Niagara Hydropower Model Evaluation Summary
Jacob Bruxer
Two models were available and compared. These included the 2005 model, which was used in the Lake
Ontario study, and the latest version of the SVM being used in the IUGLS. The 2005 model uses a
quarter monthly time step, whereas the SVM uses a monthly time step. The following quarter monthly
and monthly average values are provided as inputs to the model:
o
o
o
Lake Ontario water level
Lake Ontario outflow
Lake Erie outflow
The Lake Ontario outflow is unnecessary for this analysis. The model determines from the total Lake
Erie outflow the flow available for power production at Ontario Power Generation (OPG) Sir Adam Beck
(SAB) I and II and the New York Power Authority (NYPA) Robert Moses (RM) power plants. This process
proceeds as follows:
[1] The OPG DeCew flow (on the Welland Canal) is assumed to be a constant 195.39 cms (6900 cfs).
In reality it varies, but this is probably a satisfactory assumption.
[2] A constant monthly value denoted as “Net Basin” is added to the DeCew flow. The monthly Net
Basin values are as follows (note the sign):
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Net Basin
(cms)
87.78
79.29
99.11
-8.50
-116.10
-127.43
-124.59
-127.43
-118.93
-116.10
-96.28
-33.98
Net Basin
(cfs)
3100
2800
3500
-300
-4100
-4500
-4400
-4500
-4200
-4100
-3400
-1200
It is not entirely clear what this “Net Basin” value means, and neither OPG nor NYPA contacts
could find anything specific related to this parameter. I would think it would at least include
local inflow to the Niagara River, the outflow to the NYSBC, flow for non-power (primarily
navigation) purposes in the Welland Canal, and may also include local inflow to the Welland
Canal and the Twelve Mile Creek basin (including Lake Gibson and Lake Moodie, upstream of
DeCew) that flows through the DeCew plants (though according to Joan Frain at OPG the power
companies do not track or account for these latter flows). Neither OPG nor NYPA could provide
me with information as to what exactly the values mean or where they come from. Rich
Mueller suggested that it was what was called the "River Correction" needed to
translate the Fort Erie table flow to the flow at the Grass Island Pool, which would be
similar to my assumptions. In my opinion, the “Net Basin” values seem too high given
what I assume they include, but without knowing exactly where they come from it is
difficult to make any further conclusions.
(*** Received an e-mail from Joan Frain on Feb 22, 2011, forwarded from John Ching, that
suggested the Net Basin number came from the “Great Lakes Consumptive Use” study by
Burlington Environment Canada under Dough Cuthbert in the early 1980s, and that the number
was the sum of estimated local inflow and consumption. I have not checked this yet, though I
suspect I will still have trouble reproducing the numbers***)
[3] Regardless, these constant monthly “Net Basin” values appear to be a simplification to
determine the total flow that reaches the Chippawa-Grass Island Pool (CGIP). The combined
DeCew and “Net Basin” flow is subtracted from the total Lake Erie outflow to determine what is
denoted as the Niagara Flow, which should be the flow at the CGIP, and it is this flow that is
apportioned between Niagara Falls flow requirements (indicated as “Scenic Flow” in the model)
and the flow diverted to the Niagara River SAB I and II and RM hydropower plants
[4] The “Scenic Flows” are given in the model as constant monthly values based on the Niagara
Treaty requirements. The Treaty Falls flow requirements can be summarized as follows:
o During tourist hours, which are 8 a.m. to 10 p.m. from April 1st to September 15th
inclusive, and 8 a.m. to 8 p.m. from September 16th to October 31st inclusive,
hydropower companies must ensure that no less than 2,832 m3/s (100,000 ft3/s) passes
over Niagara Falls
o During all other non-tourist hours, including night-time flows during the tourist season
and all hours from November 1st to March 31st inclusive, the hydropower companies
must ensure that no less than 1,416 m3/s (50,000 ft3/s) flows over the Falls.
o These are the minimum amounts required by the Treaty, but the actual amount varies
depending on existing river conditions.
These requirements were included in the modelled “Scenic Flow” with the addition of a 17 cms
(600 cfs) “cushion” that is used operationally by the hydropower companies (Note: this cushion
is for operational purposes only and may not be necessary in the model). Lastly, I checked the
“Scenic Flow” values and noted that they were incorrect for the month of March for both the
Lake Ontario version and the latest SVM version of the model. I notified Yin Fan and she made
the required modifications.
[5] The remainder of the Niagara Flow (assumed at the CGIP, see [3] above) minus the “Scenic
Flow” (see [4] above) is divided between the two countries, Canada (represented by OPG) and
the US (represented by NYPA), and diverted to the hydropower plants downstream. In
allocating the allowable diversion of the remaining water between the two countries, a total
assumed diversion of 141.6 cms (5000 cfs) that is diverted into Lake Superior from Long
Lac/Ogoki (LLO) is attributed to Canada and included in its share. The remainder of the total
water available for power is divided evenly between the two countries. As it exists today, the
total water available for power (𝑃𝑇𝑜𝑡𝑎𝑙 ) can be given as:
𝑃𝑇𝑜𝑡𝑎𝑙 = 𝑃𝑆𝐴𝐵𝐼&𝐼𝐼 +𝑃𝑅𝑀 +𝑃𝐷𝐶 = 𝑂𝐸𝑟𝑖𝑒 − 𝑁𝑀𝑂𝑀 − 𝑊𝐶𝑁𝑜𝑛𝑃 + 𝑅𝐿𝑜𝑐𝑎𝑙 − 𝐷𝑁𝑌𝑆𝐵𝐶
(Eq. 1)
where 𝑃𝑆𝐴𝐵𝐼&𝐼𝐼 is the flow diverted to OPG SAB I and II; 𝑃𝑅𝑀 is the flow diverted to NYPA RM;
𝑃𝐷𝐶 is the flow diverted to OPG DeCew; 𝑂𝐸𝑟𝑖𝑒 is the total Lake Erie outflow, which includes the
LLO diversion; 𝑁𝑀𝑂𝑀 is the total flow over Niagara Falls through the MOM pool; 𝑊𝐶𝑁𝑜𝑛𝑃 is the
non-power related flow through the Welland Canal; 𝑅𝐿𝑜𝑐𝑎𝑙 is the local runoff to the Niagara
River (and possibly the Welland Canal and Twelve Mile Creek); and 𝐷𝑁𝑌𝑆𝐵𝐶 is the diversion to
the New York State Barge Canal (NYSBC). Then, the flow allocated to Canada (OPG) and the US
(NYPA), including the LLO diversion, can be determined as:
𝑃𝑇𝑜𝑡𝑎𝑙 −𝐿𝐿𝑂
)
2
𝑂𝑃𝐺=𝑃𝑆𝐴𝐵𝐼&𝐼𝐼 +𝑃𝐷𝐶 = 𝐿𝐿𝑂 + (
(Eq. 2)
𝑃𝑇𝑜𝑡𝑎𝑙 −𝐿𝐿𝑂
)
2
𝑁𝑌𝑃𝐴= 𝑃𝑅𝑀 = (
(Eq. 3)
Substituting 𝑃𝑇𝑜𝑡𝑎𝑙 into the above equations gives:
𝑂𝐸𝑟𝑖𝑒 −𝑁𝑀𝑂𝑀 −𝑊𝐶𝑁𝑜𝑛𝑃 +𝑅𝐿𝑜𝑐𝑎𝑙 −𝐷𝑁𝑌𝑆𝐵𝐶 −𝐿𝐿𝑂
)
2
𝑃𝑆𝐴𝐵𝐼&𝐼𝐼 +𝑃𝐷𝐶 = 𝐿𝐿𝑂 + (
𝑂𝐸𝑟𝑖𝑒 −𝑁𝑀𝑂𝑀 −𝑊𝐶𝑁𝑜𝑛𝑃 +𝑅𝐿𝑜𝑐𝑎𝑙 −𝐷𝑁𝑌𝑆𝐵𝐶 −𝐿𝐿𝑂
)
2
𝑃𝑅𝑀 = (
(Eq. 4)
(Eq. 5)
These are the equations for flow available for power for each of the countries as the system
exists today. Equation 4 can be rearranged to solve for SAB I & II specifically by simplifying and
moving LLO inside the brackets, such that:
𝑂𝐸𝑟𝑖𝑒 −𝑁𝑀𝑂𝑀 −𝑊𝐶𝑁𝑜𝑛𝑃 +𝑅𝐿𝑜𝑐𝑎𝑙 −𝐷𝑁𝑌𝑆𝐵𝐶 +𝐿𝐿𝑂
)−
2
𝑃𝑆𝐴𝐵𝐼&𝐼𝐼 = (
𝑃𝐷𝐶
(Eq. 6)
In the 2005 hydropower model, the flow to SAB I & II is determined as:
𝑃𝑆𝐴𝐵𝐼&𝐼𝐼 =
𝑂𝐸𝑟𝑖𝑒 −(𝑃𝐷𝐶 +𝑁𝑒𝑡𝐵𝑎𝑠𝑖𝑛)−𝑁𝑀𝑂𝑀 +(𝐿𝐿𝑂−𝑃𝐷𝐶 )
2
(Eq. 7)
Where 𝑁𝑒𝑡𝐵𝑎𝑠𝑖𝑛 represented the “Net Basin” value discussed in Section [2] above. Simplified,
this equation gives:
𝑂𝐸𝑟𝑖𝑒 −𝑁𝑀𝑂𝑀 −𝑁𝑒𝑡𝐵𝑎𝑠𝑖𝑛+𝐿𝐿𝑂
)−
2
𝑃𝑆𝐴𝐵𝐼&𝐼𝐼 = (
𝑃𝐷𝐶
(Eq. 8)
Equation 8 is the same as Equation 4 if we assume that the 𝑊𝐶𝑁𝑜𝑛𝑃 , 𝑅𝐿𝑜𝑐𝑎𝑙 and 𝐷𝑁𝑌𝑆𝐵𝐶 are
all included in the 𝑁𝑒𝑡𝐵𝑎𝑠𝑖𝑛 value. Similarly, in the 2005 hydropower model the flow to RM is
determined as:
𝑃𝑅𝑀 =
𝑂𝐸𝑟𝑖𝑒 −(𝑃𝐷𝐶 +𝑁𝑒𝑡𝐵𝑎𝑠𝑖𝑛)−𝑁𝑀𝑂𝑀 −(𝐿𝐿𝑂−𝑃𝐷𝐶 )
2
(Eq. 9)
Simplified, this gives:
𝑃𝑅𝑀 =
𝑂𝐸𝑟𝑖𝑒 −𝑁𝑀𝑂𝑀 +𝑁𝑒𝑡𝐵𝑎𝑠𝑖𝑛−𝐿𝐿𝑂
2
(Eq. 10)
Again, this is equivalent to equation 5 if we assume that the 𝑊𝐶𝑁𝑜𝑛𝑃 , 𝑅𝐿𝑜𝑐𝑎𝑙 and 𝐷𝑁𝑌𝑆𝐵𝐶 are
all included in the 𝑁𝑒𝑡𝐵𝑎𝑠𝑖𝑛 value. Therefore, the equations in the 2005 hydropower model
appear to be correct, though there remain questions about the “Net Basin” value as discussed in
Section [2]. Note that the SAB I & II share is incorrectly labeled as the “OPGShare” in the 2005
hydropower model and as the “OPG Flow” in the SVM. In reality, the OPG share also includes
the De Cew flow, which is removed earlier, so in both cases it should be labeled as the OPG SAB
I&II share or flow. Furthermore, in the SVM some further simplifications of the equation have
been made, but the equations are consistent between the 2005 and SVM model; however, I
would suggest returning to the more complete 2005 equations, as they allow the equations to
be more readily understood (for example, in the 2005 model the values for 𝑃𝐷𝐶 and 𝐿𝐿𝑂 are
given specifically as 6900 cfs and 5000 cfs, respectively, whereas in the SVM the net sum of the
two values is given as 1900 cfs, but this makes it more confusing).
[6] The tail water (TW) elevation at each of the hydropower plants must also be determined. There
are two equations used in the hydropower model to do this, one for SAB and one for RM.
According to Joan Frain (OPG), Rich Mueller (NYPA) and other documents received, both
equations are derived from analysis of water level and flow data; however, there doesn’t appear
to have been any coordination of the methods used, and as a result the TW equations and
results are quite different for the two plants.
For the OPG TW, Joan Frain informed me that for the Beck1 and Beck2 tailwater levels as
functions of Lake Ontario level and Niagara River flow at Queenston, data were provided by the
former OH Geotechnical and Hydraulic Engineering Department (DWG.No.210-A-1004, April 26,
1963; DWG.No.210-A-1089, September 19, 1967. Note: these drawings were not provided).
According to Joan, cubic polynomial equations were fit to the data. Joan also provided a plot
showing this analysis, which is also shown below. In this plot, QF indicates the Niagara River
flow at Queenston, which in the model is represented by the Niagara Flow at the CGIP. It is not
entirely clear what the QNF indicates, but the relationship QNF = QF – 140 kcfs includes an
assumption that QNF is a constant 140,000 cfs (3964 cms) less than QF, so my guess would be
that QNF is the Niagara Falls flow with an assumed constant hydropower diversion of
140,000 cfs removed from the total flow at Queenston.
The plot shows relationships developed for Lake Ontario elevations of 246 feet and 244 feet for
both SAB I (B1) and SAB II (B2). The datum is indicated as IGLD Datum, but no date is given.
However, the equations are also referenced in an e-mail string that David Fay forwarded to me.
In that e-mail, it also is indicated that the elevations are in IGLD 1955. It does not appear that
the elevations have been updated to IGLD 85 in either the 2005 model or the SVM.
Furthermore, in the models themselves, TW elevations are interpolated between 244 and 246
feet using the equation:
𝑇𝑊𝑋 − 𝑇𝑊244 𝑇𝑊246 − 𝑇𝑊244
=
𝑊𝐿𝐿𝑂𝑛𝑡 − 244
246 − 244
Which can be simplified to and solved for the TW at elevation x as:
𝑇𝑊𝑋 = 𝑇𝑊244 +
(𝑊𝐿𝐿𝑂𝑛𝑡 − 244)(𝑇𝑊246 − 𝑇𝑊244 )
2
This is the equation used in the models. However, only the Beck II relationships are used to
determine the TW elevation. The Beck I relationships shown in the plot above are not included.
This may be a simplification, but the plot shows that the TW elevations of the two plants are
quite different. In comparison of different regulation plans this might not be a significant
concern, but it’s worth noting. Probably of more concern is the IGLD datum issue, and whether
that is significant.
For the NYPA TW, Rich Mueller told me that he developed the relationship from a regression
analysis of historic data of the Niagara River CGIP flow and the level of Lake Ontario. Rich also
stated specifically that the equations are compatible with IGLD 85 elevations.
A comparison of the TW elevations computed for the two plants show that the NYPA TW is
higher than the OPG TW. This is to be expected since the NYPA plant is located upstream.
However, using the 2005 model for example, the differences range from 0.15 to 0.76 metres,
with the average difference being 0.57 metres. I’m not sure how much of a drop there is in this
part of the Niagara River, so it’s hard to say whether this large a difference is realistic, but
what’s more concerning is that the variability in the differences seems high to me. My gut
feeling tells me that the difference between the TW elevations shouldn’t have that much
variability. This could probably be confirmed if the data were obtained, but this was not
pursued.
[7] Once flow allocations and TW elevations are determined, the power generated by each
plant (in MW) is then estimated by using two different simplified equations.
For the OPG SAB I & II plants, the flow is determined as the minimum of the flow
allocated and the maximum diversion capacity. The maximum capacity was given as
2270 cms. According to Joan Frain, the current capacity of OPG is 1800 cms, and with
completion of the new tunnel currently being built the capacity will increase to
approximately 2300 cms, so the model value seems reasonable long term. After
discussing with Joan, the flow appears to be multiplied by a plant efficiency (which
according to Joan seems high), times a ratio of “heads”. Joan was not sure why the last
part was included, but apparently the first value appears to be based on minimum crossover elevation (converted from feet) minus a given tailwater elevation (which Joan
thought might be based on a long-term Lake Ontario level, but looking at it now it’s the
computed tailwater level from [6] above), while the second one appears to be close to
what OPG refers to as “normal head” (which can be considered an average value).
Basically this ratio appears to me to be another determination of plant efficiency, this
one based on head: when the head difference (which is determined from minimum
forebay, i.e. headwater, minus tailwater) is less than the “normal head” the plant
produces less power; when head difference is greater than “normal head” the plant
produces more power. However, looking at the head ratios, they are all very close to
one, and therefore the power produced by the model isn’t very sensitive to changes in
head. Note also that there is no determination of the true headwater elevation, but
rather they use the minimum cross-over elevation. NYPA, on the other hand, estimates
headwater in their model (see below). Joan also noted specifically that because the
equation does not consider individual Beck units, it is a very rough estimate. Also, since
2005, Beck1 G7 has been converted to 60 Hz and G9 has been upgraded, so whatever
they used in 2005 for Beck outputs will not reflect the current configuration.
For the NYPA RM plant, the maximum capacity of 2860 cms was confirmed to be correct
by Rich Mueller. Rich explained the power equation as being based on the equation for
converting potential energy of water into electrical energy, that is:
𝑃 = 62.4 ∙ 𝑄 ∙ 𝐻 ∙ 𝑒
Where 𝑃 is generation output; 62.4 is the specific weight of water; 𝑄 is NYPA's treaty
share of the Niagara River flow; 𝐻 is the head across the Robert Moses Plant = Forebay
elevation - Tailwater elevation; 𝑒 is the average efficiency of the Robert Moses Niagara
Power Plant, which was assumed to be 92.1%. The forebay elevation = CGIP elevation
561.5 feet - ( NYPA's treaty share in tcfs "squared" / waterways coefficient 420 ). The
waterways coefficient is a fudge factor for calculating flow through the conduit and is
analogous to a Manning’s roughness coefficient. An average value is about 420. In
addition, a multiplier of 1.356x10-6 is included in the model to convert power from ftlb/sec to megawatts.
[8] The energy (in MWh) is then determined by multiplying the power by the number of hours in a
day and the number of days in a month or quarter month.
Overall Conclusions
Overall, the model is a huge simplification of the actual hydropower production process, which
is as expected, but it also leaves some questions as to the accuracy of the results. Furthermore,
there are some outstanding issues, including what exactly the “Net Basin” values refer to, and
whether the OPG TW elevations referenced to IGLD 55 need to be updated to IGLD 85 and
whether this will affect the results. Therefore, currently I’d be wary about reading too much
into the model results.
From Len: IESO determines OPG power generation on the Niagara River; there is a similar organization
in the US apparently. Basically, the IESO decides how much power should be produced in Ontario, and
then the hydro companies bid on the power generation based on what is needed at the time. Niagara is
not baseload power. Unclear what is done at the Soo and St. Lawrence Rivers. See www.ieso.ca
With this in mind, it might not be possible to relate daily or even monthly or longer flows and levels to
power generation. Power generated fluctuates often throughout the day (every 5 minutes??) and is
based among other things on the power demand and the amount awarded to OPG by the IESO. Perhaps
on an annual basis some of these fluctuations average out, but this needs to be checked.