Available online at www.sciencedirect.com

Solar Energy 98 (2013) 167–179 www.elsevier.com/locate/solener

Ensuring long term investment for large scale solar power stations: Hedging instruments for green power
A. Radchik a,⇑, I. Skryabin b, J. Maisano c, A. Novikov d, T. Gazarian e
Mathematics & Statistics, Faculty of Science, UTS and Director GTS Pty. Ltd., Suite 2, 16 Figtree Avenue, Randwick, NSW 2031, Australia b Centre for Sustainable Energy Systems, Australian National University, Canberra 2000, Australia c Energy Markets, TTA Pty. Ltd., Suite 12, L6, 321 Pitt St., Sydney, NSW 2000, Australia d School of Mathematics & Statistics, Faculty of Science, University of Technology Sydney (UTS), P.O. Box 123, Broadway, NSW 2007, Australia e School of Mathematics & Statistics, Faculty of Science, UTS, 1 Stella Vista Pl, Greenwich, NSW 2065, Australia Available online 29 March 2013 Communicated by: Associate Editor Frank Vignola a Abstract There is a general consensus that solar power is one of the cleanest energy technologies available. Nevertheless, investment in largescale Solar Power Generators (SPGs) is largely impeded by the intermittent nature of solar power. Since the electricity market has a critical responsibility to maintain the reliability of energy supply, the SPG can be registered only as the market semi-scheduled generator (AEMC, 2011). This option excludes the advantages of providing baseload supply, which in turn impedes efficient market contracting for SPGs. The existing approach relies on energy storage or co-generation facilities to be built at the same connection point as the SPG to compensate for output shortages when there is insufficient sunlight. The co-located facilities require significant additional investment in infrastructure. This paper proposes a market based financial approach that does not require an additional construction effort. The approach financially links solar or other intermittent power generation with a gas-fired station through a set of tailored swap-type instruments. These swaps (based on solar energy forecasting) are designed to insure and hedge the SPG against a drop in its output. They contractually link physically separated solar and gas generators to form a single entity termed the Virtual Generator (VG). The VG arrangement requires the SPG to provide solar power when possible and the gas generator to kick in when there is any shortfall due to random clouds or at nightfall. Thus the proposed VG will have the capacity to produce reliable baseload supply. The profitability and design of the proposed financial setup for both the solar and gas generator has been tested in this research. The model has been prototyped on real market and solar data, the results demonstrate the benefits of implementation. While the paper is focused on links with gas generators, the developed financial setup is applicable to a broad range of fast-ramping power generators, such as hydro, including pumped-hydro storage as well as electrical batteries and biofuels. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Solar power; Energy demand forecasting; NEM; Baseload; Virtual Generator; Power Purchase Agreement

1. Introduction Despite a sustained decrease in photovoltaic (PV) solar panel costs, uptake of large-scale Solar Power Generation (SPG) has remained relatively low in Australia and contin⇑ Corresponding author. Tel.: +61 417224800.

E-mail address: alex.radchik@uts.edu.au (A. Radchik). 0038-092X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2013.02.022

ues to face a number of impediments. We suggest that progress is not being curbed by technical limitations but rather by the absence of an adequate mechanism to manage the complex interplay between existing electricity networks and intermittent renewable energy sources. The intermittency of solar output is a complicating factor. Aggregate annual solar power outputs are highly predictable, at least in the absence of catastrophic climate

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events. However, on a smaller time scale, solar power output is subject to the high volatility of local meteorological conditions (such as cloudy weather). At the same time, meeting market’s power need requires predictable and controllable sources of electricity. Further, existing local electricity grids as well as centralized dispatch and control systems are not designed to accommodate rapid ramping rates of generated electricity that are not uncommon when, for example, a cloud is passing over a large PV array. ‘PV variability can drive localized concerns, which typically manifest themselves as voltage or power quality problems. These issues are distinct from grid system level issues of balancing, and ought not to be confused. Management and remediation options for local power quality problems are generally different than options for maintaining a balance between load and supply at the system level (Mills et al., 2009)’. This distinction is illustrated in Fig. 1. While effects on local power quality are being addressed with the development of advanced power electronics and distributed storage, balancing load and supply on a market level requires different solutions. A number of solutions addressing the variability of solar generation have been developed elsewhere. For example, advanced inverters supported by locally distributed storage (e.g. batteries) have been used to address concerns over local power quality (Franquelo et al., 2006). Substantial research efforts have also been directed towards quantifying the PV power output variability of solar power plants as a function of their size, the number of plants in a fleet (Hoff and Perez, 2012), and meteorological forecasting. Detailed analysis from these studies has yielded outcomes that were intuitively expected. Results show that PV plant size has a smoothing effect on power fluctuations (Marcos et al., 2011), and that the combined output variability of N

pffiffiffiffi spaced generators decreases with 1= N (Hoff and Perez, 2012). This paper is concerned with the effects of solar variability on balancing load and supply on a market level. This balancing is complicated by the fact that energy demand is also variable and this variability is generally different to that of solar output. A number of research projects have been conducted to demonstrate that variable demand may be met by intermittent renewable generation where there is a sufficiently high quantity of solar generators. A recent study, Western Wind and Solar Integration,1 demonstrated that 35% of US renewable energy generators could be integrated into the electricity grid without dedicated storage facilities. This means that, if spread over large geographical regions, solar power stations may be treated collectively as a base-load generator. In Germany a combined power plant comprising geographically dispersed but centrally controlled solar, wind, biomass and pumped-hydro elements was demonstrated to be capable of effectively supplying 100% renewable energy to the grid.2 Generally balancing load and supply on the National Energy Market can, as shown in Fig. 1, be achieved by following two different market approaches. In the first approach the market is dominated by an oligopoly of vertically integrated retailers. Large companies combining generation and retail under a single business structure (named as ‘gentailers’) are capable of splitting generation between its intermittent (e.g. solar) and controllable components (e.g. gas or coal-fired) to balance demand as required by the retail part of the business structure. In the second approach most of generated power is traded through bidding at the National Energy Market, and intermittent solar generators are integrated through financial contracts between otherwise competing electricity generators and retailers. A spot market for energy (operated by the Australian Energy Market Operator, AEMO) was designed to facilitate an efficient and competitive trading environment for conventional power generators. One of the objectives was to encourage technical innovation and to meet consumer energy demand at the lowest cost. However, solar generators do not participate in the spot market yet. This is largely due to the volatility of solar power output and the restrictive dispatching rules enforced by AEMO to uphold energy supply security. Without firm option of trading on spot market solar generation potential remains underutilized. As an alternative to spot price bidding solar power could be contracted in the form of Power Purchasing Agreements (PPAs), which are mainly offered by one of three Australian major gentailers (see Fig. 1). However,
1 Western Wind and Solar Integration Study, prepared by GE Energy for NREL (2010). 2 SolarServer, http://www.solarserver.com/solarmagazin/ anlagejanuar2008_e.html.

Fig. 1. Issues arising from the intermittency of solar output. A solar plant or generator supplies intermittent power to the National Electricity Market in accordance with AEMO’s dispatch instructions.

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their significant market power allows them to impose PPA prices that are almost below production cost. Such market structure is anti-competitive, and prevents entry from new, smaller players. Solar generation in Australia is, therefore, facing a growth dilemma. On one hand, a large number of renewable generators are required to smooth the variability of individual outputs and to enable market acceptance of widespread combined generation. On the other hand, the present structure of the National Energy Market, coupled with low and volatile spot electricity prices, means that adequate financing for large-scale solar is difficult to secure. Novel financial and business structures are needed to kick-start a process that will invariably lead to higher market penetration of diversified renewable energy generators. This paper proposes the concept of the Virtual Generator as a separate bidding entity into the NEM. The Virtual Generator would act on behalf of a solar power generator contractually linked to a geographically separated non-intermittent generator, such as a gas-fired power station. The proposed business structure is interlinked by swap-like contracts and back-tested in the NEM conditions. The purpose of this paper is to develop market-based solutions accelerating the integration of Solar Power Generators (SPGs) into existing national energy markets. These include novel SPG business structures eliminating the need for co-located generation or storage, and financial instruments addressing the risks associated with intermittency of solar power. The former is effectively guaranteeing a reliable profile that is consistent with consumer demand, allowing its straightforward incorporation into AEMO’s pre-dispatch and dispatch processes. The latter acts as financial insurance against a drop in solar generation and is specifically tailored to a specific SPG output profile. The Virtual Generator (registrable as a market scheduled generator) is described in Section 2 of this paper along with methodology of constructing baseload supply by contractually linking SPG and a rapid ramping generator. The proposed methodology is verified by backtesting as described in Section 3. Section 4 discloses a new set of financial derivatives addressing the needs of solar generators. The derivatives are designed to mitigate financial risk caused by the variability in solar generation due to exogenous events. This paper belongs to the field of financial modeling in renewable energy market. Therefore, nomenclature used in this paper corresponds to standards established in this field, which are frequently different to notations adopted in solar engineering.3

2. The Virtual Generator model 2.1. The concept An example of solar generation profile of a single SPG (located in Melbourne) is depicted in Fig. 2 as a function of time of day (‘solar profile’). For comparison a state load as a function of time of day (‘load profile’ or ‘demand profile’) is also presented in Fig. 2 (Victoria state demand4). Despite some daily correlations between solar and demand profiles a single SPG is unable to meet state demand requirements. Consider now a Virtual Generator (VG) comprising: a Gas Powered Generator (GPG),5 a Solar Powered Generator (SPG) and a Wind Powered Generator (WPG). The intermittent generators (solar and wind) are required by the VG to provide power where possible and the gas generator compensates for any shortage in output due to a lack of wind, nightfall and/or random clouds blocking sunlight. This concept is demonstrated in Fig. 3. The VG as a joined entity is able to guarantee reliable generation. It bids into the NEM as a single bidder and is dispatched as a market-scheduled participant. Both solar and wind output can be forecasted so the gas generation required could be planned by the VG in advance with some margin for error. For the sake of simplicity, the remainder of the paper eliminates wind generation as part of the VG. It discusses the concept of the VG and the resulting cash flows between a gas and solar power generators. In this case, the SPG relies solely on the GPG to compensate for any shortage in output. Importantly, the distance between participating generators is not critical for the operation of the VG. All generators adjust their NEM bidding structures by respective Mean Loss-Factors (MLFs), taking into account how far a particular generator is from a Regional Reference Point (RRP).6 The RRP is a node in a state grid in respect to which state price and demand are defined. All MLFs are published by AEMO on a yearly basis. As the Virtual Generator is a financial, not physical aggregation of participating power stations, it is only important how far each power station is from the RRP. Therefore Virtual Generator shall adjust its bidding into the NEM to take into account loss factors of each of its participants.

3 For example, “p” in finance stands for price, whilst in engineering – for power.

We are considering demand formed in the National Energy Market, which is published by the AEMO (at half-hourly intervals) on a state-bystate basis. It is a total state demand including aggregation of cities, towns, and rural areas. 5 The Gas Powered Generator represents here a class of power generators that can be ramped up and down on demand. This class includes biomass burning stations and hydropower. Financial contracts proposed in this paper are extendable to include energy storage facilities such as pumped-hydro or batteries based in place of or in addition to the Gas Powered Generator. 6 Alternatively, in other electricity markets (e.g. NZ market) the lossfactor is taking into account how far a particular generator is from a nearest connection point in the transmission network.

4

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and weather-related variability of outputs. These swaps provide each party with revenue compensation tailored to variations in price and output over any given half hourly interval. The payoff (per MW h) of the swaps can be described at the sum of all half hourly floating payments less the sum of all half hourly fixed payments. Solar Swap Payoff ¼
S 1 X ðp S i À N s X s Þ 2S i¼1 i

N

ð1Þ

Gas Swap Payoff ¼
Fig. 2. An example of Melbourne solar profile in comparison with Victorian state load profile (Shaded areas indicate market peak periods. Peak period is defined as the NEM time interval from 7 AM to 10 PM on a business day. The remaining time periods are defined as off-peak. For NEM time conventions see www.aemo.com.au) shown for 1 week in February 2010. Both the solar profile and the state load profiles were normalized to corresponding quarterly averages (under ‘quarter’ we mean financial quarter).

g 1 X ðp Gi À N g X g Þ 2G i¼1 i

N

ð2Þ

where Xs is the Solar swap strike, as defined in (3); Xg the Gas swap strike, as defined in (4); Si the actual solar generation during the ith half hour quoted in MW h9; Gi the actual gas generation during the ith half hour quoted in MW h; pi the actual spot price (Regional Reference Prices,10 RRPi) during the ith half hour quoted in $/ MW h; Ns forecasted number of solar ticks in a quarteri.e. number of half hourly intervals (ticks) of SPG generation; Ng the forecasted number of gas ticks in a quarter-i.e. number of half hourly intervals of GPG generation; Ns + Ng = NT the total number of ticks in a quarter; and P PN g S ¼ N s S i and G ¼ i¼1 Gi are the total solar and gas eni¼1 ergy quarterly outputs correspondingly. Our aim was to allow hedging together over three variables: Regional Reference Price pi, and generations Si and Gi. We will define Solar and Gas swaps’ strikes in terms of respective percentiles of forecasted quarterly outputs as: p X s ¼ W 0a  peak p X g ¼ W  off
0 b peak

ð3Þ ð4Þ

Fig. 3. The Virtual Generator (Skryabin et al., 2010).

2.2. Solar and Gas swaps Existing standard financial contracts in the electricity market7 are inadequate hedging instruments for solar power. Since the output of a SPG varies with sunlight, its energy supply to the market is also always variable. Standard financial hedging against losses in output does not mitigate volumetric risks. The SPG needs to hedge different quantities of output at different times of day. We propose that the SPG and GPG of the Virtual Generator be linked through a set of specific solar and gas swaps that provide compensation for both – variability of spot market price8 http://d-cyphatrade.com.au/. Terms floating price, pool price, spot price and Regional Reference Price (RRP) are used interchangeably throughout the paper. Electricity load is a common term used in industry. We use it interchangeably with the expression electricity demand.
8 7

Here peak is the average (forward) peak price (Footnote 11) p over quarter (Footnote 12); off peak the average (forward) p off-peak price over quarter; Wa the a-percentile of forecasted solar output over given quarter11; Wb the b-percentile of forecasted (complementary to solar) gas output over given quarter.12 Set of values for both percentiles will be derived in subsequent section in order to make the VG arrangement mutually beneficial for the SPG and GPG.
This variable is determined in accordance with a procedure outlined in Appendix A. Historical solar radiation and temperature data were converted into ‘historical’ solar outputs (Solanki, 2009). Forecasted solar output was obtained by using Fourier Transforms in combination with the Convolution Theorem. 10 See “AN INTRODUCTION TO AUSTRALIA’S NATIONAL ELECTRICITY MARKET, JULY 2010” available from http://www.aemo.com.au/About-the-Industry/Energy-Markets. 11 This variable is determined from generated forecasted solar outputs (see Appendix A). 12 This variable is determined from our set of forecast gas output values. Forecast gas output was calculated as a function of forecast solar output and the Quantity of Confidence (Appendix B).
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for construction of baseload-profile Power Purchase Agreements. 2.3. Benefits for the Gas generator The VG arrangement is beneficial to the SPG as it gives its project long term revenue certainty, which is critical for obtaining project financing. However, what does the gas generator gain? This proves a valid question since the gas generator does not generally need to be a part of the VG to be able to reliable generation. The VG setup not only supports large-scale solar investment but also provides a number of advantages for gas generators already operating in the market. By bidding as part of the VG during the off-peak periods, the gas generator is selling the least valuable parts of its production, i.e. the off-peak profile of it is baseload profile.15 Thus by committing to the swap agreement, the gas generator is ultimately securing a fixed payment for its production during these otherwise unprofitable times. Bidding as a separate entity during peak hours with the fraction of capacity that is not committed to the Virtual Generator is an additional significant source of revenue for the gas generator. Through the VG arrangement the gas generator is effectively contracting out and securing fixed payments to sell only a portion of its peak period capacity (Gi) to the Virtual Generator. This provides it with the opportunity to bid any remaining fraction of capacity into the market independently. Furthermore, it can do so at premium prices. The gas generator also has the opportunity to offset its carbon footprint costs with the financial benefits that are awarded to renewable energy providers. As of 2011, Australian Government implemented the Large-scale Renewable Energy Target and the Small-scale Renewable Energy Scheme (LRET/SRES). These schemes aim to encourage the renewable electricity generation through the creation of Renewable Energy Certificates (RECs). RECs are awarded based on the amount of renewable electricity produced over a certain period.16 One MW h of solar electricity equates to the attainment of one REC. Retailers using gas and other non-renewable generation are liable to surrender a certain number of these certificates at the end of each reporting period passing their liabilities onto generators. Five MW h of non-renewable energy generation obliges the submission of one REC. The compulsory submission of these RECs serves as an indirect penalty to non-renewable generators for releasing pollutants. Essentially, renewable generators provide a supply of RECs and non-renewable generators – a demand for them. Consequently, a market consisting of buyers and sellers has developed and the certificates are readily traded. The VG
00:00 till 24:00 Monday to Sunday. Office of the Renewable Energy Regulator, 2011, http://ret.cleanenergyregulator.gov.au/.
16 15

Fig. 4. Futures Cash Flows with both SPG and GPG in use.

It is revealing to compare the proposed swaps (1) and (2) to an existing OTC13 profiled swap, which also incorporates variation in generation: Profield Swap Payoff ¼
NT 1 X Gi ðpi À Þ p 2G i¼1

ð5Þ

We can see that the swap in (5) is a hedge in price only whilst the proposed swaps combine price and load hedge. As shown in Fig. 4 the solar generator will receive the solar swaps fixed (strike) price of electricity (Xs). It will sell the quantity of electricity it has generated (Si) to the pool at the spot price (pi). It will therefore receive (pi  Si) and it will pass this revenue onto the gas generator. The gas generator will receive the gas strike price of electricity (Xg). It will sell the quantity of electricity it has generated (Gi) to the pool at the spot price (pi) receiving (pi  Gi) from the pool and then passing this revenue onto the solar generator as per the agreement of the swaps contract. In summary, regardless of the magnitude of solar output, the solar generator has locked in constant earnings of Xs. Furthermore, at night and other times of impeded solar performance (when we need gas generation to fill any lack in output) the gas generator has locked in constant earnings of Xg. The cash flows described above are not physically exchanged every half hour, but rather weekly settled by AEMO. Both the solar and gas swaps mature quarterly, in line with existing industry standards.14 It should be noted that the proposed VG arrangement is also applicable
OTC – over-the-counter or bilateral trading as apposite to public trading on futures exchanges. 14 http://d-cyphatrade.com.au/products.
13

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setup entails the solar generator to transfer a portion of its RECs to the gas generator. This portion is designed to offset gas generator’s carbon liability associated with the VG. Depending on the market price the RECs are trading at, this setup can provide a significant additional financial advantage for the gas generator. Let: REC – market value of one REC Therefore: Rg is the number of RECs surrendered by gas generator quarterly NT X ¼ 20%  Gi ð6Þ i¼1 Then, the additional revenue realized by the gas generator due to these ‘free’ RECs is Rg  REC. 3. Results and back-testing In this section, we present the Solar and Gas Forward Curves and the set of possible portfolio values making beneficial VG arrangement for the solar and gas generator. 3.1. Solar and gas forward output curves The Solar Forward Curve in Fig. 5 below was derived by applying the Solar Forward Curve algorithm described in Appendix A. The forecast solar output values were normalized on their quarterly maximum. The dashed curve represents the normalized Solar Forward Curve across the first week in August 2010. The black curve, displayed for the purpose of validation of results by the back-testing, plots actual solar output data across the same week. Regretfully, we did not have access to generation data from any particular GPG. Due to confidentiality reasons, specific contract data was also not available. As a proxy to baseload contract, we used a rescaled (on quarterly average) VIC state demand forecast.17 Then, the most straightforward way to forecast gas load would be to find the difference between the forecast demand curve and the forecast solar load curve. We present the details of modeling in Appendix B. Figs. 5 and 6 below display all contract profiles involved in the solar and gas swaps (shaded areas indicate market peak periods). The Solar Forward Curve is represented by the green18 line and the Gas Forward Curve (see Eq. (B8)) is represented by the blue line. The black line represents the solar contribution to baseload contract profile, and is part of generation under the green curve less some
17 Produced by TTA Pty. Ltd., Beacone Simulation Engine (see www.tta.com.au). 18 For interpretation of colour in Figs. 5 and 6, the reader is referred to the web version of this article.

Fig. 5. Normalized Solar Forward Curve from the 1st to the 7th of August 2010.

margin for error to account for any discrepancies in forecasting. The addition of the solar contract profile and the gas contract profile (shown in blue) results in the baseload contract profile (black line), i.e. rescaled VIC state demand. When solar is providing some but not enough electricity to satisfy demand gas is only required to make up the shortfall. When solar well exceeds the quantity demanded, the additional unused output can be bid into the NEM independently of the VG arrangement. It should be noted that SPG and GPG are at different grid connection points and transmission losses are incorporated into SCADA dispatch algorithm by using AEMO’s defined MLFs.19 3.2. Portfolio values Table 1 displays the forecasted gas and solar portfolio values without the Virtual Generator arrangement. These values are used as a point of comparison when analyzing the profitability of the Virtual Generator. Assuming RECs are trading at $35,20 Tables 2–5 display the forecasted portfolio values with the Virtual Generator arrangement for quarters 1–4 respectively. For each quarter, all paired combinations of a and b quantiles yielding higher gas portfolio values with the VG than without are considered. The dashes indicate that no profit can be generated for the gas station in this instance and so the figures have been omitted. Ultimately, the quantiles should be chosen based on optimal overall portfolio profitability for both the solar and gas generator. Table 2 shows the portfolio values (in thousands of dollars) for all viable combinations of a and b quantiles. For example, when a = 0.4 and b = 0.4, the gas portfolio revenue is approximately $28,500 and the solar portfolio revenue is approximately $13,200. Portfolio values presented in Table 2 are illustrated graphically in Fig. 8
See http://www.aemo.com.au/en/~/media/Files/Other/electricityops/ 0170-0003%20pdf.ashx. 20 This price is based on the average market price of a REC during 2010.
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Solar output above contract profile is sold to spot market. Solar output is allocated to contract up to point at which load profile is met.

173

Wed

Thu

Fri

Sat

Sun

Mon

Tue

Wed

VG Contract Profile Solar Profile Gas Contract Profile

Normalised Profile

0.2

0.4

0.6

0.8

Sep 16

Sep 17

Sep 18

Sep 19

Sep 20

Sep 21

Sep 22

Sep 23

Time Period

Gas generates to meet load profile to fill in at nonsolar output times. GPG can sell at spot for additional revenue.

0.0

Fig. 6. Q3 contract profiles from the 16th to the 22nd of September 2009.

Table 1 Portfolio values (in thousands of dollars) without the VG. Q3 2009 Vg Vs 22.5 19.1 Q4 2009 19.7 46.5 Q1 2010 42.1 69.3 Q2 2010 24.1 17.5

It is clear that there are ample opportunities for the gas generator to financially benefit from the VG across all four quarters of the year. SPG has the obvious advantage of becoming part of baseload generation. To ensure the values above were independent of the size of the solar module, the forecasted solar output values were

normalized on its maximum output per quarter. Thus, the overall portfolio values are based on only the normalized quantities of output. To obtain portfolio values that correspond uniquely to a particular capacity SPG, we simply multiply these portfolio values by the size of the module in question. Furthermore, the values displayed above were calculated based on data recorded from a weather station located in Melbourne. Since solar and gas output forecasts are influenced by weather conditions in a particular location, contracts’ and thus portfolio values will differ from state to state.

Table 2 Q3 2009 set of possible solar and gas portfolio values with the VG. a b = 0.1 b = 0.2 b = 0.3 27.6 27.6 27.6 27.6 26.9 – – – – 14.0 14.0 14.0 14.0 14.8 – – – – b = 0.4 28.5 28.5 28.5 28.5 27.7 – – – – 13.2 13.2 13.2 13.2 14.0 – – – – b = 0.5 29.2 29.2 29.2 29.2 28.4 – – – – 12.5 12.5 12.5 12.5 13.3 – – – – b = 0.6 29.8 29.8 29.8 29.8 29.1 – – – – 11.8 11.8 11.8 11.8 12.6 – – – – b = 0.7 30.7 30.7 30.7 30.7 29.9 – – – – 11.0 11.0 11.0 11.0 11.8 – – – – b = 0.8 31.8 31.8 31.8 31.8 31.0 23.1 – – – 9.9 9.9 9.9 9.9 10.7 18.6 – – – b = 0.9 32.7 32.7 32.7 32.7 31.9 24.0 – – – 9.0 9.0 9.0 9.0 9.8 17.7 – – –

Q3 2009: gas portfolio values with VG 0.1 25.5 26.9 0.2 25.5 26.9 0.3 25.5 26.9 0.4 25.5 26.9 0.5 24.7 26.1 0.6 – – 0.7 – – 0.8 – – 0.9 – – Q3 2009: solar portfolio values with VG 0.1 16.2 14.8 0.2 16.2 14.8 0.3 16.2 14.8 0.4 16.2 14.8 0.5 7.0 15.6 0.6 – – 0.7 – – 0.8 – – 0.9 – –

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Table 3 Q4 2009 set of possible solar and gas portfolio values with the VG. a b = 0.1 b = 0.2 b = 0.3 42.1 42.1 41.9 34.5 – – – – – 24.2 24.2 24.4 31.8 – – – – – b = 0.4 43.3 43.3 43.1 35.7 20.8 – – – – 22.9 23.0 23.2 30.5 45.5 – – – – b = 0.5 44.2 44.2 44.0 36.6 21.6 – – – – 22.1 22.1 22.3 29.6 44.6 – – – – b = 0.6 44.9 44.9 44.7 37.3 22.4 – – – – 21.3 21.3 21.6 28.9 43.9 – – – – b = 0.7 45.6 45.6 45.4 38.0 23.0 – – – – 20.7 20.7 20.9 28.3 43.2 – – – – b = 0.8 46.4 46.4 46.2 38.8 23.8 – – – – 19.9 19.9 20.1 27.5 42.4 – – – – b = 0.9 47.4 47.4 47.2 39.8 24.8 – – – – 18.9 18.9 19.1 26.5 41.4 – – – –

Q4 2009: gas portfolio values with VG 0.1 36.2 39.3 0.2 36.2 39.3 0.3 36.0 39.1 0.4 28.6 31.7 0.5 – – 0.6 – – 0.7 – – 0.8 – – 0.9 – – Q4 2009: solar portfolio values with VG 0.1 30.0 27.0 0.2 30.0 27.0 0.3 30.2 27.2 0.4 37.6 34.6 0.5 – – 0.6 – – 0.7 – – 0.8 – – 0.9 – –

Table 4 Q110 set of possible solar and gas portfolio values with the VG. a b = 0.1 b = 0.2 b = 0.3 69.9 69.9 69.9 69.3 47.7 – – – – 41.6 41.6 41.6 42.1 63.8 – – – – b = 0.4 70.7 70.7 70.7 70.2 48.6 – – – – 40.7 40.7 40.7 41.2 62.9 – – – – b = 0.5 71.7 71.7 71.6 71.1 49.5 – – – – 39.8 39.8 39.8 40.3 62.0 – – – – b = 0.6 72.3 72.3 72.3 71.8 50.1 – – – – 39.1 39.2 39.2 39.7 61.3 – – – – b = 0.7 73.0 73.0 73.0 72.5 50.8 – – – – 38.4 38.4 38.4 39.0 60.6 – – – – b = 0.8 74.0 74.0 74.0 73.5 51.8 – – – – 37.4 37.4 37.4 38.0 59.6 – – – – b = 0.9 75.4 75.4 75.4 74.9 53.3 – – – – 36.0 36.0 36.0 36.5 58.2 – – – –

Q110: gas portfolio values with VG 0.1 65.2 68.4 0.2 65.2 68.4 0.3 65.1 68.4 0.4 64.6 67.9 0.5 43.0 46.2 0.6 – – 0.7 – – 0.8 – – 0.9 – – Q110: solar portfolio values with VG 0.1 46.3 43.1 0.2 46.3 43.1 0.3 46.3 43.1 0.4 46.8 43.6 0.5 68.5 65.2 0.6 – – 0.7 – – 0.8 – – 0.9 – –

4. Hedging risks with non-linear Solar derivatives: the Solar Floor Additional solar derivatives discussed in this chapter could potentially enhance the VG setup investigated in this research. A swap, as a linear-type derivative, provides a convenient and easy to price hedge against a drop in solar output, but possesses both-upside benefit and downside risk. Existing financial markets also have instruments with built-in optionality which provide the insurance against downside risk only (but much cheaper than standard insurance policies).

Consider an unforeseen cloud that has caused an unexpected drop in solar output. We may deem the gas generator too expensive to ramp up for what we expect will be a short period of time. In this case the solar generator would be short of revenue due to lack of output. More importantly, it would not be compensated by the swap’s payoff, as the gas generator would not be operating either. Hence, it will be desirable to purchase alternative solar derivatives that can insure against a drop in solar output due to unexpected weather changes. The proposed additional specialty derivatives are Solar Floors. A Solar Floor is a series of floorlets consecutively

A. Radchik et al. / Solar Energy 98 (2013) 167–179 Table 5 Q210 set of possible solar and gas portfolio values with the VG. a b = 0.1 b = 0.2 b = 0.3 27.0 27.0 27.0 27.0 24.7 – – – – 14.6 14.6 14.6 14.6 16.9 – – – – b = 0.4 27.8 27.8 27.8 27.8 25.5 – – – – 13.8 13.8 13.8 13.8 16.1 – – – – b = 0.5 28.5 28.5 28.5 28.5 26.2 – – – – 13.1 13.1 13.1 13.1 15.4 – – – – b = 0.6 29.1 29.1 29.1 29.1 26.9 – – – – 12.4 12.4 12.4 12.5 14.7 – – – – b = 0.7 30.0 30.0 30.0 30.0 27.7 – – – – 11.6 11.6 11.6 11.6 13.9 – – – – b = 0.8 31.1 31.1 31.1 31.1 28.8 – – – – 10.5 10.5 10.5 10.5 12.8 – – – –

175

b = 0.9 32.0 32.0 32.0 32.0 29.7 – – – – 9.6 9.6 9.6 9.6 11.9 – – – –

Q210: gas portfolio values with VG 0.1 24.9 26.1 0.2 24.9 26.1 0.3 24.9 26.1 0.4 24.9 26.1 0.5 – – 0.6 – – 0.7 – – 0.8 – – 0.9 – – Q210: solar portfolio values with VG 0.1 16.6 15.5 0.2 16.6 15.5 0.3 16.6 15.5 0.4 16.7 15.5 0.5 – – 0.6 – – 0.7 – – 0.8 – – 0.9 – –

maturing at every half hour over a quarterly period. A floorlet works like a long European put option. In this case however, we are insuring against a fall in quantity and not a fall in price; hence each floorlet is based on a strike quantity instead of a strike price. The Solar Floor is essentially a sequence of put options giving the owner the right to receive money at the maturity of each floorlet if the solar output of their generator is below the specified strike quantity. The equation below describes the half hourly pay-off for each floorlet. As previously defined, pi is the spot price per MW h during the ith tick, Wa is the strike quantity on a percentile level a and is a part of contract specification,21 and Si is the actual solar output during the ith tick:
ND X

Fig. 7. Q1 contract profiles from the 14th to the 20th of February 2010.

P i Max½W a À S i ; 0Š 2N D ð7Þ National Electricity Market. Consequentially, it can participate in the bidding process as a market scheduled generator. This provides a financially attractive avenue for integration of solar generator into existing electricity markets. A set of Solar and Gas swaps has been designed to form the financial backbone of the VG model. These swaps are tailored to insure and hedge against a variation in the quantity of solar output. By testing of the proposed financial model for the electricity market of Australian state of Victoria for 2009–2010 financial year a methodology for building a profitable portfolio was demonstrated. While the testing was performed for specific market and climate conditions of the selected year and state, the proposed methodology is broadly applicable and adjustable to accommodate changes in market regulations and stateby-state variations in prices. It has been demonstrated that the proposed business structure and underpinning financial mechanisms benefit

pF ¼

i¼1

2 Â ND is the total number of a daylight hours in the financial quarter for a given state.22 The structure of this product is similar to the structure of the cap (floor) products listed on d-cyphaTrade (Footnote 15). However, the Solar Floor is based on a strike quantity rather than a strike price. 5. Conclusions It has been demonstrated that the Virtual Generator comprising complimentary arranged solar and gas generators has the capacity to supply a reliable baseload profile to the
Might be eventually included in ISDA: http://en.wikipedia.org/wiki/ ISDA_Master_Agreement. 22 Available from http://members.iinet.net.au/~jacob/risesetsyd.html.
21

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Fig. 8. Solar (a) and gas (b) revenues as functions of a and b quantiles.

both – gas and solar generators. By participating in the VG the GPG financially profits across all four quarters of the year and the SPG can participate in providing baseload supply. The results undoubtedly prove the benefits of the implementation. Further, fully renewable energy sources such as wind and biomass-burning plants used in conjunction with existing energy storage technologies, such as thermal, pumped hydro or batteries, might be explored as complimentary techniques that could potentially enhance the VG model. In addition to the VG model, novel financial instruments such as non-linear solar derivatives which can hedge solar power generators against falls in their output were proposed. The solar derivatives are applicable to a standalone solar power generator, as well as to any intermittent generators integrated in the VG structure. Once again, the implementation of the proposed financial instruments is expected to improve certainty of investment in solar power. With the cost of solar generation continuously decreasing, it has become broadly accepted that market integration and financing are the major remaining barriers for broad acceptance of solar power. In developed renewable energy markets variations in power generated by a single solar generator should be substantially smoothened by a large number of other intermittent generators connected to electricity grid and spread over a large area. There is, however, an unavoidable intermediate period when initially a small number of solar generators must be integrated with existing electricity markets designed to suit and still dominated by fossil fuel burning conventional generators. This period may last years, if not decades. A financial and business strategy for the intermediate period was proposed and analyzed in this paper. The strategy is based on initial partnering with conventional generators, relative role of which will be gradually diminished with the growth in number of solar and other renewable power stations. Further research will be focused on the

optimization contract parameters providing optimum portfolio values for power stations participating in the VG.

Acknowledgements The authors would like to thank Dr. Alberto Troccoli from the Commonwealth Scientific and Industrial Research Organization (CSIRO) and to Dr. Frank Mills from ANU for their assistance in obtaining and interpreting historical meteorological data.

Appendix A. Solar Forward Curve algorithm In commercial realization of the proposed business structures, Solar Forward Curve should preferably be obtained by a suitable solar forecasting. Techniques for detailed forecasting of solar radiation and of performance of solar power generators are being developed elsewhere ´ (Sfetsos and Coonic, 2000; Chow et al., 2011; Jose Luis Aznarte et al., 2009). Depending on time-horizon needed, forecasting goals include very short term (1–3 h) for load dispatching, short-term or day ahead for system operations, and quarterly or annual for long-term system plan´ ning and cash-flow analyses (Renne et al., 2008). As the financial contracts of this paper are based on relatively long term peak/off-peak cash-flow aggregation, preservation of overall curve profiles over the term of contracts rather than accuracy of particular values is required to demonstrate the viability of the VG setup. Commonly, long-term PV performance is evaluated using a Typical Meteorological Year (TMY) data. Such evaluation can be performed using, for example, PVWatts calculator developed by NREL.23 The TMY data comprises hourly
23

http://www.nrel.gov/rredc/pvwatts/.

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meteorological parameters derived from historical records to represent “typical” annual climate at a given location. Unfortunately the TMY data in half-hourly time intervals (time intervals of the financial contracts) was not available, and we were not able to utilize a standard TMY approach. At the same time 5 years24 of historical solar radiation and temperature records were available for Melbourne in 30 min intervals.25 A methodology for building Solar Forward Curve employed in this paper used the following steps:  Obtaining historical weather data for a location selected for the SPG (in our case – Melbourne, Australia). The historical weather data included direct and diffuse solar radiation supplemented by air temperature.  Aligning solar radiation and temperature data to a local time scale. This procedure was required since solar radiation data was available with respect to solar time.  Converting historical weather data into historical solar power output data. This was calculated for a monocrystalline Si module having temperature coefficient k = À0.5%, NOCT = 47 °C, facing north and tilted at an angle of 25° to the horizon. The calculations used a standard procedure, described for example in Solanki (2009). Resulted DC solar output data was used as a historical base for the forecasting. For the simplicity of calculations we assumed that an inverter converting DC to AC was 100% efficient.  Using calculated historical half-hourly PV output data (years 2004–2009) to predict half-hourly PV output in selected quarters of 2010, and use this prediction as an approximation of the Solar Forward Curve. The selection of an algorithm for approximating the Solar Forward Curve was driven by the following considerations. Solar output data is highly periodical with two natural cycles: daily and seasonal. Fundamentally, as it was noted in Reikard (2009), the dominance of the 24 h cycle makes it straightforward to build predicting models. This periodicity suggests the use of Fourier Analysis (Sun and Kok, 2007; Boland, 2008) as an appropriate methodology for building Solar Forward Curve as well as for data cleansing. Such approach was implemented in Beacone Simulation Engine (Footnote 25), used to forecast state demand (shown in Figs. 6 and 7). Therefore, it was convenient and logical to utilize the same principle for forecasting solar output. Fortunately, the application of Fourier Analysis for building Solar Forward Curve is more straightforward than in case of the state demand curve: solar radiation does not follow a human induced business/weekend cycle specific to state demand curve.

For the purposes of the prediction, we treated the data as a periodical signal with a superimposed noise, and applied frequency composition/decomposition and filtering techniques implemented in Beacon and well known in Digital Signal Processing.26 Apart of powerful and transparent analytics they also offer high computational efficiency. We assume that there were no dramatic weather changes from year to year over a relatively short (5 years) period. Then we can consider that the solar output is a stationary process (Kubo et al., 1978) represented by three consecutive years of historical data f1(t), f2(t), and f3(t). Respective Fourier Transforms are given by27: F 1 ðkÞ; F 2 ðkÞ; F 3 ðkÞ where 1 F i ðkÞ ¼ pffiffiffiffiffiffi 2p Z
1

dtfi ðtÞeÀikt
À1

ðA1Þ

Forward curve f(t) should belong to the same stationary process but should not include random variations which do not persist from year to year. Therefore, in order to build the 4th year projection we need a mechanism which will consecutively ‘wash out’ random variations. Here we will employ the Convolution Theorem, commonly used for signal filtering (Smith, 1997). We will use 2nd year of data to filter out random changes of the first year, 3rd year as a filter for a 2nd year (and so on, if necessary). We will repeat this process cyclically until we’ll exhaust all possible filtering combinations b and then evaluating resulting Fourier Transform ð F ½f ŠÞ: Z 1  b b Y 123 ðkÞ ¼ F duY 12 ðuÞY 23 ðz À uÞ
À1

b b ¼ F ½Y 12 ðuފ  F ½Y 23 ðuފ ¼ F 1 ðkÞF 2 ðkÞF 2 ðkÞF 3 ðkÞ ¼ F 1 ðkÞF 2 ðkÞF 3 ðkÞ 2 where Y 12 ðuÞ ¼ Y 23 ðuÞ ¼ Z
1

ðA2Þ

dtf1 ðtÞf2 ðu À tÞ ðA3Þ dtf2 ðtÞf3 ðu À tÞ

ZÀ1 1
À1

And, to ensure full symmetry of our procedure: b Y 312 ðkÞ ¼ F 3 ðkÞF 2 ðkÞF 2 ðkÞ 1 b Y 231 ðkÞ ¼ F 2 ðkÞF 2 ðkÞF 1 ðkÞ
3

ðA4Þ

Finally, our 1 year-duration forward curve could be defined as Inverse Fourier Transform of Geometric Average of all possible (filtering) convolutions: b FSC  f ðtÞ ¼ F À1 ½F 1 ðkÞF 2 ðkÞF 3 ðkފ3
26 27
4

ðA5Þ

1/08/04–1/08/09 data. Historical meteorological data was provided by Australian Bureau of Meteorology for station 086282, Melbourne Airport.
25

24

See Smith (1997). Throughout this section we will follow the definitions from Sneddon (1951).

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Transition to more years of historical data is now mathematically trivial. To avoid cumbersome mathematical formulae we have limited the above description to continuous time series. Extending to real discrete data series is straightforward (Smith, 1997) and, in any case, is included in computational packages such as Mathematicae. A resulted approximation of the Solar Forward Curve shown in Fig. 5 for 1 week of August resembles the shape of actual historical data also shown in that figure. This approximation enhances truly periodical events, and smoothens the effect of events not persisting from year to year. It has been noted, that the process routinely implemented in constructing the TMY (Dean, 2010) has a number of drawbacks, including the possibility for overestimating solar outputs, and neglecting sequential dependences between “typical months”. The proposed approach taking into an account the whole set of available historical data without any preferences to the artificial length of 1 month is expected to be free of these disadvantages. Further, our algorithm predicts a “typical PV generation year” – we used historical solar radiation and temperature data to calculate a single historical variable – energy generation A detailed assessment of the proposed technique is outside the scope of this paper, and is being conducted in a separate research effort. Appendix B. Gas Forward Curve algorithm In the absence of real gas plant and contract data, the most obvious way to forecast gas generation would be to find the difference between the forecasted state demand curve and the forecasted solar generation curve. However, it is too risky to predict gas generation based only on this difference because the forecasts are subject to some degree of error. They are only forecasts after all, not actual historical values. To account for this error, FGCi is calculated as a function of three variables. These variables are FDCi, FSCi and a third variable, which will be referred to as the Quantity of Confidence (QOC). Let: FGCi – forecasted gas generation for the ith tick. FDCi – contracted profile quantity for the ith tick. FSCi – forecasted solar generation for the ith tick. QOC – maximum deviation of actual from forecasted solar generation, measured at the 5% significance level. Also, assume: FSC i þ FGC i P FDC i 8i ðB1Þ

FSC i À QOC 6 S i 6 FSC i þ QOC

ðB2Þ

Statistically, the resulting one-sided inequality is true 97.5% of the time. S i P FSC i À QOC ðB3Þ

Hence, 97.5% of the time actual solar output will be above FSCi À QOC. Instead of holding the gas generator accountable for providing just the shortfall between FDCi and FSCi, it is more viable to hold it accountable for providing the shortfall between FDCi and FSCi À QOC. This way, Si can fall as much as QOC less than FSCi before the planned supply of electricity will fall short of FDCi. Thus QOC acts as a safety cap in case of inaccurate forecasting. Obviously the excessive solar output can be sold to the market at premium peak prices generating additional revenue for the SPG. The following scenarios demonstrate the gas generation required (FGCi) at different levels of forecasted solar output less the safety cap (FSCi À QOC). 1. If FDC i 6 ðFSC i À QOCÞ ðB4Þ

Then the forecasted solar output less the safety cap is enough capacity to fulfill all contract obligations during the ith tick. So in this case: FGCi = 0. 2. If 0 < ðFSC i À QOCÞ < FDC i ðB5Þ

Then the solar generator is forecasted to provide some output. But this quantity less the safety cap is only enough to satisfy partial contracted load during the ith tick. Gas output is required to provide the difference. Hence: FGCi = FDCi À (FSCi À QOC). 3. If ðFSC i À QOCÞ 6 0 or equivalently FSC i 6 QOC ðB6Þ

Then the forecasted solar output is minuscule and we conclude the solar generator cannot satisfy any contracted demand. The gas generator must satisfy all demanded on its own. Then, FGCi = FDCi. The following piecemeal function summarizes the values of FGCi
8 8 FDC i 6 ðFSC i À QOCÞ >0 < FGC i ¼ FDC i À ðFSC i À QOCÞ 8 0 < ðFSC i À QOCÞ < FDC i > : FDC i 8 ðFSC i À QOCÞ 6 0 ðB7Þ

Then, in mathematical terms, QOC proves the following inequality to be true 95% of the time for any given single observation of actual solar output Si.

We can capture all three constraints from B7 using a single function: FGC i ¼ Max½FDC i À MaxðFSC i À QOC; 0Þ; 0Š ðB8Þ

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Appendix C. Portfolio values for Virtual Generator In Table 3–5, each portfolio value is given in thousands of dollars. References
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