An Alberta-British Columbia Electricity Grid Model

by

Tianyang (David) Zhang Bachelor of Science, University of Victoria, 2017

An Extended Essay Submitted in Partial Fulfillment of the Requirements for the Degree of

MASTER OF ARTS in the Department of Economics

We accept this extended essay as conforming to the required standard

Dr. G. Cornelis van Kooten, Supervisor (Department of Economics)

Dr. Fatemeh Mokhtarzadeh, Member (Department of Economics)

© Tianyang (David) Zhang, 2020 University of Victoria

All rights reserved. This extended essay may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author.

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Abstract

British Columbia (BC) and Alberta (AB) have different asset mixes for generating electricity. While BC relies primarily on hydropower, AB generates its power from various sources, but primarily fossil fuels. Although both provinces currently work independently from one another due to ideological and political disagreements, one might be curious about what would happen if both provinces work together. In this research project, we introduce an integrated electricity grid model of BC and AB, based on two stand-alone grid allocation models of each province. After introducing each model, we conduct various case studies of the integrated model to address some popular topics in the economics of electricity grids, such as a carbon tax, renewable energy, and nuclear power.

Key words: grid allocation model; renewable energy; hydroelectricity

Acknowledgements

The author’s sincerest gratitude goes to Dr. van Kooten, Jon Duan and Ms. Voss for their help on this project. He also wants to thank his parents and friends for their physical and emotional support through his seven years of journey at UVic.

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Table of Contents 1. Introduction ...... 4

2. British Columbia’s Electricity System ...... 6

2.1 British Columbia Grid Allocation Model ...... 9

2.2 Reservoir Operation ...... 11

2.3 Power Generation ...... 13

2.4. Upstream and Downstream Connections ...... 14

3. Alberta Electricity System ...... 14

3.1 Alberta Grid Allocation Model ...... 18

3.2 Hydroelectricity Generation in AB ...... 21

3.3 Thermal Generator Operation ...... 21

3.4. Wind Operation ...... 22

4. Transmission Interties ...... 23

5. An Integrated Alberta-British Columbia Grid Model ...... 24

6. Data Sources ...... 24

7. Results and Sensitivity Analyses ...... 26

8. Conclusions ...... 33

9. References ...... 36

Appendix 1. Hydro Data for BC ...... 39

Appendix 2. GAMS CODE ...... 40

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1. INTRODUCTION

British Columbia relies primarily on hydroelectricity for its power needs, which makes it hard to reform its electrical generating system so as to reduce carbon dioxide (CO2) emissions. Contrarily,

Alberta generates electricity from a variety of generating assets, including primarily fossil fuel assets, which enables the Alberta grid operator more flexibility to expand or contract production from some of its generators, at least in the longer run (Canadian Energy Research Institute, 2018).

In particular, because Alberta relies heavily on fossil fuels for the generation of electricity, it has a broader scope to integrate renewable forms of energy into its generation composition, particularly solar and wind, thereby reducing CO2 emissions. In theory, it is more difficult for BC to bring in renewable sources because wind and solar energy might replace hydroelectric generation, thereby leaving CO2 emissions unchanged. Nonetheless, the two provinces can work together to lower overall CO2 emissions. Alberta can replace its fossil-fuel generators by wind and solar energy. At the same time, BC’s hydroelectric reservoirs can store excess electricity produced in Alberta against times when Alberta’s solar and wind production is low. Since Alberta has more sites and greater capacity potential for solar and wind energy, the province can utilize this advantage to reform its power-generation system, while using BC’s reservoirs as a battery to store excess energy (McWilliam, van Kooten, & Crawford, 2012; van Kooten, 2016; van Kooten &

Mokhtarzadeh, 2019). Currently, the Alberta and BC electricity grids operate independent of one another, but trade when necessary. Exchanges of power are made along extant transmission interties.

Our project is based on two stand-alone grid allocation models, each representing one province. Each model describes the electricity generating system of a province and its trade with

Page | 4 the other and the United States (U.S.).1 While each model is stand alone, they can also be integrated so that non-dispatchable renewable energy generated in AB can be stored in reservoirs behind hydroelectric dams in BC, thereby reducing the costs of ramping output from thermal power plants in Alberta to accommodate intermittent wind and solar sources of electricity. Energy stored in BC can then be used in peak times to facilitate load requirements in both provinces at the least cost.

By using BC’s storage facilities, Alberta can integrate wind and solar energy to a greater extent, thereby reducing CO2 emissions by lowering the need for thermal power plants. Electricity operators also have less need to run thermal generators at less-than-potential levels in the case of lower generation from wind and solar, thereby also lowering CO2 emissions.

The integrated AB-BC grid model aims to maximize the aggregate net revenue to the operators of the two electricity grids. It is expressed as:

Z = ZBC + ZAB (1) where Z refers to the total net revenue accruing to the grid operators and consisting of the sum of benefits to the individual provinces.2 Both provinces trade with the U.S. and with each other. From a social planner’s point of view, any import and export payments between AB and BC constitute transfers and do not affect the management of the grids. Therefore, the objective function can be interpreted as the net revenue accruing to BC and AB minus any payments to the U.S. for imported power.

The rest of this paper is organized as follows. The independent BC and Alberta grid models are introduced in sections 2 and 3, respectively. Sections 4 and 5 provide details on transmission

1 A minor transmission intertie exists between Alberta and Saskatchewan; although discussed below, exchanges of power between these provinces are assumed to be insignificant. 2 Rather than net revenue, it is more appropriate to refer to Z as the gross margin because it does not include all of the costs incurred by the system operators. For example, costs related to ancillary services are ignored, such as spinning reserves and other backup resources. Page | 5 interties and the integrated model, which links the two independent models together. Section 6 introduces the sources of data used in the model. Section 7 presents various runs of the model and discusses the results. Finally, Section 8 provides concluding remarks and acknowledges problems with the current version of the model.

2. BRITISH COLUMBIA’S ELECTRICITY SYSTEM

British Columbia has vast hydraulic resources for generating electricity. Table 1 provides a breakdown of BC’s power generation in 2017. Hydropower and biomass are the main generation sources, but hydro’s share is larger at 90%. In 2016, 96.5% of generating capacity consisted of renewables, which included biomass and wind sources in addition to hydropower; 98.4% of electricity generated in the province in 2016 came from renewable sources, with 88.0% from hydraulics (National Energy Board, 2017). For 2018, BC’s peak hourly load of 10,490 MW occurred at around 6 pm on January 2, with the smallest load of 5,033 MW occurring June 14 at about 6 am(both in pacific time). BC’s load duration curve for 2018 is depicted in Figure 1. During

2018, the hourly load varied by some 5,480 MW, or by more than 52% of peak load; 5,033MW is the lowest load, constituting the province’s baseload. Unlike Alberta, where coal and combined- cycle natural gas plants are used to satisfy peak load, British Columbia relies on hydro resources, which are also used to cover more than just baseload requirements.

Table 1: British Columbia Electricity System, Capacity and Generation, 2017 Resource Type Capacity (MW) Generation (GWh) Shares (%) Natural Gas 1371 1,528 2.0 Hydro 15,817 68,471 89.6 Wind 698 1,015 1.3 Biogas & Biomass 1,151 4,584 6.0 Oil/diesel 265 808 1.1 Total 19,302 76,406 100 Source: National Energy Board (2019a), shares are calculated accordingly.

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10,500

9,500

8,500

7,500

Megawatts (MW) 6,500

5,500

4,500 1 205 409 613 817 1021 1225 1429 1633 1837 2041 2245 2449 2653 2857 3061 3265 3469 3673 3877 4081 4285 4489 4693 4897 5101 5305 5509 5713 5917 6121 6325 6529 6733 6937 7141 7345 7549 7753 7957 8161 8365 8569 Hours Figure 1: Load Duration Curve, British Columbia, 2018. Data from BC Hydro (2018b).

British Columbia exchanges electricity with its primary trading partners (the U.S. and AB) along transmission interties. Each intertie has a capacity that is, due to political constraints, often under-utilized. Figures 2 and 3 provide an overview of BC’s trade with the U.S. and AB since

1998. BC’s trade balance oscillated around zero before 2014. High surpluses took place before

2000, and extreme deficits occurred in 2006 and 2010. A three-year stream of surpluses occurred in 2015-2017, followed by a slight deficit in 2018. BC was a net exporter in 11 out of 21 years, eight of which happened before 2014. In total, BC exported 13.1 TWh more than it imported, which implies an annual surplus of 621.4 GWh; this annual surplus becomes negative once we exclude the trade surplus in 2015-2017. Concerning Alberta, BC was a net exporter 18 out of 21 years, with a total surplus of 16.8 TWh, which averages to 798.4 GWh per year.

The period 2000-2001 was unique for BC because negative balances occurred in its trades with both the U.S. and AB. Specifically, BC’s trade deficits in 2001 were 1.92 TWh with the U.S.

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15.0 350.0 Exports Imports Balance Price (right scale) 300.0 10.0 250.0

5.0 200.0

150.0 0.0 Trade (TWh) Trade Price Price ($/MWh)

100.0 -5.0 50.0

-10.0 0.0 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Figure 2: BC Electricity Trade with the United States and Value of Exports, 1998-2018. Data from BC Stats (2018a, 2018b). Prices are calculated by dividing trade volumes by trade quantities.

3.5 Exports Imports Balance 3.0

2.5

2.0

1.5

1.0

0.5 Trade (TWh) Trade

0.0

-0.5

-1.0

-1.5 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Figure 3: BC Electricity Trade with Alberta, 1998-2018. Data from BC Stats (2018a).

Page | 8 and 1.39 TWh with AB. This might be because of a supply shortage in BC which increases its demand of imports and raises the prices of electricity.

2.1 British Columbia Grid Allocation Model

The BC grid allocation model focuses extensively on hydropower generation from two types of generators: large dams and run-of-river assets, which include dams with reservoirs but without significant storage. Hydraulic assets generate electricity by moving water through turbines. Large hydroelectric dams store water and thereby energy; importantly, system operators can control the flow of water through the turbines and thereby the production of electricity – electricity is therefore considered to be dispatchable. Run-of-river facilities are assumed not to store water so that electricity is not dispatchable – the electricity must be used when it is generated, although power from any thermal or renewable source can be sent to storage. Run-of-river assets are not able to generate the same levels of output as large dams, but they generally have less environmental impacts as well (Energy BC, 2017).

The only large dams found in BC are on the Peace River and the Columbia River. The

Shrum generating facility in the Bennett Dam on the Peace River has the largest capacity of any other generating asset in the BC system, and it has the largest reservoir, Williston Lake. The next largest generating station is on the Columbia River – the Mica dam/generator and Kinbasket Lake reservoir. The operations of these dams are modelled so that the water flow through the dams and the associated production of electricity is controlled by the system operator. On the Peace River, there are two downstream generating facilities: the Peace Canyon reservoir and dam, and Site C, which is under construction. On the Columbia River, the Revelstoke reservoir and dam are downstream from the Mica dam and Kinbasket Lake Reservoir.

BC’s aggregate net return is calculated as:

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� ��� = ∑�=1[���,����,� − ∑�(��� + �� + ���)��,� − ∑� ���,���,� + ∑�[(��,� − �)��,� −

(��,� + �)��,�]], � ∈ {Shrum, Mica}, k ∈ {AB, US} (2)

In equation (2), ZBC refers to BC’s net revenue or gross margin ($); i is the set of generators (run- of-river facilities and large dams); k refers to Alberta or the U.S.; r refers to the dams with reservoirs; and t represents the number of hours in a year (8760), with total time T=8760. DBC,t refers to the internal demand of BC consumers that has to be satisfied at each period, while PBC,t refers to the domestic price for BC consumers at time t. The product of demand and price is thus the domestic revenue at time t. OMi is the operating and maintenance cost of generator i ($/MWh); bi is the variable fuel cost of electricity production from i ($/MWh), which is assumed to be constant across time throughout the model; τ is the carbon tax rate ($/tCO2), which is the policy variable driving changes in the optimal generation mix; and φi is the CO2 emission from generator i, which is higher for fossil fuels and lower for renewable energy. The second term is thus the total variable cost of electricity generation. Sr,t refers to the amount of water spilled from a reservoir without generating electricity, generally to meet in-stream demand for water. Since in-stream demand is part of the internal demand, the associated revenue must be subtracted from equation

(2). The objective function is summed over 1 to 8760 hours. Pk,t refers to the trade price with BC’s trade partners (the U.S. and Alberta) at time t; and δ is the transmission cost. The trade prices of

AB and the U.S. are constantly changing, while the trade price of BC is assumed to be fixed. Due to the data gap in BC’s hourly price, we assume it to be fixed at $65/MWh, the average export price to the U.S. in 2018 (BC Stats, 2018a, 2018b).

The objective function (2) is maximized subjective to a set of constraints. The most important one is that the total electricity produced in BC, plus imports and minus exports, must equal or exceed the provincial load (demand) at every instant of time:

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∑� ��,� + ∑�∈{��,��}(��,� − ��,�) ≥ ���,� ∀t , (3) where the first term is the total power generation of all generators, the second term is the net import of energy. The total available power, on the left-hand side, must be equal to or greater than the total internal demand.

2.2 Reservoir Operation

Here we explain a set of constraints that describe the hydropower operation of BC. There are two major hydro generation systems with dams and downstream run-of-river facilities. The generation capacity of upstream dams depends on their height, which is affected by active storage, the inflow of water from various sources, and the outflow of water through turbines or spillage. As noted above, only water moving through the turbines contributes to electricity generation. We also assume the absence of a loss factor so that all the outflow of water from the upstream dam is available to use for downstream run-of-river facilities.

We model the hydro generation systems of Kinbasket Lake and Williston Lake. The former includes the Mica Dam and the Revelstoke Dam, and the latter includes the WAC Bennett (Shrum generating facility) Dam, the Peace Canyon Dam, and Site C Dam. Mica and Shrum are the upstream dams, and Revelstoke, and Peace Canyon and Site C are the respective downstream run of river assets. For simplicity and due to lack of data, we assume upstream flows are the only source of water for run-of-river assets. We tentatively assume no water loss due to drought but investigate drought scenarios as part of our sensitivity analysis.

For simplicity, we assume that an upstream reservoir has the shape of a rectangular box.

This makes it easier to calculate the change in height and track the existing generation capacity, which fluctuates with reservoir height, using the inflow and outflow data. Thus, the change in effective height equals the change in volume divided by the surface area of the reservoir. The

Page | 11 change in the volume in each period (ΔVt) is calculated as follows:

ΔVt = Vt – Vt-1 = Qin,t – Qout,t – Qspill,t ∀t, (4) where Qin,t, Qout,t, and Qspill,t are the volumes of water flowing into the reservoir from surrounding rivers and streams, water expelled through the turbine to generate electricity, and water that is spilled for in-stream purposes, respectively. The first term refers to the inflow into upstream reservoirs from various sources, while (Qout,t+ Qspill,t) represents the total outflow at time t, with total outflow constituting inflow into downstream run-of-river turbines. Operators would spill water only to satisfy in-stream use; otherwise, when the reservoir exceeds capacity, water will flow through the turbines with the electricity replacing that produced by another dam or a fossil fuel asset, or exported to the U.S. or Alberta. It is highly unlikely, but not impossible, that there is no demand for electricity and the reservoir is overflowing as its capacity is exceeded. Such scenarios require the operator to spill enough water. This is reflected in equation (5) where Vr,t and Vmax.r represents the current and maximum volume of reservoir r.

Qr,spill,t ≥ Vt,r – VMax,r , ∀t. (5)

The following equation then describes the head height available at any time:

Hr,t = Hr,min – Hr,tail +Vr,t–1/Ar ∀t,r. (6) where Ar is the surface area of reservoir r. The first term is the minimum height of an upstream reservoir, and the second term is the level of tailwater, which equals the maximum height of the downstream river or reservoir; the two terms together represent the inherent difference in heights between the upstream and the downstream reservoir. The change in head height in period t relative to period t–1 depends on the volume of inflow in period t–1. The term Vr,t–1/Ar is thus the change in head height of a reservoir resulting from the inflow in the previous period using a rectangular

Page | 12 volume calculation.

2.3 Power Generation

The formula for hydropower (P) production is as follows:

P = ε ρ g H q, (7) where ε is the unitless efficiency parameter, ρ is the density of water (1,000kg/m3), g is the gravitational acceleration parameter (9.81 m/s2), H is the water height measured in meters, and q is the per second flow rate into the turbine (m3/s). The unit of measurement of P is thus kg ∙ m2 ∙ s–2 ∙ s–1 = J ∙ s–1 = W, where J refers to Joule and W to Watt. Thus, P = 9,810 H q [W].

The total amount of energy (E) generated in time period Δ� is as follows:

E = P × Δt. (8)

Since the flow rate of water is usually measured in seconds, we assume Δt to be in seconds as well.

The energy unit is, therefore, W∙ s (watt-second) and should be divided by 3600 to convert to watt- hour and divided by 1000 to convert to kilowatt-hour (kWh). Therefore, energy generated in hour t is:

Et = 0.002725 ε Qt Ht, ∀t. [kWh] (9)

3 Notice Qt here is the volume of flow through the turbine measured in m . This can be thought of as the product of average discharge per second and the number of seconds in our presumed period.

Thus, we can multiply the product by 3600 to approximate the hourly flow volume and times 24 to approximate the daily flow.

We assume run-of-river dams have an efficiency parameter ɛ=0.9 and that for reservoirs

ɛ=0.83. Since run-of-river assets have constant heights, their output depends on the outflow of dams. For reservoirs, the head height and volume of flow through turbines change constantly.

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According to Loucks and Beek (2017), a linear approximation is often needed to solve complex optimization problems. The product of the unknown terms (QtHt) can be linearized as follows:

0 0 0 0 QtHt ≈ Qt Ht + Ht Qt – Qt Ht , ∀t, (10)

0 0 where �� and �� represent the average values of flow and head height at period t. Loucks and

0 0 Beek recommend running the model several times to get accurate values of �� and �� . In our model, we approximate these values using the historical inflow and head height from BC Hydro.

2.4. Upstream and Downstream Connections

Two equations are included to model the connections between upstream and downstream generators. First, we assume the water that went through the upstream turbines (QTurb,t) and the water spilled (QSpill,t) proceeds instantaneously to downstream run-of-rivers facilities:

Qdown,t = QUPspill,t + QUPturb, t ∀t (11) where Qdown,t represents the inflow into the downstream run-of-river turbines at time t.

The energy generated (E) from downstream generators is thus:

Et = 0.002725 × (QTurb,t,j + QSpill,t,j) × Hj × ε, ∀j, (12) where j represents a run-of-river generator and E is measured in kWh. The heights of run-of-river facilities are assumed fixed at their respective annual average heights.

3. ALBERTA ELECTRICITY SYSTEM

Coal and natural gas are the two dominant sources of electricity in AB, and they together account for 88.1% of AB’s generating capacity and 90.0% of electricity generation in 2018 (Table 2). The remaining 10% was generated from a diverse set of sources, predominantly wind, biomass and hydro, with a tiny part from solar and other sources. Clearly, given that coal accounts for 42.1% of the electricity produced in Alberta, it will be necessary to reduce or eliminate coal-fired power

Page | 14 if the province is to meet federal and provincial climate targets.

Table 2: Alberta Electricity System, Capacity and Generation, 2018 Resource Type Capacity (MW) Generation (GWh) Share (%) Coal 5,723.0 35,631.9 42.1 Natural Gasa 7,516.3 40,591.5 47.9 Hydro 916.4 1,914.2 2.3 Wind 1,474.4 4,196.6 5.0 Biogas & Biomass 419.6 2,033.4 2.4 Solar 15.0 22.4 0.0c Otherb 128.1 339.1 0.4 Total 16,192.8 84,728.9 100 Source: Alberta Utilities Commission (AUC) (2018a, 2018b). Shares calculated accordingly. a Includes cogen of 4,949.1 MW and generation of 32,168.2 GWh, with difference assumed to be produced by peak gas (simple cycle gas plants). b Includes fuel oil and waste heat. c The exact number is 0.02644.

The change in AB’s generation capacity is shown in Figure 4. The system composition remained relatively stable before 2000. After that, natural gas began to take a larger share of power generation, so did hydro, wind, and biomass, although to a lesser extent. While there might be increasing demand for eco-friendly generators from the public, there is no sign of significant decommissioning of coal power plants at the system level, except for the temporary capacity reductions around 2011 and in 2018. The system instead introduced more renewable energy in the recent decade, which lowered the share of coal-generated power.

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16,000.00

14,000.00

12,000.00

10,000.00

8,000.00 Megawatts (MW) Megawatts

6,000.00

4,000.00

2,000.00

0.00

Coal Natural Gas sub total Renewables

Figure 4: AB’s Generation Capacity by Source, 1985-2018. Data from AUC (2018b)

Figure 5 shows Alberta’s load duration curve in 2018. Upon comparing Figure 5 to Figure

1, one finds that Alberta’s load duration curve lies well above that of BC. Alberta’s peak load in

2018 was 11,720 MW and occurred at 6:30 pm on January 11; the minimum load of 7,819 occurred on May 6 at 5 am (both in mountain daylight time). The difference between the peak load and baseload amounted to 3,878 MW (33.2% of peak load) compared to a difference of 5,480 MW

(52%) for the BC grid. This reflects that Alberta’s industrial base is much larger than that of British

Columbia. Further, Alberta residents rely almost exclusively on natural gas to heat their homes, with a much smaller proportion of residents relying on electricity than is the case in BC.

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12,000

11,500

11,000

10,500

10,000

9,500

Megawatts (MW) 9,000

8,500

8,000

7,500 1 205 409 613 817 1021 1225 1429 1633 1837 2041 2245 2449 2653 2857 3061 3265 3469 3673 3877 4081 4285 4489 4693 4897 5101 5305 5509 5713 5917 6121 6325 6529 6733 6937 7141 7345 7549 7753 7957 8161 8365 8569 Hours

Figure 5: Load Duration Curve, Alberta, 2018. Data from AESO (2019).

Finally, Alberta trades electricity with BC, the U.S. (Montana) and Saskatchewan. It trades with BC along an intertie with a rated capacity of 1,200 MW, but, in practice, only at a capacity of 1,000 MW for imports; with Saskatchewan along an intertie rated at 150 MW capacity (153

MW for exports, 75 MW for imports);3 and with the U.S. (Montana) along an intertie rated at 300

MW, although export capacity is slightly higher at 325 MW (Maloney, 2017). For simplicity and due to the insignificance of trade capacity, trade with Saskatchewan is not modelled. Overall, the province imported 2,684 GWh of electricity more in 2018 than it exported. BC accounted for

64.3% of AB’s imports of electricity and 74.2% of exports (Table 3). Assuming the price at which trade took place between the provinces was the same as the average value of exports to the U.S.,

BC profited from interprovincial trade by at least $107.5 million. This profit arises likely because

3 In 2018, the Saskatchewan grid had a capacity of 4,528 MW, with baseload of 1,442 MW and peak capacity of 3,723 MW – a difference of 2,281 MW or 58.2% of baseload power (a greater difference than in BC or Alberta). Of total generating capacity, 33.8% is coal-fired, 40.6% is natural gas, 19.6% is hydraulic, 5.3% is wind, and the remainder is based on waste heat. Page | 17 exports from AB to BC are valued less than imports from BC since exports occur at night when electricity is not intensely demanded, and the import of power occurs at peak hours when prices are high (see Carr, 2018).

Table 3: Alberta Exports and Imports along Interties (GWh), 2018 Interconnections Exports Imports Net Imports British Columbia 542.1 2,196.3 1,654.2 Saskatchewan 144.9 260.5 115.6 Montana 43.6 957.8 914.2 Total 730.7 3,414.7 2,684.0 Source: AESO (2018a, 2018b)

3.1 Alberta Grid Allocation Model

The Alberta grid allocation model has been described by van Kooten et al. (2013, 2016, 2020), and van Kooten and Mokhtarzadeh (2019). In this section, we briefly introduce the model based on its earlier developments. The Alberta Electric System Operator (AESO) is assumed capable of allocating Alberta’s load across generators in the system to maximize the following net revenue

(gross margin) function.

� ��� = ∑�=1[���,��� − ∑�(��� + �� + ���)��,� + ∑�[(��,� − �)��,� − (��,� + �)��,�]] −

∑�(�� − ��)Δ�� , � ∈ {��, ��} (13)

AB’s objective function is constructed in a similar format to that of BC, with the notation of the variables also identical to that in the previous sections. ZAB is the gross margin ($); i refers to the generator source (coal, natural gas, wind, hydro, etc.); T is the number of hours (t) in the one-year time horizon (8760); Dt refers to the load (demand) that has to be met in hour t (MW); Ei,t is the amount of electricity produced by generator i in hour t (MW); OMi is operating and maintenance cost of generator i ($/MWh); and bi is the constant variable fuel cost of producing electricity from

Page | 18 generator i ($/MWh). We define PAB,t to be Alberta’s price ($/MWh) of electricity in each hour, while Pk,t refers to the prices in BC and the U.S., k∈{BC, US}. We implement the same price assumptions as in the BC model, which lets the Alberta and U.S. prices vary hourly and BC price to be fixed at $65/MWh (see section 2.1). Mk,t refers to the amount imported by Alberta from region k∈{BC, US} at t, while Xk,t refers to the amount exported from Alberta to region k; and δ represents the transmission cost ($/MWh).

The first term in square brackets is simply the gross revenue earned by selling electricity in AB, while the second refers to the overall costs of internal power generation. For each generator, the total cost is simply the variable operating & maintenance cost plus fuel cost multiplied by the generator output over the year, with the carbon tax paid by each generator simply treated as a cost.

The carbon tax ($/tCO2) is denoted by τ and assumed to be $50 per tonne of CO2; φi is the CO2 emitted when producing electricity from generation source i and is assumed to be higher for coal power plants. The third term in square brackets refers to the revenue from the sale of exports minus the cost of buying imports, with net exports accounting for the difference between load and internal generation in an hour. The terms in square brackets are then summed over the 8760 hours in a year.

The AB model also has to satisfy the demand constraint. The hourly demand from consumers in AB must be met. This constraint is expressed as:

∑� ��,� + ∑�(��,� − ��,�) ≥ ��, ∀� = 1, … , �, � ∈ {��, ��} , (14) where Ei,t is the total generation, and the second term on the left-hand side is the net import of electricity.

Contrary to BC, AB has the flexibility to adjust its electricity generation system by ramping up and down its generators. The total cost of system capacity reform is captured by the final term in (13), where ai and di refer to the annualized cost of adding or decommissioning assets ($/MW),

Page | 19

Ci refers to the capacity of generating source i (MW), and ∆Ci is thus the capacity added or removed. For wind assets, the change in capacity is measured in the number of wind turbines of a particular capacity that are added (no reduction in numbers is permitted). For simplicity, we assume that all wind turbines are at a capacity of 3.5 MW, at an installation cost of $1,250,000 per

MW. Given that wind energy is non-dispatchable (‘must run’), storage is assumed to be available in each period in neighbouring jurisdictions via transmission interties (whose capacity is limited).

Excess energy can be exported to or retrieved from BC or the U.S. if the AB system cannot respond quickly enough because of extreme variability in wind power output from one period to the next; alternatively, thermal power plants can be forced to reduce or increase output subject to ramping constraints, although this could be costly. Excess intermittent power can be ‘wasted’ by sending energy to a sink or simply preventing turbine blades from turning or darkening solar panels.

Ri is the maximum proportion of the capacity of generator i that can be ramped in a given hour. The change in capacity is reflected in the hourly power generation; thus, we include equations (15) and (16) as the ramping-up/down constraints.

Ei,t – Ei,(t–1) ≤ Ci×Ri, ∀ i,t=2,…,T (15)

Ei,t – Ei,(t–1) ≥ –Ci×Ri, ∀ i,t=2,…,T (16)

AB also faces constraints in trades with its partners (BC and the U.S.), reflected on the transmission intertie capacities; the capacities for imports and exports are different. The maximum capacities of import and export are denoted TRMkt and TRXkt, respectively, with k∈ {��, ��}. The constraints are expressed as.

Mk,t ≤ TRMk,t, ∀ k,t (17)

Xk,t ≤ TRXk,t, ∀ k,t (18)

In any given hour, electricity can only flow in one direction along a transmission intertie. To model

Page | 20 this constraint requires the use of a binary variable for each intertie in the model. To avoid such a nonlinear constraint, we assume that the import and export capacities at any time are equal, and

4 that they equal the total capacity of the line at that time (TRMk,t = TRXk,t = TCAPk,t, ∀k,t). The following linear constraint appears to limit the flow of electricity to one direction:

Xk,t + Mk,t ≤ TCAPk,t, ∀ k,t (19)

Finally, the electricity produced in any generator should not exceed its capacity. At the same time, generation, exports and imports cannot be negative. The capacity and non-negativity constraints are expressed as follows:

Gi,t ≤ Ci, t,i (20)

Gi,t, Mk,t, Xk,t ≥ 0, ∀ t,i,k (21)

3.2 Hydroelectricity Generation in AB

Our initial approach was to model the hydroelectricity generation in Alberta as a single dam with a reservoir since the generators are at much smaller scales compared to BC. Due to the lack of current inflow data, we decided to model hydro generation as a run-of-river facility, subtracting the hydro generation from load according to the hydro data in 2018 (AUC, 2018b).5

3.3 Thermal Generator Operation

Our model includes four types of thermal energy sources in Alberta: coal, biomass, combined- cycle natural gas (NG), which serves baseload needs and is referred to as NG, and open-cycle NG used to address peak load (denoted ‘peak’). Each generator source has an assigned initial capacity that is open to adjustment by the AESO. We assume all generators have the same capacity as in

4 Currently, the capacity of the AB-BC intertie varies in each period due to internal transmission constraints in AB. In both the stand alone and the integrated model, this constraint is assumed not to be an issue. 5 AB’s hydro generation in 2018 was 1914.2 GWh, which is the generation of a 218.5 MW dispatchable generator; this amount is subtracted from the load of each period. Page | 21

Table 2, with the capacities of NG and peak plants to be 4949.1 MW and 2567.2 MW, respectively.

While the above four are the existing generators, nuclear plants are also modelled as a potential generator, since the Alberta Nuclear Consultation Report found a plurality of 45% prefers nuclear plants to be considered on a case-by-case basis (Innovative Research Group, 2009).

Considering the lack of nuclear power, we will discuss this further in the sensitivity analysis.

The post-adjustment capacity of a thermal generator f is expressed as:

��,����� = ��,������� + ∆��, � ∈ {����, �������, ����, ��, �������} (22) where Cf, intial and Cf, final each refers to the generating capacity before and after adjustments from

AECO, and ΔCf,t refers to the capacity added or removed. The construction time for each generator differs. For instance, it takes up to five years to put a coal-fired power plant into operation, and 3.5 years for an NG plant (U.S. Energy Information Administration, 2020; Fickling, 2019).6 To reflect this, we set an hourly ramp-up/down rate for each generator: 1% for nuclear power, 2.5% for coal and biomass, 12.5% for combined-cycle NG, and 100% for a peak plant. Costs are incurred during the expansion and deconstruction of generators. We assume all thermal power plants to have a lifetime of 40 years, during which their construction costs are paid annually (U.S. Energy

Information Administration, 2020). The decommissioning costs of all dispatchable generators are assumed to be one-time payments of $10,000/MW.

3.4. Wind Operation

Wind energy has become popular due to its eco-friendly features and cheap generation costs. AB has great potential for wind energy, especially in the south part of the province (Hastings-Simon,

Dronkers, & Cretney, 2016). Up to December 2019, AB has 38 wind power projects with an installed capacity of 1,685MW (Canadian Wind Energy Association, 2019, 2017). The capacity of

6 These times include construction and regulatory procedures. Page | 22 wind energy depends on the number of turbines and the capacity of each turbine. In our model, the

AESO has the option to adjust the number of wind turbines at the beginning. For simplicity, we assume all turbines are at the capacity of 3.5MW; the initial number of turbines is set at 425, which leads to a capacity slightly higher than the 2018 capacity of 1474 MW. The wind generator capacity is expressed as follows:

Cw = 3.5 (Wbase + Aw). (23) where Cw is the total capacity, Wbase is the initial number of turbines, and Aw is the number of new turbines; in other words, the AESO is not allowed to take down turbines. On the other hand, since there is a limited number of spots for wind energy in Alberta, we set the maximum number of turbines to be 5000. The installation cost of a wind facility is assumed to be $1,250,000 per MW, which is paid evenly over 20 years. The unique nature of wind energy is that its output depends on the turbine height and uncontrollable environmental factors such as wind speed and wind duration; details of our output data are provided in section 6.

4. TRANSMISSION INTERTIES

Electricity trading provides each province with the opportunity to import electricity during peak times and export electricity when there is an energy surplus. The BC-U.S. intertie has a north-to- south capacity of 3150 MW and the south-to-north capacity of 3000 MW, and the BC-AB intertie has a west-to-east capacity of 1200 MW and an east-to-west capacity of 1200 MW (Maloney,

2017). Alberta trades with BC, the U.S. and Saskatchewan, its trade capacity with the U.S. is 325

MW north to south and 300 MW south to north. While electricity trading enables provinces to satisfy their internal demand at lower costs, such opportunities might be exploited to generate profits. Sopinka, van Kooten and Wong(2013) find evidence of BC arbitraging electricity for revenue: importing electricity at a low price and exporting at a high-price. In 2017-2018, BC Hydro

Page | 23 generated $710 million of trade revenues which were 11.4% of its total revenue (BC Hydro, 2018a).

Our model allows both provinces to arbitrage, thereby enabling each province to satisfy its internal demand at least cost and earn profit by selling their excess electricity at higher prices.

Take BC as an example, when (��,� − ��� − �) > 0, BC would earn higher profit by exporting electricity to another region; when(��,� − ��� − �) < 0, BC would save money by importing electricity from another region, thereby fulfilling its demand at a lower cost and avoiding the variable costs of generating this electricity. While AB’s arbitrage decision is made in each hour,

BC has the potential to arbitrage intertemporally by using its reservoirs to store energy at off-peak hours against peak hours when prices are high.

5. AN INTEGRATED ALBERTA-BRITISH COLUMBIA GRID MODEL

As shown in Table 2, Alberta produces 42.1% of its power from coal and 47.9% from natural gas, leading to a high level of CO2 emissions compared to BC; at the same time, BC’s massive hydroelectricity system can provide storage for imbalances in AB generation. Thus, instead of having to employ peak NG plants, AB can rely on BC to meet its demand in peak hours, while reducing overall CO2 emissions. Such a strategy requires BC and AB to work together, which motivates the integrated model.

The integrated model maximizes the sum of the revenue margins of AB and BC, with cash flows associated with such trade considered to constitute transfer payments. In the model, Alberta is designed to be a more diverse and flexible electricity generator. Not only do we allow for a diverse electricity generation system, but we also allow the system to transform at a limited rate as stated in Section 3.3.

6. DATA SOURCES

The BC model utilizes four sets of data. The hydrometric data of Mica and Shrum are constructed Page | 24 based on the 2018 inflow, outflow and elevation data from BC Hydro (details in Appendix 1). The load data are the balanced authority load of 2019 from BC Hydro; this is the total internal demand, which also includes facilities not operated by BC hydro and from other power sources, and the generation of these sources are subtracted from the internal load (BC Hydro, 2019b). We also obtained the flow and level data of 10 run-of-river generators in BC from Environment Canada and calculated their generation according to equation (9). The hydrometric data of each generator is approximated by the available data of the nearest active flow-monitoring station; we obtain the latest complete year (January to December) of data from each river-flow monitoring station.

Important model parameters such as rated generation capacity and average electricity price are collected from or calculated based on the 2019 BC Hydro Quick Facts (BC Hydro, 2019a).

The AB model utilizes the 2018 hourly load and pool price data from the AESO. The model also utilizes the wind output data of a 3.5MW Enercon E-101 wind turbine from van Kooten, Duan, and Lynch (2016). Since our model does not account for the locations of new wind turbines, we simply assume an arbitrary turbine and approximate its output with a weighted average of the regional power production7.

Table 4 shows the cost matrix of all generators in AB. The operating and maintenance

(O&M) costs of generators consist of a fixed and a variable component. The fixed O&M costs include labour and material costs of equipment maintenance and administrative and general expenses such as facility rent and office utility; these costs are assumed not to vary with output.

Variable costs, on the other hand, do change with output level; these expenses include water consumption, the cost of waste management, and consumable materials for machines such as

7 The weighted averaged is calculated from the 2014 output data of north AB and 2015 output data of south and southwest AB. Page | 25 lubricant and calibration gas (U.S. Energy Information Administration, 2020). The overnight construction costs of materials are accounted for by the AESO to decide the optimal capacity of each generator, and these costs are assumed to be paid annually over a lifetime of 40 years with a discount rate of 5%.

This model also utilizes a series of Mid-Columbia prices (for the U.S.) simulated by Jon

Duan based on historical values; they are then converted to Canadian dollars using the daily exchange rates of from the Bank of Canada8.

Table 4: Cost of Electricity by Generating Asset in Alberta a,b Fixed O&M Var O&M CO2 Emission Overnight Fuel Cost Cost (t/MWh)b Construction Cost source ($/MWh)a ($/MWh) ($/MW)

Coalc 5.00 2.00 0.32 4,809,396 NG 2.43 6.15 0.18 1,537,280 Biomass 7.00 2.49 0 922,368 Nuclear 18.17 3.10 0 8,765,767 Peakd 5.25 7.44 0.22 2,368,065 Wind 3.93 0 0 1,655,029 a Fixed and variable O&M cost data are from Table 2 of the U.S. Energy Information Administration (2020). The fixed O&M costs are converted from dollars per kW per year to dollars per MWh by assuming that generators operate 8760 hours per year. This implies that the values are only approximate as the model itself treats operating hours as a control variable. b In 2018 Canadian dollars. c The fixed and variable costs of coal are lowered significantly from the source data to calibrate the affordability of coal-fired power. d To incorporate emissions from heating the peak plants, we multiply their emission level by 1.2.

7. RESULTS AND SENSITIVITY ANALYSES

In this section, we present some applications of our model. We start by presenting the base-case

scenario, which is shown in Table 5. The integrated grid generates about $5 billion of gross

margin, with BC having a slightly larger margin than AB. BC’s hydropower facilities are more

8 Mid-Columbia prices are available on the website of the U.S. Energy Information Administration, these are daily prices that’s only available on business days (when the auctions are open). Future researches can utilize this information to produce more accurate prices. Page | 26 than enough to satisfy its internal demand, thereby making the province a net exporter of energy overall. That said, BC is a net exporter to the U.S. but a net-importer to Alberta. Alberta’s outcome is interesting because of its enormous generation capacity, which is twice as large as its actual generation in 2018 (National Energy Board, 2019b); arbitrage seems to be the reason for this high level of generation since more than 1/3 of its power is exported to BC and the U.S.

Biomass, coal and NG are the top three generators of the province, with biomass taking a 40- percent share of total generation. This seems unrealistic but is justifiable because biomass has relatively lower O&M costs and zero CO2 emissions. Our results on AB’s system capacity changes further support our explanation as we see an increase in biomass capacity and a decrease in peak NG facilities, primarily due to the low overnight costs of biomass. Overall, our base-case results suggest both provinces should increase their trade with the U.S., while biomass should be the primary facility to expand in Alberta.

Although biomass helps to generate electricity in an eco-friendly way, a massive expansion of biomass facilities might not be realistic because there might not be residuals from mills and timber supply areas. On the other hand, the cost of biomass fuel rise as more wood residuals are transported, this variation in marginal cost is not considered in our model.

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Table 5: Base-case Model Output Total Gross Margin ($M) 5,391 BC’s Gross Margin 2,830 AB’s Gross Margin 2,561

BC Outcome Generation (GWh) 58,216 Net Export to US 27,382 Net Export to AB -10,410

AB Outcome Generation (Gwh) 163,674 Coalb 46,035 (28%) Biomass 68,921 (42%) NG 42,305 (26%) Peak 1,382 (1%) Wind 5,032 (3%) Net Export to US 67,583 CO2 Emission (M ton) 22.65

AB System Capacity Changes Coal 0 Biomass +311 NG 0 Wind 0 Peak -77 Notes: The Carbon tax rates of BC and AB are respectively $50 and $20 per ton. The transmission intertie capacities are: 1200MW between BC and AB, 3150MW between BC and the U.S., and 1000MW between AB and the U.S.

Next, we explore the effects of a carbon tax on Alberta’s integrated electricity grid.9 In particular, we are curious about how much of a loss AB might suffer and what actions will the

AESO take to mitigate the effect of a tax increase. To do this, we run the model under two more cases with the carbon tax in AB set higher at $30/tCO2 and $40/tCO2, while BC’s carbon tax is

9 AB’s and BC’s attitudes towards carbon pricing are different. Currently, BC’s carbon tax is $40/tCO2 and is expected to reach $50/tCO2 in 2021. Conversely, Alberta has repealed its carbon tax and issued a court challenge against the federal carbon tax (Government of BC, n.d.; Government of Alberta, 2020). Page | 28 fixed at $50/tCO2. The outputs are shown in Table 6. Despite the two provinces works together, the tax has a negligible spillover effect on BC’s energy economy. An interesting issue is the inconsistent reaction of BC’s net export to AB as AB’s carbon tax rises. The impacts on AB’s grid is more significant. The first ten dollars of tax increase makes Alberta to disband its coal-fired power plants and shrinks its NG sector quite a bit; the following ten dollars of increase shrinks the

NG sector while biomass takes up more than 90% of total generation. As for AB’s system capacity changes, the first ten-dollar increase in tax incentivizes the province to ramp down the more pollutive generators of coal and peak power generator to a greater extend, but no further ramp down is incurred after the tax becomes $50/tCO2. The increase in biomass capacity, on the other hand, has a positive relationship with the tax level. For the same reasons in the previous paragraph, such a ramp up of biomass might be unrealistic; since the biomass costs we use refer to the conversion of coal plants to fire with biomass, there is a capacity limit from the existing coal plants capacity. Nevertheless, by comparing AB’s results before and after the tax increase, we can conclude that a carbon tax increase of $10 provides considerable incentives to the AESO in implementing renewable energy while not leading to a significant loss. We also find that the effect of the tax diminishes with its level, which suggests that unnecessary efficiency losses will be incurred if the tax is too high.

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Table 6: Model Output – Carbon Tax AB Base Case $10 increase $20 increase Total Gross Margin ($) 5,391 5,263 5,231 BC’s Gross Margin 2,830 2,830 2,830 AB’s Gross Margin 2,561 2,433 2,402

BC Outcome Generation (GWh) 58,216 58,217 58,209 Net Export to US 27,382 27,382 27,382 Net Export to AB -10,410 -10,409 -10,417

AB Outcome Generation (Gwh) 163,674 163,748 163,989 Coal 46,035 0 0 Biomass 68,921 124,814 151,456 NG 42,301 33,901 7,499 Peak 1,382 0 0 Wind 5,032 5,032 5,032 Net Export to US 67,583 67,644 67,864 CO2 Emission (M ton) 22.65 6.10 1.35

AB System Capacity Change Coal 0 -238 -238 Biomass +311 +578 +707 NG 0 0 0 Wind 0 0 0 Peak -77 -107 -107 Note: The proposed tax increases apply to AB only, while BC’s tax is fixed at $50/tCO2.

Next, we explore the effects of a higher-capacity intertie between BC and AB; in particular, we want to see whether such an increase leads to a higher overall margin and whether both provinces can benefit from it. To look into that, we present two more model runs that assume higher capacities of 2,000MW and 2,500MW. According to the model results in Table 7, the gross margin increases with the intertie level; AB’s gross margin increases, but that of BC falls. Upon comparing the 2000-MW-intertie case to the base case, we find that BC’s generation goes down by about 7,000 GWh, which is made up by an increase of the same magnitude in its imports from

AB. It’s trade with the U.S. also increases slightly, which likely reflects arbitrage. AB’s generation

Page | 30 increases by about 7,000MWh, mostly made up of biomass power; this is the reason why AB’s increase in emissions is insignificant, despite its higher generation compared to the base-case level.

The increase in biomass generation also leads AB to expand its biomass capacity by about 30MW more than the base case. The pattern above remains the same once we further increase the intertie capacity. Overall, a higher transmission intertie capacity brings benefits to the integrated grid as a whole; the benefit to the gross margin is, however, not mutual, as we see AB benefiting from the higher intertie, BC’s benefit decreases. This does not fit our expectation since BC benefits massively from its trade with Alberta in real life by importing electricity at off-peak hours where prices are low and selling them at peak hours where prices are high. Table 7: Model Output - Intertie Base Case 2000MW 2500MW Total Gross Margin ($) 5,391 5,661 5,830 BC’s Gross Margin 2,830 2,761 2,718 AB’s Gross Margin 2,561 2,900 3,112

BC Outcome Generation (GWh) 58,216 51,300 46,959 Net Export to US 27,382 27,487 27,433 Net Export to AB -10410 -17,367 -21,718

AB Outcome Generation (Gwh) 163,674 170,666 175,041 Coal 46,035 46,065 46,066 Biomass 68,921 75,870 80,243 NG 42,305 42,300 42,301 Peak 1,382 1,399 1,400 Wind 5,032 5,032 5,032 Net Export to US 67,583 67,579 67,577 CO2 Emission (M ton) 22.65 22.66 22.66

AB System Capacity Change Coal 0 0 0 Biomass +311 +344 +364 NG 0 0 0 Wind 0 0 0 Peak -77 -77 -77

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Next, we allow nuclear power to enter AB’s generation mix to determine its impact on CO2 emissions. To do this, we add a nuclear plant with a capacity of 200 MW. It turns out that nuclear was neither used nor adjusted by the AESO so that our model results are very close to the base case. Our results are different from the finding of van Kooten, Duan, and Lynch (2016), which, based on the AB grid allocation model, suggests that nuclear is the best option to reduce CO2 emissions since it lowers the cost of doing so significantly. Nuclear is not used in our model probably because its variable O&M and overnight costs are high. This does not mean the government should shut the door on nuclear since these costs might be lowered in the future by technological developments.

For our next case, we simulate a drought in BC and examine its impacts on the integrated grid. Since hydro is BC’s only source of power, BC will likely make up its generation needs by increasing its imports from AB and the U.S. For simplicity, we assume drought to only affect large hydro dams with a reservoir and conduct our analysis by presenting two model runs that apply loss factors of 10% and 20% for reservoir inflow and outflow.10 The results are displayed in Table 8.

As expected, as the drought parameter increases, BC’s gross margin and generation decrease. The decrease in BC’s margin is not large because BC is able to compensate its lower generation by importing more biomass energy from AB. That said, BC’s economy is still affected due to lower arbitrage revenue. The drought has minor impacts in AB, its generation, exports to BC, and gross margin all increase. An explanation is that, as BC cannot generate as much electricity, it needs to import power from Alberta to benefit from arbitrage, thereby leading to the increases in Alberta’s margin and generation. The increase in external demand also incentivizes Alberta to increase its

10 The same loss factors are applied to average head height and outflow as in equation (10). Page | 32 generation capacity, thereby expanding its biomass facilities while slowing down the decommissioning of coal power plants. To some extent, Alberta helps BC to mitigate its revenue losses from the shock, while making additional profits from it.

Table 8: Model Output – Drought Base Case Low loss Medium loss Total Gross Margin ($) 5,391 5,338 5,205 BC’s Gross Margin 2,830 2,776 2,718 AB’s Gross Margin 2,561 2,562 2,562

BC Outcome Generation (GWh) 58,216 53,946 45,567 Net Export to US 27,382 23,141 14,766 Net Export to AB -10,410 -10,439 -10,443

AB Outcome Generation (Gwh) 163,674 163,696 163,700 Coal 46,035 46,013 46,008 Biomass 68,921 68,956 68,974 NG 42,305 42,307 42,308 Peak 1,382 1,379 1,378 Wind 5,032 5,032 5,032 Net Export to US 67,583 67,575 67576 CO2 Emission (M ton) 22.65 22.64 22.64

AB System Capacity Change Coal 0 0 0 Biomass +311 +311 +311 NG 0 0 0 Wind 0 0 0 Peak -77 -77 -77

8. CONCLUSIONS

In this paper, we introduce an Alberta-British Columbia electricity grid model. BC is modelled as the province with a stable electricity generation system that primarily relies on hydroelectricity, while AB is the province with multiple generating sources and more opportunities to reform the

Page | 33 generation system to reduce CO2 emissions. The model maximizes one year’s aggregate gross margin of BC and AB and provides guidance to the operating strategies of both provinces in terms of internal generation, system reform, and trade activities with each other and the U.S. According to our base-case scenario, BC should import electricity from Alberta and export its excess energy to the U.S., while AB should generate a lot of electricity and export it to its trading partners while limiting its emissions by expanding biomass facilities and taking down coal-fired power plants.

We continue our analysis by using our models to answer some popular questions in the field of natural resources and electricity generation. For instance, what are the effects of a carbon tax increase in Alberta; what will happen if both provinces increase their scale of trade; and should

AB implement nuclear energy? Our analyses produce intuitive answers to the questions: a carbon tax is effective to incentivize renewable energy, but its effects diminish with its level; a higher intertie capacity increases the aggregate margin, but the benefit is primarily in AB; it is not optimal to bring nuclear into AB because of its high overnight costs, that said, it should still be considered as an alternative source of energy due to its high capacity, cheap variable costs of generation, and low emission (Renewable Energy Coalition, 2016). We also find that both provinces can help each other to mitigate profit losses during productivity shocks.

For simplicity, our model assumes biomass to be carbon neutral and has constant marginal costs, such assumptions might not be practical. The carbon neutrality assumption comes from the carbon life-cycle analysis from biomass energy, which suggests any CO2 emissions will be removed in the future by tree growth (as cited in Johnson and van Kooten, 2015). Actually, biomass has higher incremental CO2 emissions than coal, and it will take years for tree to grow and start of offset the higher emissions. If global warming is urgent, governments should focus on programs that facilitate immediate carbon removal, as opposed to expanding biomass electricity.

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The problem with our second assumption is the marginal cost of biomass will rise because of increases in the demand for wood residuals, which will also lead biomass producers to purchase residuals from further forest areas. Thus, the hauling distance from the forest the power plants will increase, with transportation of wood residuals also leading to higher CO2 emissions. Other factors can also constraint the capacity of biomass, such as the availability of timber (Johnson and van

Kooten, 2015; van Kooten, 2017). Future researches can consider the facts above when trying to quantify the costs of biomass.

We would also like to acknowledge some other problems with the current version of our model. First, the BC model does not successfully enforce our assumption that interties can only run one way in each hour, which means BC’s export and import to the U.S. can be positive at the same time. The problem seems to disappear if we set the intertie capacity between BC and AB to a large amount, say, 10 GW. Second, the BC model does not project water spills at any time of the year, which is unrealistic as spills are common in June/July when the snowpack melts. This might be due to the bad quality of our run-of-river data, since Environment Canada does not have a river- flow monitoring station close to the facility. Active stations with the required data available are not necessarily on-site at each facility, making the data less accurate. A solution is to find the historical generation of the run-of-river facilities and subtract their load from BC’s internal load.

Currently, the electricity prices in our model are exogenous. This approach is likely unrealistic since electricity prices are usually determined in a market environment by supply and demand. One way to address this is to endogenize prices. Since we already have a fair picture of the suppliers, prices can be determined by estimating a demand function. Additionally, we can apply quadratic cost functions to generators, which will help to capture the change in variable costs our time. All of the above will make the model nonlinear but will increase its realism.

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Carr, J. (2018). How Alberta can hurt B.C.’s anti-pipeline NDP with a painful electric shock. Financial Post. February 14. Retrieved from https://business.financialpost.com/opinion/how-alberta-can-hurt-b-c-s-anti-pipeline-ndp- with-a-painful-electric-shock Energy BC. (2017). Run of river power. Retrieved from http://www.energybc.ca/runofriver.html Fickling, D. (2019). The world’s last coal plant will soon be built. The Washington Post. Retrieved from https://www.washingtonpost.com/business/energy/the-worlds-last-coal- plant-will-soon-be-built/2019/05/14/56d4425e-76be-11e9-a7bf-c8a43b84ee31_story.html Government of Alberta. (2020). Carbon tax repeal. Retrieved from https://www.alberta.ca/carbon-tax-repeal.aspx Government of British Columbia. (n.d.). British Columbia’s carbon tax. Retrieved from https://www2.gov.bc.ca/gov/content/environment/climate-change/planning-and- action/carbon-tax Hasting-Simon, S., Dronkers, B., & Cretney, S. (2016). Wind and Solar in Alberta: Infographic. The Pembina Institute. Retrieved from https://www.pembina.org/pub/wind-solar-alberta Innovative Research Group. (2009). Alberta nuclear consultation. Report prepared for: The Alberta government – Ministry of Energy. Retrieved from https://open.alberta.ca/publications/4646714#detailed Johnson, C.M.T., & van Kooten, G.C. (2015). Back to the past: Burning wood to save the globe. Ecological Economics, 120(15 Dec): 185-193. Loucks and Beek. (2017). Water resource systems planning and management. The Springer. Retrieved from https://www.springer.com/gp/book/9783319442327 Maloney, J. (2017). Strategic electricity interties: Report of the Standing Committee on Natural Resources. Parliament of Canada. Retrieved from https://www.ourcommons.ca/Committees/en/RNNR/StudyActivity?studyActivityId=963 7720 McWilliam, M.K., van Kooten, GC., & Crawford, C. (2012). A method for optimizing the location of wind farms. Renewable Energy,48 (12 Dec): 287-299. National Energy Board. (2017). Canada’s renewable power landscape 2017 – Energy market analysis. Ottawa, ON: National Energy Board. 36pp. At https://www.neb- one.gc.ca/nrg/sttstc/lctrct/rprt/2017cndrnwblpwr/2017cndrnwblpwr-eng.pdf National Energy Board. (2019a). Provincial and territorial energy profiles – British Columbia. Ottawa, ON: Government of Canada. Retrieved from https://www.cer- rec.gc.ca/nrg/ntgrtd/mrkt/nrgsstmprfls/bc-eng.html National Energy Board. (2019b). Provincial and territorial energy profiles – Alberta. Ottawa, ON: Government of Canada. Retrieved from https://www.neb- one.gc.ca/nrg/ntgrtd/mrkt/nrgsstmprfls/ab-eng.html Renewable Resources Coalition. (2016). Nuclear energy: Pros & cons. Retrieved from https://www.renewableresourcescoalition.org/nuclear-energy-pros-cons/

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Sopinka, A., van Kooten, GC., & Wong, L. (2013). Reconciling self-sufficiency and renewable energy targets in a hydro dominated system: The view from British Columbia. Energy Policy ,61(5): 223-229. U.S. Energy Information Administration. (2020). Capital cost and performance characteristic estimates for utility scale electric power generating technologies. Retrieved from https://www.eia.gov/analysis/studies/powerplants/capitalcost/ van Kooten, G.C. 2016. The economics of wind power, Annual Review of Resource Economics, 8(1): 181-205. van Kooten, G.C., Withey. P, & Duan, J. (2020). How big a battery? Renewable Energy 146(20 Feb): 196-204. van Kooten, G.C., & Mokhtarzadeh, F. (2019). Optimal investment in electric generating capacity under climate policy, Journal of Environmental Management, 232(15 Feb): 66- 72. van Kooten, G.C. (2017). California dreaming: The economics of renewable energy, Canadian Journal of Agricultural Economics 65(1): 19-41. van Kooten, G.C., Duan, J., & Lynch, R. (2016). Is there a future for nuclear power? Wind and emission reduction targets in fossil-fuel Alberta, PLoS ONE 11(11): e0165822. van Kooten, G.C., Johnston, C., &Wong, L. (2013). Wind versus nuclear options for generating electricity in a carbon-constrained world: Strategizing in an energy-rich economy, American Journal of Agricultural Economics 95(2): 505-511.

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APPENDIX 1. HYDRO DATA FOR BC

The average inflow and outflow data of BC dams (m3/s) are constructed based on the 2018 hourly

data from BC Hydro, each takes the unit m3/s. The data were not directly used for two reasons: 1.

The data contain negative entries, which did not fit the model’s definition of inflow and outflow

(this means their data are probably net inflow, which takes into account other factors not

considered in this model). 2. The data have an outlier problem. To best utilize this information, I

smoothed the data using a 24-period moving average and scaled it to get rid of any negative entries,

the new series is then downscaled to calibrate the mean of the original data. The smoothing helped

to show the trend of the data. Take the inflow data of the Mica Dam as an example, the raw data

shown in Figure A1 have quite a number of outliers. The cleaned data, shown in Figure A2, are

not only less volatile but also has a more realistic distribution, which reflects the high hydro inflow

in summer and lower inflow in winter.

Figure A1. Raw and scaled hydro inflow for the Mica Dam. Source: BC Hydro and author’s calculation.

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APPENDIX 2. GAMS CODE

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