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By C. Rhodes, P.Eng., Ph.D.

Total wind electricity generation in Ontario is characterized by random short term output power variations, likely daily output power variations and predictable seasonal output power variations. As shown on this web page, useful wind generation of electricity in Ontario is constrained by availability of sufficient balancing hydraulic generation with the necessary: hydraulic turbo-generator capacity, reliable load and seasonal energy storage to filter the wind power. Wind generation must also bear the high costs of intermittent energy transmission back and forth between the wind generator and the hydraulic generator as well as the cost of transmission of filtered wind power to the load.

The cost of usable wind energy delivered to the end user is many times the present Ontario end user electricity price. This high cost is caused by Ontario geography where most of the electricity load is in southern Ontario whereas most of the economic wind generation is in northern Ontario and most of the available hydraulic balancing generation with sufficient energy storage is in Quebec. It is generally more economic to meet the electricity load in southern Ontario with nuclear energy than it is to build sufficient transmission, hydraulic generation and energy storage to filter and transmit the available wind power.

However, there may be some special case circumstances in small communities in northern Ontario that can reduce their electricity costs through use of local wind generation balanced by local hydro electric generation. These circumstances tend to occur at locations where the interruptible electricity load is comparable to the electricity base load.

Via a number of 20 year wind power purchases the Independent Power System Operator (IESO) has determined that the cost of unconstrained on-shore wind generation, with no energy storage and no transmission, is about:
$.115 / kWh.
A wind generator located at a favorable site typically has a winter capacity factor of 40%, a summer capacity factor of 20% and an annual capacity factor of 30%.

One kW of such generator peak plate capacity produces its owner a gross revenue of about:
(8766 h / year) X 0.3 X ($.115 / kWh) = $302.43 / kW plate capacity-year

The OPA (Ontario Power Authority) and its successor the IESO (Independent Electricity System Operator) have further found that the capital cost of land based wind generation is about $2800 / kW of wind generator peak plate capacity, indicating that the maximum simple payback period for wind generator financing is:
($2800 / kW wind generator peak plate capacity) / ($302.43 / kW wind generator peak plate capacity-year) = 9.26 years

The actual payback period for investors is longer due to the costs of site leasing and wind generator maintenance. However, an investment in unconstrained wind generation may make financial sense to an investor if this investment shelters other income from tax.

It is generally accepted that the capital cost of rural dual circuit 500 kVAC transmission is about:
$3,000,000 / km-3000 MW peak = $1.00 / km-kW peak

To allow for occasional branch service outages the transmission system should be designed to have a 20% safety margin between normal maximum operating power and maximum load conditions. Hence the actual capital cost of transmission is given by:
$1.00 / km-kW peak X (1 / 0.8) = $1.25 / km-kW peak plate capacity

The annual blended cost of interest, capital amortization and maintenance for the transmission of 1 kW of peak unconstrained wind generation without energy storage is about:
0.1 / year X $1.25 / km-kW plate capacity = $.125 / kW plate capacity-km-year

When the average transmission distance from the wind generator to the energy storage is 1000 km, the annual cost of that 1 kW of peak transmission becomes:
1000 km X $.125 / kW-km-year = $125.00 / kW-year

If the wind generator capacity factor is 30%, this cost must be amortized over:
0.3 X 8766 kWh / kW-year = 2629.8 kWh / kW-year
leading to a transmission cost per kWh of:
($125.00 / kW-year) / (2629.8 kWh / kW-year) = $.0475 / kWh

Neglecting transmission losses the minimum cost of unconstrained wind energy delivered to a distribution system 1000 km from the wind generator is:
$.115 / kWh + $.0475 / kWh = $.1625 / kWh

Assume that the local distributor adds a further $0.03 / kWh, there are debt service and regulatory charges of $.0144 / metered kWh and that the combined transmission/distribution loss is 9.2%. Then the cost of unconstrained and unfiltered wind energy delivered to the end user, before taxes is:
($.1625 / kWh + $.03 / kWh + $.0144 / kWh) X 1.092 = $.226 / kWh

The fundamental problem with this unfiltered wind power is that it is unreliable. The energy that is delivered only has commercial value as interruptible electricity with a potential market value in the range $.02 / kWh to $.04 / kWh. That is, the cost of supplying the unfiltered wind generated electricity is of the order of 10X the market value of that electricity.

In principle the market value of wind generated electricity can be increased if the surplus wind energy available in the winter and at times of random peak wind generation is stored for use during the following summer and at times of random minimum wind generation.

In the summer the average wind generation is 0.2 X plate capacity and in the winter the average wind generation is 0.4 X plate capacity. The annual average wind generation is 0.3 X wind generation plate capacity.

Now assume that when 4 units of electric power are generated in the winter on average 3 units are immediately used and 1 unit goes into storage. In the summer on average 2 units of electric power are generated and 1 unit is drawn from storage. Assume that the storage system is a hydraulic dam that provides balancing generation. The storage system efficiency is assumed to be 100%. Since in the summer the wind generation can actually drop to zero the dam must be fitted with 3 units of hydraulic electricity generation capacity that are dedicated to balancing wind generation.

Notice that the capacity of each unit of generation is 0.1 X wind generation plate capacity.

The storage requirement per kW of wind generation plate capacity is:
1 unit of generation X (8766 hours / 2)
= 0.1 kW / kW wind generator plate capacity X 4383 h
= 483.3 kWh / kW wind generator plate capacity

The minimum amount of other hydraulic generation plus load required to absorb random peaks in wind generation is:
0.7 kW / kW wind generator plate capacity

The hydraulic system must provide:
a) Energy storage of at least 483.3 kWh / kW-wind generator plate capacity;
b) Dedicated hydraulic turbo-generator capacity of at least 0.3 kW / kW-wind generation plate capacity;
c) Other generation and load before connection of the wind generation of 0.7 kW / kW wind generator plate capacity
d) Hence the total hydraulic turbine capacity must exceed the total wind generator plate capacity.

The average filtered wind generation power output is 0.3 kW / kW wind generation plate capacity.

Note that the ratio of hydraulic energy generation with storage to wind energy generation must be at least:
0.7 kW / 0.3 kW = 2.33
In Ontario this ratio places a hard limit on the total amount of unconstrained wind generation.

Since the hydraulic generation plate capacity with accompanying seasonal energy storage is known a maximum unconstrained wind generation plate capacity is easily calculated. This maximum wind generation plate capacity leads to a maximum annual wind energy generation capacity.

Note that the unconstrained wind generation plate capacity is limited to the hydraulic turbo-generator plate capacity of dams with substantial energy storage. This issue limits the total amount of unconstrained wind generation that the electricity grid can accept.

The required storage time for the average wind generation is:
483.5 kWh / 0.3 kW = 1611.66 h

The costs of filtering the wind generator output include:
a) Cost of building and maintaining (0.7 kW of energy transmission) / (kW of wind generator plate capacity) from the wind generator to the hydraulic dam site;
b) The cost of adding (0.3 kW of dedicated hydraulic turbo-generators) / (kW wind generator plate capacity);
c) The cost of dedicating (energy storage of 483.3 kWh) / (kW of wind generator plate capacity).

There is a further issue that at times of minimum wind generation the hydraulic facility downstream water flow increases by a factor of:
1.0 / 0.7 = 1.428
and at times of maximum wind generation the hydraulic facility downstream water flow falls to zero. Maintenance of minimum downstream water flow for preserving fish species further constrains the maximum amount of unconstrained wind generation.

Clearly there are many constraints on filtering wind power and transmitting wind energy from northern Ontario to southern Ontario. The IESO has attempted to mitigate the delivered cost of wind energy by restricting wind generation to locations within 500 km of major electricity markets. However, the over riding issue is that unconstrained wind energy generation is capped by the amount of hydraulic energy generation that has sufficient hydraulic energy storage. In Ontario, absent strong transmission interties to Quebec, this cap on annual wind energy generation is less than 5% of total Ontario electricity energy generation.

It has been shown that a hydro-electic facility can be used for balancing unconstrained wind generation provided that the plate capacity of the hydro-electric turbogenerators exceeds the plate capacity of the wind turbine turbogenerators and that the same hydro-electic facility provides energy storage of at least 483.3 kWh / kW of wind generator plate capacity. The unfortunate reality is that in Ontario there are very few hydro-electric dams with sufficient energy storage for balancing wind generation. The cost of interconnecting the Ontario and Quebec electricity grids to allow use of available energy storge in Quebec should not be underestimated. This issue places a hard limit on the total amount of unconstrained wind generation that the Ontario electricity grid can accept.

Due to the cost of the required additional hydraulic generation, hydraulic energy storage and transmission facilities for filtering wind generation it is less expensive for Ontario to build new nuclear generation than to build more wind generation for meeting new electricity load in southern Ontario.

There are special cases in which wind generation might be more economic than nuclear generation. For the special case of a remote community in northern Ontario in which size matched wind generation and hydraulic generation with sufficient energy storage are located within the same local distribution system then the cost of transmission is zero, the transmission loss is zero and the energy storage is local. Under these special circumstances, if the hydraulic generation is average water flow constrained but is not storage constrained, the cost of incremental wind energy may be less than the cost of distant nuclear generation.

Another special case for wind generation is when a size matched wind turbine, small bio-methanol plant and conventional small electricity load all co-exist on the same property so there is no need to feed power to the grid or to invest in other forms of energy storage. If half of the wind turbine output can be fed behind the meter of the conventional load to displace $.20 / kWh electricity otherwise drawn from the grid, then the cost $X / kWh of the remaining power for generating electrolytic hydrogen is given by:
[($X / kWh) + ($.20 / kWh)] / 2 = $.115 / kWh
$X / kWh = $.03 / kWh

When these special circumstances apply there is an opportunity for economic application for wind power.

This web page last updated March 7, 2016.

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