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 hight 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 height squared.
Maximum harvesting power: 0.7 MW.
Storage capacity: 2 MWh.
Minimum energy that the flywheel need to store: 0.05 MWh.
Maximum dispatch power: 2 MW.
Flywheel self-discharge rate: 0.2135% per hour. Self-discharge rate of 5% in 24 hours means an hourly sdr of (1-.95^(1/24))=0.002135.
Ring charge efficiency: 0.93. 7 % of energy is lost during transfer to the ring. (Roundtrip storage efficiency =.865); http://css.umich.edu/factsheets/us-grid-energy-storage-factsheet: 85-87%
Ring discharge efficiency: 0.93. 7 % of energy is lost during transfer from the ring to the wire.
Allowable shortage time 7 hours, or 7.990867610^{-4} % of time. Average demand for a representative community: 612
Storage capacity: 0 MWh.
If no storage is deployed, the WEC produces excess electricity 0.978296 % of the time. The generation factor is 2574.5798771. The genration 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 the WEC i.e. the cost.
Let the ESS capacuty be equal to one hour of yearly peak demand.
Storage capacity: 1025.3608347 MWh.
We define a function that outputs the energy storage and dispatch schedule of a hybrid energy generation and storage system given its energy generation schedules, demand, the self discharge rate of the energy storage system, energy storage capacity and the minimum storage required for the system to function.
Flywheel enegry storage systems can have a self-discharge rate as low as 3 % and require as little as 3 % of energy storage capacity as its minimal energy. The function allows the user to set any input parameters for sensitivity analysis.
dispatch_storage_schedule_2 <- function(generation, demand, self_discharge, storage_capacity, min_storage, charge_efficiency, discharge_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
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))
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$storage[i] - min_storage* 1/(1-self_discharge))*discharge_efficiency ,dat$demand[i])
dat$storage[i] <- max(dat$storage[i]-(dat$demand[i]-dat$genertion[i])*1/discharge_efficiency,min_storage* 1/(1-self_discharge))
}
}
return(dat)
}Satisfyind demand during low power months requires a combination of sufficient energy generation capacity and energy storage
Number of hours with shortages: 33
Shortages occurance by month
## # A tibble: 5 x 2
## month n
## <dbl> <int>
## 1 2 13
## 2 3 4
## 3 6 1
## 4 7 4
## 5 9 11dispatch_storage_schedule <- function(generation, demand, self_discharge, storage_capacity, min_storage){
#Inputs: equal length vectors of generation and demand schedules,the self discharge rate, and minimum energy storage required
dat <- as.data.frame(cbind(generation, demand))
dat$storage <- 0
dat$dispatch <- 0
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))
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], storage_capacity)
} else {
dat$dispatch[i] <- min(dat$generation[i]+dat$storage[i] - min_storage* 1/(1-self_discharge) ,dat$demand[i])
dat$storage[i] <- max(dat$generation[i]+dat$storage[i]-dat$demand[i],min_storage* 1/(1-self_discharge))
}
}
return(dat)
}The AquaRing Energy system can react to ambient wave conditions, submerge when wave power exceeds its generation capacity, and adjust its energy storage and dispatch schedule in reaction to these conditions.
we assume that the system will be able to react to ambient wave conditions in real time. Therefore we treat the wave condition data as known.
The day-ahead or long-term forecasts are made based on the past data from BOEM. A day-ahead forecast is simply the current day’s data, and the year-ahead forecast is the current year’s data.
The inputs into the model include design parameters of the AquaRing system - parameters that can vary within certain limits depending on the design choice, external parameters, including physical properties of materials, and market costs of materials and energy demand and wave resource data used to train the model.
Maximum harvesting power: 0.7 MW.
Storage capacity: 2 MWh.
Minimum energy that the flywheel need to store: 0.05 MWh.
Maximum dispatch power: 2 MW.
Flywheel self-discharge rate: 0.2135% per hour. Self-discharge rate of 5% in 24 hours means an hourly sdr of (1-.95^(1/24))=0.002135.
Ring charge efficiency: 0.93. 7 % of energy is lost during transfer to the ring. (Roundtrip storage efficiency =.865); http://css.umich.edu/factsheets/us-grid-energy-storage-factsheet: 85-87%
Ring discharge efficiency 0.93. 7 % of energy is lost during transfer from the ring to the wire.
We use the hourly energy demand for Tacome adjusted downward to generate sample energy demand of a small coastal community. The wave energy data comes from the Bureau of Ocean Energy Management for a loacation near the coast in the Gulf of Alaska.
The energy demand data is the data generated to resemble the fluctutuations in energy demand of a coastal Alaskan community such as Yakutat.
sample data for a representative Northern coastal community with a population of about 600 residents such as Yakutat, Alaska. The sample data is created by using the hourly demand for Tacoma Power in 2018 provided by EIA and scaling it down to to have the average demand equal to a demand of a community with 600 residents.
Wave resource data is the hourly wave height data for 2018 collected near the Island of Montauge, Alaska provided by the Bureau of Ocean Energy Management (BOEM).
Objective Function Minimize the cost of the system while keeping outages under the U.S. average of 7.8 hours/ year (EIA, 2017).
The ARE energy storage system (ESS) can react to real time requests for power within 4 seconds (Beacon Power).
Source: Demand for Tacoma Department of Public Utilities Light Division Hourly https://www.eia.gov/opendata/qb.php?category=2122628&sdid=EBA.TPWR-ALL.D.HThe energy generation must be sufficient to charge the battery
We determine the cutoff for wave height. When the waves are below the cutoff wave energy genertion cannot satisfy peak demand. The duration of such weak waves should not exceed the number of hours that the ESS can dispatch power at full dispatch rate.
The red line shows the 0.0799087 th percentile of wave height
Wave power is proportional to the square of the wave height.The plot below shows the variability of wave power given the wave hight data.
The wave energy generation will vary with the wave power. For a community with an average demand for power of 612 kW (or 612 kWh/h ) and the demand profile given in Figure 1, the energy generation capacity that allows for under 8 hours of outages per year needs an energy generation capacity+energy storage capacity
Minimal energy generation and storage capacity
To limit blackouts the storage capacity should be able to satisfy every energy demand except 7 hours out of 365, or 990 kiloWatt.
Maximum hours of blackout allowed 7.
Minimum amount of dispatch power 989.8194961 allows the system to dispatch power for all but 7 hours with the highest energy demand.
To guarantee that in case of small waves the ESS can satisfy peak demand we set the minimum ESS capacity to 989.8194961.
The generation capacity should be sufficient to charge the ESS for daily, monthly and yearly peak demand.
Let the minimum energy generation
Let the average energy generation be set at 989.8194961
AquaRing Energy submerges in stronger waves to match its energy generation capacity to the ambient wave power.