1. Valuing The Time- Varying Production of Solar PV Cells Severin Borenstein Haas School of Business, UC Berkeley University of California Energy Institute March 18, 2005

2. Importance of Time-Varying Electricity Generation  Wholesale prices reflect higher value of power at peak times  In summer-peaking systems, photovoltaic production is higher at high price times  But PVs are on the customer side of the meter, so the power may be misvalued, because retail prices don’t time vary  TOU vs flat-rate retail tariff?

3. Many other issues in PV debate  Direct subsidies  Indirect subsidies from avoiding other costs loaded into retail price  Value of reducing transmission and distribution usage, including losses  Security value of distributed generation  Grid stability/backup costs due to supply intermittency

4. Basic Approach  Find data on time-varying PV production  Find data on time-varying wholesale prices  Put them together  Calculate premium value of PV power due to its timing compared with value at flat rate  Adjust for positive residual correlation between PV production and price

5. PV Production Data  Simulation versus Production data  Problems with actual production data availability idiosyncracy  Best simulation source, TRNSYS, gives output with stochastic weather variation  Still has surprising result: SF > Sacramento

6. Wholesale Price Data  CAISO real-time price data for five years, 1999-2003 Not in long-run equilibrium: over-capacity reduces price spikes  Simulated long-run real-time price data using small demand elasticity Based on CSEM WP #133r Uses CAISO load for same time period large price spikes in a few peak hours

7. Simple Analysis  Calculated average per-kWh valuation Weigthed by CAISO load to get flat rate Weighted by PV production to get value of PV corrected for time of production  Using actual CAISO prices, value increase ~10% from production-time correction for south-facing panels  Using simulated prices, value increase per kWh is 20%-30% for south-facing panels  Value increases, but total production falls when panel is turned away from South

8. Correction for Residual Correlation  PV production higher when price is higher  Adjustment: reorder PV production data so high system load corresponds to high PV production within month/hour/weekperiod  Very favorable assumption for PV Still omits out-of-sample superpeaks, but PV production doesn’t superpeak  Effect of correction is fairly small

9. TABLE 1

10. TABLE 2

11. TABLE 3

12. How much does TOU improve valuation of solar PV power?  If customer is on TOU retail rate, then retail prices are higher on average at times when wholesale prices are high.  Still doesn’t capture superpeak prices, but solar PV production doesn’t superpeak when prices do.  Result: with TOU retail prices, retail price variation approximates true wholesale value overall

13. TABLE 4

14. TABLE 5

15. Conclusion  Adjusting for time-varying production of solar PV can make a significant difference in the value of PV production  Less dramatic impact using actual CAISO prices than long-run simulated prices that cover fixed costs with large price spikes  Customers on time-of-use pricing face prices that fairly accurately reflect the time-varying value of PV production