Energy procurement in the presence of intermittent Adam sources Wierman (Caltech) JK Nair (Caltech / CWI) Sachin Adlakha (Caltech) get about energy for a second lk is really about the role of uncertainty in newsvendor get about energy for a second lk is really about the role of uncertainty in newsvendor decide today how many newspapers you want to se Estimate demand, Purchase, uncertainty

Demand is realized lost revenue wasted inventory get about energy for a second lk is really about the role of uncertainty in newsvendor decide today how many newspapers you want to se seasonal products perishable goods compute instances energy Now, back to energy Generation Load

Key Constraint: Generation = Load (at all times) low uncertainty Now, back to energy Generation Load Key Constraint: Generation = Load (at all times) controllable via markets low uncertainty Electricity markets markets

long term int. /day ahead Utility buys power to meet demand real time time newable energy is coming! MW China Americas

Solar PV: Europe MW Wind: Worldwide newable energy is coming! but incorporation into the grid isnt ea y Each line is wind generation over 1 da They are typically d) an m de n

o e bl la ai av ot (n e bl lla Uncontro ) Intermittent (large fluctuations Uncertain (difficult to forecast) Tomorrows grid Key Constraint: Generation = Load (at all times)

less controllable low uncertainty high uncertainty 1) Huge price variability, leading to generator opting out of markets! 2) More conventional reserves needed, countering sustainability gains! Key Constraint: Generation = Load (at all times) less controllable low uncertainty high uncertainty ery peculiar v g in th e m

so th 6 1 ON JUNE market. The y it ic tr c le e s y n a happened in Germ minus 100 to ll fe

y it ic tr c le e f wholesale price o generating , is t a h T ). h W (M r u

per megawatt ho e managers of th y a p to g in v a h companies were ir electricity. e th e k ta to d ri

g e th far o s s a h e d n Energiewe d, e s a e r c e

d t no increased, ouse h n e e r g f o emissions gases. What can be done? Reduce the uncertainty Better prediction Aggregation in time (storage) in space

(distributed generation) in generation (heterogeneous mix) Design for the uncertainty Redesign electricity markets this session Increase amount of demand response PIRP markets long term int. /day ahead real time

time markets long term int. /day ahead real time time 4 hr market talk: What is the impact of long term wind con As renewable penetration increases: 1)Should markets be moved closer to realtime?

2)Should markets be added? First step: hould utilities procure electricity in the presence of renewabl talk: What is the impact of long term wind con As renewable penetration increases: 1)Should markets be moved closer to realtime? 2)Should markets be added? long term price int. /day ahead

real time long term price volatility [ ] > int. /day ahead [ | ] >

real time price wind uncertainty long term ^ ^ ^

1 = int. /day ahead ^ real time ^ 2 = Assumption: and are independent

(A generalization of the martingale model of forecast evolution) price wind uncertainty long term ^ int. /day ahead

^ real time Key Constraint: Generation = Load + + + (we ignore network constraints) min [ + + ] Utility goal: Subject to causality constraints price

wind uncertainty long term ^ int. /day ahead ^

real time min [ + + ] Utility goal: Subject to causality constraints Variant of the newsvendor pro [Arrow et. al. 51], [Silver et. al. 98], [Khouja 99], [Porteus 02], [Wang et. al. 12]. long term

^ int. /day ahead ^ real time

Theorem: The optimal procurement strategy is characterized by reserve levels and such that where and uniquely solves Scaling regime baseline, e.g., average output of a wind farm scale, e.g., number of wind farms aggregation, e.g., degree of correlation between win long term int. /day ahead ^

^ ^ 1 = ^ ( )= ( ) = ^ real time ^ 2 = ( ) =

Scaling regime baseline, e.g., average output of a wind farm scale, e.g., number of wind farms aggregation, e.g., degree of correlation between win Theorem: Procurement with zero uncertainty Extra procurement due to uncertainty Scaling regime baseline, e.g., average output of a wind farm scale, e.g., number of wind farms aggregation, e.g., degree of correlation between win

Theorem: Depends on wind aggreg - =1/2 (independent) Depends on markets & predictions - =1 (correlated) - prices - forecasts Scaling regime baseline, e.g., average output of a wind farm scale, e.g., number of wind farms aggregation, e.g., degree of correlation between win Theorem: This form holds more generally than the model studied here: e than three

markets: [Bitar et al., 2012] n prices are endogenous: [Cai & Wierman, 2014] n small-scale storage is included: [Hayden, Nair, & Wierman, Electricity markets markets long term int. /day ahead real time time talk: What is the impact of long term wind con As renewable penetration increases:

1)Should markets be moved closer to realNo! (See paper) time? 2)Should markets be added? Electricity markets markets long term talk: What is the real int. /day 4 hr time ahead ahead marke t? term impact of long

time wind con As renewable penetration increases: 1)Should markets be moved closer to realtime? 2)Should markets be added? long term real time v/s long term int.

real time What happens to if a market is added? What happens to if a market is added? 2 Gaussian long term int. /day 6

2 markets ] 3 markets are always better! 3 markets 6 6.5 7 7.5 8 8.5

When does this happe 9 9.5 10 Theorem: If is increasing for , decreasing for , and satisfies: is decreasing for is decreasing for then the expected procurement is lower with 3 markets than with 2 markets. Satisfied by the Gaussian distributio 2 Weibull long term

int. /day 6

6 real time 8 When does this happe 8.5 9 9.5 10 Estimation errors are heavy-tailed (specifically, long-tailed) Theorem: If satisfies the condition: =0 ,

then there exist prices such that the expected procurement is higher with 3 markets than with 2 markets. markets long term int. /day ahead real time time 4 hr market talk: What is the impact of long term wind con

As renewable penetration increases: 1)Should markets be moved closer to realNo! (See paper) time? It depends, Gaussian or heavy-tai 2)Should markets be added? PIRP markets long term int. /day ahead real time

time talk: What is the impact of long term wind con stion: How should wind be incorporated into th Energy procurement in the presence of intermittent Adam sources Wierman (Caltech) JK Nair (Caltech / CWI) Sachin Adlakha (Caltech)