Economic Assessment of a Price-Maker Energy StorageFacility in the Alberta electricity market

Soroush Shafieea, Payam Zamani-Dehkordia, Hamidreza Zareipoura,∗, AndrewM. Knighta

aSchulich School of Engineering, University of Calgary, Alberta, Canada

Abstract

Dynamic price fluctuations in the Alberta electricity market bring potential

economic opportunities for electricity energy storage technologies. However, stor-

age operation in the market could have significant impact on electricity prices.

This paper evaluates the potential operating profit available through arbitrage

operation for a price-maker storage facility in Alberta. Considering a five-year

period from 2010 to 2014, hourly generation and demand price quota curves

(GPQCs and DPQCs) are constructed to incorporate price impact as an input to

the self-scheduling problem of a price-maker storage facility. The self-scheduling

model is applied to the historical hourly GPQCs and DPQCs of the Alberta elec-

tricity market to investigate the potential economic performance of a price-maker

energy storage facility.

Keywords: Economic assessment, energy storage technology, price-maker,

Self-scheduling, price quota curves.

∗Corresponding Author: Hamidreza Zareipour;Email: h.zareipour@ucalgary.ca; Phone:+1-403-210-9516 ; Fax:+1-403-282-6855

Preprint submitted to Energy April 28, 2016

Nomenclature

Indices

t Index for operation intervals running from 1 to T .

s Index for the steps of generation price quota curves from 1 to ndt .

s′ Index for the steps of demand price quota curves from 1 to nct .

Parameters5

µ Roundtrip storage efficiency.

V OMd Variable operation and maintenance cost of discharging.

V OM c Variable operation and maintenance cost of charging.

P dmax Maximum discharging capacity.

P cmax Maximum charging capacity.

Emin Minimum level of energy storage.

Emax Maximum level of energy storage.

Eint Initial level of energy storage.

πdt,s Price corresponding to step number s of the GPQC at hour t.

πct,s′ Price corresponding to step number s′ of the DPQC at hour t.

qd,mint,s Is the summation of power blocks from step 1 to step s− 1 of GPQC

for hour t.

qc,mint,s′ Is the summation of power blocks from step 1 to step s′−1 of DPQC

for hour t.

bd,maxt,s Size of step s of the GPQC at hour t.

bc,maxt,s′ Size of step s′ of the DPQC at hour t.

2

Functions

πdt (P

dt ) Stepwise decreasing function that indicates the market price as a

function of the price-maker discharge quantity at time t.

πct (P

ct ) Stepwise increasing function that indicates the market price as a

function of the price-maker charge quantity at time t.

Variables10

P dt Discharging power of the storage unit at hour t.

P ct Charging power of the storage unit at hour t.

OCt Operation cost of the plant at time t.

Est Level of energy storage at time t.

uxt Unit status indicator in either modes x, i.e., discharging (d) or charg-

ing modes (c) (1 is ON and 0 is OFF).

bdt,s The fractional value of the power block corresponding to step s of

the GPQC to obtain discharging quota P dt in hour t.

bct,s′ The fractional value of the power block corresponding to step s′ of

the QPQC to obtain charging quota P ct in hour t.

xdt,s Binary variable that is equal to 1 if step s of GPQC is the last step to

obtain discharging quota P dt in hour t and 0 otherwise.

xct,s′ Binary variable that is equal to 1 if step s′ of DPQC is the last step

to obtain charging quota P ct in hour t and 0 otherwise.

1. Introduction

The implementation of large-scale energy storage systems has been shown to

be technically feasible in the province of Alberta [1]. Such systems are able to

3

provide load-shifting [2] and potentially provide the necessary flexibility to deal15

with uncertainties associated with the growing penetration of renewable resources

[3, 4, 5]. Load shifting is one of the best-comprehended and analyzed applications

of energy storage , i.e., to buy and store electricity at low demand, low price peri-

ods, and sell at high demand, high price periods [6]. This is referred to as energy

arbitrage. It has been shown that the dynamics of the Alberta electricity market20

and relatively high price variations provide desirable opportunities for energy ar-

bitrage [7]. As an example, the hourly electricity prices in this market for 2013

are shown in Fig. 1. Over the year, electricity prices averaged $80.20/MWh. For

3208 hours, the price was below $25/MWh and for the remaining hours, the av-

erage price was over $115/MWh with 204 hours settling between $800/MWh and25

$1,000/MWh, the market price cap. As a result of this variation, energy storage

systems have attracted the attention of investors; in 2014, a 160 MW compressed

air energy storage (CAES) plant was filed with the Alberta Electric System Op-

erator (AESO) in 2014 [8]. It is important for the investors to know the potential

profitability of a large-scale investment in bulk energy storage; economic feasi-30

bility is the deciding factor for developing new energy storage facilities. Projects

must be attractive to capital from the investors’ viewpoint and it is crucial to eval-

uate the potential profit available to be earned through energy arbitrage in the

Alberta electricity market.

The profitability of providing energy arbitrage by energy storage systems in35

various electricity markets are shown in [6, 9, 10, 11, 12, 13, 14]. These studies

assume that the energy storage facility is a ”price-taker”, i.e, storage operation

4

in the market does not affect the pool price [15, 16]. However, in the case of a

large-scale energy storage facility it can be assumed that charging and discharg-

ing operations change the net demand and supply. As a consequence, a large-scale40

energy storage facility can be expected to be a price-maker, i.e., its actions could

affect the market price. A few studies have modeled the impacts of energy stor-

age operation on market price. The operation of large-scale price-maker energy

storage systems is optimized in [17]. The profitability of energy arbitrage for a

price-maker energy storage in the PJM [6], the Iberian Electricity Market [18, 19]45

and the Alberta electricity market [20] is investigated. In [20], one representative

supply curve is considered for all the hours. The impact of energy storage charg-

ing and discharging operation on market prices should be accurately formulated

and historical hourly data should be employed to achieve a better understanding

of the energy storage profitability in the Alberta electricity market.50

Several efforts have been devoted in modeling of price-maker generation com-

panies (Gencos). The developed modeling methods can be divided into two cate-

gories: game based and non-game based. Game based methods aim to calculate

the Nash Equilibrium in a market with a single or multiple price-maker Gencos

using the mathematical program with equilibrium constraints (MPEC) approach55

and binary expansion techniques [21, 22, 23, 24]. In [21, 22], the bidding strategy

problem of a price-maker Genco is initially formulated as a bi-level optimization

problem, consisting of bidding strategy and market clearing problems in the upper

and lower levels, respectively. Then, using Karush-Kuhn-Tucker (KKT) optimal-

ity conditions, the problem is converted to its equivalent single nonlinear MPEC60

5

problem. Binary expansion is used in [22] to transform the nonlinear MPEC prob-

lem to a mixed-integer linear programming (MILP) form and then solve the bid-

ding strategy for one price-maker thermal generator in an electricity market. In

[23], this work is further extended to find the Nash equilibrium for a market with

multiple price-maker firms. Bakirtzis et al. [24] apply the approach in [22] to65

construct multi-step price-quantity offer curves for a single price-maker producer.

In non-game based methods, the impact of a participant’s operation on the

market price is modeled by generation price quota curves (GPQCs) [25]. The

GPQC for a given hour, is a stepwise decreasing curve that indicates the market

price as a function of the total accepted production of the price-maker generator.70

Figure 2-(a) shows an example of a GPQC with steps of 10 MW up to 100 MW.

The use of GPQCs enables self-scheduling of price-maker producers to be formu-

lated efficiently [26, 27, 28, 29]. In [26], the self-scheduling problem of a price-

maker thermal producer is addressed using a MILP approach with PQCs. This

work illustrates the efficient and proper functioning of the proposed formulation.75

PQCs are used to address the short term operation planning of a price-maker hydro

producer in a day-ahead electricity market [27, 28]. A mid-term self-scheduling

model for a price-maker hydro producer is developed in [29], in which PQCs are

used to model the producers interaction with other market participants.

This paper addresses the economic assessment of energy arbitrage for a large-80

scale energy storage facility in the Alberta electricity market, considering its im-

pact on pool prices. Self-scheduling of a merchant price-maker storage plant is

proposed, using an approach which incorporates the impact of storage operation

6

on market clearing price by means of price quota curves. The impact of large-

scale energy storage discharging activities in the market is modeled by hourly85

GPQCs. However, the storage plant must decide not only when to sell electricity

to the market, but also when to purchase the electricity from the market for charg-

ing with the lowest cost. Purchasing electricity from the market will increase the

demand and consequently may negatively impact market prices. Thus, the impact

of energy storage charging activities on market prices should also be modeled in90

the self-scheduling problem in order to achieve an optimal scheduling solution.

In so doing, in addition to the GPQCs for discharging operations, an hourly de-

mand price quota curve (DPQC) is also defined here for discharging operations.

The DPQC states how electricity price changes as the demand quantity of the load

changes. The DPQC is a stepwise non-decreasing curve; the more power absorbed95

from the grid, the more the electricity price will increase. Hourly DPQCs help a

price-responsive load to participate efficiently in the market in order to meet de-

mand at the lowest cost. Figure 2-(b) shows an example of a DPQC with steps of

10 MW up to 100 MW.

The formulation, presented in this paper, is non-linear and is therefore con-100

verted to its equivalent linear formulation to be enable solution by conventional

solvers. Thereafter, the historical hourly supply curves and hourly pool prices of

the Alberta electricity market for years 2010 to 2014 are extracted to construct the

hourly GPQCs and DPQCs in this period. The developed self-scheduling model

is then applied to the historical hourly GPQCs and DPQCs of the Alberta electric-105

ity market to investigate the economic feasibility of a price-maker energy storage

7

during these years. The model is used to explore the sensitivity of the storage

plant profit to a range of design and performance parameters.

The main contributions of this paper can be stated as follows:

• To develop a linear self-scheduling formulation for a price-maker energy110

storage facility using hourly GPQCs and DPQCs

• To construct the hourly GPQCs and DPQCs of the Alberta electricity market

during years 2010 to 2014 using actual hourly supply curves.

• To assess the economic feasibility of large-scale energy storage systems

providing energy arbitrage in the Alberta electricity market considering im-115

pacts of storage operations on market price.

The remainder of the paper is outlined as follows. Section 2 reviews the litera-

ture on the economic assessment of energy storage systems in different electricity

markets. In section 3, the process of constructing GPQCs and DPQCs for the Al-

berta electricity market is described, and the non-linear self-scheduling problem120

of a merchant price-maker storage and, its equivalent linear formulation are devel-

oped. In Section 4, the developed model is employed. A base case of the potential

revenue gained by energy arbitrage is presented along with sensitivity analyses.

Finally, the paper is concluded in Section 5

2. Literature Review125

This section reviews the literature on scheduling of energy storage systems

and estimation of the energy arbitrage value. The study presented in this paper is

8

compared with the literature.

In the price-taker approach for self-scheduling of energy storage systems ([6,

9, 10, 11, 12, 13, 14]), it is assumed that storage operation in the market does130

not affect the pool price. The arbitrage value of a storage device in the PJM and

New York are explored in [6] and [9], respectively. It is shown that the value of

arbitrage for an 80% efficient storage device has a range from $60/MW-year to

$110/MW-year in PJM market. The effects of natural gas and electricity price

fluctuations on the energy arbitrage revenue of a pure storage device and a CAES135

facility are investigated in [10]. It is concluded that the annual arbitrage value of

a CAES facility is lower than that of an 80% efficient pure storage device due to

the effect of the cost of burning natural gas in the CAES system. It is shown that

the energy arbitrage revenue of a CAES facility could be improved by distributing

compressors near heat loads in the Alberta electricity market[11, 12]. The value140

of providing energy arbitrage as well as operating reserves for energy storage

systems in different electricity markets in US and UK are evaluated in [13, 14].

The limitation of all all these studies is the assumption that storage operations

have no impact on price. However, purchasing and selling activities will change

the net demand and supply, and consequently, the market price. Thus, storage145

operation could reduce the peak price differential and consequently decrease the

net energy arbitrage revenue for storage operators.

An optimization framework for the optimal operation of a price-maker energy

storage system is developed in [17]. In this paper, MPEC approach is applied to

model the price impacts of the energy storage facility. The impact of large-scale150

9

storage on arbitrage value in PJM is investigated in [6]. In that paper, in order to

model the price impacts, only one linear supply curve is assumed for each month

based on the historical price and load data. The self-scheduling of a price-maker

PHS is developed in [18, 19]. In these papers, the impact on price is modeled

by residual demand curve, which is defined by an approximated sigmoid func-155

tion. This leads to a mixed-integer non-linear formulation. In [20], profitability

of energy arbitrage by different storage technologies are evaluated in the Alberta

electricity market in year 2012 considering the price impacts. In this report, one

representative supply curve is considered for all the hours in this market.

Compared to [9, 6, 10, 11, 12, 13, 14], in this paper, the impacts of energy160

storage operation on market price are taken into account, i.e., we consider the fa-

cility to be price-maker. This is important in the case of large storage facilities.

Compared to [17], instead of MPEC approach, a non-game based method using

PQCs is used to model the impacts of energy storage operation on market prices.

The proposed methodology in the present paper makes it possible to use real-life165

market data with high volume at a reasonable computational cost. Compared to

[6], instead of using a monthly supply curve, which is estimated using load and

price data, actual hourly supply curves and pool prices are extracted to model the

impacts of energy storage operation on market price for each hour. Compared

to the model presented in [18, 19], instead of using an approximated function to170

model the residual demand curves, the GPQCs and DPQCs are constructed using

actual hourly supply curves. Moreover, compared to the non-linear model pre-

sented in [6, 18, 19], a mixed-integer linear programming approach is developed

10

in this study, the global optimality of which is guaranteed. Compared to [20],

instead of using one representative supply curve for all hours in the Alberta elec-175

tricity market, the hourly supply curves of this market for years 2010 to 2014 are

extracted and used to investigate the economic feasibility of energy storage sys-

tems in this market during recent years. The importance of considering hourly

supply curves is going to be explained later in Section 3.1. As a summary, the

comparison of our work with the related literature are presented in table 1.180

3. Methodology and Formulation

The methodology, used in this paper, requires pre-process of significant data

in order to develop the required DPQCs and GPQCs. These curves are the input

to the nonlinear formulation, which can then be linearized

3.1. The Alberta Electricity Market Database185

In order to model the potential impacts of an energy storage facility, a first

necessary step is to build a historical database of market operations over the pe-

riod of interest. In Alberta, the data required is publicly available, published by

the Alberta Electric System Operator (AESO) through its online data-publishing

portal [30]. The database for the study includes hourly generator offers and pool190

price data for the period of January 1, 2010 to December 31, 2014.

In the Alberta electricity market, generators submit their offers in the form

of quantity and price pairs to sell energy in the market to the AESO through the

Energy Trading System (ETS). Sorting the price-quantity offers from the lowest-

priced to the highest-priced, a supply curve is constructed for each hour. The195

11

sensitivity of market price to changes in supply or demand depends on the market

structure and particularly, the system supply curve. As an example, the supply

curve of the Alberta electricity market for the hour 1 on December 31, 2014 is

shown in Fig. 3. As can be seen, the supply curve is very steep towards the right

side of the curve. This could cause significant price fluctuations as a result of a200

relatively small change to supply offers. Moreover, the steep supply curve could

lead to a significant change in pool price if the demand in the market varies. As

a result, the impacts of storage operation on market pool prices in Alberta should

be incorporated in economic analyses in order to prevent profit overestimation.

As stated earlier, this study uses the actual supply curve data for each of the205

43,824 hours in the study period. The importance of using actual hourly data,

rather than a representative curve, can be seen by considering Fig. 4 and Fig. 5.

Figure 4 plots the supply curves for each of the 24 hours in a single day, August 1

2014; Figure 5 plots the supply curves for a given hour of all the days in a specific

month, hour 1 for each day of October 2014. Both plots demonstrate significant210

variability in the supply curves. This is an indication that market participants sub-

mit their offers strategically depending on market conditions. Thus, using a single

supply curve for all hours of a long study period, as that of considered in [20], may

not fully capture the realities of market participants offering strategies. Moreover,

with lower resolution data (e.g., using one representative supply curve per day215

instead of hourly supply curves) we might overestimate the energy arbitrage op-

portunities that exist during a period of say a week or a year. Thus, it could cause

overestimation of the potential profit gained through energy arbitrage. Conversely,

12

low resolution data could also cause underestimation of the arbitrage opportunity

and consequently failure to capture an arbitrage opportunity. Therefore, use of220

high resolution data leads to more effective scheduling and revenue prediction.

The Alberta Internal Load (AIL) is reported by the AESO on a hourly basis.

However, the AIL data does not provide sufficient information to determine price

from a supply curve such as that in Fig.3. The supply curves in the database only

consider dispatchable generation above 5MW. To determine equivalent system225

load on a supply curve such as that developed in the study, the pool price is cross-

referenced against the supply curve, with the intercept providing the load supplied

by the dispatchable generation in the merit order. We refer to this value as the

”Market Equivalent Demand”.

3.2. Construction of GPQCs and DPQCs of the Alberta Electricity Market230

In order to investigate the economic performance of a price-maker energy stor-

age system in the Alberta electricity market, the hourly GPQCs and DPQCs are

created. Construction of the PQCs requires the database of hourly supply curves,

pool prices and market equivalent demand. For each hour of years 2010-2014,

the impact of additional generation or additional demand have on on market pool235

prices is explored. The impact of [rice is determined by incrementally adding ei-

ther demand or generation, in 10 MW steps, up to 200 MW. Additional generation

is added to the merit order at an offer price of $0/MWh. Figure 6 illustrates the

case of a new supply of 150 MW; as a result of the new supply, the supply curve

is extended to the right. The impact of the new supply offer can be seen as the240

difference between the original and modified supply curves, at the equivalent mar-

13

ket demand. At 10,800 MW of demand, the original price is $500/MWh, the new

price is $259.12/MWh; a $240.88/MWh decrease in price due to the new supply

in the system.

Figure 7 shows the impact of an additional 100 MW demand on market price.245

The original price is $32.28/MWh and the market equivalent demand is 9110 MW.

As can be seen in the figure, the 100 MW additional demand cause the price to

increase to $39.4/MWh.

Two sets of data are created, one consists of hourly GPQCs and the other

hourly DPQCs. Each set of data has 43824 rows and 20 columns. The curves250

shown in Figs. 2-(a) and 2-(b) are GPQC of hour 1043 and DPQC of hour 39 in

2010 up to 100 MW, respectively. Note that, the described process is based on the

assumption that during the analyzed period, historical supply offers and demand

bids remain unchanged.

3.3. Energy Storage self-scheduling Formulation255

A merchant storage plant, designed for energy arbitrage, purchases electricity

during low price periods to charge the plant. The stored energy is later used to

discharge the power and sell it to the market during peak price hours. The stor-

age device characteristics consist of charging power capacity, discharging power

capacity, energy capacity, and efficiency. The efficiency of a storage facility is ex-260

pressed as the amount of output energy per unit of energy consumed for charging

during the off-peak hours.

In this section, a general optimization-based formulation for the self-scheduling

of a merchant price-maker energy storage plant is presented. The developed model

14

can be modified depending on the characteristics of the storage technology such265

as battery [31, 32] or CAES [10]. The goal of the storage plant is to maximize

profit through energy arbitrage as a participant in the electricity market. To for-

mulate the operation of the facility, it is assumed that the storage operator has the

forecasts of the GPQCs and DPQCs for the upcoming hours. Publicly available

data of electricity markets can be used to forecast the DPQCs and GPQCs. For270

instance, in this paper, the historical hourly supply curves and pool prices of the

Alberta electricity market for five years, which are available online at [30], are ex-

tracted to build the hourly PQCs for five years. Different forecasting methods can

be used and the historical PQCs can be fed to those forecasting engines to forecast

PQCs for the upcoming day or week. Hourly GPQCs and DPQCs allow the self-275

scheduling profit maximization problem to be precisely formulated. The objective

function and constraints for the self-scheduling optimization are as follows.

maxT∑t=1

[P dt × πd

t (Pdt )− P c

t × πct (P

ct )−OCt] (1)

Subject to:

OCt = P dt × V OMd + P c

t × V OM c ∀t ∈ T (2)

udt + uct ≤ 1 ∀t ∈ T (3)

0 ≤ P ct ≤ P c

max.uct ∀t ∈ T (4)

0 ≤ P dt ≤ P d

max.udt ∀t ∈ T (5)

15

Esmin ≤ Es

t ≤ Esmax ∀t ∈ T (6)

Est+1 = Es

t + P ct × µ− P d

t ∀t ∈ T (7)

Es(0) = Es

int (8)

The objective function (1) consists of three terms. The first term is the revenue

from electricity sales to the market from discharging the stored energy. The sec-

ond term is the cost of purchasing the electricity from the market. The third term280

of the objective function represents the operating cost of the plant. It is expressed

as the variable operation and maintenance (VOM) cost of the storage plant during

charging and discharging hours in (2). The operational constraint is expressed in

(3) i.e., the storage can operate in only one of charging or discharging modes at

a time. The charging and discharging power and energy limits of the storage are285

specified by (4)-(6). The dynamic equation for the storage level is provided by

(7). The initial level for the air storage cavern is specified by (8).

3.4. Equivalent Linear Formulation

In the objective function, the market clearing price is not an input parameter.

The price is a variable, which is a function of charging or discharging quanti-290

ties. The relation between the price and charging and discharging quantities is

expressed through hourly GPQCs and DPQCs. Due to the products between these

variables, i.e., hourly charging and discharging power and hourly market price,

the formulation is nonlinear. A mixed-integer linear programming approach is

presented in [26] to convert the non-linear problem of a price-maker generation295

company to its linear equivalent. The optimization problem developed above can

16

be also converted to its equivalent linear formulation in a similar manner to that

described in [26]. However, since the charging side should be also scheduled, the

proposed approach in [26] is modified and extended further for energy storage

charge/discharge scheduling.300

Figs. 8 and 9 demonstrate the linearization process for a sample five step

GPQC and a sample four step DPQC, respectively. Based on this approach, the

linearization process may be written as follows:

maxT∑t=1

[ ndt∑

s=1

πdt,s(b

dt,s + xdt,sq

d,mint,s )−

nct∑

s′=1

πct,s′(b

ct,s′ + xct,s′q

c,mint,s′ )−OCt

](9)

Subject to:

(2)− (8)

P dt =

ndt∑

s=1

(bdt,s + xdt,sqd,mint,s ) ∀t ∈ T (10)

0 ≤ bdt,s ≤ xdt,sbd,maxt,s ∀t ∈ T (11)

ndt∑

s=1

xdt,s = udt ∀t ∈ T (12)

P ct =

nct∑

s′=1

(bct,s′ + xct,s′qc,mint,s′ ) ∀t ∈ T (13)

0 ≤ bct,s′ ≤ xct,s′bc,maxt,s′ ∀t ∈ T (14)

nct∑

s′=1

xct,s′ = uct ∀t ∈ T (15)

17

The objective function (9) states the profit of the price-maker energy stor-

age during the scheduling horizon. As seen in 9, the profit consists of three

terms, which are respectively discharging revenue, charging cost, and operat-

ing cost. Figure 8 illustrates the variables, i.e., bdt,s, xdt,s, and parameters, i.e.,

πdt,s, q

d,mint,s , bd,max

t,s , used to linearize the revenue of the storage plant as a func-305

tion of its hourly discharging power. The shaded area in this figure represents

the revenue, which is the discharging power multiplied to the market price at that

discharging level. It is mathematically expressed in the first term of objective

function. In (10), the discharging power is linearly expressed as a function of

variables bdt,s, xdt,s, shown in Fig. 8. Equation (11) expresses the limit on the block310

of the GPQC at each hour, which is between zero and the size of that step. Equa-

tion (12) states that at each hour of discharging period, only one instance of the

variable xdt,s is nonzero, which shows the corresponding step of GPQC the storage

is operating at that hour. Based on (12), all instances of the variable xdt,s are zero

at time t if storage is not in discharging mode at that hour. Based on (11) and315

(12), during a discharging hour, only one instance of the variable bdt,s could vary

between zero and the size of selected step of GPQC of that hour. All the others

are forced to be zero. Based on above discussion, for each hour, The revenue is

the sum of the product of the corresponding price of each step of GPQC with the

corresponding term of the discharging power constraint (10). If the storage is not320

in discharging mode, all terms of (10) are zero, which means no revenue at that

hour.

The linearization process for charging is similar to that used for discharg-

18

ing. The second term in the objective function (9) indicates the charging cost

of storage. Figure 9 shows the variables, i.e., bct,s′ , xct,s′ , and parameters, i.e.,325

πct,s′ , q

c,mint,s′ , bc,max

t,s′ , used to linearize the charging cost of storage plant as a function

of its hourly charging power. In (13), the charging power is linearly formulated as

a function of variables bct,s′ , xct,s′ shown in Fig. 9. The charging cost is shadowed

in this figure, which is formulated in second term of the objective function (9).

4. Results and Discussions330

The model developed in Section 3 is used to assess the potential operating

profit gained by a merchant price-maker storage plant participating in the Alberta

electricity market. A period of seven days is selected as the scheduling horizon in

order to take advantage of hourly and daily fluctuations in electricity prices. It is

assumed that the perfect forecast of hourly GPQCs and DPQCs are available. The335

hourly PQCs of the Alberta electricity market from 2010 to 2014 are used as the

input to the storage self-scheduling problem. A base case and sensitivity analyses

are presented

4.1. Base Case Analysis

The base case evaluates a storage facility with 140 MW discharging power, 90340

MW charging capacity, 1400 MWh energy capacity, i.e, 10 hours generation at

full discharging capacity, and 70% roundtrip efficiency. $1/MWh VOM cost [33]

is considered for charging and discharging modes.

Single Week Example: To demonstrate the importance of the price-maker for-

mulation, a single week of operation is scheduled under each of price-taker and345

19

price-maker assumptions. Figure 10 plots the scheduling plan when the impact

of storage operations on the electricity price is neglected. It is clear that with

this price-taker assumption, the storage facility charges during low price hours

and discharges during high price hours. It is also clear that the majority of these

operations are conducted at maximum power capacity.350

Figure 11 plots the storage scheduling when the impact on market price is con-

sidered. The hourly price without and with the storage operation are also plotted.

As with the price-maker assumption, the overall operational trend of the storage

facility with responsive price is to charge when prices are low and discharge when

prices are high. However, the price curves indicate that even a 140/90 MW stor-355

age facility has a significant impact on the electricity price specially during peak

hours. The peak generation capacity of Alberta’s electric system for the period

in the study is 12.35 GW, with peak net demand of 10.51 GW. Comparison of

Fig. 10 and Fig. 11 demonstrates that with responsive price optimization, charg-

ing and discharging operations are sometimes curtailed when their impacts on360

price are significant, making energy arbitrage less profitable. Under the price-

maker assumption, the price profile becomes smoother with higher prices during

charging and lower prices during discharging. The proposed self-scheduling so-

lution prevents excessive price impacts during operation hours. This leads to a

more profitable solution and higher net operating profit than would be obtained365

if scheduling was carried out using price-taker formulation. Figure 11 demon-

strates that the impact of energy storage operation on the electricity price should

be taken into account, since ignoring its impact causes high errors in results and

20

overestimation in the potential revenue of energy storage facility.

Dispatch Characteristics of the Storage Facility During Five Years: The per-370

centage of time the storage facility is charging, discharging or idle for the five-year

period from 2010 to 2014 is plotted in Fig. 12. Considering the asymmetric nature

of the storage facility, with 140MW discharge capacity and only 90MW charge

capacity and with 70% roundtrip efficiency, 100% utilization corresponds to 69%

charge time and 31% discharge time. From Fig. 12, one can see that the facility375

is idle for between 41% and 54% of the time, and that generation occurs for less

than 24% of the available hours, with charging occurring between 27% to 35% of

the hours.

Considering the charging operations first, between 37% to 45% of the charging

hours, the storage facility charges at the rate lower than it charging capacity. It380

shows that considering charging impacts on market price, the charging power is

limited to lower rates to reduce price increment. Instead, it charges for more hours

to store sufficient amount of energy. moreover, it can be seen that the majority of

the charging occurs at full capacity. This implies that during majority of charging

hours, which is likely to coincide with low price periods, the market is relatively385

insensitive to an additional load; charging is not curtailed by increasing prices.

Conversely, much of the generation is conducted at a rate below maximum power.

This result is unlike that which may be expected from [13]. It is reported in [13]

that the energy storage mostly operates at full discharge when providing energy

arbitrage. The result of our study shows that at high price periods, the Alberta390

market price is sensitive to additional supply, and that during most of the hours

21

discharging should be curtailed below maximum power in order to balance price

and generated volume.

Based on Fig. 12, during years 2010 and 2014 the number of operating hours

is lower than other years. This implies that there are fewer arbitrage opportunities395

during those years (e.g., lower price volatility) whereas during 2013, the plant

operates for more hours than that of other years, 59% hours. This result implies

that among these five years, the highest price volatility occurs during 2013, which

brings profitable opportunities for energy arbitrage.

Weekly Profit Analysis During Five years: Figure 13 plots the weekly oper-400

ating profit earned through arbitrage in years 2010 to 2014. Table 2 also provides

the statistics of weekly profit during these years. Based on the total profit reported

in this table, the level of gained profit is much lower compared to the cases pre-

sented in price-taker studies [11, 12]. This shows the fact that storage operation

in the market noticeably impacts market price, which leads to significant overes-405

timation of potential profit in the case of price-taking assumption. As a result, the

price impact should be necessarily considered in the economic analysis.

It can be observed from Fig. 13 that the profit varies significantly week by

week and also year by year. For example, for year 2014, the weekly profit could be

as low as $ 0.006 million or as high as $2.55 million. This can be also concluded410

from Table 2; the standard deviation of the weekly profit is higher than the average

profit in all these years, implying significant variation in the number and level of

arbitrage opportunities in different weeks of the year. The comparison of weekly

profit for these five years and also the results provided in Table 2 show that in year

22

2013, the average weekly profit is higher than in the other years. The data in Table415

2 and Fig. 13 indicate that in the years 2010 and 2014, although the price varied

hourly and daily, the energy arbitrage opportunities rarely happened and are not

highly profitable. Thus, the weekly profit is mostly low compared to the other

years. As provided in the fifth column of Table 2, i.e., median column, for half of

the weeks in years 2011, 2012, and 2013, the obtained profit is higher than $0.247420

M, $0.258 M, and $0.198 M, respectively. This level is as low as $0.053 M and

$0.060 for years 2010 and 2014, respectively. Moreover, the comparison of Figs.

12 and 13 demonstrates that although the number of charging and discharging

hours in years 2011 and 2012 are slightly higher than those of years 2010 and

2014, the final annual profit in years 2011 and 2012 is almost two to three times425

as that of 2010 and 2014. This implies that there are a few highly profitable energy

arbitrage opportunities in 2011 and 2012, which makes a noticeable difference in

total profit between these two years, and years 2010 and 2014. Furthermore, based

on this table, the median of profit for the year 2013 is lower than that of years 2011

and 2012 in spite of total higher operating profit of year 2013 than that of years430

2011 and 2012. As shown in Fig. 13, there are a few weeks with significantly

high profit, which makes the total profit of year 2013 higher than the other years.

All these descriptions show the fact that the energy storage should be able to take

advantage of high price spikes and price drops as much as possible to get the most

out of energy arbitrage.435

Overall Impact on Market Price: The price duration curves for the year 2013

without and with the operation of storage unit are presented in Fig. 14. According

23

to Fig. 14, the operation of storage facility has a significant impact on the elec-

tricity price during peak hours, since the energy storage is only likely to discharge

during peak hours. At this time, the market supply curve is very steep and the440

storage discharging reduces the electricity price significantly.

Table 3 presents an analysis of the impact of energy storage discharging activ-

ities on the electricity price in each year. During discharging operation, the energy

storage facility causes a noticeable decline in the average price. For instance, the

average price during discharging periods in year 2013 decreases by $35.3/MWh,445

from $217.87/MWh to $182.58/MWh. Furthermore, even though the percentage

price changes are similar for the first three years and about 3% higher than that of

2013, the overall impact is obviously more significant when discharging at higher

prices (e.g., the average price decrease is higher in years 2011, 2012, and 2013

than the other years).450

Table 4 presents the impacts of charging operation on market price. Based on

the data plotted in Fig. 14 and presented in table 4, the charging of energy storage

has a smaller impact on price than discharging. This is because storage facility

mostly charges during low price periods during which both the demand and the

gradient of the supply curve are low. As a result, a small increase in demand does455

not significantly impact the price. The lowest increase in price is for year 2014,

which is on average $1.75/MWh. Charging operations have the highest impact on

market prices during year 2012 and 2013.

Considering both charging and discharging operations, table 5 presents the net

impact on average electricity price for each year in the study. The table indicates460

24

that the operation of energy storage leads to a decrease in the annual mean price

as the price reduction due to discharging operation is more substantial than the

price increase due to charging operation. The highest price decrease is in 2011

by $9.26/MWh, following by the years 2012 and 2013, which are respectively,

$7.89/MWh and $7.39/MWh. During years 2010 and 2014, the storage operation465

does not have as significant effect on prices as that of the other years.

4.2. Sensitivity Analysis

The sensitivity of the annual profit of the storage plant to different design

changes is explored to provide information to economically optimize storage en-

ergy, charging and discharging capacities. In the sensitivity analysis, only one470

characteristic is varied at a time, all other characteristics are assumed to be the

same as that of base case.

Figure 15 shows the impact of the discharging capacity on the annual and total

profit of the energy storage facility. It can be seen that larger discharging capacity

leads to higher profit. Expanding the discharging capacity from 60 MW to 100475

MW, or from 100 MW to 180 MW, increase the total profit by 40.7% and 36.5%,

respectively. This is because with larger discharging capacity, the unit is able to

generate more power. Consequently, more power could be sold during the hours

with the highest prices. This increases sales profit as well as the number of hours

when energy arbitrage is profitable. The increment rate differs from year to year.480

This rate is higher for years 2011, 2012, and 2013 compared to that of year 2010

and 2014. This is due to more frequent price spikes during years 2011-2013. Thus,

25

a storage with larger discharging capacity could better exploit these opportunities.

According to Fig. 15, the marginal incremental profit declines as discharging

power increases. The higher the level of injected power, the higher the (nega-485

tive) impact on price. Based on the developed formulation, when the discharging

power capacity is high, the operator sometimes decides to limit its production

level and not to sell high level of power to the market in order to avoid high level

of price drop. Thus, the storage would not benefit much from higher level of dis-

charging capacity. However, in studies in which the storage facility is assumed490

to be price-taker [13, 11], larger discharging power would almost linearly lead to

profit increment, since the impact of energy storage operation on market price is

ignored. Hence, even with larger discharging power, the price is assumed not to

change and consequently higher revenue is obtained.

Figs. 16 presents the effect of charging capacity, ranged between 10 MW to495

190 MW, on the storage profit in different years. Figs. 16 shows that increasing the

charging power improves the operating profit. For instance, increasing charging

capacity from 50 MW to 90 MW improve total profit by 12.8%. However, Fig.

16 demonstrates that the incremental rate of profit improvement is lower than that

of discharging capacity. Additionally, the incremental increase in profit declines500

with charging capacity such that there is negligible improvement for charging

power larger than 130 MW. This is due to the fact that in the Alberta electricity

market, the hours of low price happens frequently and thus, with not necessarily

large charging capacity, there is enough time for charging sufficient amount of

energy and taking advantage of peak prices. Therefore, a larger charging power505

26

does not noticeably improve system total operating profit.

Figure 17 shows the sensitivity of the annual profit to the energy capacity.

Storage size larger than 18 hours does not provide significant incremental arbi-

trage opportunity. This results implies that the additional storage is not used by

the unit. Due to the price pattern, the unit does not need to charge large amount of510

energy and at most 18 hours of storage is sufficient to take advantage of all hourly

and daily energy arbitrage opportunities. Moreover, Fig. 17 indicates more than

72% of the total potential value comes from the first 4 h of storage, i.e., intra-day

arbitrage. Additional operating profit is achieved by longer-term storage; 10 h of

storage captures about 91.6% of the potential profit, while 20 h of storage captures515

about 99% of potential profit.

Figure 18 represents the relationship between the operating profit gained by

the storage facility and the unit efficiency. The efficiency of the unit impacts the

annual profit as a higher efficient unit needs less energy to purchase to generate

one MWh of energy. Thus, a lower gap between the purchasing and selling price520

is required to make profit out of energy arbitrage. Figure 18 illustrates that im-

proving the storage efficiency from 60% to 70% would lead to around $7.35 M

additional revenue in five years. The additional gained profit can be used to com-

pare with the additional capital cost required to improve system efficiency and

determine profitability of the investment.525

The results presented in this paper are based on a general modeling of an

energy storage system. It is not the purpose of this paper to conduct financial

analysis for every storage technology. However, for a specific storage technology,

27

depending on technology and planned application, fixed and variable cost of the

device, as well as efficiency, the reported results can be useful for optimal sizing of530

that storage device. There is no universal optimal size of storage and the marginal

cost of the next incremental MW of charging or discharging or hour of storage is

wildly ranged depending on the technology.

5. Conclusion

This paper conducts a comprehensive study on the economic evaluation of a535

large-scale energy storage facility in the Alberta electricity market, incorporat-

ing the impacts of energy storage activities on market price. Hourly GPQCs and

DPQCs are utilized to precisely formulate the self-scheduling of a price-maker

energy storage in an electricity market. Then, the developed model is applied

using the historical hourly GPQCs and DPQCs of the Alberta electricity mar-540

ket to explore the economics of energy storage in this market. The results show

that energy storage operation significantly affect market price, especially during

high price hours. During high price hours the supply curves are steep and a rel-

atively small change in supply may change the price substantially. As a result,

the proposed formulation mat curtail charging and discharging operations relative545

to price-taking self-scheduling, when their impacts on price are high and energy

arbitrage becomes unprofitable. In this way, the predicted gained profit is lower

than that reported in price-taker studies, demonstrates the necessity of incorporat-

ing price impacts during economic studies.

Sensitivity analyses are performed to investigate the impacts of different stor-550

28

age characteristics on its profit. The results illustrate that larger discharging ca-

pacity leads to a higher level of profit due to the ability to sell more power during

peak price periods. However, the incremental return declines due to the impact of

discharging power on the market price. The sensitivity analysis on charging power

shows that, larger charging capacity up to 180 MW can return higher profit. How-555

ever, the profit increment saturates quickly as low prices occur frequently in the

Alberta electricity market. Even with a low charging power capacity, there is time

to store sufficient energy. It is shown that 4 and 10 hours of energy storage capac-

ity are able to capture 72% and 91.6% of potential profit profit, respectively. The

Higher storage efficiency decreases the cost of purchasing the electricity and con-560

sequently increase the annual profit. The presented results can be used to optimize

the size of storage device depending of the storage technology.

In the developed self-scheduling model, forecasts of DPQCs and GPQCs are

require inputs to the problem. In our study, the actual historical DPQCs and

GPQCs are used, since we focus on evaluating the economic feasibility of a stor-565

age facility based on historical market data. In other words, we say what would

have been the revenues if this facility was in operation and had a perfect knowl-

edge of the market. The outcomes are the upper bound of the economic feasibil-

ity, and real-life uncertainties could make the economics less attractive depending

how the actual curves deviate from forecast curves. However, the focus of our pa-570

per in not designing bidding strategies under forecast uncertainty of these param-

eters. The authors are currently working on bidding strategies for such a facility

under various sources of uncertainty and revenue streams.

29

Moreover, the database of GPQCs and DPQCs and the developed linearized

scheduling model can be used to formulate an optimization framework to find the575

optimal size for an specific energy storage technology. This is an ongoing study

in our research group.

The important assumptions that are made for this study are (i) market partic-

ipants do not react to the presence of an energy storage facility and act the way

they did without it, and (ii) no demand charges are considered when calculating580

profit values. As for assumption (i), it is hard to model how market participants

would have reacted if the the facility was in service in each of those years. The

authors are investigating alternative methodologies that could be used for doing

just that. For the second assumption, demand charges are sometimes high and

could significantly impact the profitability of a facility. These two assumptions585

need to be kept in mind when interpreting the findings of this research.

Acknowledgment

The authors would like to thank the NRGStream company for providing us

with the software by which we could extract the database used in our study.

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35

Figures

0 1000 2000 3000 4000 5000 6000 7000 8000 87600

200

400

600

800

1000

Hours

Pri

ce (

$/M

Wh

)

Figure 1: Hourly electricity price during 2013 in the Alberta electricity market

Figure 2: An example of a typical a) GPQC, b) DPQC

Figure 3: Sample supply curve for hour ending 1, December 31, 2014

36

Figure 4: Supply curves for each of the 24 hours on August 1, 2014

Figure 5: Supply curves for hour ending 1 for the month of October 2014.

Figure 6: an example of price decrease due to a 150 MW new supply to the system

37

Figure 7: an example of price increase due to a new 100 MW demand to the system

Figure 8: Generation PQC, the linearization process [26].

38

Figure 9: Demand PQC, the linearization process.

Figure 10: scheduling of storage plant and price of electricity during an arbitrary week in the caseof ignoring the impact of storage operation on electricity price

Figure 11: scheduling, price of electricity before and after operation, for a price-maker storageplant during an arbitrary week

39

Figure 12: Dispatch characteristic of a price-maker storage facility during 2010 to 2014

Figure 13: Weekly profit of a price-maker energy storage facility during a) 2010, b) 2011, c) 2012,d) 2013, and e) 2014.

40

0 1000 2000 3000 4000 5000 6000 7000 80000

200

400

600

800

1000

Time (Hour)

Price($

/MW

h)

Without storage operationWith storage operation

Figure 14: Price duration curve without and with operation of a price-maker storage facility during2013.

Figure 15: Profit of storage facility as a function of discharging capacity (Charging capacity isfixed at 90 MW, storage capacity is fixed at 10-hr )

Figure 16: Profit of storage facility as a function of charging capacity (discharging capacity isfixed at 140 MW, storage capacity is fixed at 10-hr )

41

Figure 17: Profit of storage facility as a function of storage capacity (Discharging capacity is fixedat 140 MW, charging capacity is fixed at 90 MW)

Figure 18: Profit of storage facility vs. energy storage efficiency (Discharging capacity is fixed at140 MW, charging capacity is fixed at 90 MW, the storage capacity is 10 hours of full dischargingcapacity)

42

Tables

Table 1: Summaries of comparison with previous worksReference Price-taker/maker Modeling Approach for Impact on Price

[6, 9, 10, 11][12, 13, 14] Price-taker N/A

[6] Price-maker Monthly linear supply curve[17] Price-maker MPEC-Game based

[18, 19] Price-makerapproximate residual demand curve(RDC) and nonlinear optimization

[20] Price-makerOne representative supply

curve for all hours

This Study price-makerHourly price quota curves

and non-game based linear optimization

Table 2: Weekly Profit Analysis for a Price-Maker storage facility during 2010 to 2014 [Million$]

Year Min. Max. Mean Median StandardDeviation Total

2010 0.006 2.55 0.194 0.053 0.418 10.102011 0.015 2.69 0.578 0.247 0.682 30.052012 0.002 3.20 0.494 0.285 0.635 25.672013 0.021 3.39 0.615 0.198 0.895 31.992014 0.020 2.50 0.269 0.060 0.494 14.00Total - - - - - 111.81

Table 3: Price analysis without and with storage operation during discharging hours

Year No.Hours

Price average[$/MWh] Price change

Without With [$/MWh] %2010 1597 128.32 103.69 -24.62 -19.22011 2089 216.17 174.41 -41.75 -19.32012 1974 198.05 158.60 -39.45 -19.92013 2110 217.87 182.58 -35.30 -16.22014 1810 122.81 106.24 -16.58 -13.5

43

Table 4: Price analysis without and with storage operation during charging hours

Year No.Hours

Price average[$/MWh] Price change

Without With [$/MWh] %2010 2408 24.52 27.23 2.71 11.12011 2696 21.78 23.90 2.12 9.72012 2976 18.69 21.70 3.01 16.12013 3023 24.26 27.53 3.27 13.52014 2879 21.13 22.88 1.75 8.3

Table 5: Price analysis without and with storage operation for all hours

YearPrice average

[$/MWh] Price change

Without With [$/MWh] %2010 50.95 47.20 -3.75 -7.42011 76.27 67.01 -9.26 -12.12012 64.64 56.75 -7.89 -12.22013 80.22 72.83 -7.39 -9.22014 49.66 46.81 -5.75 -5.7

44