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Re-posted from Wind Concerns Ontario with permission

Math lesson on power costs for Minister Bob Chiarelli: Parker Gallant

Don't despair Mr Chiarelli: Parker Gallant explains it all nice and slow
Don’t despair Mr Chiarelli: Parker Gallant explains it all nice and slow

January 5, 2016

Open “Tongue in cheek” letter to:

The Honourable Bob Chiarelli, Minister of Energy, Queen’s Park, Toronto
Dear Minister Chiarelli:

First, I hope you and your family had a Merry Christmas and a Happy New Year.

Second, I hope you found the time to make it through the exercises I described in my recent letter so you now understand the difference between “profit” and “loss” in respect to the energy portfolio.

With that behind you, I believe it’s time for a second math lesson. We will again use the chart for November 12th, 2015 prepared by my friend Scott Luft. See below.

This lesson is focused on allowing you to understand how the cost per megawatt hour (MWh) by generating source can be calculated using the chart Scott prepared versus the IESO daily summary which is not at all as transparent as Scott’s.

Let’s start! Note the second portion of the chart with the subject line “IESO Transmission (Tx)”.  The first heading “Nuclear” is a reflection of the generation source and on this day it provided 58.1% of all generation.  How to get that calculation is simple.  Look at the first line; add the “Ontario” column of the generation of 429,668 MWh to the 2nd line “est. Distribution (Dx)1. giving you 447,177 MWh. Divide it into Nuclear total of 259,444 MWh and you get 58%!  Including curtailed it becomes 61.8%.

Now let’s calculate the cost of each megawatt hour of Nuclear generation. We will include “est. Curtailed” in our calculations as it is generation that could have been delivered, but because IESO was concerned with the grid crashing it was “curtailed” i.e., not produced.  Bruce Nuclear has the ability to “steam off” and that is what they were told to do, because wind/solar was generating too much power at a particular point in the day. Now the total of nuclear generation plus the curtailed (steamed off) nuclear is 276,301 MWh and that should be divided into the last line “Cost ($000s)” of $18.062 million —which demonstrates each MWh of nuclear cost $65.37/MWh.   Still with me, I hope!

OK, so let’s calculate the cost per MWh for hydro: that was 86,965 MWh + est. Distribution (Dx) of 1,867 MWh and curtailed (spilled) of 208 MWh for a total of 89,040 MWh. Divide that into the “Cost” of $4.671 million and you will see the cost per MWh was $52.46.  Hydro contributed 20.2% of Ontario’s total generation (ignoring curtailed generation) this day, so combined with nuclear those two sources generated or curtailed/steamed off 78.2% (365,341 MWh) of all electricity generated in the province, and 100.4% of total Ontario demand (refer IESO daily summary) of 363,960 MWh.

Hope you are paying attention Bob. Here’s why: our exercise up to now doesn’t include generation from wind, solar, gas, biomass or biofuel sources, yet they were were completely CO 2 free!   Worth pondering, eh?

Now, time to look at costs of those other sources of generation. Let’s start with gas and its role in providing “peaking power”!  On this day, gas provided 5.5% of Ontario generation (including “est. Distribution (Dx).”  The calculation: 24,511 MWh divided by 447,177 MWh = 5.5%.  The cost of those megawatt hours is simply: divide the “Cost” of $5.360 million by 24,511 MWh, giving a shocking total of $218.68/MWh!

Contracting for gas plants is to back up wind and solar generation when the wind doesn’t blow and the sun doesn’t shine!

Here is an example that requires some math calculation so read this carefully before trying the calculations. Specifically let’s review  the TransCanada 900-MW gas plant (planned but canceled) for Oakville (most of the $1.1 billion cost) and moved to Bath!  The OPA contract (negotiated by the OPA) will pay them $15,000 per MW per month to be “at the ready.” The annual cost of the 900 MW is $162 million (900 MW X $15,000 X 12 = $162 million).

Bob, what the foregoing means is that if that plant produced just one (1) megawatt hour of electricity in a year, the cost would be $162 million.

Now let’s do a “what if” exercise: assume it will operate at 10% of rated capacity of 900 MW which means it will produce 788,400 MWh (10% X 900 MW X 8760 [hours in a year] = 788,400 MWh).  Actual generation costs from the gas peaking plants are based on the cost of the natural gas fuel plus a small mark-up but we will ignore those latter two costs in the next calculation just to keep it simple.  Here we go: if you divide the annual cost of $162 million by 788,400 MWh, your answer should be $205.50/MWh.  Pretty expensive, eh?

The requirement to back up industrial wind turbines is old news as noted in a Memorandum submitted to the U.K. Parliament which stated:  “Dr Paul Golby CEO of E.On UK, says 90% whilst Mr Rupert Steele of Scottish Power says, “Thirty Gigawatts of wind maybe requires twenty-five GW of backup.”  In other words, that means, if you contract for 1,000 MW of industrial wind generation you need a 900 MW gas plant to “back-up” its capacity!

So, doing math is important: you can see that you are almost doubling up on the cost of producing a single MWh of electricity.

That brings us to the actual cost of wind generation on the chosen day in November.

On November 12, 2015 (refer to Scott Luft’s chart) wind produced 63,203 MWh, i.e., the lines “IESO Transmission (Tx)” + “est. Distribution (Dx)” equals 63,203 MWh. On this day wind produced 14.1% of Ontario’s generation at a cost of $153.55/MWh (based on the calculations applied above) —or at least this is what one would assume.  That is an assumption you shouldn’t make though, Bob, and I will try to explain why.  Adding curtailed wind production (13,500 MWh) to the 63,203 MWh produced would reduce the per MWh cost to $126.52/MWh, but, and it’s a big but—it doesn’t include gas back-up costs.   Now pay attention!

The outstanding contracts for gas generation total about 9,000 MW of capacity and the contracts guarantee them (including the 2,100 MW of  Lennox owned by OPG) a monthly price similar to the TransCanada contract mentioned above.   So, knowing that, let’s assume the “average” contracted price is only $10,000 per MW per month.  Bearing that in mind the backup for wind (solar to a lessor extent) is costing Ontario ratepayers $1.080 billion annually to be on “standby”!  In other words, if they produced one (1) MWh in a year the cost would be $1,080,000,000.   Shocking eh?  If operated at 100% of rated capacity (which they can’t) they would produce almost 79 TWh (terawatts2.) or over 50% (9,000 MW X 8760 hours in a year) of Ontario’s annual consumption.

OK, now back to Scott’s chart of November 12 and let’s figure out the full cost. On November 12, gas generators operated at around 11.3% of capacity (79 TWh divided by 365 days in a year = 216,438 MWh and 24,511 MWh divided by 216,438 MWh = 11.3%).  The cost of that day’s gas generation combined with wind generation would be $171.75/MWh, i.e., combined cost of $15,065,000 divided by combined generation of 87,714 MWh (ignore the curtailed generation) = $171.75/MWh.  Now that cost coupled with the losses of $7.9 million from our exports of 74,352 MWh (cost of $108 per/MWh3.) Nov. 12th, produces a combined cost of $279.75/MWh or 4.3 times the cost of nuclear generation.

At this point, Bob, I hope you have grasped the math so I won’t go through the exercise for Scott’s other headings of biofuel, solar etc. I will leave you to work those out on your own.

I certainly hope this exercise gives you sufficient math skills to at least understand the basic steps you should go through before making either rash remarks or issuing directives to IESO telling them what to do. Instead perhaps you could instruct them to produce information similar to what Scott Luft produces.  The latter would also back up your leader’s wishes or intent to be “transparent” for the taxpayers and voters in Ontario.

Good luck with the math exercises and with demonstrating your Ministry’s intention to become more transparent.


©Parker Gallant

  1. Distribution (Dx) reflects the generation sources (principally small wind and solar) hooked up directly to local distribution companies (LDC).
  2. One Terawatt hour is equal to 1,000,000 MWh.
  3. Refer letter of November 17, 2015.
(C) Scott Luft
(C) Scott Luft