Energy Sorage and Renewables in New Jersey: Complemenary Technologies for Reducing Our Carbon Fooprin ACEE E-filliaes workshop November 14, 2014 Warren B. Powell Daniel Seingar Harvey Cheng Greg Davies 2014 Warren B. Powell, Princeon Universiy
Frequency regulaion PJM sends charge/discharge signals o generaors every 2 seconds o smooh ou frequency/volage variaions 1 hour MW
Solar from PSE&G solar farms Solar from a single solar farm Solar energy from a single solar farm 1 week
Energy from wind Wind power from all PJM wind farms 1 year Jan Feb March April May June July Aug Sep Oc Nov Dec
Energy from wind Wind from all PJM wind farms 30 days
Wind energy in PJM Toal load vs. oal curren wind (January)
Winer load and solar Toal PJM load plus facored solar (January)
Wind energy in PJM Toal PJM load plus acual wind (July)
Summer load and wind Toal PJM load plus acual wind (July)
99.9 percen from renewables! Wind & solar Baery sorage Fossil backup }20 GW
Lead-acid or lihium-ion Ulracapacio rs
Research challenges How do we conrol a baery sorage sysem? Challenges include:» Managing a single sorage device o handle muliple revenue sreams, over muliple ime scales» Conrolling a sorage sysem in he presence of a mulidimensional sae of he world» Conrolling dozens o hundreds of sorage devices spread around he grid. How do we design sorage sysems?» Wha ype of sorage device(s)?» How many are needed?» How should hey be disribued across he grid? How does sorage change he economics of renewables?
Revenue sreams Frequency regulaion Power qualiy managemen Baery arbirage Energy shifing Demand peak managemen - Many uiliies impose charges based on peak usage over a monh, quarer or even a year. Peak managemen for avoiding capaciy expansion Backup power for ouages seconds minues hours days-weeks weeks-monhs monhs-years
Research goals To design an algorihm ha produces near-opimal policies ha handle he following problem characerisics:» Responds o predicable ime-dependen srucural paerns over hourly, daily and weekly cycles in generaion and loads.» Able o simulaneously opimize over muliple revenue sreams, balanced agains maximizing he lifeime of he baery.» Able o handle ime scales ranging from seconds o minues, hours and days.» Handles uncerainy in energy generaion, prices and loads.» Handles sae of he world variables such as weaher condiions, nework condiions and prices.» For some applicaions, we need o scale o large numbers (ens o hundreds, bu perhaps housands) of grid-level sorage devices.» Abiliy o incorporae forecass of wind or solar energy, loads, and weaher.» Needs o be compuaionally very fas.
A sorage problem Energy sorage wih sochasic prices, supplies and demands. wind E D grid P baery R E = E + Eˆ wind wind wind + 1 + 1 P = P + Pˆ grid grid grid + 1 + 1 D = D + Dˆ load load load + 1 + 1 R = R + x baery baery + 1 W + 1 = Exogenous inpus S = Sae variable x = Conrollable inpus
A sorage problem Bellman s opimaliy equaion V( S ) = min C( S, x ) + γ EV( S ( S, x, W ) ( ) x X + 1 + 1 E P D R wind grid load baery x x x x x wind baery wind load grid baery grid load baery load Eˆ Pˆ Dˆ wind + 1 grid + 1 load + 1
Managing a waer reservoir Backward dynamic programming in one dimension Sep 0: Iniialize V ( R ) = 0 for R = 0,1,...,100 T+ 1 T+ 1 T+ 1 Sep 1: Sep backward = TT, 1, T 2,... Sep 2: Loop over R = 0,1,...,100 Sep 3: Loop over all decisions 0 x Sep 4: Take he expecaion over all rainfall levels (also discreized): R 100 max { } W Compue Q( R, x ) = C( R, x ) + V (min R, R x+ w ) P ( w) End sep 4; End Sep 3; * Find V ( R) = max x QR (, x) * + 1 w= 0 π Sore X ( R) = arg max QR (, x). (This is our policy) End Sep 2; End Sep 1; x
Managing cash in a muual fund Dynamic programming in muliple dimensions Sep 0: Iniialize V ( ) 0 for all saes. T+ 1 ST+ 1 = Sep 1: Sep backward = TT, 1, T 2,... ( R D p E ) Sep 2: Loop over S =,,, (four loops) Sep 3: Loop over all decisions x (a problem if x is a vecor) M + 1 + 1 1 ( Dˆ ˆ ˆ p E) Sep 4: Take he expecaion over each random dimension,, Compue Q( S, x ) = C( S, x ) + End sep 4; End Sep 3; * 100 100 100 w = 0 w = 0 w = 0 1 2 3 * Find ( ) = max x (, ) ( ( )) π Sore X ( S) = arg max QS (, x). (This is our policy) End Sep 2; End Sep 1; V S QS x x W V S S, x, W = ( w, w, w ) P ( w, w, w ) 2 3 1 2 3
Approximae dynamic programming Bellman s opimaliy equaion» We approximae he value of energy in sorage: ( x( x γ )) V ( S ) = min C( S, x ) + V S ( S, x ) x X Invenory held over from previous ime period
Approximae dynamic programming We updae he piecewise linear value funcions by compuing esimaes of slopes using a backward pass: δ R» The cos along he marginal pah is he derivaive of he simulaion wih respec o he flow perurbaion.
Approximae dynamic programming Tesing on a deerminisic problem demonsraes ha we can precisely capure opimal ime-dependen behavior:
Approximae dynamic programming 120 Benchmarking agains opimaliy on a sochasic model 100 Percen Percen of opimal opimal 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sorage problem
Approximae dynamic programming 101 Benchmarking agains opimaliy on a sochasic model 100 Percen Percen of opimal opimal 99 98 97 96 95 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sorage problem
Grid level sorage Slide 25
Grid level sorage conrol Slide 26
Grid level sorage conrol Monday Time :05 :10 :15 :20 Slide 27
Grid level sorage conrol Monday Time :05 :10 :15 :20 Slide 28
Grid level sorage conrol Monday Time :05 :10 :15 :20 Slide 29
Grid level sorage conrol Approximae dynamic programming (blue) vs. opimal using linear programming (green)
Heerogeneous flees of baeries
Heerogeneous flees of baeries A ale of wo baeries» Ulracapacior High power, high efficiency, low capaciy» Lead acid Lower power, lower efficiency, high capaciy Lead acid Ulra capacior
Heerogeneous flees of baeries Conrol algorihm adaps o characerisics of each sorage device Cumulaive disribuion Time (hours) energy is held in sorage device
Handling muliple ime scales Daily (hourly incremens) ( γ E ) V( S ) = min C( S, x ) + V( S x X + 1 0 1 2 3 4... 23 24 Hourly (5-min. incremens) V( S ) = min ( C( S, x ) + γ EV( S ) x X + 1... 0 5 10 15 20 55 60
Handling muliple ime scales Daily (hourly incremens) ( γ E ) V( S ) = min C( S, x ) + V( S x X + 1 0 1 2 3 4... 23 24 Hourly (5-min. incremens) ( γ E ) V( S ) = min C( S, x ) + V( S x X + 1... 0 5 10 15 20 55 60
Handling muliple ime scales Daily (hourly incremens) ( γ E ) V( S ) = min C( S, x ) + V( S x X + 1 0 1 2 3 4... 23 24 Hourly (5-min. incremens) ( γ E ) V( S ) = min C( S, x ) + V( S x X + 1... 0 5 10 15 20 55 60 5 min (2-sec. incremens) V( S ) = min ( C( S, x ) + γ EV( S ) x X + 1... 0 2 4 6 8 298 300 There are 43,200 2-second incremens in a day, over 300,000 in a week.
Solar energy Princeon solar array Wha is he value of sorage in managing he variabiliy from renewables?
Our model, SMART-Sorage simulaneously opimizes he ramping of generaors as well as sorage.
Solar-sorage experimens Sorage level Load Solar inensiy LMP Mixed sun/cloud Sunny day Cloudy day Mixed sun/cloud
Sunny day Solar = 2.3GW Sorage = 12Gwh/600MW Pumped sorage Gas urbine Seam Nuclear CC Solar = 23GW Sorage = 12Gwh/600-MW Solar Energy from sorage Cloudy day
Solar-sorage experimens Load covered by solar % Solar capaciy 23MW 230MW 2.3GW 11.5GW 23GW % of solar used Solar capaciy 23MW 230MW 2.3GW 11.5GW 23GW
Solar-sorage experimens Some conclusions:» The model will only pu energy in sorage when sorage is he only way o mee fas variaions in generaion and loads.» The reason is he losses ha are incurred when convering energy is sored. I is always beer o ramp down a generaor during periods of high energy generaion from wind or solar, han o sore he energy and use i beer.» The idea ha he conversion losses do no maer when he energy is free is a myh. I only applies when he oal generaion from renewables exceeds he oal load (which was never he case in our experimens).
Research goals To design an algorihm ha produces near-opimal policies ha handle he following problem characerisics:» Responds o predicable ime-dependen srucural paerns over hourly, daily and weekly cycles in generaion and loads.» Able o simulaneously opimize over muliple revenue sreams, balanced agains maximizing he lifeime of he baery.» Able o handle ime scales ranging from seconds o minues, hours and days.» Handles uncerainy in energy generaion, prices and loads.» Handles sae of he world variables such as weaher condiions, nework condiions and prices.» For some applicaions, we need o scale o large numbers (ens o hundreds, bu perhaps housands) of grid-level sorage devices.» Abiliy o incorporae forecass of wind or solar energy, loads, and weaher.» Needs o be compuaionally very fas.
Thank you! For more informaion see: hp://energysysems.princeon.edu