1 The Problem

Remote communities not connected to the large electricity grid typically rely on diesel generated electricity. Diesel generation emits greenhouse gases and other pollutants. The electricity generated from diesel is up to 10 times more expensive compared to the main electric grid due to the cost of fuel transportation and delivery Bay (2013). In addition, delivery can be unreliable leading to frequent power shortages (“Microgrid Market” 2018).

For these reasons, remote rural communities seek alternatives to diesel that can decrease energy costs and improve reliability.

This report evaluates the benefits of integrating a renewable energy generation and storage system, AquaRing Energy (ARE) into the electricity system of a representative Northern coastal community. The report investigates what proportion of yearly energy demand of a remote coastal community can be served by a wave energy converter, compared to a wave energy converter with integrated energy, such as as ARE, and compared to an offshore wind system.

Section I of the report describes the assumptions used for analysis, and Section II lists the parameters used in the model. Section III describes the external data used to create an energy load of a coastal community, and the wave and wind resource data.

Sections IV - VII include models of alternative power provision for the small community, including powering a community with a wave energy converter without storage, with a wave energy converter with storage, and with offshore wind. For each case we describe a system that reliably serves load without supplemental diesel generation, and then allow for supplemental diesel generation.

2 Modeling Energy Provision by an Energy Generation and Storage System for a Remote Alaskan Community

We assess the wave energy resource in coastal Alaska, model hour-by-hour energy generation, energy storage and dispatch of energy generation and storage systems at various scales that can reliable serve the demand of a rural Alaskan community. By reliability we mean energy provision with the numbers of outages being at least as rare as the actual number of outages occurring in Alaskan villages. According to Rural Utilities Service, the residents of the villages served by the Alaska Village Electric Coop experienced power outages for 11 hours in 2014 (Allen and Brutkoski (2016)). The average hours that an average U.S. resident experienced in 2017 was 7.8 hours (“Today in Energy” 2018).

2.1 Model Assumptions

Energy demand is assumed to be known in real time.

Energy generation depends on the wave power resource per meter of shoreline, the width of the wave energy converter, and the efficiency with which a device of a certain width can harvest wave power.

The AquaRing submerges in strong waves. Then, it generated energy at its generation capacity when the wave height is below the maximum wave height, and continues generating at capacity in stronger waves.

The wave power per meter of shore is proportional to the wave period and wave height squared.

with \(P\) the wave energy flux per unit of wave-crest length, \(H_{m0}\) the significant wave height, \(T_{e}\) the wave energy period, \(\rho\) the water density and \(g\) the acceleration by gravity (Wikipedia contributors (2019)).

The wind power generation is proportional to the speed of wind cubed

2.2 Model Parameters

The parameters used in modeling the energy dispatch and storage include design parameters of the energy generation and energy storage system, parameters related to the energy demand characteristics of the community, and parameters related to the ocean energy resources, waves and offshore wind.

Table 1. Model Parameters

Variable Units Description
Engineering Parameters
Energy Generation
Generation kW Hourly energy generation at a given location throughout the year
Baseline_generation kw Wave energy generation profile when average energy generation is equal to average community demand. The energy generation needed to meet demand is always above baseline.
Generation_factor Generation = baseline_generation * generation_factor
Generation_capacity kW Energy generation capacity or the maximum output of the energy system
max_wave_height meters Wave height at which the wave energy system submerges
Energy Storage
Storage_capacity kWh Energy Storage Capacity
Round_trip_efficiency rate The proportion of energy put into the ESS that can be retrieved from the ESS. This rate accounts for the losses during the charging and discharging of the ESS
Min_storage_rate rate Minimum energy that the energy storage system (ESS) needs to store as a proportion of the energy storage capacity.
Self_discharge_per_day rate Proportion of energy stored in the ESS lost to self-discharge per day. Flywheel ESS can have a self-discharge rate of 5 % per day (“Flywheel storage power system - Wikipedia” 2019).
Energy Resource Characteristics
Baseline_generation kW Hourly wave power profile for a given location over 1 year
Wind_power_profile kW Hourly wind power profile for a given location
Energy Demand Characteristics
Demand kW Hourly energy demand profile for a given location over 1 year
Max_shortage_hours hours per year Acceptable hours of shortages per year. In the U.S. each resident experienced about 8 hours of shortages on average in 2017. In remote communities shortages are more frequent (“Microgrid Market” 2018).
Economic Parameters
Generation_capex $/kW Capital expenditure per kW of generation capacity
Generation_opex $/kW/year Operating expenditure per kW of generation capacity per year
ESS_capex $/kWh Energy Storage Cost per kWh of ESS capacity
ESS_opex $/kWh/year Operating expenditure per kWh of ESS capacity per year

Initial Values for Input Parameters 

max_wave_height = 2.8 # meters. The average wave height in the Alaska Bay is 2 meters and peak wave height is 10 meters. The ARE system submerges to more closely match its energy generation capacity with the ambient wave power. At a max_wave_height of 2.8 meters ARE will harvest energy from the strongest ambient waves 80% of the time. 


round_trip_efficiency = 0.87  # Wikipedia: https://en.wikipedia.org/wiki/Flywheel_energy_storage, round-trip efficiency up to 90%. http://energystorage.org/energy-storage/technologies/flywheels: 85 - 87%
min_storage_rate = 0.03 #Proportion of energy storage capacity required at all times. Our estimate for the FESS is based on the engineering estimated from the ARE Overall Feasibility Model.

min_storage_rate = 0.03 #Proportion of energy storage capacity required at all times

self_discharge_per_day =  0.05  #Proportion of energy stored in the ESS lost to self-discharge per day.  (https://en.wikipedia.org/wiki/Flywheel_storage_power_system#Energy_loss. The Wikipedia article refers to the German technology company ATZ (http://www.atz-gmbh.com) that claim that the flywheel ESS that they developed has under 5% self-discharge rate per day.)


max_shortage_hours = 10 #According to Rural Utilities Service, the residents of the villages served by the Alaska Village Electric Coop experienced power outages for 11 hours in 2014 (@Allen2016). The average hours that an average U.S. resident experienced in 2017 was 7.8 hours @EIA2018.

generation_capex = 5027.88 #$/kW. Source: ARE Overall Feasibility Model
generation_opex = 70 #$/kW/year. 1.4 % of CapEx. Source: ARE Overall Feasibility Model. 
ess_capex =  224.265 #$/kWh. Source: ARE Overall Feasibility Model
ess_opex = 3 # $/kWh. 1.4 % of CapEx. OpEx are low because the ESS is protected from the elements and movement in the ESS occurs without friction. We expect virtually unlimited number of charge and discharge cycles. 

#Lithium Ion Battery Parameters
li_ion_ess_round_trip_efficiency = 0.9 # http://css.umich.edu/factsheets/us-grid-energy-storage-factsheet: Battery storage efficiency: 60-95%
li_ion_ess_min_storage_rate = 0.03
li_ion_ess_self_discharge_per_day =  0.001 # low
li_ion_ess_capex = 652 # $/kWh. Lazard reorts that the average capital cost needed to integrate a compressed air, pumped hydro, thermal, or lithium ion battery storage system is $159/kWh, $263/kWh, $331/kWh, and $652/kWh, respectively. (http://www.intertek.com/blog/2017-10-06-grid-scale-energy/)
li_ion_ess_opex= 10# $/kWh

3 Wave Energy Converter without the Energy Storage System (ESS)

Storage capacity: 0 kWh.

3.1 Hourly Energy Demand and Wave Energy Generation Profiles

#Energy Demand and wave power data 
dload <- dload[dload$year==2018,] #Tacoma power hourly energy demand for 2018. 
average_community_demand = 612 # Mean yearly power demand (in kW) for a representative Community. Yakutat's average hourly demand for power was 612 kW in 2017. This number is used to generate the community demand series. 
dload$demand <- dload$demand/mean(na.exclude(dload$demand))* average_community_demand #We use hourly demand for Tacoma Power. We find that the demand patterns for the Pacific Northwest Utilities are similar to those of Alaska. We scale demand to have the average the same as the average demand of a given coastal community 

dwaves$wave_height_for_generation <- ifelse(dwaves$WVHT<max_wave_height, dwaves$WVHT,max_wave_height) #Cap wave height for energy generation at max_wave_height. WVHT is significant wave height, defined as the average of the highest one-third of all of the wave heights during the 20-minute sampling period. 

dwaves$wave_power_profile <- dwaves$wave_height_for_generation^2*dwaves$APD # This hourly series is used to estimate the distribution and the variability of wave power throughout the year

data <- inner_join(dwaves,dload, by='time') #Join the demand profile and the wave power data by time

data <- data %>% filter(!is.na(demand)& !is.na(WVHT))# 98 hours excluded, due to missing values. Assume that missing values are uncorrelated with demand or waves.

data$baseline_generation <- mean(data$demand)/mean(data$wave_power_profile)*data$wave_power_profile #scale the wave power profile to have the mean = mean demand

generation_factor <- (-1)*sort(-data$demand/data$baseline_generation)[max_shortage_hours] # generation should exceed demand for all except the 10 most extreme hours (hours with greatest demand and weakest waves). This condition keeps shortages under 10 hours. The generation factor is determined by the lenth of the WEC that is perpendicular to the waves and that harvests energy. The generation factor is proportional to the size of WEC or material costs.
data$generation <-  data$baseline_generation*generation_factor

Allowable shortage hours set to 10.

Average community demand is 612 kW.

Average energy generation is 11835 kW.

The system energy generation capacity is 40342 kW.

The generation factor is 19. Generation factor is the ratio of average yearly generation to average yearly demand.

4 Wave Energy Converter with ESS

4.1 Storage and Dispatch Schedule Algorithm

We define a function that outputs the energy storage and dispatch schedule of a hybrid energy generation and storage system.

The inputs of the function are the hourly energy generation and community load schedules in kW and the parameters of the performance parameters of the ESS: the energy storage capacity in kWh, the self-discharge rate per day, minimum energy storage needed at all times for ESS to function, and round-trip efficiency.

Flywheel energy storage systems can have a self-discharge rate as low as 5 % per day and require as little as 3 % of energy storage capacity as its minimal energy. The round-trip efficiency is set to 87 %. The function can be used to judge the sensitivity of the system performance to these input parameters.

4.2 A Dispatch Storage Schedule Function

dispatch_storage_schedule <- function(generation, demand, storage_capacity, self_discharge_per_day, min_storage_rate, round_trip_efficiency){
  self_discharge_per_hour = 1 - (1-self_discharge_per_day)^(1/24) 
  charge_efficiency = sqrt(round_trip_efficiency) #We assume that energy is lost at the same rate during the charge and discharge of the ESS 
  discharge_efficiency =  sqrt(round_trip_efficiency)
  #Inputs: equal length vectors of generation and demand schedules,the self discharge rate, minimum energy storage required, charge efficiency, and discharge efficiency
  dat <- as.data.frame(cbind(generation, demand))
  dat$storage <- 0
  dat$dispatch <- 0
  min_storage <- min_storage_rate*storage_capacity
  initial_storage <- min_storage
  
  for (i in 1:nrow(dat) ){
  dat$storage[i] <- ifelse(i==1,initial_storage,dat$storage[i-1]*(1-self_discharge_per_hour))
  
    if (dat$generation[i]> dat$demand[i]){
      dat$dispatch[i] <- dat$demand[i]
      dat$storage[i] <- min(dat$storage[i]+(dat$generation[i]-dat$demand[i])*charge_efficiency, storage_capacity)
      } else {
        dat$dispatch[i] <- min(dat$generation[i]+(dat$storage[i] - min_storage/(1-self_discharge_per_hour))*discharge_efficiency ,dat$demand[i])
        dat$storage[i] <- max(dat$storage[i]-(dat$demand[i]-dat$generation[i])/discharge_efficiency,min_storage* 1/(1-self_discharge_per_hour))
      }
  }
  return(dat)
}

4.3 Application to a Sample Energy Generation and Storage System

We apply the algorithm to a system with the following characteristics:

Energy generation exceeds demand 75 % of the time. Then, 75% the time the system will be able to satisfy demand and store excess energy and 25% of the time it will use stored energy.

Energy generation capacity = 2033 kW

Energy storage capacity equal to 2 hours of peak yearly energy community demand.

storage_capacity = 2051 kWh.

Energy demand is met 84 % of the time. Total hours with insufficient dispatch are 1392.

The generation factor is 3. Generation factor is the ratio of average yearly generation to average yearly demand.

Shortages in winter are more costly and less desirable, as diesel is more expensive and less reliable in winter and electricity is essential for community’s heat and lighting. The system is not able to meet demand for 91 hours in winter.

4.3.1 Seasonal Performance of the Energy Generation and Storage System.

The plot below looks at the system performance during three days of weak wave power in July. The plot demonstrates the operation of the energy storage and dispatch algorithm starting from the state when the ESS stores energy at capacity to the state when the ESS reaches its minimum level and dispatch drops below demand.

The plot below shows the system performance when waves are strong.

4.4 Wave Energy Generation and Storage System for Reliable Power

Satisfying demand during low power months requires a combination of sufficient energy generation capacity and energy storage.

The system generates energy that exceeds demand 90% of the time and includes an ESS that stores 8 hours of peak demand of the community.

Mean community demand is 612

The energy generation capacity is 13293 kW, and ESS capacity is 8203 kWh.

The generation factor is 6. Generation factor is the ratio of average yearly generation to average yearly demand.

The system is able to completely meet demand 99 % of the time. The predicted shortages are 111 hours per year.

In winter (December - February) energy dispatch falls below demand for only 14 hours.

5 References

Allen, Riley, and Donna Brutkoski. 2016. “Sustainable Energy Solutions for Rural Alaska.” Ernest Orlando Lawrence Berkeley National Laboratory. https://www.denali.gov/wp-content/uploads/2018/10/Sustainable-Energy-Solutions-For-Rural-Alaska-April-2016.pdf.

Bay, Hartley. 2013. “Remote Grids System Performance Monitoring and Assessment.” https://www.nrcan.gc.ca/sites/www.nrcan.gc.ca/files/canmetenergy/files/pubs/2013-035{\_}en.pdf.

“Flywheel storage power system - Wikipedia.” 2019. Accessed August 10. https://en.wikipedia.org/wiki/Flywheel{\_}storage{\_}power{\_}system{\#}Energy{\_}loss.

“Today in Energy.” 2018. U.S. Energy Information Administration. https://www.eia.gov/todayinenergy/detail.php?id=37652.

Wikipedia contributors. 2019. “Wave Power.” https://en.wikipedia.org/wiki/Wave_power.