Optimization of carbon emissions in smart grids E.T. Lau 1 Q. Yang 1 - - PowerPoint PPT Presentation

9th International EnKF workshop , Os (Bergen) Norway

Optimization of carbon emissions in smart grids

E.T. Lau1

• Q. Yang1

G.A. Taylor1 A.B. Forbes2

• P. Wright2

V.N. Livina2

1Brunel University, UK 2National Physical Laboratory, UK

June 23 – 25, 2014

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9th International EnKF workshop , Os (Bergen) Norway

• 1. Problem statement
• 2. Electrical power system
• 3. Carbon footprints
• 4. Methodology

(a) Ensemble Kalman Filter (EnKF) (b) Ensemble Close-Loop Optimisation (EnOpt)

• 6. Results
• 7. Future work & conclusion

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Outline

9th International EnKF workshop , Os (Bergen) Norway

Minimisation of carbon emissions (gCO2eq) with suitable control settings in electrical systems. Estimation of uncertainties.

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Problem statement:

9th International EnKF workshop , Os (Bergen) Norway Lau et. al., ECM 2014

Electrical power system

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9th International EnKF workshop , Os (Bergen) Norway

• 1. Generated time series should have daily and annual periodicities.

𝑌𝑙(𝑢) = 𝑇 𝑢 𝑈

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+ 𝐸 𝑢 𝑈2 + 𝜁

Annual Cycle Diurnal Cycle Signal noise

Electrical signal - periodicities

• 2. The electrical voltage can be expressed into state space, with

seasonal cycle, combined with annual and diurnal cycle and noises.

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9th International EnKF workshop , Os (Bergen) Norway

• 1. Reported in kilograms (or grams) of carbon dioxide CO2

equivalent per unit of energy (kWh) – kgCO2/kWh.

• 2. Calculated by: Ricardo – AEA, an UK research company.

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Carbon footprints

9th International EnKF workshop , Os (Bergen) Norway

Types of Fuel Carbon footprints (gCO2eq/kWh) Coal 788-899 Oil 600-699 Open cycle gas turbine (OGCT) 466-586 Combined cycle gas turbine (CCGT) 367-487 Wind 20-94 Nuclear 20-26 Hydro 2-13

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Carbon factors in UK electricity generation

9th International EnKF workshop , Os (Bergen) Norway

Estimation of UK electricity grid carbon factors:

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𝐹𝐹𝐹𝐹(𝑢) = ∑ ∑ (𝐹𝑙 × 𝐹𝑙(𝑢))

𝐿 𝑙=1 𝑈 𝑢=1

∑ 𝐹𝑙(𝑢)

𝑈 𝑢=1

Where, Ck - Carbon footprints for different fuels (gCO2eq/kwh) Ek - The energy generated (kWh) t - Time index, k- Fuel type index

UK variable electricity grid carbon factor

9th International EnKF workshop , Os (Bergen) Norway Data courtesy of Balancing Mechanism Reporting System (BMRS).

UK electricity grid carbon factor with uncertainties

Average EGCF = 493.85 gCO2eq/kWh

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9th International EnKF workshop , Os (Bergen) Norway

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Carbon emissions The product of activity data and the carbon footprints.

𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑢 = 𝐹𝐹𝐹𝐹𝐹𝐹 𝑢 × 𝐹𝐷𝐹𝐷𝐹𝐹_𝑔𝐹𝐹𝑢𝑔𝐹𝐹𝐹𝑢𝐹(𝑢)

Units = kgCO2eq

9th International EnKF workshop , Os (Bergen) Norway

The difference between the emissions (BAS) and the innovations employed.

𝐹𝐷𝐹𝐷𝐹𝐹_𝐹𝐷𝑡𝐹𝐹𝐹𝐹(𝑢) = 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐶𝐶𝐶(𝑢) − 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽(𝑢)

Units = kgCO2eq

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Carbon savings

9th International EnKF workshop , Os (Bergen) Norway

Methodology for carbon emissions and savings

• 1. Ensemble Kalman Filter (EnKF) for ensemble estimation of

grid state and the associated uncertainties.

• 2. Ensemble Close-Loop Optimisation (EnOpt) for maximisation
• f carbon savings.

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9th International EnKF workshop , Os (Bergen) Norway

EnKF

• 1. Ensemble realizations - model state and state updates.
• 2. Adjust an ensemble of the model to be consistent with real-time

production data.

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9th International EnKF workshop , Os (Bergen) Norway

Collect variable of interests in grid state vector ‘y’

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y = 𝐹 𝑒

Where, m=state variables (e.g., working families, pensioners, industrials,

• ffices)

d=observation variables (energy production and consumption data, carbon emissions)

EnKF - general formulations

9th International EnKF workshop , Os (Bergen) Norway

State vector y consists of energy usages corresponds to various consumers:

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y = 𝑈𝐹𝑔𝐹1, 𝑈𝐹𝑔𝐹2, 𝑈𝐹𝑔𝐹3, ⋯ , 𝑈𝐹𝑔𝐹𝑂 𝑈

Ensemble of state vector y is denoted in Matrix ‘Y’:

𝑍 = 𝐹1, 𝐹2, 𝐹3, ⋯ , 𝐹𝑂𝑂

Where N = Total number of variables; Ne=Total number of ensembles

EnKF - Ensembles

9th International EnKF workshop , Os (Bergen) Norway

Apply EnKF to propagate the ensemble to obtain forecasted ensemble:

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𝐹𝑗

𝑣 = 𝐹𝑗 𝑞 + 𝐹𝑍𝐼𝑈(𝐼𝐹𝑍𝐼𝑈 + 𝑆)−1(𝑒𝑝𝑝𝑝,𝑗 − 𝐼𝐹𝑗 𝑞)

Where, yu=updated state yp=predicted state CY=covariance matrix of state vector y H=measurement operator relating the model state to the observation variables d R=covariance matrix of the measurement error (positive definite) d=perturbed observations

EnKF – Ensemble updates

9th International EnKF workshop , Os (Bergen) Norway

EnKF – Artificial data of energy consumption

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9th International EnKF workshop , Os (Bergen) Norway

• 1. Search direction used in the optimization is approximated by

an ensemble.

• 3. Combined with EnKF to reduce the uncertainty of the model.
• 4. Sequential updating method - updated parameters are to be

consistent with the energy production data in time.

• 5. Optimises both control settings x and expectation of the
• bjective function f.

(Chen at al., SPE, 2008)

Ensemble-based close-loop production optimisation (EnOpt)

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9th International EnKF workshop , Os (Bergen) Norway

Ensemble of control variables ‘x’ is created:

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𝑦 = 𝑦1, 𝑦2, 𝑦3, ⋯ , 𝑦𝑂𝑂

Where Nx=Total number of control variables

EnOpt – Control variables

x = energy data (generator properties, controlled generation, consumption, consumer usage behaviour)

9th International EnKF workshop , Os (Bergen) Norway

EnOpt – ensembles

• 1. Ensemble of grid state vector y :
• resultant energy generation, consumption

and carbon emissions.

• 2. Ensemble of controlled variables x:
• generator properties, controlled generation,

consumption, consumer usage behaviour.

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9th International EnKF workshop , Os (Bergen) Norway

EnOpt – ensembles

Ensemble x acts as the controller that integrates with Ensemble y in controlling energy generations and consumptions.

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Objective function = carbon emissions (gCO2eq):

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𝑔(𝑦, 𝐹) = 𝐹𝐹𝐹𝐹𝑗

𝑂𝑢 𝑗=1

× 𝐹𝑗(𝑦, 𝐹)

Where, Nt=total number of time steps Ei=Energy consumptions (kWh) EGCFi=Electricity Grid Carbon Footprints x=control variables y=grid state vector

EnOpt – Objective function

9th International EnKF workshop , Os (Bergen) Norway

Optimise control variable x:

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Where, λ =iteration index Cx=covariance matrix of control variable x Cx,fY(x)=cross covariance between control variables x and fY(x) α=tuning parameter

𝑦λ+1 = 1 𝛽 𝐹𝑂𝐹𝑂,𝑔𝒁(𝑂) − 𝑦λ

EnOpt – Steepest descent

9th International EnKF workshop , Os (Bergen) Norway

Cross-covariance:

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Where, 𝑦λ=mean of control variables x 𝑔 𝑦λ, 𝐹 =mean of the objective function f Ne=Total number of ensembles λ =iteration index

𝐹𝑂,𝑔𝒁(𝑂) = 1 𝑂𝑂 − 1 (𝑦λ,𝑗 − 𝑦λ)(𝑔 𝑦λ,𝑗, 𝐹𝑗 − 𝑔 𝑦λ, 𝐹 )

𝑂𝑓 𝑗=1

EnOpt

9th International EnKF workshop , Os (Bergen) Norway

Start Time step k=1 Propagate state vector y with control variable x

• ne step at a time

Use EnKF to update y Start optimisation at 𝜇=1 Calculate fY(x) and xλ+1 Initialise ensembles of state vector y and control variables x Update fY(xλ+1) Evaluate fY(xλ+1) and fY(x) fY(xλ+1) < fY(x) ? Check stopping criteria Stopping criteria satisfied? All data assimilated? Finish

Increase α No Yes Yes Yes keep α Proceed to next iteration No No

2 1 1 2

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9th International EnKF workshop , Os (Bergen) Norway

• 1. Maximum optimisation step 𝜇max.
• 2. Unsuccessful search for tuning parameter α.
• 3. The relative increase of the objective function fY(x) is less

than 1 percent.

• 4. Not allowed to increase α more than twice.

EnOpt – Stopping criteria

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9th International EnKF workshop , Os (Bergen) Norway

Consumers and generators considered:

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Quantity Restaurant 10 Pensioner 20 Office/retailer 10 Industrial 5 School/university/college 5 Working Family 50 Green Generator 2 Non-green Generator 3

Ensemble

9th International EnKF workshop , Os (Bergen) Norway

EnOpt – Artificial data of usual vs. optimised carbon emissions

Carbon savings (24 hrs, 105 ensembles) = 153.8 ± 4.51 tonnesCO2eq

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9th International EnKF workshop , Os (Bergen) Norway

• 1. Carbon footprints.
• 2. Consumers (behavioural usage).
• 3. Generators (green and non-green power stations).

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Uncertainties

9th International EnKF workshop , Os (Bergen) Norway

• 1. Use of Lagrange multipliers in the steepest descend technique in

determining the effect of perturbations on the optimal solution. Given a system constraint, the new modified objective function:

𝑔̅ = 𝑀[𝐹 𝑙 + 1 , 𝐹 𝑙 , 𝑦 𝑙 , 𝜇 𝑙 + 1 ]

𝐿 𝑙=1

where L is Lagrangian. (Naevdal et al., CG, 2006)

Future work – constrained EnOpt

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9th International EnKF workshop , Os (Bergen) Norway

Summary of EnKF and EnOpt

1. Uncertainties are reduced through EnKF. 2. The updated ensemble estimates (EnKF’ed) are able to match with the real-time production data. 3. Through EnOpt, maximisation of carbon savings can be achieved along with optimised control variables.

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9th International EnKF workshop , Os (Bergen) Norway

• 1. E.T. Lau, Q. Yang, A.B. Forbes, P. Wright, V.N. Livina

“Modelling carbon emissions in electrical systems”, Energy Conservation and Management, vol. 80, no. 59, pp. 573-581, 2014.

• 2. E.T. Lau, Q. Yang, G.A. Taylor, A.B. Forbes, P. Wright, V. N.

Livina “Optimization of carbon emissions in smart grid: a mathematic model”, UPEC2014 conference proceedings (accepted).

• 3. E.T. Lau, Q. Yang, G.A. Taylor, A.B. Forbes, P. Wright, V.N.

Livina “Carbon savings in smart interventions in electrical systems”, IEEE Transactions on Smart Grid, in preparation.

Publications

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9th International EnKF workshop , Os (Bergen) Norway

Thank you!

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9th International EnKF workshop , Os (Bergen) Norway

Bibliography

• 1. Energy use and behaviour change, Postnote 417, 2012.
• 2. BMRS data, available at: http://www.bmreports.com/
• 3. Efficient ensemble-based close loop production
• ptimisation, Chen et. al, SPE, 2008.
• 4. Carbon footprints of electricity generation, Postnote 268,

2006 and Postnote Update 383, 2011.

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9th International EnKF workshop , Os (Bergen) Norway

Add-ons

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9th International EnKF workshop , Os (Bergen) Norway

• 1. Based on four seasons, with

different rates of power consumptions in every season.

1st

Periodicities

Annual Cycle

• 1. Represents one period of cycle (24

hours per cycle)

• 2. Cycles are continuous.
• 3. Based on four categories:

(1) Working family; (2) Pensioner; (3) Industrial daytime office; (4) Industrial (1 shift).

Diurnal Cycle

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9th International EnKF workshop , Os (Bergen) Norway

Annual cycle

𝐵 𝑢 = 𝐹1 + tanh 𝑢 − 𝐷𝑙 − 𝑈

1(𝑙 − 1)

𝑀

𝐿 𝑙=1

Where: T1 – 365 days C1 – y-axis adjustment L - width of HTF ak - particular time interval k-index of data subset

Lau et.al., ECM 2014

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9th International EnKF workshop , Os (Bergen) Norway

Diurnal cycle

𝐸 𝑢 = 𝐹1 + 𝐹2 𝑙 · tanh 𝑢 − 𝐷 − 𝑈2(𝑙 − 1) 𝑀

𝐿 𝑙=1

Where: T2 – 24 hours C1 – y-axis adjustment L - width of HTF a - particular time interval k-index of data subset C2 – adjustment constant at particular HTF term

Lau et.al., ECM 2014

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9th International EnKF workshop , Os (Bergen) Norway Data courtesy of Brunel University

Photo-voltaic data of Brunel installation

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9th International EnKF workshop , Os (Bergen) Norway

Constraints : 𝐹𝑗

𝑛𝑗𝑛 ≤ 𝐹𝑗 ≤ 𝐹𝑗 𝑛𝑛𝑂

𝐹𝑗 ≤ 𝐹𝑗

𝐽 𝑗=1

𝐹𝑗 ≥ 𝐹_𝐹𝐹𝐹 _𝑒𝐹𝐹𝐷𝐹𝑒

𝐽 𝑗=1

i = 1,2,3,…, I is the corresponding energy consumption of consumers

Optimisation constraints

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9th International EnKF workshop , Os (Bergen) Norway

Optimisation constraints - results

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9th International EnKF workshop , Os (Bergen) Norway

UK Carbon footprints with uncertainties

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9th International EnKF workshop , Os (Bergen) Norway Source: Chen et. al (2008) EnOpt, SPE.

EnOpt (EnKF + optimisation)

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