Expected dispatch values for the system at a levelized hydrogen cost of 67.5 JPY/m3.

