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

Math lesson # 2 for Bob Chiarelli—Calculating the cost per megawatt hour of Ontario’s power

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



Bob knows everything. Just ask him. He even knows more than the Auditor General.

Pat Cusack

Be prepared. He’s a slow learner. Recommend moving him to special ed.

Andre Lauzon

WOW, thanks again Mr. Gallant.
I can understand your math so Chiarelli should be capable of doing it, or at least have someone from his family circle or dept. explain it to him.
Having digested this message, if he has a tiny bit of moral integrity, he should resign his job as a member of this Gov’t.

Leda Millar

I ditto what Andre Lauzon commented.. However I have come to realize that through the years and there are many, no one in Polictics is honest it was said many years ago has to be a CROOK to be a Polictian, they very rarely tell you truth, they lie before an election ,,tell you what they want you to Hear, and then the rules change, TRUTH — FICTION –equals. LIES.that is the Liberal Balance Sheet. Just saying.

Bob Lyman

Parker, This is very useful analysis but there are a few things I don’t follow. I can see the usefulness of adding to the costs of generation the costs of distribution (which I have never seen split out that way), but why not add in the costs of transmission as well? I am also perplexed as to why the cost of transmission for wind and solar is so low. Is it because we cannot accurately attribute the transmission costs to these sources, despite the many kilometres of transmission lines needed to connect these distant generation sources to the grid? Is it because, especially in the case of solar, much of the generation is “embedded” in the distribution systems’ costs, not in the costs monitored by IESO? Similarly, does it really make sense to attribute the cost of curtailment of nuclear energy generation to nuclear when the curtailment would not even arise if it were not for the surplus of wind and solar generation and the “first-to-the-grid” rights that these high cost generation sources enjoy? I would suggest that the costs of curtailment should all be attributed pro rata to wind and solar. That, of course, makes them even ore expensive and more of a bad idea.

Parker Gallant

Bob, The “Transmission TX” is referencing only the power that IESO agreed was generated from the power source and doesn’t include the “costs of transmission” which is generally levied by Hydro One (they hold a virtual monopoly). Likewise the “Distribution DX” is what IESO have agreed is to be paid for “embedded generation” as reported by the LDC where the embedded generation is located. Scott’s chart and the numbers contained are strictly for the cost of the generation from the power source without either the resulting transmission costs (now included in the “delivery” line on your bill) or local distribution charges from your local distributor in which you are also charged for line losses.

Scott Luft

Bob, I’m inspired by your economist’s comments to write a bit of a response with some links I think you may find of interest, and worthy of exploration.

First off, I hope Parker’s explained Dx (for distribution) is meant here as generation that is not part of the IESO’s reporting on Transmission connect generators, but embedded in distribution networks. I try to demonstrate in my last post at my own blog, “2015 Ontario Electricity Data Summary Part 2: component costs, and cost shifting”.

More importantly, for an economist, are your correct comments about not attributing the cost of curtailment to the curtailed source.
In July 2011 Benjamin Dachis and Donald Dewees wrote a short paper: “Plugging into Savings: A New Incentive-Based Market Can Address Ontario’s Power-Surplus Problem”
The IESO explained its typical ostrich-type response in this January 2012 paper (
It’s a sophisticated topic, but an important one. The curtailment I can’t estimate much of is hydro and OPG seems to me to be reporting about 10% of production being curtailed. They may get paid 4 cents for that curtailment, which is required because we pay much more for other source we commit to. Certainly that spillage isn’t a cost of hydro, and the cost of that surplus is far higher than whatever is paid for the curtailed hydro (similar for nuclear).


Chiarelli has no moral integrity. He will not resign. Chiarelli knows exactly what he’s doing. It’s surprising how many people can’t be bothered-or maybe just arent capable to think at a higher level and figure things out for themselves.
Chiarelli is misleading, disgusting. I expect much more from a person in his position.
Our government is guilty of stealing billions of dollars from the people of Ontario. This must stop. Government dignitaries must be held accountable.
A person at such a level of responsibility and power knows better than to perform shoddily, illegally. Therefore penalties need to be much more severe. This may be a step to straighten out the corruption evident in our government.
We can point fingers and make accusations of all parties. The Liberals, by far, take the cake.

R Budd

Thanks again for this Parker and Scott. We’re lucky to have this information. It boggles that the Liberals can continue to intentionally sabotage the system at the expense of both the economy and environment.
What will it take for news providers like the Star and the CBC to be shamed out of their willful ignorance of what is happening in Ontario. This “cloak of green” hides much right now.

Bob Lyman

Parker and Scott, Thanks for your additional comments and clarifications. There is one other notable point about Scott’s tables I would like to confirm or clarify. The quantity of solar energy purchased by IESO on November 12 is listed as 38 MWh plus 2,231 Dx, which I assume to be solar embedded in distribution systems, plus 1 MWh of curtailment for a total of 2,320 MWh. For this, IESO paid $1,101,000, or almost $475 per MWh. Can that be correct?

Scott Luft

yes, that could be correct Bob.
Which is not to say that it is, as it’s an estimate. The “est. curtailed” should be ignored when it’s that small.

The day Parker shows in the report precedes Kinston Solar entering IESO (Tx) generator reporting, so that Tx is one enormous installation (Grand Renewable solar) and embedded (Dx) capacity would have been about 18 times that capacity (1800+ megawatts). My estimates for embedded are based, partly, on IESO estimates, so the relationship of Tx:Dx is not 1:18, but sometimes more and sometimes less.

That is a very low solar day.
The Auditor’s report showed 2014 solar generation as 1.8 TWh (million megawatt-hours), and that $475 pricing I use should be from the OEB/Navigant RPP price reporting. These are firm data sources, and my math puts that cost in 2014 at $2.34 million a day.
I suspect 2015 was about 50% higher, so average is $3.5 millionish each day

I produced a report for one of the higher priced days for lowly “Class B” consumers, which was a sunny and windy weekend day in April:

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