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FORECAST VALUE CONSIDERING ENERGY PRICING IN CALIFORNIA

Jennifer Luoma

Patrick Mathiesen

Jan Kleissl

University of California, San Diego 1 1. INTRODUCTION 2 3 Forecasting of weather conditions such as global horizontal irradiance (GHI), wind speed, direction, and expected power 4 production is essential for the efficient integration of renewable power into the energy portfolio. For solar, there are two 5 prominent groups that require forecasts: solar power generators and system operators. Solar power generators are entities 6 that own production facilities and profit from the sale of energy. Independent System Operators (ISOs), however, are 7 primarily concerned with grid reliability and require energy forecasts to plan the dispatch of energy, determine spinning 8 reserve requirements, and calculate energy procurement needs. As these two entities have varied interests, there is a 9 mismatch between their individual definitions of the best possible forecast. For instance, it is possible for a power generator 10 to benefit economically from using biased (rather than accurate) forecasts. This is detrimental to the systems operator‟s goal 11 of reliability of the power grid [1]. As such, system operators cannot rely solely on market commitment information and 12 generally contract with third party forecasting services to provide independent energy production forecasts. 13 14 For the system operator, forecast accuracy is the accepted standard for evaluating forecast effectiveness. Also known as 15 quality [2], accuracy is the deviation between a forecast and a co-located observation. ISOs prefer high-accuracy forecasts as 16 these are most useful for grid reliability purposes. Solar power generators, however, rely on forecast value. Forecast value is 17 the direct monetary benefit of the forecast [2]. As the price of energy is not fixed, forecast quality does not necessarily 18 directly translate to forecast value. For example, a forecast that is of high quality during peak net load times of the day (when 19 energy prices are high and errors are more costly) may be more valuable than a forecast with higher quality only at less 20 critical times. For ISOs, forecast value is a secondary consideration and used to minimize energy generation, transmission, 21 and reserve costs on the grid. For example, an underforecast (predicting too little energy production) would result in over-22 procurement of energy and possibly result in transmission congestion near the solar power plant. Alternatively, an 23 overforecast (predicting more energy than is ultimately produced) would result in under-procurement of energy and a 24 purchase of energy from reserves or regulation at additional cost. 25 26 In California, the California Independent Service Operator (CAISO) allows solar power producers to participate in the 27 Participating Intermittent Resource Program (PIRP). PIRP requires day- and hour-ahead forecasts in addition to historical 28 observations of energy production and local meteorological data (global horizontal irradiance (GHI), direct normal irradiance 29 (DNI), temperature, and wind) [3]. On the net monthly forecast deviation, „uninstructed imbalance energy‟ charges are 30 assessed. These monthly settlements can be positive or negative (reimbursement). However, no penalties for individual day- 31 or hour-ahead forecast errors are applied. As such, there is currently no incentive for generators to provide accurate daily 32 forecasts. However, utility-scale solar power plants will eventually participate in the energy market following the same 33 bidding and settlement rules as conventional power sources (as is already the case for Red Electrica in Spain), including wind 34 power (in most energy markets). 35 36 Previous studies have investigated the integration of renewable energy (predominately wind power) into energy markets. 37 Using Midwest ISO (MISO) pricing data, Botterud et al. (2011) found that optimal day-ahead wind energy bids are primarily 38 driven by price expectations (rather than forecast energy production) when no deviation penalty is applied. However, adding 39 a deviation penalty diminished the difference between the optimal wind energy bid and the most accurate wind energy 40 forecast [4]. In the Spanish energy market, Fabbri et al. (2005) estimated the costs associated with wind energy forecast 41 errors by assuming that forecast deviations are balanced in real-time by reserve energy and found that error prediction costs 42 can be as much as 10% of the total income annually from the energy generation [5]. Bathurst et al. [6], found that forecast 43 revenue is dependent on the difference between the contract (DAM) price and the imbalance (RTM) price for the UK energy 44 market. There, a Markov-Probabilistic forecast was used to determine the most profitable energy commitment. Pinson et al. 45 [7] devised an optimum bidding strategy using forecast uncertainty to dramatically increase revenue. Additionally, Mills and 46

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Wiser [8] found that in a 30% solar photovoltaic (PV) penetration scenario day-ahead forecast error and ancillary services 47 costs were $3.0/MWh and decreased capacity and energy value of PV by 11% (23% for CSP). 48 49 From the ISO perspective, the integration of solar energy results in additional cost due to increased uncertainty and 50 variability. Porter et al. (2013) quoted a Public Service Company of Colorado (PSCo) study as directed by the Colorado 51 Public Utilities Commision (CPUC) in which integration costs ranged from $1.25/MWh to $6.06/MWh [9]. There, each 52 additional 100 MW of installed solar resulted in an increased cost of $1/MWh. To reduce these costs, energy forecasts are 53 relied upon. Milligan et al. (1995) found that the most accurate forecast provides the lowest cost of operations when 54 integrating wind power. However, improving a forecast to 100% accuracy has declining marginal benefits [10]. Using price 55 data from the New York ISO (NYISO), Ruiz et al. (2009) showed that a stochastic-based forecast system reduced the cost of 56 operations by up to 2% over a deterministic-based forecast when optimized to the constraints of the power system [11]. In 57 California, assuming 7.5 GW of wind generation, a GE Energy study found that using existing wind forecasting technology 58 saved $68 million/year in operation costs [12]. Furthermore, the Western Wind and Solar Integration Study (WWSIS, Lew et 59 al., 2010) found that using state-of-the-art day-ahead wind and solar forecasts in the unit commitment process would reduce 60 Western Electricity Coordinating Council (WECC) operating costs by up to $5 billion/yr for 25% wind and 5% solar (by 61 energy) penetrations. Using a perfect forecast would result in additional cost savings of $500 million/yr [13]. A complete 62 review of forecast value studies for renewable energy applications can be found in Chapter 7 of Giebel et al., 2011 [14]. 63 64 In this study, the value of a solar power forecast in the CAISO system is examined. This is particularly of interest as the 65 CAISO market contained 47% of the nation‟s installed solar power as of 2010 [15]. Ideally, the value of a forecast would be 66 evaluated from both a power generator‟s and system operator‟s perspective. However, modeling forecast value to a system 67 operator is complex and requires knowledge of available resources, start-up and running costs, and the system operator unit 68 commitment rules. These factors vary among system operators and, consequently, such a study would be ISO-specific. 69 Large-scale studies such as WWSIS have already generalized these factors to investigate cost savings due to wind and solar 70 forecasts. Rather, this paper will focus on market participants such as solar power generators (after discontinuation of PIRP). 71 Using CAISO pricing data (Sec. 2.1), the price difference between the day-ahead market (DAM) and real-time market (RTM) 72 will be examined (Sec. 3.1). Next, using numerical weather prediction (NWP) solar forecasts (Sec. 2.2), forecast value (Sec. 73 2.3) will be determined for 63 sites in California and geographic data trends explained. Previous studies have not calculated 74 a monetary forecast value in this manner. Furthermore, the effect of a hypothetical deviation penalty on forecast value will 75 examined (Sec. 3.2). Finally, solar forecasts will be corrected using a simple model output statistics (MOS) bias-correction 76 function. The value of corrected forecasts will be compared to uncorrected. Overall, it will be shown that when no deviation 77 penalty is included, positively biased forecasts have the highest value to solar power generators. However, when a deviation 78 penalty is included, the most accurate forecast yields the highest value. 79 80 81 2. METHODS 82 83 2.1 Energy Price Data and Market Structure 84 85 Energy price data was obtained from the CAISO Open Access Same-time Information System (OASIS). OASIS has over 86 4,500 nodes at which a Locational Marginal Price (LMP) is reported. These nodes represent locations in the CAISO power 87 grid where energy can be bought or sold into the market. The LMP is the sum of three components: energy, loss, and 88 congestion. The energy component represents the average price of generating a MWh of electricity and by convention is the 89 same at all price nodes. The loss component represents the cost of transmission losses associated with the delivery of 90 electricity to that price node. Lastly, the congestion component monetizes the transmission constraints in delivering 91 electricity to a price node. All LMP components are reported for the day-ahead (DA), hour-ahead (HA), and real-time (RT) 92 markets. DA forecasts must be submitted at 0530 (local time) on the day prior (Day 0 in Table 1) to the operating day. The 93 operating day (Day 1 in Table 1) begins at midnight (0000) and extends 24 hours. DA forecasts are provided on an hourly 94 basis for each of the 24 hours of the operating day (Table 1). Therefore, the DA forecast horizon is 18.5 to 42.5 hours. 95 Similarly, the HA forecast is submitted 105 minutes prior to each operating hour. However, in this study, HA prices and 96 forecasts are not used.. 97 98 TABLE 1: DAY-AHEAD FORECAST SUBMISSION TIMELINE 99 100

Day 0 Day 1

3

Hour (Local) 00 03 06 09 12 15 18 21 00 03 06 09 12 15 18 21 24

FH (Hours) - - 00 03 06 09 12 15 18 21 24 27 30 33 36 39 42

DA Forecast X 101 DAM LMP (the market price at which a DA forecast is committed) and RT market (RTM) LMP (the price at which 102 settlements are made) from June 1, 2010 to May 31, 2011 were used in this study. Additionally, hour-beginning DAM LMP 103 (e.g. the 0800 DAM LMP applies to 0800-0900) are averaged to correspond to instantaneous hourly GHI data (e.g. for 0800, 104 the mean of the 0700 and 0800 DAM LMP is used). For the RTM, LMP are reported every five minutes and are valid 105 through the next five minutes (e.g. the 0800 RTM LMP is used for 0800-0805). To determine hourly RTM LMP, prices were 106 averaged between 30 min from the hour (e.g. for 0800, the mean of values from 0730 – 0825 RTM LMP were taken). 107 108 In calculating revenue from energy sales, we assume that PIRP is discontinued and that solar photovoltaic (PV) plants 109 participate in the wholesale energy market like other generating resources. Furthermore, it is assumed that the 2010/2011 110 LMP is representative of typical years and that the LMP will not change due to additional PV plants participating in the 111 market. In reality, DAM prices would be reduced with increasing solar generation and the RTM price could fluctuate 112 depending on systematic solar forecast biases and daily production values [16]. 113 114 Since forecasts are submitted in the DAM and deviations settled in the RTM, the value of a forecast must be dependent on 115 the difference between the DAM and RTM LMPs in addition to the magnitude of forecast error (Table 2). For example, if 116 the RTM LMP is greater than the DAM LMP, energy is more expensive to procure in real-time. If an overforecast should 117 occur there will be a large loss in revenue as additional units of energy will need to be purchased at the higher RTM price. 118 Conversely, underforecasts are potentially profitable as excess energy produced can be sold at the high RTM price. 119 However, energy is not guaranteed to sell in the RTM. In fact, a significant excess of energy in the RTM at a particular node 120 is likely to drive the local RTM price down, negating any potential profit. For this reason, excess energy sold in the RTM 121 will be considered only as a potential gain in revenue and RTM LMP will be set to zero when underforecasts occur. The case 122 when the RTM price is less than the DAM price is also considered. Here, underforecasts result in a loss of revenue as the full 123 amount of produced energy was not sold in the higher-priced DAM. In this situation, overforecasts produce higher revenues 124 than accurate forecasts as energy can be procured in the RTM inexpensively. Table 2 summarizes the possible outcomes 125 considering forecast error and the price difference between the RTM and DAM. 126 127 TABLE 2: SUMMARY OF MARKET/FORECAST OUTCOMES 128 129 DAM price –

RTM price

Forecast

Bias Outcome

Restrictions

Imposed

< 0 Over-

forecast

Must purchase additional energy at the higher RTM price:

loss of revenue

If RTM LMP < 0,

then RTM LMP = 0

> 0 Over-

forecast

Must purchase additional energy to cover the under delivery of DA-

committed energy, but at the lower RTM price and thus total revenue

will be greater than if no forecast error occurred: gain of revenue

If RTM LMP < 0,

then RTM LMP = 0

< 0 Under-

forecast

Potential to sell additional energy at higher RTM price: potential gain of revenue

(only monetized when implementing a deviation penalty)

If RTM LMP > 0, then RTM LMP = 0

> 0 Under-

forecast

Missed opportunity to sell additional energy at higher DAM price:

loss of revenue

None

130 131 2.2 Solar Energy Forecasts and Actual Generation 132 133 The California Irrigation Management Information System (CIMIS) is a statewide network of over 120 meteorological 134 observation stations [17]. At each station, Li-Cor LI-200S pyranometers measure GHI to within 5% [18] each minute. 135 However, GHI is reported as hourly-average values. In addition to the automatic CIMIS-provided quality controls [19]-[20], 136

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data exceeding historical limits, missing data, and stations with obvious shading were excluded in this study. Ultimately, 63 137 stations with complete and accurate records were chosen. All other sites and price nodes were omitted. 138 139 In order to simulate solar energy production, it was assumed that a 1 MW PV plant was co-located at each CIMIS station. 140 Power was calculated to be proportional with observed GHI (Eq. 1). In actuality, PV plant efficiency decreases with 141 increasing panel temperature. This effect, known as the panel de-rate factor, was ignored for this study. As such, Equation 1 142 overestimates solar energy production when panel temperatures are high such as in the afternoon. Overall, this simplification 143 is reasonably accurate and may affect estimated power production by up to 10%. 144 145 Day-ahead solar irradiance forecasts are generated using the North American Mesoscale (NAM) numerical weather 146 prediction model [21]-[22]. Published by the National Centers for Environmental Prediction (NCEP), the NAM predicts 147 irradiance on a 12 km x 12 km grid and is available hourly for forecast horizons up to 36 h. In this study, only the 1200 UTC 148 (0400 PST) NAM initialization time is used. Using nearest neighbor interpolation, hourly NAM irradiance forecasts were 149 established at each CIMIS station and power calculated according to Equation 2. 150 151

h (1) 152

153 154

h (2) 155

156 Additionally, to investigate the effect of forecast accuracy on forecast value, model-output-statistics (MOS) was used to bias-157 correct NAM forecasts. Previously, Mathiesen and Kleissl (2011) found that, over a year, NAM forecasts are positively 158 biased by up to 150 W m-2 on average [23]. Futhermore, coastal locations exhibited the largest positive bias especially 159 during summer months. This was attributed to issues in modeling the prevalent summer marine layer clouds. Here, MOS was 160 employed to remove bias error as a function of forecast clear sky index (irradiance normalized by clear-sky GHI) and solar 161 zenith angle. This correction was applied independently for each CIMIS station using a dynamic training set of 8 weeks of 162 rolling, up-to-date data. Overall, for this dataset, bias-corrected NAM forecasts reduced forecast GHI MBE from 57.5 W m-2 163 to 7.0 W m-2. Additionally, the root mean square error (RMSE) was reduced from 134.2 W m-2 to 114.1 W m-2. 164 165 2.3 Revenue and Forecast Value 166 167 To determine forecast value, the total yearly revenue from the sale of solar energy, R, is calculated. Generally, R is 168 calculated by first selling the forecasted energy in the DAM and then settling (either selling excess energy or purchasing 169 energy to meet shortfalls) in the RTM (Eq. 3). In some cases, LMP (especially in the RTM) may be negative. This generally 170 occurs when there is an oversupply of energy or transmission difficulties near a single node. In these instances, energy 171 suppliers are paid to curtail production. To ensure that negative LMP are not unfairly beneficial, energy is never allowed to 172 be “bought” at a negative price in this study. However, energy is allowed to be procured at zero cost. Effectively, when an 173 overforecast occurs, negative RTM LMP are set equal to zero (Table 2). Conversely, when underforecasts occur, there is no 174 guarantee that energy can be sold in the RTM. To simulate this, RTM LMP that are greater than zero are set to zero in these 175 situations (Table 2). To determine the value of forecasts, we assume that a non-revenue-biased bidding strategy is used; solar 176 power providers bid at the forecast level exactly. 177 178

∑ ( - ) (3) 179

180 Additionally, the effect of a deviation penalty, Pdev., is investigated in an alternative market structure. PDev. is defined as 181 182

( ) | | (4) 183 184 where DPF is the deviation penalty factor. There is no precedent for the magnitude of the DPF, but any DPF greater than one 185 ensures that a the maximum possible revenue results from using an unbiased forecast. In this study, a factor of 1.5 is used to 186 ensure that the deviation penalty is always 50% larger than the possible revenue gain of a biased forecast. A proper DPF 187 ensures that the highest quality forecast is the most valuable forecast without excessively diminishing total revenue for the 188 solar energy generator (i.e. if the DPF is too high solar energy generators will be harshly penalized for providing even near 189 perfect forecasts). An optimal DPF was not investigated. When implementing a deviation penalty, excess energy is allowed 190

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to be sold in the RTM and the restrictions for underforecasts are lifted (Table 2). Subsequently, the total yearly revenue 191 considering a deviation penalty becomes: 192 193

∑ ( - ) - (5) 194

195 Finally, revenue from a perfect forecast was calculated assuming that the delivered energy calculated using CIMIS data (Eq. 196 1) was bid exactly into the DAM and no RTM settlement took place. 197 198

∑ (6) 199

200 201 3. RESULTS AND DISCUSSION 202 3.1 Day-Ahead and Real-Time Market Price Trends 203 204 Figure 1 shows the DAM and RTM LMPs averaged across all studied price nodes. Mean hourly DAM LMP range from $25 205 to $41 / MWh with highest prices occurring in the late afternoon during July through September. Price trends vary by time of 206 year. Between November and May, the highest daily prices occur in the morning and prices decrease by approximately $10 207 throughout the day. In summer months (May – October), the trend is reversed; morning prices are low and increase by 208 approximately $40 throughout the day, peaking in the late afternoon. Presumably, this is due to higher demand on the grid 209 resulting from increased air conditioning load. In the RTM, mean-hourly LMP are similar ($21 to $34, Fig. 1e). 210 Additionally, similar diurnal and yearly trends are observed with highest prices occurring in the afternoon during July to 211 October. Overall, RTM prices are slightly less than DAM prices but are more volatile. 212 213 Geographically, DAM and RTM prices vary by location. In general, the highest yearly averaged prices for the DAM occur 214 near the coast. However, not all sites follow this trend and the difference from coastal to inland sites is small (less that 215 $7/MWh). Additionally, locations with the highest yearly averaged RTM prices are dispersed across the state, indicating that 216 geographical trends in prices are weak. Lastly, it is expected that year-to-year variations in pricing will occur. For this study, 217 it is assumed that 2011 represents a typical year. 218 219 As presented in Eq. 1 and Eq. 2, forecast revenue is largely dependent on the difference between the DAM and RTM LMP. 220 For most months and times, the DAM and RTM prices differ by less than $5/MWh. Differences are largest in the afternoon 221 between July and October, with RTM prices approximately $10-$15/MWh larger. Over the entire year, price differences are 222 largest in morning and evening (Fig. 1f). Overall, however, DAM prices are greater than RTM prices by about $5/MWh. 223 This price difference provides an incentive for overforecasting in the DAM as additional energy can likely be procured at 224 relatively low RTM prices. Furthermore, overforecasts are particularly profitable in mornings between May and September 225 as DAM prices tend to be much higher than RTM prices. Similarly, evenings in June through September could yield high 226 profits for underforecasts because excess energy could be sold at high RTM prices. Since there is no guarantee the energy 227 would be purchased in the RTM, profits from underforecasts are not allowed in this study (Table 2). 228 229 3.2 Comparison of Forecast Value 230 231 For each CIMIS station, revenue was calculated for a 1 MW power plant for NAM forecasts (Eq. 3), bias-corrected NAM 232 forecasts, and perfect forecasts (Eq. 6). To determine forecast value relative to a perfect forecast, the ratio of forecast yearly 233 revenue to perfect forecast yearly revenue was calculated. For the NAM forecast, this ratio is depicted in Figure 2a. On 234 average, using NAM forecasts yield yearly revenues of 96% of perfect forecast revenue (Fig. 2b). Inland, NAM forecast 235 revenue is as large as 98% of the perfect forecast revenue. In these areas, NAM forecasts are more accurate due to lower 236 cloud occurrence. 237 238 Figure 2b summarizes the distribution of forecast revenue for all sites using the standard and bias-corrected NAM forecasts 239 under market structures with and without deviation penalties. When no deviation penalty was enforced, the standard NAM 240 forecast was most profitable at 96% of perfect forecast revenue. When bias error was reduced, forecast revenue decreased to 241 93% of perfect (Sec. 3.4, later). Conversely, when a deviation penalty was included, the standard NAM forecast yielded 242 revenue of 59% of a perfect forecast. After MOS bias-correction was applied, revenue increased to 76% (Fig. 2b). 243 244 3.3 Example for Coastal Sites 245

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246 When no deviation penalty is considered, bias-correction of NAM forecasts results in a large loss in value at coastal 247 locations. Figure 3a shows the ratio of bias-corrected NAM forecast revenue to standard NAM forecast revenue. At the 248 coast, this ratio is smallest. To illustrate why the bias-corrected NAM forecast is less valuable at coastal sites, the Revenue 249

Improvement Factor (RIF) is defined as -

. Positive RIF indicate that the bias-correction increases total 250

revenue when compared to the standard NAM forecast. Averaged by hour of day and month of year for all sites within 20 251 miles of the coast, Figure 3b shows that RIF is typically negative. Specifically, the bias-corrected NAM is less valuable than 252 the standard NAM for all times of day from July to November. During this time, DAM prices are generally up to $5/MWh 253 higher than RTM prices. As a result, overforecasts produce larger revenues than perfect forecasts as the cost of RTM energy 254 procurement is less than the commitment price in the DAM. Since the standard NAM typically overforecasts irradiance at 255 this time, it follows that the standard NAM would be more profitable than the relatively unbiased corrected NAM forecast. 256 Moreover, this effect is amplified in the mornings of July, August, and September. At this time, NAM overforecasts are 257 more frequent as the prevalent marine layer clouds are rarely predicted. In general, if the DAM price is higher than the RTM 258 price, the most profitable bid for a market structure without deviation penalties would be to forecast energy output at 259 maximum capacity. Since bias-corrected forecasts trend away from maximum capacity, revenues are generally lower. 260 However, when deviation penalties are considered, forecast errors are de-incentivized, ensuring that bias-corrected forecast 261 are more valuable. 262 263 3.4. Forecast Value Versus Error Metrics 264 265 Figure 4 shows the RIF as a function of - and ) for 266 each site. Without a deviation penalty (Fig. 4a), forecast revenue improvement decreases with increasing MBE. However, 267 decreasing RMSE has little effect on forecast revenue. Together, this indicates that positively biased, low RMSE forecasts 268 are the most profitable. If RMSE could be reduced without removing the positive bias, forecast revenue could potentially be 269 increased further. However, when a deviation penalty is added, allowing for excess energy to be sold in the RTM, forecast 270 value increases as MBE and RMSE are improved (Fig. 4b). 271 272 4. CONCLUSIONS 273 274 In this study, the value of a solar power forecast was estimated for 63 locations within the California energy market. Day-275 ahead solar irradiance forecasts for one year were based on the NAM numerical weather prediction model. Using CAISO 276 LMP prices, total forecast revenue was calculated for standard NAM forecasts and bias-corrected NAM forecasts under two 277 simple market structures and compared to the theoretical revenue of a perfect forecast. Overall, the yearly revenue of the 278 NAM numerical weather prediction model irradiance forecasts is always less than that of a perfect forecast. However, for 279 some locations forecast revenue is as much as 98% of perfect forecast revenue. When model-output-statistics (MOS) was 280 used to reduce forecast bias, a decrease in forecast value was observed. Since DAM prices are typically higher than RTM 281 prices, positively biased NAM forecasts produce greater revenue than less-biased forecasts for all sites. This effect was 282 exacerbated for coastal California, in which irradiance overforecasts are more common and DAM prices much greater than 283 RTM. 284 285 These simulations confirm findings [1] that biased forecasts can be more valuable to solar power generators. Since there 286 currently is no penalty for providing an incorrect forecast, there is motivation to submit an incorrect, biased forecast that 287 produces higher revenue. Subsequently, if forecasts from generators are not representative of the actual energy that is 288 expected to be received, market inefficiencies are created by forcing system operators to procure additional reserves to 289 balance the additional uncertainty in the forecast. System operators can respond by producing internal forecasts or procuring 290 forecasts from independent 3rd parties. Market inefficiencies could also be mitigated through deviation penalties, which (by 291 design) cause the value of an accurate forecast to increase (Sec. 3.4). In this way, deviation penalties can internalize the 292 external costs of inaccurate forecasts to the owner / operator, but the penalty factor must be chosen carefully to be reasonable 293 to forecast providers. 294 295 We assume that solar power plants participate in the open market and that the LMP does not change due to participation of 296 the additional solar power plants in the market. In reality, DAM prices would be reduced with increasing solar generation and 297 the RTM price could be driven up or down if solar forecast trend to either over- or under-predict. Inclusion of the feedback of 298 PV participation in the energy market is likely to promote accurate forecasts. Also, these results are specific to California 299

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with unique forecast biases and DAM and RTM price spreads. Regardless, our approach to determining forecast value allows 300 for the analysis of impact of different energy market structures on the value of accurate forecasts to market participants. 301 302 5. ACKNOWLEDGEMENTS 303 304 We appreciate support by Jim Blatchford, Jenny Pedersen, and Julianne Riessen (CAISO) for assisting in obtaining 305 information about CAISO operations and market structure. 306 307 6. REFERENCES 308 309 [1] Botterud A, Zhou A, Wang J, Bessa R, Keko H, Mendes J, Sumaili J, Miranda V. “Use of Wind Power Forecasting in 310 Operational Decisions.” Argonne National Laboratory, 2011. 311 312 [2] Murphy A H. “What is a good forecast? An essay on the nature of goodness in weather forecast,” Weather and 313 Forecasting, Vol. 8, pp. 281-293, 1993. 314 315 [3] Blatchford J and Zack J. “Integration of Solar Energy into the Participating Intermittent Resource Program (PIRP).” 316 CAISO Issue Paper, April 2008. 317 318 [4] Botterud A, Wang J, Miranda V, Bessa R. “Wind Power Trading Under Uncertainty in LMP Markets.” IEEE Transaction 319 on Power Systems. 320 321 [5] Fabbri A, Gomez San Roman T, Rivier Abbad J, and V. H. M. Quezada,“Assessment of the cost associated with wind 322 generation prediction errors in a liberalized electricity market,” IEEE Trans. Power Syst., Vol. 20, 323 No. 3, pp. 1440–1446, Aug. 2005. 324 325 [6] Bathurst, G.N., Weatherill, J., and Strbac, G. “Trading Wind Generation in Short Term Energy Markets.” IEEE 326 Transactions on Power Systems, Vol. 17, No. 3, pp 782-789, 2002. 327 328 [7] Pinson, P., Chevallier, C., and Kariniotakis, G.N. “Trading Wind Generation From Short-Term Probabilistic Forecasts of 329 Wind Power.” IEEE Transactions on Power Systems, Vol. 22, No. 3, pp 1148-1156, 2007. 330 331 [8] Mills, A. and Wiser, R. “Changes in the Economic Value of Variable Generation at High Penentration Levels: A Pilot 332 Case Study of California.” Ernest Orlando Lawrence Berkeley Technical Note, LBLN-5445E. Available online at 333 http://emp.lbl.gov/sites/all/files/lbnl-5445e.pdf. 2012. 334

[9] Porter, K., Fink, S., Buckley, M., Rogers, J., and Hodge, B.-M. “A Review of Variable Generation Integration Charges.” 335 National Renewable Energy Laboratory Technical Report, NREL/TP-5500-57583. Available online at 336 http://www.nrel.gov/docs/fy13osti/57583.pdf. 2013. 337

[10] Milligan M, Miller A, Chapman F. “Estimating the Economic Value of Wind Forecasting to Utilities.” NREL. 338 Windpower. 1995. 339 340 [11] Ruiz P, Philbrick C R, Zak E, Cheung K W, Sauer P. “Uncertainty Management in the Unit Commitment Problem.” 341 IEEE Transaction on Power Systems, Vol. 24, No. 2, pp 642-651, 2009. 342 343 [12] Porter, K., Fink, S., Rogers, J., Mudd, C., Buckley, M., and Clark, C. “PJM Renewable Integration Study: Review of 344 Industry Practice and Experience in the Integration of Wind and Solar Generation.” GE Energy Technical Report. Available 345 online at http://pjm.com/~/media/committees-groups/task-forces/irtf/postings/pris-task3b-best-practices-from-other-markets-346 final-report.ashx. 2012. 347 348 [13] Lew D, Piwko D, Miller N, Jordan G, Clark K, Freeman L. “How Do High Levels of Wind and Solar Impact the Grid? 349 The Western Wind and Solar Integration Study. NREL. December 2010. 350 351 [14] G. Giebel et al., “The State-of-the-Art in Short-Term Prediction of Wind Power: A Literature Overview, 2nd Ed.” 352 ANEMOS. 2011. 353

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354 [15] Ardani K, Margolis R. “2010 Solar Technologies Market Report.” NREL Report, November 2011. 355 356 [16] Jonsson T, Pinson P, Madsen H. “On the market impact of wind energy forecasts.” Energy Economics, Vol. 32, pp 323-357 320, 2010. 358 359 [17] CIMIS, CIMIS Overview 2009 [Online]. Available: http://www.cimis.water.ca.gov/cimis/infoGenCimisOverview.jsp 360 361 [18] Campbell Scientific, 1996: LI200S Pyranometer instruction manual. Campbell Scientific Technical Specifications, 362 Revision 2/96. 363 364 [19] CIMIS, QC Overview 2009 [Online]. Available: http://www.cimis.water.ca.gov/cimis/dataQc.jsp 365 366 [20] CIMIS, Current Hourly Flags 2009d [Online]. Available: http://www.cimis.water.ca.gov/cimis/dataQcCurrentHourly. jsp 367 368 [21] Janjic, Z., R. Gall, and M.E. Pyle, 2010: Scientific documentation for the NMM solver. NCAR Technical Note 369 NCAR/TN 477+STR. 370 371 [22] Janjic, Z., T. Black, M. Pyle, B. Ferrier, H.Y. Chuang, D. Jovic, N. McKee, R. Rozulmalski, J. Michalakes, D. Gill, J. 372 Dudhia, M. Duda, M. Demirtas, L. Nance, T. Slovacek, J. Wolff, L. Bernardet, P. McCaslin, and M. Stoelinger, 2011: User‟s 373 guide for the NMM Core of the Weather Research and Forecast (WRF) Modeling System Version 3. 195 pgs. 374 375 [23] Mathiesen P, Kleissl J. “Evaluation of numerical weather prediction for intra-day solar forecasting in the continental 376 United States. Solar Energy, Vol. 85, No. 5, pp. 967–977, May 2011. 377 378

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Figure 1: Average DAM LMP (a), RTM LMP (b), and DAM LMP-RTM LMP (c) for June 1, 2010 – May 31, 2011 for all 63 379 price nodes by time of day (for hours with a non-zero solar forecast) versus month. Box plots for DAM LMP (d), RTM LMP 380 (e), DAM LMP-RTM LMP (f) indicating mean, 25th and 75th percentiles, ends, and outliers (red crosses). For RTM LMP, 381 outliers greater than 115 $/MWh (83) are not shown. For DAM LMP –RTM LMP, outliers less than -100 $/MWh (66) are 382 not shown. 383

384 Figure 2: (a) Ratio of yearly revenue using NAM forecast (Eq. 3) over using a perfect forecast (Eq. 6). (b) Box plot showing 385 distribution of site revenue performance based on yearly revenue ratio using a real forecast to a perfect forecast (Eq. 6); real 386 forecasts consist of (from left to right) NAM („NAM‟, mean 0.96), corrected NAM („NAMcorr‟, mean 0.93) (Eq. 3), NAM 387 with deviation penalty („NAM_Pen‟, mean 0.59) and corrected NAM with deviation penalty („NAMcorr_Pen‟, mean 388 0.76)(Eq. 5). Box plots indicate mean, 25th and 75th percenticles, ends, and outliers (red crosses). 389

390 Figure 3: (a) Ratio of yearly revenue using corrected NAM forecasts to NAM forecasts (Eq. 3). (b) Revenue improvement 391 factor [-] using corrected NAM to NAM plotted by time of day and month averaged for all sites within 20 miles of the coast. 392

393

Figure 4: Revenue Improvement Factor (RIF, defined as -

) as a function of change in MBE and RMSE 394

due to the forecast bias correction for each site without deviation penalties (a, Eq. 3) and with deviations penalties (b, Eq. 5 395 396