The Input Parameters of the Technology

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.

Case 1: Low Dispatch Power. Dispatch Power = 2 MW.

Daily Revenue by Storage Capacity, and Marginal Yearly Revenue for an Additional MWh of Storage. Harvesting Power = 0.7 MW, Dispatch Power = 2 MW
storage_capacity daily_revenue marginal_yearly_revenue
0.05 500 0
1.05 520 7300
2.05 535 5475
3.05 544 3285
4.05 548 1460

Case 2: High Dispatch Power. Dispatch Power 9 MW or More.

Daily Revenue by Storage Capacity, and Marginal Yearly Revenue for an Additional MWh of Storage. Harvesting Power = 0.7 MW, Dispatch Power = 9 MW
storage_capacity daily_revenue marginal_yearly_revenue
0.05 500 0
1.05 520 7300
2.05 539 6935
3.05 554 5475
4.05 566 4380
5.05 576 3650
6.05 586 3650
7.05 600 5110
8.05 612 4380
9.05 624 4380
10.05 631 2555
11.05 644 4745
12.05 656 4380
13.05 663 2555

Seasonal Variation in Wave Size and Prices (Northern California)

The months with the smallest waves are August and September. These are also the months with the highest variability in prices and highest peak prices. The waves are largest in January and February. These are also the months with the lowest variability in prices, when storing energy has a lower payoff.

Revenue in January. High Dispatch Power, Storage Capacity = 7.05 MWh, Harvesting Power = 1 MW

Daily Revenue is $722. Revenue if we had no usable storage is $702, and the value of 7 MWh storage is $20/day ($3/ day per MWh).

Revenue in August. High Dispatch Power, Storage Capacity = 7.05 MWh, Harvesting Power = 0.5 MW

Daily Revenue is $564. Revenue if we had no usable storage is $435, and the value of 7 MWh storage is $129/day ($18/ day per MWh).

Additional Results

  • The value of storage capacity does not vary greatly by the power of the device. For example, the value of 7 MWh of usable storage is $106/ day on average for a 1 MW average power device, $130/ day for a 2 MW average power device, $135/ day for a 5 MW average power device, and then gradually declines as the power harvested in one hour becomes greater than thestorage capacity.

Cost-Benefit Analysis

The marginal cost of a MWh of storage for our technology $88,000 per MWh. This is favorable compared to the battery costs in the market which are over $200,000 per MWh.

The marginal revenue of a MWh of storage is about $20 per day.

NREL cost benefit analysis of solar plus storage describes a 30 MW and 4 hours of capacity storage system (120 MWh), that earns about $19/ day per 1 MWh of storage based on 2014 hourly prices in California. We need to adopt the methodology of the NREL cost-benefit analysis to demonstrate the viability of our technology.