The Wikipedia explains engineering redundancy with the following formula:
Each duplicate component added to the system decreases the probability of system failure according to the formula:
- n - number of components
- c pi - probability of component i failing
- P - the probability of all components failing (system failure)
The failure in this case would be the failure of wind components of the grid. For wind temporary component failure would be the rule rather than the exception, and the high likelihood of failure means that redundancy is necessary for any wind penetrated grid system, almost to the extent the system relies on wind generated electricity.
Here is an example of a suggested use for redundancy to increase the reliability of a wind system:
the power guaranteed by 7 and 19 interconnected farms was 60 and 171 kW, giving firm capacities of 0.04 and 0.11, respectively. Furthermore, 19 interconnected wind farms guaranteed 222 kW of power (firm capacity of 0.15) for 87.5% of the year, the same percent of the year that an average coal plant in the United States guarantees power. Last, 19 farms guaranteed 312 kW of power for 79% of the year, 4 times the guaranteed power generated by one farm for 79% of the year.
Thus by lining up an array of 19 geographically dispersed wind generators, the authors. Cristina L. Archer AND Mark Z. Jacobson propose to increase the reliability of wind generating systems. The one question which Archer and Jacobson did not answer is how much would it cost. If we assume that system operators will want the 87.5% reliability, that means, the authors tell us a firm capacity of .15, then we will be able to count part of the capital cost of the generators in the system. The most recent Wind Generators for the most recent West Texas wind project, are priced at $2.5 million per MW installed. At .15 capacity the cost of one MW of 87.5% reliable wind generating capacity would be $2.5 million divided by .15 or a $16.75 in wind investments per every kW of reliable wind generating capacity. But that would not be the end of the investment, because the Archer-Jacobson system would require a large number of high voltage electrical lines to gather the electricity produced at 19 separate locations in 4 different states. More high voltage lines would be required to carry electricity from the central location or locations to Texas or California cities where electricity would be consumed.
Drew Thornley offers a discussion of ERCOT wind transmission cost studies. Thornley reports:
According to ERCOT, 138-kV lines cost $1 million per mile, while 345-kV lines cost $1.5 million per mile. See Competitive Renewable Energy Zones (CREZ) Transmission Optimization Study, ERCOT System Planning (2 Apr. 2008).That is overnight costs. According to Thornley, 500-kV or 765-kV lines are even more expensive. Thus
Energy consultant Jeffry C. Pollock quantified the rate impact of future transmission investment on various customers.† Taking into account rising material and la- bor costs, interest/financing costs, and routing issues, the installed cost for CREZ Scenario 2 is estimated to be $7.8 billion ($3,282,828.28 per mile).In the case of the Archer-Jacobson plan, the gathering and transmission system would be far more ambitious and expensive than ERCOT's CRUZ plans which only transmit electricity from wind farms in West Texas.
A further and until now unnoticed consequence of the Archer-Jacobson plan is what I call its carbon penalties. Carbon penalties are the added and usually hidden CO2 costs of attempts to make renewable schemes work. Professor Manfred Lenzen from the University of Sydney estimates that CO2 costs related to wind generator construction amount to from 30 and 60 grams of C02 per kilowatt hour. But redundancies inherent in the Archer-Jacobson plan would multiply the CO2 penalty for wind by from 6.67 times. The carbon penalties for Archer-Jacobson reliable wind will run from 200 to 400 grams per kW hour, but in addition there would be further carbon penalties for the electrical gathering and transmission systems necessitated by the Archer-Jacobson plan. I am unaware of studies that address the carbon costs of transmission systems, but surely there must be some. Thus not only would reliable power under the Archer-Jacobson plan cost far more than than equally reliable power from conventional nuclear generators, but carbon emissions from the construction of large numbers of redundant wind generators, necessitated by the Archer-Jacobson plan, would lead to far higher carbon penalties for reliable wind, than for reliable nuclear electricity.