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

9 th International EnKF workshop , Os (Bergen) Norway Optimization of carbon emissions in smart grids E.T. Lau 1 Q. Yang 1 G.A. Taylor 1 A.B. Forbes 2 P. Wright 2 V.N. Livina 2 1 Brunel University, UK 2 National Physical Laboratory, UK June 23 – 25, 2014 1

9 th International EnKF workshop , Os (Bergen) Norway Outline 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 2

9 th International EnKF workshop , Os (Bergen) Norway Problem statement: Minimisation of carbon emissions (gCO 2 eq) with suitable control settings in electrical systems. Estimation of uncertainties. 3

9 th International EnKF workshop , Os (Bergen) Norway Electrical power system Lau et. al., ECM 2014 4

9 th International EnKF workshop , Os (Bergen) Norway Electrical signal - periodicities 1. Generated time series should have daily and annual periodicities. 2. The electrical voltage can be expressed into state space, with seasonal cycle, combined with annual and diurnal cycle and noises. 𝑢 𝑢 𝑌 𝑙 ( 𝑢 ) = 𝑇 + 𝐸 + 𝜁 𝑈 𝑈 2 1 Signal noise Annual Diurnal Cycle Cycle 5

9 th International EnKF workshop , Os (Bergen) Norway Carbon footprints 1. Reported in kilograms (or grams) of carbon dioxide CO 2 equivalent per unit of energy (kWh) – kgCO 2 /kWh. 2. Calculated by: Ricardo – AEA, an UK research company. 6

9 th International EnKF workshop , Os (Bergen) Norway Carbon factors in UK electricity generation Types of Fuel Carbon footprints (gCO 2 eq/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 7

9 th International EnKF workshop , Os (Bergen) Norway UK variable electricity grid carbon factor Estimation of UK electricity grid carbon factors: 𝑈 𝐿 𝐹𝐹𝐹𝐹 ( 𝑢 ) = ∑ ∑ ( 𝐹 𝑙 × 𝐹 𝑙 ( 𝑢 )) 𝑢=1 𝑙=1 𝑈 ∑ 𝐹 𝑙 ( 𝑢 ) 𝑢=1 Where, C k - Carbon footprints for different fuels (gCO 2 eq/kwh) E k - The energy generated (kWh) t - Time index, k- Fuel type index 8

9 th International EnKF workshop , Os (Bergen) Norway UK electricity grid carbon factor with uncertainties Average EGCF = 493.85 gCO 2 eq/kWh Data courtesy of Balancing Mechanism Reporting System (BMRS). 9

9 th International EnKF workshop , Os (Bergen) Norway Carbon emissions The product of activity data and the carbon footprints. 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑢 = 𝐹𝐹𝐹𝐹𝐹𝐹 𝑢 × 𝐹𝐷𝐹𝐷𝐹𝐹 _ 𝑔𝐹𝐹𝑢𝑔𝐹𝐹𝐹𝑢𝐹 ( 𝑢 ) Units = kgCO 2 eq 10

9 th International EnKF workshop , Os (Bergen) Norway Carbon savings The difference between the emissions (BAS) and the innovations employed. 𝐹𝐷𝐹𝐷𝐹𝐹 _ 𝐹𝐷𝑡𝐹𝐹𝐹𝐹 ( 𝑢 ) = 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐶𝐶𝐶 ( 𝑢 ) − 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽 ( 𝑢 ) Units = kgCO 2 eq 11

9 th 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 of carbon savings. 12

9 th 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. 13

9 th International EnKF workshop , Os (Bergen) Norway EnKF - general formulations Collect variable of interests in grid state vector ‘ y’ y = 𝐹 𝑒 Where, m=state variables (e.g., working families, pensioners, industrials, offices) d=observation variables (energy production and consumption data, carbon emissions) 14

9 th International EnKF workshop , Os (Bergen) Norway EnKF - Ensembles State vector y consists of energy usages corresponds to various consumers: y = 𝑈𝐹𝑔𝐹 1 , 𝑈𝐹𝑔𝐹 2 , 𝑈𝐹𝑔𝐹 3 , ⋯ , 𝑈𝐹𝑔𝐹 𝑂 𝑈 Ensemble of state vector y is denoted in Matrix ‘ Y’ : 𝑍 = 𝐹 1 , 𝐹 2 , 𝐹 3 , ⋯ , 𝐹 𝑂𝑂 Where N = Total number of variables; N e =Total number of ensembles 15

9 th International EnKF workshop , Os (Bergen) Norway EnKF – Ensemble updates Apply EnKF to propagate the ensemble to obtain forecasted ensemble: 𝑞 + 𝐹 𝑍 𝐼 𝑈 ( 𝐼𝐹 𝑍 𝐼 𝑈 + 𝑆 ) −1 ( 𝑒 𝑝𝑝𝑝 , 𝑗 − 𝐼𝐹 𝑗 𝑣 = 𝐹 𝑗 𝑞 ) 𝐹 𝑗 Where, y u =updated state y p =predicted state C Y =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 16

9 th International EnKF workshop , Os (Bergen) Norway EnKF – Artificial data of energy consumption 17

9 th International EnKF workshop , Os (Bergen) Norway Ensemble-based close-loop production optimisation (EnOpt) 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 objective function f . (Chen at al., SPE, 2008) 18

9 th International EnKF workshop , Os (Bergen) Norway EnOpt – Control variables Ensemble of control variables ‘ x’ is created: 𝑦 = 𝑦 1 , 𝑦 2 , 𝑦 3 , ⋯ , 𝑦 𝑂𝑂 Where N x =Total number of control variables x = energy data (generator properties, controlled generation, consumption, consumer usage behaviour) 19

9 th 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. 20

9 th 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. 21

9 th International EnKF workshop , Os (Bergen) Norway EnOpt – Objective function Objective function = carbon emissions (gCO 2 eq) : 𝑂 𝑢 𝑔 ( 𝑦 , 𝐹 ) = � 𝐹𝐹𝐹𝐹 𝑗 × 𝐹 𝑗 ( 𝑦 , 𝐹 ) 𝑗=1 Where, N t =total number of time steps E i =Energy consumptions (kWh) EGCF i =Electricity Grid Carbon Footprints x=control variables y=grid state vector 22

9 th International EnKF workshop , Os (Bergen) Norway EnOpt – Steepest descent Optimise control variable x: 𝑦 λ+1 = 1 𝛽 𝐹 𝑂 𝐹 𝑂 , 𝑔 𝒁 ( 𝑂 ) − 𝑦 λ Where, λ =iteration index C x =covariance matrix of control variable x C x,f Y(x) =cross covariance between control variables x and f Y (x) α =tuning parameter 23

9 th International EnKF workshop , Os (Bergen) Norway EnOpt Cross-covariance: 𝑂 𝑓 1 𝐹 𝑂 , 𝑔 𝒁 ( 𝑂 ) = 𝑂 𝑂 − 1 � ( 𝑦 λ , 𝑗 − 𝑦 λ )( 𝑔 𝑦 λ , 𝑗 , 𝐹 𝑗 − 𝑔 𝑦 λ , 𝐹 ) 𝑗=1 Where, 𝑦 λ =mean of control variables x 𝑔 𝑦 λ , 𝐹 =mean of the objective function f N e =Total number of ensembles λ =iteration index 24

9 th International EnKF workshop , Os (Bergen) Norway 1 Start Time step k=1 Proceed to 2 next iteration Calculate f Y (x) and x λ +1 Initialise ensembles of Stopping criteria state vector y and control satisfied? No variables x Update 1 f Y (x λ +1 ) Yes Propagate state vector y All data with control variable x assimilated? Evaluate f Y (x λ +1 ) and f Y (x) one step at a time No Increase 2 α No Yes Use EnKF to update y f Y (x λ +1 ) < f Y (x) ? Finish Yes keep α Start optimisation at 𝜇 =1 Check stopping criteria 25

9 th International EnKF workshop , Os (Bergen) Norway EnOpt – Stopping criteria 1. Maximum optimisation step 𝜇 max . 2. Unsuccessful search for tuning parameter α . 3. The relative increase of the objective function f Y (x) is less than 1 percent. 4. Not allowed to increase α more than twice. 26

9 th International EnKF workshop , Os (Bergen) Norway Ensemble Consumers and generators considered: Quantity Restaurant 10 Pensioner 20 Office/retailer 10 Industrial 5 School/university/college 5 Working Family 50 Green Generator 2 Non-green Generator 3 27

9 th International EnKF workshop , Os (Bergen) Norway EnOpt – Artificial data of usual vs. optimised carbon emissions 4 x 10 7.5 Emissions Optimised emissions 7 Carbon emissions (kgCO2eq) 6.5 6 5.5 5 4.5 4 0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 Time (hours) Carbon savings (24 hrs, 105 ensembles) = 153.8 ± 4.51 tonnesCO2eq 28

9 th International EnKF workshop , Os (Bergen) Norway Uncertainties 1. Carbon footprints. 2. Consumers (behavioural usage). 3. Generators (green and non-green power stations). 29