Optimizing microgrid deployment for community resilience

Abstract

The ability to (re)establish basic community infrastructure and governmental functions, such as medical and communication systems, after the occurrence of a natural disaster rests on a continuous supply of electricity. Traditional energy-generation systems consisting of power plants, transmission lines, and distribution feeders are becoming more vulnerable, given the increasing magnitude and frequency of climate-related natural disasters. We investigate the role that fuel cells, along with other distributed energy resources, play in post-disaster recovery efforts. We present a mixed-integer, non-linear optimization model that takes load and power-technology data as inputs and determines a cost-minimizing design and dispatch strategy while considering operational constraints. The model fails to achieve gaps of less than 15%, on average, after two hours for realistic instances encompassing five technologies and a year-long time horizon at hourly fidelity. Therefore, we devise a multi-phase methodology to expedite solutions, resulting in run times to obtain the best solution in fewer than two minutes; after two hours, we provide proof of near-optimality, i.e., gaps averaging 5%. Solutions obtained from this methodology yield, on average, an 8% decrease in objective function value and utilize fuel cells three times more often than solutions obtained with a straight-forward implementation employing a commercial solver.

Appendices

Appendix A: Disaster cost components

More than one dozen public and private sector data sources help capture the total, direct costs (both insured and uninsured) of the weather and climate events. These costs include physical damage to residential, commercial, and municipal buildings; material assets (content) within buildings; time element losses such as business interruption or loss of living quarters; damage to vehicles and boats; public assets including roads, bridges, levees; electrical infrastructure and offshore energy platforms; agricultural assets including crops, livestock, and commercial timber; and wildfire suppression costs, among others. However, these disaster costs do not take into account losses to natural capital or environmental degradation; mental or physical healthcare-related costs, the value of a statistical life; or supply chain, contingent business interruption costs. Therefore, our estimates should be considered conservative with respect to what is truly lost, but cannot be completely measured due to a lack of consistently available data (Smith 2021).

Appendix B: Taxonomy feeders

See Table 10.

Table 10 Summary of distribution feeders used to create electrical load profile

Table 11 Projected costs of solid oxide fuel cells

Appendix C: Additional solid oxide fuel cell costs

Assumptions

• U.S. Energy Information Administration (2020) estimates “owner costs” though the applicability of those to this context is unclear: “typically include development costs, preliminary feasibility and engineering studies, environmental studies and permitting, legal fees, project management (including third-party management), insurance costs, infrastructure interconnection costs (e.g., gas, electricity), and owner’s contingency.”

• O &M costs from U.S. Energy Information Administration (2020) are orders of magnitude different from Battelle Memorial Institute (2017a) as the former estimates are much more inclusive.

• High capital cost case assumes high equipment costs and a high sales markup.

• Costs over time are based on the assumption that production volumes increase, reducing the costs of production.

• Equipment cost includes the cost of heat recovery equipment for combined heat and power and sales markup.

• Costs assume a 5% discount rate, but given current economic conditions, a higher value may be more appropriate and would increase the low and medium case fixed O &M.

• With all sources pooled together, there was agreement that production volume matters for costs, but not system size (except at very small system sizes, 1 kW and 5 kW, which we do not consider in the model).

• The levelized cost of energy (LCOE) estimates only factor in the electricity delivered, not the heat energy, assuming a 5% discount rate, a 10-year system lifetime, a 5-year stack and inverter replacement, and a capacity factor of 93%.

Based on these assumptions, we estimate fuel cell costs and report them in Table 11.

LCOE$_{Nj}$ is the levelized cost of energy for technology j, at a life expectancy of N, where AEP is the annual electricity production, and is computed as:

$$\begin{aligned} \text {LCOE}_{ij}=\frac{\kappa _j \frac{i(1+i)^{N_j}}{(1+i)^{N_j}-1}+\text {FOM}}{\text {AEP}}+\text {VOM} \end{aligned}$$

Figure 13 shows the projected costs over time for each category: high, medium, and low. The purple circle shows the value we use for our modeling efforts.

Fig. 13

Projected levelized cost of energy for power-only solid oxide fuel cells. Projections extend to 2050 based on the values found in Table 11