Applied Energy 125 (2014) 93–102
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
The value of energy storage in South Korea’s electricity market: A Hotelling approach q Anastasia Shcherbakova a,⇑, Andrew Kleit b, Joohyun Cho b a b
The University of Texas at Dallas, 800 W Campbell Road, Richardson, TX 75080, United States The Pennsylvania State University, 201 Hosler Building, University Park, PA 16802, United States
h i g h l i g h t s We evaluate lifetime economic potential for energy arbitrage in South Korea. We simulate lifetime energy flows and profits for small price-taking NaS and Li-ion batteries. We devise optimal battery operating strategy using Hotelling’s depletion rule. Cumulative profits depend on intraday price differences and social discount rate. At current electricity prices, neither battery generates enough arbitrage revenue to offset capital costs.
a r t i c l e
i n f o
Article history: Received 14 September 2013 Received in revised form 19 February 2014 Accepted 22 March 2014 Available online 16 April 2014 Keywords: Electricity market Energy storage Arbitrage profits Hotelling’s rule Empirical simulation
a b s t r a c t In this study we evaluate the economic potential for energy arbitrage by simulating operation and resulting profits of a small price-taking storage device in South Korea’s electricity market. As demand for electricity continues to grow, maintaining a balanced power system at all times has become more challenging in Korea and other developed nations. Along with demand response programs and increased renewable energy utilization, energy storage devices may provide a viable way to contribute to diurnal peak demand shaving. In some parts of the U.S. storage arbitrage has proven to be profitable. Treating a battery’s ability to charge and discharge as a scarce resource, we apply the Hotelling (1931) rule to determine a strategy for maximizing the value of the battery. Results show that present market conditions in South Korea do not provide sufficient economic incentives for energy arbitrage using sodium–sulfur (NaS) or lithium-ion (Li-ion) batteries, with the capital cost of the storage devices exceeding potential revenues. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Phasing storage devices into existing electricity networks can potentially help to address the challenge of rising peak generation costs by making lower-cost power generated during off-peak times available to meet peak-time demand. However, storage remains a weak link in electricity markets, partly due to the high cost of storage devices. Empirical studies differ on the economic viability of storage. Some authors find that potential storage arbitrage profits are not always sufficient to offset the capital cost of the storage device [1–7], while other simulations demonstrate more promising
q This research was supported by a Grant from Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Korea government Ministry of Knowledge Economy (No. 20118530020010). ⇑ Corresponding author. Address: 800 W Campbell Road, SM 31, Richardson, TX 75080, United States. Tel.: +1 972 883 5871. E-mail address:
[email protected] (A. Shcherbakova).
http://dx.doi.org/10.1016/j.apenergy.2014.03.046 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.
results [2–9]. In this study we evaluate the economic viability of storage in the South Korean electricity market. Specifically, using hourly day-ahead system marginal electricity prices (SMPs) for the years 2009–2011, published by Korea Power Exchange (KPX), and a set of charging and discharging rules, we calculate potential lifetime profits resulting from arbitrage activities using a small battery in Korea’s energy market. South Korea faces many of the challenges common to developed-world electricity sectors, including fluctuating costs of input fuels, regulated retail rates, and a continually growing demand for electric power. A large-scale blackout that roiled Seoul on September 15, 2011 caused much concern among citizens about the resilience of the country’s existing power infrastructure [10,11]. During the summer of 2013, the country faced another potential electricity supply crisis as operation of three nuclear power plants was suspended during unusually hot summer weather due to corruption-related safety concerns [12,13]. The government responded with a public commitment to strengthen the nation’s electricity
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networks through a combination of more efficient management via the smart grid and complementary increases in utilization of renewable energy and demand response programs [14,15]. At this time, demand response consists mainly of periodic mandates for power use reduction from large commercial and industrial users. Although these two measures can provide an effective stopgap solution to peak demand reduction, alone they are unlikely to resolve concerns about reliability. In fact, both demand response and renewable generation bring additional uncertainty into the power market: uncertainty in compliance in case of DR, and uncertainty in supply availability (intermittency) in case of renewables. Storage devices can in principle complement the use of demand response and renewable generation in achieving a more stable and secure supply. The needed infrastructure can potentially be provided through private entry by independent owners of small-scale storage devices as long as the current diurnal variation in generation costs is sufficiently high to generate profits from storage operation (via energy arbitrage). Such private storage devices can prove to be particularly valuable to power markets facing peak reliability challenges. In this study we set out to determine whether South Korea’s power markets offer sufficient financial incentives in the energy market to induce private entry into storage operations. The next section summarizes existing literature on the topic of storage value; Sections 3 and 4 detail our simulation approach for two alternative storage technologies, NaS and Li-ion batteries, describe all utilized assumptions about market conditions and technological parameters, and present our findings. In particular, we present a strategy for maximizing a battery’s charge and discharge capacity, following the classic Hotelling rule [16]. Section 5 concludes with a summary of main results for both technologies and a discussion of policy implications. 2. Literature review Empirical studies on the economic viability of storage are largely dependent on the economic and technological circumstances surrounding any given storage project. All studies reviewed for this article point out that a storage device’s ultimate profitability is a function of chosen storage technologies and their specifications, the level of regional electricity prices, prices of generation fuels, the particular market selected for storage operation (e.g. energy, regulation, ancillary), the quality of price forecasts, existence of government subsidies and their levels, and so on, and that all of these factors tend to vary over time, making accurate profitability analysis rather challenging. For example, Ekman and Jensen [1] find that profits generated from energy arbitrage on Denmark’s spot power markets were quite a bit lower than the capital costs of installing storage devices, rendering storage uneconomic. Similar financial results are obtained by [3–7]. Mulder et al. [3], studying solar energy systems in Western Europe find that it is not economic, without increases in electricity prices, to use batteries to support household photovoltaic installations. Similarly, in a 2007 paper analyzing regional New York grids, Walawalkar et al. [2] concluded that running peaking generators is generally more economic than using storage, given the economic and technological conditions surrounding markets under their evaluation. The authors also find, however, that storage operators in New York City had a high probability of earning positive profits from energy arbitrage and regulation activities using sodium–sulfur (NaS) and flywheel storage devices. The opportunities for positive economic returns in eastern and western parts of upstate New York, however, were much lower. A thorough review of storage literature by Aucker et al. [6] points out that most studies of storage economics conclude that energy arbitrage by itself is not a profitable activity. A study of seven real-time U.S. electricity markets and 14 different storage
technologies by Bradbury et al. [17] found that the optimal profit maximizing size of a storage device depends largely on its technological characteristics, rather than the magnitude of market price volatility. He and Zachmann [18] note that since power prices tend to stay low for longer duration of time than they remain high, the most profitable storage devices will be those that have low charging rates and high discharging rates, enabling them to take advantage of short peak pricing intervals. On an larger scale, studies of pumped hydro and compressed energy storage systems to supply peak demand or support renewable integration [4,5], [9], and [19] find that such systems are not likely to be effective without appropriate government subsidies (e.g. feed-in tariffs) [4,5,19] or sophisticated high-frequency reserve markets in which generators can take advantage of real time price differences by trading hourly contracts [5]. In only one of our reviewed studies (that of a wind farm in southeastern Australia [9]) do the authors found positive rates of return to complementing the wind farm with pumped hydro, compressed air, or thermal energy storage systems. Generally, although the social or system benefits of storage integration can be high [20], lack of financial incentives prevents capital from seeking out storage projects. Incorporating storage systems in South Korea’s power industry is one component of the government’s green growth strategy [21,22], which focuses on renewable energy and smart grid development. With several South Korean companies, including Samsung and LG Chem, having recently emerged as leading energy storage manufacturers, the country appears to be a good candidate for government-driven storage investment initiatives. However, private entry does not require large-scale coordination of resources and likely allows for faster implementation and a more flexible adjustment toward efficient storage capacity levels as market conditions change and technology evolves. In August 2013, the South Korean government announced plans to promote energy storage devices by encouraging their use by large enterprises and providing financial subsidies to small and medium-sized companies investing in storage systems, along with revising the electricity rate structure to further discourage peak power purchases directly from the grid [23]. In order to determine whether incentives for private entry exist, we devise a strategy to simulate operations of a hypothetical storage device. 3. Simulation approach Our empirical approach is structured around maximizing the battery owner’s operating profits. Let t index the year under analysis; Pt denote the price differential (call this the discharging premium) between charging and discharging SMPs in year t; St denote number of full cycles a battery completes in year t, as a function of the discharging premium, St = St(Pt); S be the total cycle capacity in the battery over its useful life; r denote the interest rate and Rt the discount factor, Rt = 1/(1 + r)t. Define pt = pt(St) = pt(St(Pt)) as the net operating revenues per year as a function of the discharging premium that year. Abstracting from the battery’s fixed acquisition (capital) costs, the battery owner seeks to maximize operating revenues over the stream of Pt, given the lifetime capacity constraint S:
Max Pt
X
pt ðSt ðPt ÞRt Þ
ð1Þ
t
subject to
X St ðP t Þ ¼ S t
We estimate the maximum operating revenues for our hypothetical storage device owner through a three-stage analysis. The first stage of this process involves using historic Korean electricity data from the years 2009–2011 to devise an optimal battery
A. Shcherbakova et al. / Applied Energy 125 (2014) 93–102
operating strategy. This optimal strategy enables us to calculate energy arbitrage potential across these three years and calibrate a more general model of storage profitability for South Korea. In the second stage of our analysis, we use results from the first stage to derive an econometric relationship between two dependent variables—annual operating revenues and battery usage levels—and our primary explanatory variable—the premium for which a storage owner can sell stored energy back to the grid (the discharge premium). Finally, in the third stage of our analysis, we use coefficient estimates from the second-stage regression models to simulate a stream of discounted operating revenues for the full useful life of the storage device. We maximize the present value of this stream using an approach based on the classic work by Hotelling [16]. This analysis is performed for a variety of discharging premium levels and interest rates. We present the details of all three of these empirical steps in this section, beginning with an optimal threeyear operating strategy. 3.1. Three-year operating revenue potential Imagine an individual who owns a battery that can be connected to the electric grid and both draw power from the grid, and discharge it back into the grid. suppose this individual begins to track marginal generation costs (assumed to be equal to the system marginal price – SMP) of electricity throughout the day. In principle, he can use this price information to formulate an arbitrage strategy: utilize his battery to purchase power from the grid during hours when the SMP is at its lowest levels, and resell it back into the grid during hours when the SMP is at its highest levels. We assume that the battery in question is necessarily a small device, the operation of which has no effect on equilibrium prices (i.e. our hypothetical battery owner is a price taker). This assumption allows us to avoid challenges of dynamic estimation whereby, given a large enough battery, the actions of the battery operator will lead to an increase in off-peak demand for electricity during charging hours and an increase in peak supply of electricity during discharging hours. This battery storage and discharge will cause generation plants to produce slightly more electricity in off-peak hours and slightly less electricity during peak hours. Assuming that South Korea’s bid stack is upward sloping (that is, power providers dispatch generating assets in order of increasing marginal cost), the additional cost of producing e kWh of electricity during offpeak hours should be less than the cost savings from not producing e kWh of electricity during peak hours. Thus, the total system generation costs should fall as battery devices redistribute available generation from off-peak to peak demand periods, leading to a decrease in SMPs and a consequent adjustment in the battery operator’s charging and discharging strategy. We account for common frictions of battery operations by incorporating imperfect charging and discharging efficiency and assuming a gradual degradation of the battery’s physical capacity over time. We pair technological battery specifications with economic parameters and a set of charging and discharging rules to produce an estimate of a battery’s lifetime profits, which are then compared to the battery’s estimated capital cost to determine whether private investors face sufficient economic incentives to purchase a storage device and enter the energy market. Before beginning our empirical analysis, we identify appropriate parameters for our hypothetical storage device, specify market conditions under which operation will take place, and devise a set of rules under which an arbitrage strategy will be formulated. 3.1.1. Battery specifications Consistent with views on commonly accepted viable grid-scale storage devices in economic and engineering literature, we
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introduce into South Korea’s present electricity market a hypothetical sodium–sulfur (NaS) battery. Although many grid-storage studies reference pumped hydro and compressed air energy storage systems due to their maturity and commercial viability, these technologies are limited by geological constraints. Pumped hydro relies on large differences in elevation and is thus optimally sited at mountaintops. The success of compressed air storage, on the other hand, depends on availability of underground caverns in which compressed air could be stored. Such locational features, by contrast, do not restrain electro-chemical storage systems. Of the presently available electro-chemical storage systems, sodium–sulfur batteries are the most advanced in terms of commercial applications and typically have a larger capacity, longer discharging durations and high power ratings than either advanced lead-acid or lithium-ion batteries, which are not yet used for commercial grid applications [24]. For these reasons, we select a NaS battery as the most promising storage system for taking advantage of energy arbitrage opportunities. Our hypothetical NaS battery has a total capacity of 7.5 MWh; maximum power flow of 1 MW per hour (both into and out of the battery); a useful life of 4320 full cycles at a depth of discharge of 90%,1 with a single full cycle taken as 7.5 MWh of discharged energy; and round-trip charging efficiency of 86%.2 3.1.2. Rules governing battery operation For the sake of simplicity, we assume that our hypothetical price-taking storage owner has perfect foresight with respect to prices, which allows us to calibrate the optimal operating strategy for the storage device – i.e. one that yields the maximum available profit during the analyzed three-year time period, and a one-day forward horizon for storage decisions. This assumption serves to overestimate the actual profits from storage strategies. To maximize profits from storage operating decisions, we introduce a minimum discharging SMP premium, below which the battery owner will not operate his storage device. This premium accounts for physical degradation of the battery’s capacity over the course of its useful life and informs a battery operator’s energy selling activities, such that power will be discharged back to the grid only when SMP exceeds that at which power was purchased by at least this minimum premium, after accounting for charging efficiency losses. Consider a simple example in which a battery operator draws 1000 kWh of energy from the grid, all at a price of 100 Korean won3 per kWh. Given a one-way efficiency of 93%, 930 kWh would end up stored in the battery, costing a total of 100,000 KRW. Suppose price rises to 170 KRW per kWh and the operator decides to discharge all of the stored electricity. After further efficiency losses during the return trip, 865 kWh (or 93% of 930 kWh) would reach the grid, putting revenue at 147,050 KRW. Your net revenue is thus 47,050 KRW. The last layer of complexity we introduce into the simulation strategy is that of time preference. Since our assumed storage device is likely to last for many years, during which the battery’s 1 The extent of the battery’s useful life, measured in full cycles, is affected by its depth of discharge (DoD). Our assumed useful life of 4320 full cycles under a DoD of 90% comes from NaS product documentation of NGK Insulators Ltd., a battery developer (see [24], Section 4, pages 4–9). While engineering studies typically suggest estimating useful life in full cycle terms by multiplying assumed DoD by the number of actual utilized cycles, in our economic approach we rely on an empirical review of field studies, commercial application studies, and related sensitivity analyses for NaS projects for specified DoD. For more details, see [2,17,25]. 2 This figure is based on a one-way battery charging and discharging efficiency of 93 percent, commonly cited in engineering literature. See, for example, [26]. All storage parameters are derived from [24,26,27]. 3 Since we are working with Korean data, all monetary figures in this manuscript are expressed in Korean won (KRW). At the time of writing, the exchange rate was approximately 1100 KRW per USD.
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L¼
X
pt ðSt ðPt ÞÞRt þ k S
t
! X St ðPt Þ
ð2Þ
t
dL dpt dSt t dSt ¼0 ¼ R k dPt dSt dP t dP t
ð2aÞ
X dSt dL ¼ S ¼0 dk dPt t
ð2bÞ
The Lagrangian in Eq. (2) is composed of the present value of P t cumulative revenues to be maximized and the t pt ðSt ðP t ÞÞR constraint that the number of cycles used must equal the number P of battery cycles available ( tSt(Pt) = S). The first FOC (Eq. (2a)) dpt t yields k ¼ dSt R , with k translating to the present value of the marginal revenues from an additional charge–discharge cycle. The second FOC (Eq. (2b)) collapses to the original lifetime cycle constraint. Note that given Pt, dpt/dSt = Pt, as the lowest valued cycle in any year t will have marginal revenues of Pt. Substituting in dpt/dSt = Pt, and cancelling terms yields Pt = k/Rt. Thus, when t = 0, P0 = k. When t = 1, P1 = k/R, and so on. As we will see, this reduces the choice set to choosing the initial discount premium k that maximizes profits. 3.1.3. Economic parameters The only remaining parameters to specify are prices and the interest rate. The battery owner’s optimal arbitrage strategy is based on Mainland Korea hourly SMPs from January 1st, 2009 through December 31st, 2011. These prices are published by Korea Power Exchange in the Electric Power Statistics Information System (EPSIS).4 The appropriate discount rate is initially chosen to be 5.5% – a standard discount rate applied to public projects in South Korea, according to the Korea Development Institute [28]. The effect
of discount rate choice is evaluated via sensitivity analysis by varying the rate between 2% and 10%. To begin the simulation, we identify charging and discharging opportunities in the three years of hourly data available to us by pairing hours with lowest SMPs of the day, during which energy is bought, with the day’s high-SMP hours on which energy is sold back to the grid. We begin by pairing the highest SMP observation with the lowest SMP one, then the second highest with the second lowest, and so on, until the gap between highest and lowest SMPs reaches Pt (zero KRW, for the limiting case). Next, we apply the following constraints and reassign hour pairs that do not satisfy them: 1. No energy can be sold during the first time period (it must be purchased first). 2. The amount of energy sold at any given point in time cannot exceed the amount stored in the battery, after accounting for all efficiency losses. 3. The amount of energy stored cannot exceed the assumed battery capacity. 4. The SMP of discharging hours on any given day must exceed the SMP of charging hours by P0 KRW/kWh during the first year of operations, and, following the Hotelling t rule, by P0 ð1 þ iÞ KRW/kWh for subsequent years, with i denoting the relevant interest rate and t denoting the year under analysis. 5. If any energy remains in the battery at the end of any given day, it must be sold the following day for a price greater than or equal to the price at which it was bought plus the discharging premium required during the year under analysis. This leaves us with a set of hourly buying and selling decisions that we can use to calculate revenues. Fig. 1 displays an example of charging and discharging activities at given hourly SMPs during three days in January 2009. Gray vertical bars in the positive (negative) x-axis range denote instances of battery charging (discharging), with the amount of energy bought (sold) reflected in the bars’ length. The solid black line denotes hourly SMPs. Note that charging activity occurs during the day’s lowest SMPs, and discharging activity occurs during daily SMP highs. Table 1 details cumulative operating revenues (net of energy purchasing costs) resulting from the three-day arbitrage strategy displayed in Fig. 1, which are calculated via Eq. (3):
p¼
X ðSMPSh Q Sh e SMPBh Q Bh =eÞ
where SMPSh and SMPBh are system marginal prices of sold and bought electricity, respectively, at hour h; Q Sh and Q Bh are quantities
Jan 1
EPSIS can be accessed at http://epsis.kpx.or.kr/.
Jan 2
Jan 3
4,800
250
3,800
200
2,800
150
1,800 100 800 -200 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70
50 0
-1,200
Hour Energy Flows (KWh)
4
ð3Þ
h
SMP(KRW/KWh)
Fig. 1. Example of a three-day arbitrage strategy, January 1–3, 2009.
SMP (KRW/kWh)
storage capacity will slowly erode, the storage owner faces an opportunity cost of using the battery today (i.e. today’s use leads to diminished capacity and therefore reduces opportunities for future use). Hotelling’s rule [16] tells us that the efficient (that is, value-maximizing) path of extraction of an exhaustible resource is one under which marginal revenues grow at the rate of interest. This equilibrates discounted marginal revenues across time and eliminates producer incentives for changing the timing of extracting activities. Here the battery’s capacity can be viewed as an exhaustible resource. We account for Hotelling’s rule by requiring the discharging premium to increase at the rate of interest across time. For example, assume that the initial (year 0) required discharging premium is 20 Korean won, and the interest rate is five percent. This implies that the spread in the first year will be 20*(1.05) = 21 KRW. The spread in the second year will be 20*(1.05)2 = 22.05 KRW, the spread in the third year is 20*(1.05)3 = 23.1525*KRW, and so on. This translates intuitively into an increase in the opportunity cost of battery use over time, since the more the battery is used as time goes by, the greater the extent of deterioration in its capacity, and the fewer opportunities for its future use remain. The insight offered by Hotelling will lead us to look for the optimal opportunity cost (i.e. discharging premium) in the first period of battery operation. To evaluate sensitivity of our results to the choice of initial required discharging premium, we will calculate the net present value of revenues to the storage operator across the starting discharge premium (opportunity cost) ranging between zero and 139 KRW per kWh. The constrained maximization problem in Eq. (1) results in the following Lagrangian and first order conditions (FOCs):
Energy Flows (kWh)
96
A. Shcherbakova et al. / Applied Energy 125 (2014) 93–102
97
Table 1 Operating revenues from three-day arbitrage strategy, January 1–3, 2009. Date
Hour
Quantity charged (kW)
January 1
10 11 12 19 23 24
1000 1000 1000
2 3 4 5 6 11 12 15 18 24
1000 1000 1000 1000 1000
22 24
1000
January 2
January 3
SMP (KRW/kWh)
Revenues – running total (KRW)
594.7 1000 1000
55.51 55.51 55.51 151.90 166.13 203.07
55,510 111,020 166,530 76,195 89,935 293,005
1000 1000 324.5 1000 1000
100.05 92.15 90.44 93.81 104.71 178.24 179.86 178.24 180.18 178.79
192,955 100,805 10,365 83,445 188,155 9,915 169,945 227,784 407,964 586,754
864.9
104.10 180.00
482,654 638,336
Quantity discharged (kW)
Total operating revenues
638,336
sold and bought, respectively, at hour h; and e is one-way efficiency (assumed to be 93%, following engineering literature. See, for example, [24]). The levels and dispersion of observed SMPs during the three years under our analysis differed, with 2010 presenting the most opportunities for profitable arbitrage and 2009 presenting the fewest (see Fig. 2). Average differences for 2009, 2010, and 2011, respectively, were 43 KRW, 76 KRW, and 50 KRW. These important variations help us to account for some of the inter-temporal differences that could be brought on by changes in weather patterns, economic activity, and other factors. We do this by calculating revenues and associated levels of battery use (measured in full cycles) at the annual level and averaging annual figures. Three-year averages of both outcomes are calculated for discharging spreads between 0 and 139 KRW/kWh, leaving us with 140 observations of revenues and cycle use, which we use in subsequent regression analysis. Annual averages of operating revenues and battery use are shown in Figs. 3 and 4, respectively. Both decline as the required discharging premium increases, since this precludes the battery operator from discharging during hours with relatively low SMPs. Annual operating revenues start at above 40 million KRW for discharging premiums below 10 KRW/kWh, and fall to below 20 million KRW as discharging premium surpasses 50 KRW/kWh. The battery’s usage level for the same discharging premium range declines from more than 200 full cycles per year to less than 40. 3.2. Econometric models of annual operating revenues and battery usage 2009–2011 data allows us to evaluate short-term revenue potential for a chosen battery technology. However, we need a longer-term perspective in order to identify economic viability of storage technology in Korea’s power markets. We can gain such perspective econometrically, by establishing a relationship between annual operating outcomes (battery usage and revenues) and the required initial discharging premium, as specified in Eqs. (4) and (5).
St ¼ f ðPt Þ ¼ b0 þ b1 P t þ b2 P2t þ b3 P3t þ b4 P4t þ et
ð4Þ
Fig. 2. Annual distributions of daily differences between peak and off peak system marginal prices.
pt ¼ gðPt Þ ¼ d0 þ d1 Pt þ d2 P2t þ d3 P3t þ d4 P4t þ mt
ð5Þ
where St and pt denote the number of full cycles a battery operates and the operating revenues the battery operator gains over the course of year t; Pt is the discharging premium during year t, varying here between 0 and 139 KRW/kWh; b and d are parameters to be estimated; and et and mt are i.i.d. error terms. Regression results are presented in Tables 2 and 3. Table 2 indicates that an increase in the discharging premium likely reduces revenues, but this happens at a decreasing rate as the premium rises higher and higher. Table 3 reveals a similar relationship between the discharging premium and battery usage, which makes intuitive sense, since a higher discharging premium limits the number of profitable operating opportunities that the storage owner is likely to face. Storage operator facing an opportunity cost of battery use of 20 KRW/kWh will face more opportunities to sell stored energy back to the grid than an operator facing an opportunity cost of 50 KRW/kWh. This is illustrated in Fig. 2. In the third and final stage of our analysis, we use these regression results to simulate a battery’s lifetime operating revenues and length of useful life.
A. Shcherbakova et al. / Applied Energy 125 (2014) 93–102
Operating Profits, 1,000 KRW
98
the number of battery cycles that will be used and the amount of revenues that will be earned during this initial year of storage operations. 2. At the start of the second year of operations, we increase the required discharging premium by a factor of 1.055 (recall that the official published interest rate for public projects in South Korea is 5.5%). This new premium is then used to estimate the number of battery cycles that will be used and the amount of operating revenues that will be earned during the second year of storage operations. a. The second year’s utilized cycles are added to those of the first year to obtain cumulative usage, while the second year’s operating revenues are discounted at the public project discount rate and added to first year’s revenues.
50,000 45,000 40,000 35,000 30,000 25,000 20,000 15,000 10,000 5,000 0 0
10
20
30
40
50
60
70
80
90 100 110 120 130
Discharging premium (KRW/kWh) Fig. 3. Annual operating profits for varying discharging premium levels for a NaS battery, average over 2009–2011.
Number of full cycles utilized
250
3. At the start of year three, the required discharging premium is increased by a factor of 1.0552 and this new spread is used to generate the third year’s revenues and battery usage. a. The third year’s cycles are added to the cumulative total of the first two years. The third year’s revenues are discounted back to the initial year of operations and added to the cumulative present value of revenues of the first two years.
200 150 100 50 0 0
10
20
30
40
50
60
70
80
4. This process continues until the cumulative number of cycles reaches the battery’s assumed life span of 4320, as summarized in Eqs. (6) and (7).
90 100 110 120 130
Discharging premium (KRW/kWh) Fig. 4. Number of full battery cycles utilized per year for varying discharging premium levels for a NaS battery, average over 2009–2011.
S¼
T T T X X X St ¼ f ðPt Þ ¼ f ðP0 ð1 þ rÞt Þ ¼ 4320 t¼0
Table 2 Regression output modeling annual operating revenues as a function of discharging premium for NaS battery.
Pt Pt2 Pt3 Pt4 Intercept R2 N
(1)
(2)
(3)
(4)
343.261*** (31.77) – – – – – – 38,366.910*** (44.17)
795.557*** (49.12) 3.254*** (28.85) – – – – 48,769.700*** (100.10)
615.724*** (16.84) 0.008 (0.01) 0.016*** (5.37) – – 46,724.054*** (79.88)
51.540 (1.79) 21.775*** (25.66) 0.260*** (28.29) 0.001*** (26.80) 42,236.275*** (147.00)
0.880 140
0.983 140
0.986 140
0.998 140
Log-likelihood ratio tests (H0: the expanded model fits the data no better, statistically speaking, than the abbreviated model) X2 (df = 1)
–
273.95***
26.96***
258.16***
Note: dependent variable is average annual operating revenue, in thousands of KRW; t-statistics in parentheses. * Significance level: 10%. ** Significance level: 5%. *** Significance level: 1%.
3.3. Lifetime operating revenues and utilization potential In the final stage of our analysis, we combine coefficient estimates displayed in Tables 2 and 3 with the increasing opportunity cost of battery use suggested by Hotelling’s rule of optimal resource depletion. The simulation proceeds as follows: 1. We begin with the first year of battery operation and an initial required discharging premium of zero KRW/kWh. Applying coefficient estimates from Tables 2 and 3 and a initial Pt of 0 to the models specified in Eqs. (4) and (5), we estimate
t¼0
T X
T T X X gðPt ÞRt ¼ gðP 0 ð1 þ rÞt ÞRt
t¼0
t¼0
pt ¼
ð6Þ
t¼0
ð7Þ
t¼0
The above process is repeated for initial required discharging premiums (P0) of 0–139 RW, in increments of 1 KRW, and for discount rates (r) between 2 and 10%, in half percentage point increments. Abbreviated results of discounted lifetime revenues and length of useful life are reported in Table 4 and displayed in Figs. 5 and 6.5 Initial discharging premium of 5 KRW/kWh (about half of a cent/ kWh) generates the highest lifetime revenue potential, yielding 664 million KRW (about $667,000) over the course of about 40 years. We can see from the figures that the actual peak of revenues occurs at a premium of between 5 and 6 KRW/kWh. It is also apparent from Fig. 5 that changes in initial required premium have two effects on lifetime discounted revenue stream. As the premium begins to rise, lifetime revenues initially increase because per unit revenues are increasing. As the required premium continues to rise, however, revenues begin to fall because the storage operator faces fewer annual opportunities to engage in arbitrage, so more arbitrage income is earned further in the future and hence is more discounted. At about the same premium level, the length of useful life begins to increase significantly as the battery operator cycles the battery less and less each year. To zero in on the optimal discharging premium, we repeat steps 1–4 above for premium increments of 0.05 KRW/kWh in the 5– 6 KRW/kWh range. Results appear in Table 5 and Figs. 7 and 8 and show that, under the assumed conditions, the most profitable strategy for the battery operator is to begin selling stored power back to the grid at an initial SMP that is 5.50 KRW/kWh higher than the SMP at which power was purchased. Selected sensitivity results due to changes in the discount rate are presented in Table 6. An increase in the discount rate has the 5
Complete results are available from the authors.
99
Pt Pt2 Pt3 Pt4 Intercept R2 N
(1)
(2)
(3)
(4)
1.027*** (19.71) – – – – – – 107.647*** (25.69)
3.257*** (48.87) 0.016*** (34.57) – – – – 158.936*** (79.28)
4.852*** (67.96) 0.045*** (37.49) 1.381e-04*** (24.42) – – 177.083*** (155.09)
5.223*** (38.19) 0.057*** (14.16) 2.737e-04*** (6.29) 4.880e-07** (3.14) 179.574*** (131.90)
0.738 140
0.973 140
0.995 140
0.995 140
Log-likelihood ratio tests (H0: the expanded model fits the data no better, statistically speaking, than the abbreviated model) X2 (df = 1)
–
318.45***
235.74***
9.87**
Note: dependent variable is average number of full cycles utilized in a year; t-statistics in parentheses. * Significance level: 10%. ** Significance level: 5%. *** Significance level: 1%.
700,000 600,000 500,000 400,000 300,000 200,000 100,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Discharging premium (KRW/kWh) Fig. 5. Simulated lifetime discounted operating revenues for varying discharging premium levels for a NaS battery.
Years of useful life
Table 3 Regression output modeling number of annual cycles as a function of discharging premium for NaS battery.
Operating profits, 1000 KRW
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4000 3500 3000 2500 2000 1500 1000 500 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Table 4 Simulated lifetime discounted operating revenues and length of useful life for NaS battery, by initial discharging premium. Initial discharging premium (KRW)
Operating Revenues (1000 s KRW)
Length of useful life (years)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
586,655 604,146 620,990 636,917 651,587 664,262 650,667 625,879 602,622 578,365 555,227 533,256 508,994 489,301 466,742 449,271 428,582 408,627 389,439 371,039 353,438
24.1 25.6 27.4 29.7 32.9 38.3 560 976 1,299 1,619 1,882 2,173 2,350 2,498 2,690 2,860 3,011 3,070 3,187 3,290 3,381
expected negative effect on the lifetime revenue stream as future income is discounted more heavily. 4. Lithium-ion battery as an alternative electricity energy storage (EES) device In order to increase the robustness of our analysis, we compare our NaS results with those generated for an alternative storage technology. We choose a Lithium-Ion (Li-ion) battery as our alternative due to its comparable characteristics of fast response time, long duration of discharge, and no self-discharge. The technical specification of our Li-ion battery are as follows: storage capacity of 1 MWh, power rating of 250 kW for both charging and discharging, 3000 lifetime cycles at 80% Depth of Discharge (DoD), roundtrip efficiency of 95%, and operation and maintenance (O&M) cost of 5 cents/KWh [24,29].
Discharging premium (KRW/kWh) Fig. 6. Simulated length of useful life for varying discharging premium levels for a NaS battery.
Table 5 Simulated discounted lifetime operating revenues for NaS battery, for discharging premium between 5 and 6 KRW/kWh. Initial discharging premium (KRW/kWh)
Discounted lifetime operating revenues (1000 KRW)
Length of useful life (years)
5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00
664,262 664,821 665,373 665,913 666,448 666,977 667,499 668,026 668,568 669,171 670,433 662,895 661,346 659,786 659,877 658,366 656,846 655,316 653,777 652,227 650,667
38.3 38.8 39.2 39.7 40.3 40.9 41.5 42.3 43.3 44.6 47.8 307 344 381 418 456 420 455 490 524 560
Note: simulations were carried out in discharging premium increments of 0.05 KRW/kWh
4.1. Three-year operating profit potential We apply the same simulation strategy to generate a revenue stream from a Lithium-ion battery as we did for sodium–sulfur battery. In the first stage of the process we simulate hourly storage activities of a profit maximizing operator, given initial discharging premiums between 0 and 150 KRW/kWh and battery specifications outlined above, to calculate hourly and annual revenues and cycle usage. As with the NaS simulation, the daily revenue is calculated according to Eq. (3).
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Operating profits, 1,000s KRW
675,000
rises. For very low discharge premiums, total revenue potential amounts to nearly 10 million KRW with over 250 full cycles utilized per year. As the discharge premium rises to 50 KRW/kWh, revenues drop by 50% and cycle usage falls by nearly 80%. Higher unit revenues from total arbitrage activity offset part of the revenues lost to lower frequency of sufficient price spreads.
670,000 665,000 660,000 655,000 650,000 645,000 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00
640,000
Discharging premium (KRW/kWh) Fig. 7. Simulated discounted lifetime revenues for a NaS battery, for discharging premium between 5 and 6 KRW/kWh. Note: simulations were carried out in discharging premium increments of 0.05 KRW/kWh.
Years of useful life
600 500 400 300 200 100
4.2. Econometric models of annual operating revenues and battery usage In the second stage of our simulation, we use our first-stage results to develop general models of revenue and battery usage as functions of the initial discharging premium, as outlined in Eqs. (4) and (5). Our first stage annual revenue results show that energy arbitrage activities yielded non-negative revenues in 2009 and 2001 for initial discharge premium of up to 115 KRW/kWh and 106 KRW/kWh, respectively. In order to avoid negative revenue outcomes in our data sample, we right-censor our revenue distribution at 106 KRW/kWh initial discharging premium. Regression results for the operating revenue and battery usage regressions are summarized in Tables 7 and 8, respectively. Regression results are consistent with those obtained for the NaS battery and with the findings presented in Figs. 9 and 10. 4.3. Lifetime operating revenue and utilization potential
5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00
0
Discharging premium (KRW/kWh) Fig. 8. Simulated length of useful life for a NaS battery, for discharging premium between 5 and 6 KRW/kWh. Note: simulations were carried out in discharging premium increments of 0.05 KRW/kWh.
Next, we collapse hourly estimates into three-year revenue and cycle use averages (2009–2011) for each initial discharging premium. Fig. 9 shows the variation of average annual revenues over initial discharging premiums, while Fig. 10 demonstrates the same variation for average annual cycle use. Results are similar to those obtained for the NaS battery, with revenues and cycle usage declining as the discharging premium
The final stage of the simulation procedure is carried out as outlined in Section 3.3 above. Results are demonstrated in Figs. 11 and 12. The former shows the lifetime revenue potential accumulated over 3000 available charge–discharge cycles of the Li-ion battery, with maximum revenue of 112,521,000 KRW (approximately 103,000 USD) occurring at the initial discharging premium of 18 KRW/kWh – three times higher than the premium that maximized revenues for a NaS battery. The total lifetime of the battery at the point of maximum potential revenue is nearly 25 years– 15 years less than the NaS lifespan. 4.4. Comparison of technologies As demonstrated in the included figures, employing a Li-ion battery with technical specifications outlined above for energy
Table 6 Sensitivity of simulated discounted lifetime revenues to changes in the interest rate. P0 (KRW/kWh)
5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00
i (%)
Lifetime discounted operating revenues (1000 s KRW) 2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
934,851 936,205 937,560 938,917 940,275 941,634 942,995 944,357 945,720 947,085 948,451 949,796 951,140 952,485 953,831 955,179 956,528 957,879 959,230 960,583 961,938
888,620 889,901 891,182 892,437 893,694 894,952 896,212 897,473 898,736 900,001 901,267 902,535 903,804 905,075 906,333 907,578 908,824 910,073 911,322 912,574 913,827
845,587 846,772 847,959 849,148 850,339 851,522 852,685 853,849 855,014 856,182 857,352 858,523 859,696 860,871 862,047 863,207 864,355 865,505 866,657 867,810 868,966
805,484 806,577 807,672 808,769 809,868 810,969 812,044 813,115 814,188 815,263 816,339 817,418 818,499 819,581 820,638 821,690 822,744 823,800 824,858 825,918 826,980
767,974 768,979 769,986 770,995 771,995 772,972 773,952 774,933 775,916 776,902 777,889 778,850 779,806 780,763 781,722 782,684 783,646 784,581 785,512 786,445 787,379
732,749 733,654 734,538 735,424 736,311 737,201 738,085 738,941 739,799 740,658 741,519 742,363 743,190 744,018 744,847 745,668 746,462 747,257 748,052 748,833 749,592
699,364 700,131 700,885 701,641 702,395 703,113 703,831 704,549 705,235 705,912 706,589 707,228 707,861 708,479 709,065 709,648 710,183 710,714 711,193 711,655 712,071
667,086 667,636 668,150 668,644 669,091 669,511 669,882 670,194 670,444 670,615 670,684 670,600 670,303 – – – – – – – –
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Table 8 Regression output modeling annual cycles as a function of discharging premium for Li-ion battery.
Operating profits, 1,000 KRW
12,000 10,000 8,000 6,000
Pt
4,000
Pt2
2,000
Pt3
0 0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Pt4
Discharging premium (KRW/kWh) Cons R2 N
(2)
(3)
(4)
2.39*** (34.61) – – – – – – 212.28*** (50.51)
5.06*** (108.74) 0.03*** (59.23) – – – – 258.52*** (244.50)
5.29*** (46.93) 0.03*** (12.36) 3.51e-05** (2.24) – 260.49*** (191.43)
5.81*** (27.02) 0.05*** (6.37) 3.69e-04*** (3.07) 5.68e-07*** (2.80) 263.10*** (163.10)
0.9193 106
0.9977 106
0.9978 106
0.9979 106
Log-likelihood ratio tests (H0: the expanded model fits the data no better, statistically speaking, than the abbreviated model)
300
X2 (df = 1)
250
377.05***
5.10**
7.92***
Note: dependent variable is average number of full cycles utilized in a year; tstatistics in parentheses. * Significance level: 10%. ** Significance level: 5%. *** Significance level: 1%.
200 150 100 50 0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Discharging premium (KRW/kWh) Fig. 10. Number of full battery cycles utilized per year for varying discharging premium levels for a Li-ion battery, average over 2009–2011.
Table 7 Regression output modeling annual operating revenues as a function of discharging premium for Li-ion battery.
Pt Pt2 Pt3 Pt4 Intercept R2 N
(1)
(2)
(3)
(4)
105.53*** (76.96) – – – – – – 1.07e04*** (128.04)
115.98*** (21.64) 0.10** (2.02) – – – – 1.08e04*** (89.11)
0.89 (0.22) 2.70*** (29.23) 0.02*** (31.23) – – 9.85e03*** (199.46)
21.88*** (2.86) 1.71*** (5.72) 0.003 (0.72) 2.00e-05*** (3.45) 9.96e03*** (173.35)
0.9831 106
0.9834 106
0.9984 106
0.9985 106
Log-likelihood ratio tests (H0: the expanded model fits the data no better, statistically speaking, than the abbreviated model) X2 (df = 1)
–
4.10**
249.86***
11.80***
Note: dependent variable is average annual operating revenue, in thousands of KRW; t-statistics in parentheses. * Significance level: 10%. ** Significance level: 5%. *** Significance level: 1%.
arbitrage in South Korea’s power markets would at best generate nearly 113 million KRW (approximately 104,000 USD), in present value terms, over the course of the battery’s 25 year useful lifespan. In order to make comparison easier, we need to scale our Li-ion battery capacity up to 7.5 MWh assumed for NaS simulations. Since 4 MWh is the largest technical Li-ion capacity available at this time (although not yet commercially), we could imagine employing two batteries, one of 4 MWh capacity, and another of 3.5 MWh capacity. Using both at the same time would enable us to increase cumulative lifetime revenue potential by as much as
Operating profits, 1,000 KRW
0 120,000 100,000 80,000 60,000 40,000 20,000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Discharging premium (KRW/kWh) Fig. 11. Simulated lifetime discounted operating revenues for varying discharging premium levels for a Li-ion battery, assuming operation at 80% depth of discharge.
Years of useful life
Number of full cycles utilized
Fig. 9. Annual operating revenues for varying discharging premium levels for a Li-ion battery, average over 2009–2011.
(1)
40 35 30 25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Discharging premium (KRW/kWh) Fig. 12. Simulated length of useful life for varying discharging premium levels for a Li-ion battery, assuming operation at 80% depth of discharge.
7.5 times to nearly 850 million KRW (roughly $800,000) over the course of 25 years. By comparison, the present value of the highest revenue generated by our NaS battery was 664 million KRW (about $612,000) over the course of about 40 years – a significantly lower sum over a longer time period. 5. Discussion of results and policy implications In this study, we evaluated arbitrage profit potential for a private storage device owner in South Korea’s electricity markets.
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Using an empirical dataset, a set of assumption on prevailing technological and market characteristics, and Hotelling’s optimal depletion conditions, we simulated a stream of operating revenues accruing to an operator of two alternative storage technologies in the energy market over the course of the devices’ useful lives. Since revenues are dependent on the timing and extent of charging and discharging actions, our research objective reduced to identifying the optimal starting difference between prices at which energy is purchased from the market and is resold back to the grid. This optimal price difference for a NaS battery operator, given the employed assumptions, was 5.5 KRW/kWh, which generated for the battery owner discounted lifetime real operating revenues of 664 million KRW (about $667,000) over the course of slightly less than 40 years. For a Li-ion battery owner, the optimal price difference was 18 KRW/kWh, with arbitrage revenues amounting to 850 million KRW (about $800,000) over 25 years. To comment on the economic implications of these operating revenue figures, we can compare them to the total installed cost of a typical NaS battery, which is detailed by the Electric Power Research Institute in a 2010 white paper [24] to vary between $3,200 and $4,000 per kW of capacity for NaS batteries and between $1,800 and $4,100 for Li-ion batteries. A 7.5 MW NaS battery would therefore carry a capital cost of $27 million, which would leave the battery owner with a net loss of over $20 million. The cost of 7.5 MW of capacity for a Li-ion battery owner would range between $13.5 and $30.75 million, leaving the storage owner with a net loss of roughly $12.5–$30 million. Although the economics of the lithium-ion battery appear to be relatively more appealing than those of a sodium sulfur battery, generating a greater amount of revenues over a shorter time period, neither technology generates a sufficient amount of arbitrage revenue to cover the battery’s capital costs. The NaS battery, however, has an important advantage in that it maximizes lifetime profits at a lower price spreads. In markets with less volatile power prices, this could be a significant benefit. Under present market conditions, energy arbitrage in Korea is not profitable enough to attract private entry. Successful integration of storage would require both more price volatility and lower capital costs of storage technologies. However, as we noted in the literature review, storage likely has additional welfare (i.e. nonfinancial) benefits for consumers and electric utility companies. [20] Considering non-financial benefits would then raise the implied value of storage (e.g. value to system operator from lower peak demand or value to society of improved network resilience) to the Korean power system. In addition, the present analysis considers only revenues earned in the energy market through arbitrage activity, and further financial gains may exist in the regulation market, ancillary services, and other applications. Though outside the scope of this study, considering these other benefits of storage would provide a more complete picture of the effectiveness of storage technology in mitigating important balancing concerns currently faced by many developed markets. Acknowledgments We thank participants of the 2013 International Conference of the International Association for Energy Economics and two anonymous referees for valuable comments. References [1] Ekman Claus Krog, Jensen Soren Hojgaard. Prospects for large scale electricity storage in Denmark. Energy Convers Manage 2010;51:1140–7. [2] Rahul Walawalkar, Apt Jay, Mancini Rick. Economics of electric energy storage for energy arbitrage and regulation in New York. Energy Policy 2007;35:2558–68.
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