HELCO rate structures

The NELHA research park's electricity needs are serviced by the Hawai'i Electric Light Company (HELCO). Two rate structure options are available to the NELHA research campus through HELCO - Schedule J¹³ and Time-of-Use (TOU) Schedule J.¹⁴ Both rate schedules include three major components:

• • Demand Charge - $13/kW for the maximum power measured in the month

• • Energy Charge - ₵/kWh rate for energy use

  • ◦ The most significant contributors to this are flat energy cost recovery rates, which fluctuate monthly from 16-18 ₵/kWh based on utility calculations of fuel costs, and non-fuel energy charges, which is an additional ₵/kWh that can have hourly time-of-use options.

• • Power Factor Adjustment - Either a credit or charge calculated as:

  (1.1)$$\matrix{ {C_{PF} = PF_{adj}\lpar {C_{dem} + C_E + R_{PF}\cdot E_{total}} \rpar } \hfill \cr {PF_{adj} = \displaystyle{{0.1} \over {100}}\lpar {85-\overline {PF} \cdot 100} \rpar } \hfill \cr } $$

where C_PF, C_dem, and C_E are the monthly power factor, demand, and energy charges, respectively, PF is the power factor, R_PF is a power factor adjustment rate of 10.2440 ₵/kWh, and E_total is the amount of energy purchased in the month.^13,14

The non-fuel energy charge under Schedule J is 9.6448 ₵/kWh at all times of day under Schedule J. Table 1 shows the non-fuel energy charges with Schedule TOU J.

Table 1. Time-of-Use Schedule J Pricing and Demand Windows

Table 2. Projected annual electricity cost statistics with different tariffs and hydrogen production scenarios

Unlike other areas of the country with time-of-use options, the electricity prices are lowest in the middle of the day from 9:00AM to 5:00PM, which incentivizes energy use outside of peak sun hours. This is likely because of the high penetration of solar generation in Hawaii, which greatly reduces net loads in the middle of the day and leads to a swift increase in generation demands in the evening as solar production ends. To combat this, HELCO is now beginning to incentivize mid-day energy use to shift loads to coincide with solar production. The implications of this versus fixed energy pricing will be discussed further later in the paper.

Research campus modeling framework

The load schedule of the hydrogen production facility was optimized to minimize the cost of hydrogen production by solving a linear program assuming perfect foresight of the demand of the research park and solar generation. This optimization was performed subject to the constraints on the system shown below where C denotes a $/kW price, c denotes a $/kWh price, P denotes power in kW, ¢t is the measurement interval in hours, and H indicates a binary array with a 1 for each hour the given price is in effect.:

(1.2)$$\matrix{ {\mathop {\min }\limits_{P_C,P_D,P_{H2}} } & {P_{\,peak}\cdot C_{Dem} + \Delta t\cdot \sum\limits_{t = 1}^T {P_{FG,t}c_{total,t} + \displaystyle{{\sum\limits_{t = 1}^T {\sigma _{t + } + \sigma _{t-}} } \over K}} } & {\left( a \right)} \cr {where} & \matrix{c_{total,t} = c_{E,t} + c_{other} \cr c_{E,t} = c_{on-peak}\cdot H_{on-peak,t} \cr \quad\quad\quad+ c_{off-peak}\cdot H_{off-peak,t} \cr \quad\quad\quad+ c_{mid-day}\cdot H_{mid-day,t}} & {\left( b \right)} \cr {s.t.} & {P_{FG,t} = P_{Dem,t} + P_{H_2,t}-P_{sol,t} + P_{curt,t}} & {\left( c \right)} \cr {} & {P_{FG,t} \ge 0} & {\left( d \right)} \cr {} & {P_{curt,t} \le P_{sol,t}} & {\left( e \right)} \cr {} & {P_{\,peak} \ge P_{FG,t}} & {\left( f \right)} \cr {} & {\sigma _{t + }-\sigma _{t-} = P_{FG,t}-P_{FG,t-1}} & {\left( g \right)} \cr } $$

Subscripts Dem, FG, sol, E, H₂, and curt represent demand, power purchased from the grid, solar generation, energy, hydrogen facility power, and curtailed power, respectively. The other per kWh charges (c_other) include relatively small fixed prices for energy cost recovery, purchased power adjustments, revenue balancing account provisions, and public benefits funds as defined in the rate schedules.^13,14

The cost function in Eqn. (1.2) is essentially equal to the monthly power and energy charges for the research park. The terms σ_t+ and σ_{t -} in the cost function are non-negative variables that relate to increases or decreases, respectively, in the net power draw of the research campus. A slight penalty is associated with fluctuations in the net demand (K = 1000) to smooth the system dispatch and consequently limit the number of on/off operations of the hydrogen production facility. The resulting dispatch schedule is more reflective of realistic facility operations and preliminary analyses showed that this was less computationally intensive with the same effect than directly limiting facility operations. Non-fuel energy charges are a fixed 9.6448 ¢/kWh with Schedule J in lieu of the definition in Eqn. (1.2)b. Net energy metering is not in effect here, hence constraint (1.2)e specifies that energy coming from the grid be greater than or equal to 0 at all times. The power factor adjustment is calculated after the optimization algorithm completes to avoid excessive computational expense. Besides these constraints, additional constraints were also needed for the hydrogen production facility to simulate the capabilities and limitations of the system.

Hydrogen facility modeling framework

The hydrogen production facility consists of a Proton C30 electrolyzer, and the requisite balance-of-plant components to produce up to 65 kg/day of hydrogen at 30 bar.^{Reference Virji, Randolf, Ewan and Rocheleau15} Previous work with this system was undertaken to ensure that the system could quickly vary its load to perform frequency response operations.^{Reference Ewan, Rocheleau, Swider-Lyons, Devlin, Virji and Randolf16} Hydrogen produced by the system is stored in one of three transport trailers that can store up to 100 kg of hydrogen each.

For the optimization algorithm, the hydrogen facility demand was added to the power balance constraint as shown in Eqn. (1.2)d. Additional constraints on the electrolysis facility are imposed to reflect the on-site hydrogen storage capabilities, efficiency of the system across its operating envelope, and minimum operation levels proposed by HNEI. The amount of hydrogen stored on-site is modeled with the following constraints:

(1.3)$$\displaylines{S_{H_2\comma t} = S_{H_2\comma t-1} + \Delta t\cdot G_{H_2\comma t}-D_{H_2\comma t} \cr 0 \le S_{H_2\comma t} \le S_{H_2\comma \max }} $$

where S_H2,t is the amount of hydrogen stored in the transport trailer in kg, G_H2,t is the hydrogen production rate at time t in kg/hr, and D_H2,t is the hydrogen fueling demand at time t in kg. For this study, it was assumed that only one of the 100 kg transport trailers was in use, making S_H2,max equal to 100 kg. It was further assumed that hydrogen withdrawals occurred at a steady rate from 6pm-7pm daily at the end of the buses’ daily routes.

The relationship between the hydrogen production rate and facility power draw for this electrolysis system was modeled in a previous study.^{Reference Virji, Randolf, Ewan and Rocheleau15} This model includes the considerations of the demand for total system, including the balance-of-plant components, and yielded data for the hydrogen production rate and across the full range of the facility's power consumption as shown in Figure 2. The relationship between power and hydrogen production rate is highly linear below ~70% of the maximum load, but the production efficiency drops off above this level of power consumption because of the limitations of the electrolyzer itself. This loss in production efficiency should be reflected in the optimization algorithm to give a better representation of the proper dispatch schedule and a more accurate representation of the minimum cost of production.

To do this, the model presented in^{Reference Virji, Randolf, Ewan and Rocheleau15} was incorporated into the optimization as a piecewise linear correlation between the facility power output and hydrogen production rate using type 2 special ordered sets (SOS2):

(1.4)$$\matrix{ {P_{H_2\comma t} = \sum\limits_{k = 1}^B {b_k\cdot x_{k\comma t}} } \hfill \cr {G_{H_{&2}\comma t} = \sum\limits_{k = 1}^B {g_k\cdot x_{k\comma t}} } \hfill \cr {1 = \sum\limits_{k = 1}^B {x_{k\comma t}} } \hfill \cr {x_{k\comma t} \le \gamma _{k\comma t}} \hfill \cr } $$

where k denotes the break points in the piecewise linear approximation, b_k is the power at breakpoint k, g_k is the associated hydrogen production rate at breakpoint k, x_k‘s are continuous variables introduced by the SOS2 representation for interpolation between break points, and γ_k's are binary variables for which only consecutive values can be non-zero. This imposes a continuous relationship between the hydrogen production and facility power that is linear between the break points. Break points at 0%, 74%, 90%, and 100% of the full rated facility power were used for this analysis. Analysis results using this variable efficiency method versus a constant efficiency model will be shown to highlight the importance of including this consideration in valuation studies.

HNEI further specified that the facility would only be operated between 10% and 100% of its full rated power when online. To reflect this, the following constraints were imposed:

(1.5)$$\matrix{ {P_{H_2\comma t}-\alpha _{H_2\comma t}\cdot P_{H_2\comma \max } \le 0} \cr {P_{H_2\comma t}-A\cdot \alpha _{H_2\comma t}\cdot P_{H_2\comma \max } \ge 0} \cr } $$

where α_H2,t is a binary variable that equals 1 if the hydrogen facility is in operation at time t and 0 if it is shutdown, and A is the minimum load fraction for the facility of 10%. This ensures that if the facility was to run at less than 10% of its full rated capacity, it would instead be shut down in the optimization algorithm (α_H2,t = 0).

Lastly, the kVAR demand of the hydrogen facility needed to be estimated to give the correct total kVAR demand of the research park for the power factor adjustment. This was estimated by comparing the original data set (including hydrogen facility testing) and the filtered data set. The kW and kVAR differences between these two data sets were assumed to be contributed by the hydrogen production facility. From this, it was found that the kVAR demand of the hydrogen facility was approximately 18.5% of the kW demand on average. This relationship was used to calculate the total kVAR demand for the campus for the calculation of the power factor adjustment after the optimization was performed. The linear program was implemented using Pyomo^{Reference Hart, Watson and Woodruff17,Reference Hart, Laird, Watson, Woodruff, Hackebeil, Nicholson and Siirola18} in Python and solved using Gurobi.¹⁹

Rate structure comparison

Firstly, we will look at the effect of the rate structure on both the electricity cost of the NELHA campus without hydrogen production, and the added cost of hydrogen production under each rate structure in the optimal case. Again, the two rate structure options are SCH-J, which uses flat energy and demand charges, and TOU-J, which has three energy charge rates depending on the time of day. Figure 3 shows sample optimal dispatch schedules for each rate structure over a three-day period in July. This figure shows time series of the demand of the NELHA research park without hydrogen production (Demand), the on-site solar generation(Solar), the optimal power draw for hydrogen production (H2 Prod), and the net power demand for the research park including hydrogen production that would need to be purchased from HELCO (From Grid). Recall that the variable component of this scenario that is being optimized by the algorithm is the hydrogen production power requirements, and by extension the power purchased from HELCO at each time.

Figure 3. Electrolyzer efficiency and production rate versus % full power and selected SOS2 break points

The optimal dispatch profiles for SCH-J and TOU-J are fairly similar, with the demand of the electrolysis facility being varied to maintain a steady power draw from the utility. This optimally supports the electricity needs of the entire research park while minimizing the increase in the monthly peak demand to limit the increase in demand charges. The major difference between the optimal dispatch for SCH-J and TOU-J is the hours of operation over which this function is performed. Under TOU-J, hydrogen production is stopped during the on-peak period of 5:00PM-10:00PM when energy prices are at their highest. As a result, a consistent demand is maintained during the daily mid-day and off-peak pricing windows, but the limited production hours every day necessitates a higher peak demand to minimize the non-fuel energy charges.

The projected electricity costs of the research park while optimally generating 31 kg of hydrogen daily in addition to the normal loads are $629k ($38k demand charges) under SCH-J and $667k ($43k demand charges) under TOU-J. This is something of a surprising result as the natural assumption is that the ability to shift most of the hydrogen production to mid-day hours with low electricity prices would minimize charges. However, as the rest of the research campus load cannot be moved to low price times of day, the non-fuel energy charges increase due to elevated prices outside of the Mid-Day window and the continued overnight loads for the campus. This fact alone is sufficient to make SCH-J the preferable option for the NELHA campus, despite the potential to move hydrogen production to lower cost times of day.

With regards to the increase in electricity cost caused by the hydrogen production, it turns out again that the time-of-use option is also slightly worse in this case for a few key reasons. Firstly, despite the fact that the non-fuel energy costs from hydrogen production can be reduced versus SCH-J, this is at the expense of increasing demand charges as the available window for low cost production contracts, necessitating higher powers be used during the Mid-Day window. This also leads to a loss in the efficiency of the electrolysis system, which increases the total amount of energy that needs to be purchased. This ultimately leads to a slight increase in the energy cost recovery charge under TOU-J of about $1k versus SCH-J. Secondly, for the amount of hydrogen being produced and the peak production rate of the system, not all of the production can be shifted to the Mid-Day window, meaning that additional energy must be purchased at a higher price than with SCH-J (14.6448¢/kWh Off-Peak vs. 9.6448¢/kWh flat SCH-J).

It should be noted that this is very much a function of the specifics of the rate structure options and pairing with the NELHA campus, which has significant overnight loads that cannot be shifted to Mid-Day windows. The energy cost recovery charges comprise approximately 50% of the monthly expense in both cases, and electrolyzer scheduling has very little effect on this. Results could be significantly different if 1) demand charges also had a time-of-use component, as is used in some areas or 2) if the fixed “energy cost recovery” charge was not so large a portion of overall charges.

The effect of considering variable efficiencies

It is also important to consider the loss in efficiency of the system at high loads in the optimization routine to yield a more realistic estimate of the optimal cost of production and dispatch schedule. Neglecting this can lead to very different optimal dispatch schedules and projected costs. Figure 4 compares the optimal dispatch of the system with and without consideration of the change in efficiency of the system at high loads under TOU-J.

Figure 4. Sample optimal dispatch profiles for mid-July under a) SCH-J and b) TOU-J

If the loss in efficiency at high loads is not considered, the “optimal” dispatch schedule moves much more of the hydrogen generation to the Mid-Day window to decrease the non-fuel energy charges as shown in Figure 5b. This further increases the peak demand for the month, but without acknowledging the additional penalty of needing to use more energy to produce the same amount of hydrogen when operating at high powers, this tradeoff appears more beneficial than it would be in reality. In this case, assuming a fixed efficiency for the electrolyzer leads to a $10k reduction in the estimated annual cost of production as shown in Table 3.

Figure 5. Sample optimal dispatch schedule with TOU-J pricing using a) variable electrolyzer efficiency and b) fixed electrolyzer efficiency

Table 3. Projected annual electricity cost statistics under TOU-J variable and fixed efficiency assumptions

Such a misappropriation of benefits leads to an underestimation in the potential cost of hydrogen production and with a real time implementation would deviate operations from actual optimal use of the system. This shows the importance of increasing the accuracy of the system representation when performing valuation studies to make financial decisions for potential installations, particularly for technologies whose performance can change significantly across its operating range.

Optimal dispatch versus simple operation

The previous section showed how electricity charges for the NELHA research campus would change with the addition of optimally scheduled hydrogen production with the current on-site resources. To be clear, this assumes perfect foresight of the load and solar generation to give the absolute minimum cost for the production of hydrogen while limiting the peak monthly demand as much as possible. While this is a useful metric for valuation studies, in practice this requires real-time forecasting algorithms that would not be able to reach the full optimal results and would necessitate additional controls that could increase the cost of the system. Practically, it may be more beneficial to select a simpler dispatch schedule, which perhaps would not be able to minimize production costs but could be consistently implemented without increasing the cost of the system and with more transparency for operators.

There are many reasonable options for what could be considered a “simple” dispatch method. For instance, the electrolyzer production could be set to a fixed rate during the major hours of solar production to generate the necessary amount of hydrogen. This may increase the peak demand more than is necessary but would utilize low cost solar generation effectively. Conversely, the electrolyzer could be run at a fixed rate 24 hours a day, which would limit the increase in peak demand but not take full advantage of the midday increase in solar generation. Here we compare the cost of hydrogen production using an optimal dispatch to that using constant rates of production from 6am to 6pm (solar utilizing) and 24 hour (peak demand limiting) dispatch schedules. These comparisons give a sense of the financial benefit of optimal dispatch scheduling using forecasting methods in this case. Given the discussion in the previous section, comparisons will be made using the SCH-J rate structure on a $/kg,H₂ basis. Figure 6 shows how the timeseries of power purchased from the utility would vary with the three different dispatch methods of the hydrogen production facility.

Figure 6. Net demand profile comparison with different dispatch methods

Constant production from the hydrogen facility increases the peak monthly demand relative to what is possible by optimally varying the demand of the facility. For the amount of solar generation currently available at the research campus, the increase in demand would be far more pronounced if production was limited to the major solar generation hours because the amount of energy being produced would not be sufficient to offset the increase in demand for electrolysis. Furthermore, limiting the hours of operation to half of the day would require operating at a less efficient point for the electrolyzer and increases the amount of energy needed to produce the necessary amount of hydrogen. Table 4 summarizes the projected electricity and hydrogen production costs using different dispatch methods with the current available resources at the research park.

Table 4. Projected annual electricity and hydrogen production cost statistics under SCH-J with different scheduling methods

The analysis estimates that limiting production between the hours of 6am and 6pm would increase the production costs by 13.5% relative to the optimal case. By comparison, operating the facility 24 hours a day at a constant rate would only increase production costs by 4.6% relative to the optimal case. This shows that monthly demand charges are a significant driver of the variable production costs in this scenario. Furthermore, it seems that constant around-the-clock operations would be a viable method to keep production costs low for the current system configuration, particularly since optimal methods would not have the benefit of perfect foresight in reality and the optimal cost shown here could not be reached.

The effect of solar generation and operation method

Figure 7 shows how the cost of production would change with increasing solar generation capacity when hydrogen production is paired with the NELHA research park or if the same system were operated independently under the same electricity rate structure. Note that the production costs do not include the cost of the installed solar for simplicity. Regardless of the dispatch schedule of the hydrogen production facility or location of the system, the cost of production initially decreases linearly with increasing solar capacity. This is because the energy cost recovery charges, which again are a flat $/kWh rate, account for the largest portion of the bill. As such, simply reducing the amount of energy that needs to be purchased with additional on-site generation has a direct impact on reducing electricity charges. The analysis shows that approximately doubling the current solar generation from 170kW to 350kW would reduce the cost of production by 26-30% when the system is paired with the NELHA campus load.

Figure 7. Standalone and NELHA park coupled hydrogen production cost versus increasing solar with different operation methods

However, this trend only continues to a certain level of solar penetration, at which point further increases in solar capacity become less effective. With enough installed solar generation, there will be times when more energy is being produced than can be consumed by the electrolysis facility and the rest of the research campus combined. This would occur with an installed capacity above approximately 450-500kW in this case. As there is no net-metering option in effect, any excess energy would need to be curtailed without additional financial benefit. The dispatch schedule also affects the effectiveness of added solar. At low solar penetrations, the 24-7 mode of operation leads to lower production costs, and very nearly approximates the optimal solution. However, as solar production increase, it becomes increasingly important to schedule the load to coincide with the generation and the 6am-6pm mode of operation leads to lower production costs as shown in Figure 8.

Figure 8. NELHA park coupled hydrogen production cost versus solar capacity with different operation methods

The analysis shows a transition from a peak demand limiting focus (24-7 operation) to a solar generation utilization focus (6am-6pm operation) around 500kW of installed solar. The crossing point of course depends on the specifics of the individual case, but it is likely that a similar shift in operational focus would be seen in any situation where demand and energy charges are in effect for production. In all cases, optimal dispatch of course leads to the lowest production costs, and this becomes more pronounced as the installed solar capacity increases. This implies that more advanced control and scheduling methods would do more to reduce the cost of hydrogen production as renewable resources are relied upon more heavily. These trends could likely be applied to any behind-the-meter hydrogen production scenario without net-metering but could be significantly different where net-metering prices are in effect or for front-of-the-meter applications where systems may be able to participate in different market mechanisms.

Potential for standalone production

It is possible that the dependence of optimal electrolyzer dispatch schedule on the load profile of the rest of the research may increase the cost of production. Operating as a standalone unit could be beneficial as decisions could be made to make the best use of the electrolyzer without regard to other demands. To be clear, this is likely not an option for the HNEI system, but could offer some insight into the operation of standalone electrolysis units in other areas. Figure 9 compares the cost of hydrogen production operating the facility as a single unit under SCH-J versus operating at the NELHA research park.

Figure 9. Standalone and NELHA park coupled hydrogen production cost versus increasing solar

At low solar penetration levels, production costs would be lower when operating as a standalone unit rather than coupling the electrolysis system with the load of the rest of the research park. However, as the amount of solar generation increases, there is a distinct benefit to sharing solar generation between multiple loads and ultimately this configuration leads to the lowest production cost potential. This is again because of the lack of net-metering options under SCH-J, making it such that excess generation must simply be curtailed. Pairing multiple loads in high renewable penetration scenarios improves the utilization of renewable energy and maximizes the associated savings potential. Figure 10 shows the annual savings potential with increasing solar capacity for the NELHA research campus, the hydrogen production facility acting as a standalone unit, and when pairing the electrolyzer and research campus loads.

Figure 10. Annual savings from increasing solar generation

The savings potential from solar generation increases significantly when the two loads are paired at high solar penetration levels. If the loads are coupled, energy that would be curtailed in either single load scenario can be utilized by the other load, increasing the overall solar utilization and the resulting savings. In fact, in the very high solar penetration scenarios, the annual savings from solar with coupled loads is 36-45% higher than the same amount of solar for the individual loads. There will be an inherent benefit from locating the electrolyzer on the NELHA campus with future expansions of generation resources, despite the fact that this pairing it is not inherently beneficial with the current level of solar production. Similar symbiotic relationships will likely become possible in other areas as renewable generation assets continue to be installed.