optimization with variable energy...

MotivationScheduling with Energy Costs

Predicting PricesExtension to Building Management

Optimization with Variable Energy Prices

Helmut Simonis

Cork Constraint Computation CentreComputer Science Department

University College CorkIreland

CPAIOR 2012, Nantes

Helmut Simonis Optimization with Variable Energy Prices 1



Take away message

Electricity suppliers move to time variable pricesScheduling should take this into accountA Family of resource cost aware constraintsProblem generatorWhere do forecast prices come from?Improved forecast does not imply improved scheduleInteresting extension to building energy management




Working with

4CTarik HadzicDiarmuid GrimesGeorgiana IfrimBarry O’Sullivan

IndustryCharles Sheridan, IntelAnnabelle Pratt, Intel

Campus21 FP7 projectUCC, TU Wien, Cartif, BAM, NEC, UTRC-I, Sirus,HSG-Zander, City of Valladolid, ESB




Funding Sources

SFI TIDA Grant: Energy Cost Aware SchedulingIRCSET Post Doctoral Fellowship (Intel)SFI PI Grant (O’Sullivan)FP7 Campus21 Project




Outline

1 Motivation

2 Scheduling with Energy Costs

3 Predicting Prices

4 Extension to Building Management




A Changing World for Electricity Supply

Many countries moving away from single, nationalelectricity suppliersAllow customers to switch between suppliersStill use shared distribution networksIncreasing use of renewable sources (wind, solar PV)Political aims to reduce CO2 productionPrimary energy cost increasing rapidlySecurity of supply not guaranteed




The Rising Cost of Electricity (Source: Eurostat)




Auction Based Electricity Markets

National/Regional price finding mechanismNew price produced every 30 minutes (Ireland)Generators bid for productionBids accepted in merit orderFill predicted/real demand for time slotPrice defined by last accepted bidAdditional uplift price, start-up/shut-down/reserve costsConsumer price includes distribution costs, margins andtaxes




Demand and Prices (Source: SEMO)

Demand Price

Figure: Electricity Demand and Price, ROI, Comparing January andJune data 2010




Why Time Variable Prices?

Determine “fair” price for variable demand/productionCapacity of renewable resources variable

“Zero” marginal costCapacity profile not linked to demand

Penalize CO2 intensive generatorsMove demand away from peak periods




Consumer Prices

Most consumers (residential and industrial) still pay fixedprice per kWhSome customers use simple day/night tariffs (2 meters)Smart-meters required to allow more flexibilityTime-of-Use (ToU) tariffs offered by some utilitiesConsumer real-time prices still experimental




Time-of-Use Tariffs

Price changes during day for certain periodsWeekend prices are differentSummer/Winter prices possibleCost at each time period known well in advance (6months?)Not really linked to market price




Summer Tariff




Winter Tariff




Why are real-time prices difficult to sell?

Customers face uncertainty about costLet supplier worry about problem

Pay premium for fixed prices

How to exploit changing prices?Opportunity to reduce costs by intelligent use

But impact on other cost factors (social, environmental)




Further Complication: Feed-in

Customers may have their own electricity sourcesWindCHP (Combined heat and power)Solar PV

These sources are cheaper than grid (sunk investmentcost)Feed-in prices can be low, fair, subsidized




Use CaseCost Aware CumulativeIntegrating Energy Cost into Other Scheduling ConstraintsAn Instance Generator

Outline

1 Motivation

2 Scheduling with Energy CostsUse CaseCost Aware CumulativeIntegrating Energy Cost into Other SchedulingConstraintsAn Instance Generator

3 Predicting Prices






Scheduling with variable energy cost

Extend existing scheduling constraints with a variableresource cost componentAllow prices to vary in time and in volumeAt each time, use cheapest source firstAdd-on to existing constraint-based schedulingMainly affects cost objective





Surely somebody is doing this already?

One reference found for production schedulingP.M. Castro, I. Harjunkoski and I. E. Grossmann. A New

Continuous-Time Scheduling Formulation for Continuous

Plants under Variable Electricity Cost, IND ENG CHEMRES , vol. 48, no. 14, pp. 6701-6714, 2009.Continuous processTime of use tariff

Large body of work on energy efficient scheduling insideprocessors, not time variableDatacentre scheduling (follow the moon)





Use Case: Feed Mill Scheduling (Simonis 2006)

Animal feed production in UKFeed in different sizesFor different speciesHuman health risk

ContaminationBSE

Strict regulationsConstraints

Avoid contamination risksMachine setup timesMachine choice (quality/speed)Limited storage of finished productsVery short lead times (8-48 hours)Factory structure given as data

Status (COSYTEC Product)Operational since Nov 96





Product Made: Feed Pellets (Image: Wikipedia)





Feed Mill Schematic (www.feedmachinery.com)

Pellet Press: Rating 375kWYearly UK production (2009-2010): 10M tonnes (Defra)





Why this use case?

Day-by-Day scheduleMake during night for delivery tomorrow morningOnly need to know prices for 24/36 h aheadEnergy use depends on recipeCurrent day/night tariff limits production capacityMargins extremely tight





Reminder: Cumulative

Aggoun, Beldiceanu 1993Core global constraint for constraint-based schedulingLarge number of algorithmic developments, few changes ofbasic constraintTime/volume dependent resource cost not considered sofar

Cumulative([s1, s2, ...sn], [d1, d2, ...dn], [r1, r2, ...rn], l , p),





New Constraint Variant: CumulativeCost

Add cost elementPer unit cost expressed with areasIntersection of resource use profile with areas defines costGlobal reasoning required





Formally: CumulativeCost

∀ 0 ≤ t < p : prt :=�

{i|si≤t<si+di}

ri ≤ l

∀ 1 ≤ i ≤ n : 0 ≤ si < si + di ≤ p

ov(t , prt ,Aj) :=

�max(0,min(yj + hj , prt)− yj) xj ≤ t < xj + wj

0 otherwise

∀ 1 ≤ j ≤ m : aj =�

0≤t<p

ov(t , prt ,Aj)

cost =m�

j=1

ajcj





Toy Example

12

1

23

1

45

1

34

1

01

1

3

← j

← cj

← aj

2 52

1t1

1 52

2t2

0 5

3

1

t3





Toy Example: Optimal Solution

12

1

23

1

45

1

34

1

01

1

3

← j

← cj

← aj

cost = 15

2 52

1t1

1 52

2t2

0 5

3

1

t3

23 2 02





How to implement this?

element Element constraints linking start and costA greedy assignmentB greedy assignment

Flow flow from tasks to areasLP1 Flow + extra inequalitiesLP2 Flow + extra inequalitiesDLP time indexed LP model

DMIP MIP variant of DLP





Comparative Power of Algorithms

Element

Alg A

Flow

Alg B

LP 1 LP 2 DLP DMIP





Clear Winner: DLP

Based on LP relaxation of Cumulative by HookerMost others can be quite weakMIP is too expensive to solveDLP has very good cost boundScalable for 100s (not 1000s) of tasksCost based pruning: Reduced Cost Filtering





LP Lower Bound

lb = minq�

j=1

aj cj

prt ∈ [0, l] yit ∈ {0, 1} zjt ∈ [0, hj ]

∀ 1 ≤ j ≤ q : 0 ≤ aj ≤ wj hj

∀ 1 ≤ i ≤ n : si =p−1�

t=0

tyit

∀ 1 ≤ i ≤ n :p−1�

t=0

yit = 1

∀ 0 ≤ t < p : prt =�

1≤i≤n

�

t�≤t<t�+di

yit� ri =q�

j=1

zjt

∀ 1 ≤ j ≤ q : aj =

xj+wj−1�

t=xj

zjt





Toy Example: DLP and DMIP

Direct LP Direct MIP

12

1

23

1

45

1

34

1

01

1

3

← j

← cj

← aj

lb = 1233 1 11

12

1

23

1

45

1

34

1

01

1

3

← j

← cj

← aj

cost = 1523 2 02





Can we use this for something else?

Scheduling problems with manpower costsMan/hour cost varies over timeOffice Hours/Nights/Weekends/HolidaysExtra staff costs more: Temps/FreelanceNatural, otherwise change hire rules





Why don’t we just use CumulativeCost with otherresource constraints?

Combine a CumulativeCost with a Disjunctiveresource constraintCost estimate does not take non-overlapping into accountToo optimistic cost valueWorks if we have one global LP relaxation





DisjunctiveCost

The DisjunctiveCost constraint allows one task to be runon a machine at any time. We can describe the constraint byadding

∀ i , j |i �= j : si + di ≤ sj ∨ sj + dj ≤ si

to constraints.In the LP/MIP model, we extend constraints with the condition

∀ 0 ≤ t < p :�

1≤i≤n

�

t �≤t<t �+di

yit � ≤ 1





ParallelMachineCost

The ParallelMachineCost constraint consists of constraintsplus the constraints

∀ 1 ≤ k ≤ b, ∀ i , j |i �= j : mi �= mj ∨ si + di ≤ sj ∨ sj + dj ≤ si

We can express this condition in the LP/MIP model by addingconstraints of the form

∀ 1 ≤ k ≤ d , ∀ 0 ≤ t < p :�

{i|mi=k}

�

t �≤t<t �+di

yit � ≤ 1

to constraints.





MachineChoiceCost

∀ 0 ≤ t < p : prt :=�

{i|si≤t<si+dimi}

rimi≤ l

∀ 1 ≤ i ≤ n : 0 ≤ si ≤ si < si + dimi≤ si + dimi

≤ p

ov(t , prt ,Aj) :=

�max(0,min(yj + hj , prt)− yj) xj ≤ t < xj + wj

0 otherwise

∀ 1 ≤ j ≤ q : aj =�

0≤t<p

ov(t , prt ,Aj)

cost =q�

j=1

ajcj





Instance Generator

An instance generator is available in the form of a Java jar fileCostInstance.jar which can be downloaded from

http://4c.ucc.ie/∼thadzic/CostInstance.jar

To create an instance, execute:

java -cp CostInstance.jar Instance <parameters>

where <parameters> are:





Instance Generator

-instanceType 0 - CumulativeCost, 1 - DisjunctiveCost,2 - ParallelMachineCost

-n number of required tasks-m number of required areas-d_max maximum duration of a task-r_max maximum resource consumption of a task-s_diff_portion portion of the horizon restricting the start time domain-util utilization of the total available area-cost_distr cost distribution, 0 - explicitly given, 1 - random-w width of each area-machineNo number of machines for parallel machine instances-randomSeed initial random seed-maxCost maximal random cost of an area-costFileName a valid file name containing a vector of costs (or input "no-file")





XML Output Example

<?xml version = ”1.0” encoding = ”UTF − 8” standalone = ”yes”? >< instance resource − limit = ”6” horizon = ”21”

xmlns : xsi = ”http : //www.w3.org/2001/XMLSchema − instance”xsi : noNamespaceSchemaLocation = ”resourcecost.xsd”/ >

< tasks number = ”5” >< task id = ”0” start_min = ”4” start_max = ”4” duration = ”3” resource = ”2”/ >< task id = ”1” start_min = ”1” start_max = ”5” duration = ”4” resource = ”5”/ >< task id = ”2” start_min = ”8” start_max = ”8” duration = ”6” resource = ”5”/ >< task id = ”3” start_min = ”0” start_max = ”10” duration = ”3” resource = ”2”/ >< task id = ”4” start_min = ”3” start_max = ”9” duration = ”3” resource = ”3”/ >< /tasks >< areas number = ”7” >< area id = ”0” x = ”0” y = ”0” width = ”3” height = ”6” cost = ”14”/ >< area id = ”1” x = ”3” y = ”0” width = ”3” height = ”6” cost = ”11”/ >< area id = ”2” x = ”6” y = ”0” width = ”3” height = ”6” cost = ”7”/ >< area id = ”3” x = ”9” y = ”0” width = ”3” height = ”6” cost = ”7”/ >< area id = ”4” x = ”12” y = ”0” width = ”3” height = ”6” cost = ”0”/ >< area id = ”5” x = ”15” y = ”0” width = ”3” height = ”6” cost = ”7”/ >< area id = ”6” x = ”18” y = ”0” width = ”3” height = ”6” cost = ”7”/ >< /areas >< machines number = ”2” >< machine id = ”0” tasks = ”2 4 3”/ >< machine id = ”1” tasks = ”0 1”/ >< /machines >





Integration into JSR-331 API

We have integrated our experimental code into the JSR-331:

Constraint Programming API. We extended a standardResource class with ResourceWithCost class that supports acost-declaring method:

Var setCost ( i n t x1 , i n t x2 , i n t y1 , i n t y2 , i n t cost )




Outline

1 Motivation


3 Predicting Prices





Where do the prices come from?

We need to know prices in advance, for completescheduling horizonWhen we publish schedule, we are commitedSEMO publishes a 24h day-ahead priceThis is a forecast, not the actual priceIt is not known how this forecast is computedCan we do better?




Price Linked to Load




Surprises Happen




SMP (System Marginal Price) in 2009-2011

Year Min Median Mean Max2009 4.12 38.47 43.53 580.532010 -88.12 46.40 53.85 766.352011 0 54.45 63.18 649.48




Features Used in Forecast

Historical SMPShadow priceLoadNational/Local Weather ForecastWind ForecastCalendar InformationScheduled OutagesSupply Bids




Two Forecasting Models

FR1 Predict the SMP using historical and forecastedSMP, shadow price, load and supply.

FR2 Predicting the SMP using the local average-SMPand a learned difference-from-average model.Average price in each time period is quite stable,predict difference from average price.




Details

Using SVM (Support Vector Machine) modelsNot all features are useful/required for forecast

e.g. load forecast already based on calendar




Evaluation (Errors and paired t-tests)

Model MAE MSESEMO 12.64 1086.25FR1 11.14 821.01FR2 11.21 781.72Baseline Price SEMO FR1 FR2Actual L 761.8 513.5 486.9

U 1410.7 1128.4 1076.4SEMO L - 172.4 209.7

U - 358.0 399.3FR1 L - - 11.5

U - - 66.9




Apply this to Schedule

Our forecast prices are significantly betterFor many applications this is enoughDoes this mean we produce better schedule?Apply to feedmill problem, but abstract detail to solve tooptimalityOnly consider task assignment to machines beforedue-dateOptimize energy cost with forecast, evaluate with actualpriceIgnore product sequence, set-up costs, etc.

These will only reduce impact of price prediction




Simplified Scheduling Model

cost =�

t

pr∗t at

where pr∗t

is the profile value at time t of the optimal solution tothe following MIP problem:

min�

t

prtvt

subject to:

∀i :�

txit = 1

∀t :�

i

�t−di+1≤t �≤t

pixit � = prt ≤ lt

∀m∀t :�

i|mi=m

�t−di+1≤t �≤t

xit � ≤ 1∀i∀t |t+di>ei

: xit = 0




Results over 880 runs

Price Min Median Mean MaxActual 4,383,718 5,934,654 6,093,365 9,805,821SEMO 4,507,136 6,054,220 6,272,768 10,218,804FR1 4,499,811 6,058,093 6,266,800 10,070,541FR2 4,570,552 6,094,818 6,283,261 10,059,264




The Good News

Given only the forecast information, we can producehigh-quality schedules5-10% off optimal solution with perfect knowledge of futurepriceThis is lower than the mark-up that suppliers require forfixed/ToU pricesFor most cost-sensitive case, side constraints will onlyreduce overhead




But: t-test Comparison between forecasts

Price SEMO FR1 FR2Actual L −200, 564.9 −193, 646.7 −211, 094.4

U −158, 241.3 −153, 222.5 −168, 697.4SEMO L - −1, 506.1 −17, 262.6

U - 13, 443.1 −3, 722.9FR1 L - - −23, 968.3

U - - −8, 954.2




Can we fix it?

MAE and MSE are bad predictors for quality of scheduleHow to change the forecast generation to use schedulequality?Relative ranking of time periods is important for scheduleIt is more important to predict when peaks occur, ratherthan their magnitudeWe tested this in paperHow to do this: Current research




HEMSCampus21

Outline

1 Motivation


3 Predicting Prices

4 Extension to Building ManagementHEMSCampus21




HEMSCampus21

Energy Cost Aware Buildings

HEMS (home energy management system)Public spaces (campus, sports arena)Work in progress




HEMSCampus21

What is different?

Time of use tariff, rather than real-time pricingThermal model in addition to electricityEnergy storage (EV, thermal envelope)pre-heat, pre-coolFew scheduled resourcesData babel




HEMSCampus21

HEMS Architecture

SoftwareComponent

HEMS

User

Appliances

WeatherForecast

PriceForecaster

DistributionGrid HVAC

HomeElectricity

Grid

EV

EV Charger

Baseload

Zone Outside

ActivitiesTemperature RequestBattery Charge Request

start

setpoint

charge/discharge

ratePriceSignal

heating/cooling

heat-loss

electricity

thermal

command

information




HEMSCampus21

EV Charging with Car-to-Home Capability




HEMSCampus21

Pre-Heating of Rooms




HEMSCampus21

Huerta del Rey Sports Center, Valladolid




HEMSCampus21

Heating and DHW: Principle of Operations




HEMSCampus21

Conclusions

Electricity suppliers move to time variable pricesScheduling should take this into accountA Family of resource cost aware constraintsProblem generatorWhere do forecast prices come from?Improved forecast does not imply improved scheduleInteresting extension to building energy management




HEMSCampus21

References

H. Simonis and T. Hadzic. Constraint-based scheduling for reducing peak

electricity use. CompSust’10, Boston, MA, June 2010.H. Simonis and T. Hadzic. A resource cost aware cumulative. ModRef 2010, StAndrews, Scotland, September 2010.H. Simonis and T. Hadzic. A Family of Resource Constraints for Energy Cost

Aware Scheduling. CROCS 2010, St Andrews, Scotland, September 2010T. Hadzic and H. Simonis. Creating Tests for a Family of Cost Aware Resource

Constraints. CSCLP 2010, Berlin, December 2010D. Grimes, H. Simonis, A. Pratt and C. Sheridan. Automated Energy Usage

Optimization for the Residential Sector: Impact of Price Tariffs. CompSust’12,Copenhagen, Denmark, July 2012.G. Ifrim, B. O’Sullivan and H. Simonis. Energy-Cost Forecasting for Scheduling.

Submitted for publication.


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