quancol . ........ . . . ... ... ... ... ... ... ... - PowerPoint PPT Presentation

quan�col . ........ . . . ... ... ... ... ... ... ... www.quanticol.eu Quantitative modelling of residential smart grids Vashti Galpin Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh MoKMaSD 2015, York 8 September 2015 1 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Outline www.quanticol.eu Motivation 1 Residential smart grids 2 Modelling 3 Policies 4 Scenarios 5 Results 6 Conclusion 7 2 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Motivation www.quanticol.eu � changes in the way electricity is generated � more producers, small producers, prosumers � use of information technology � modelling to investigate different approaches � residential smart grid � sharing of renewable energy between neighbourhoods � stochastic HYPE � process algebra � continuous, instantaneous, stochastic behaviour � simulation, generation of trajectories for variables in model � quantitative modelling of collective adaptive systems 3 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Residential smart grids www.quanticol.eu [Oviedo et al , 2012, 2014] 4 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Suburb energy scheme www.quanticol.eu 5 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Quantifying residential smart grids www.quanticol.eu � n neighbourhoods where neighbourhood N i has m i houses � at each house H ij at time t � generation of r i p t q renewable energy � consumption: a ij appliances and background consumption a ij ÿ l ij p t q “ b p t q ` o ijk p t q ¨ app ijk k “ 1 � use of local renewable energy e ij p t q “ min p l ij p t q , r i p t qq � local excess demand d ij p t q “ l ij p t q ´ e ij p t q � local excess renewable energy x ij p t q “ r i p t q ´ e ij p t q 6 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Quantifying residential smart grids www.quanticol.eu � assume maximal allocation of renewable energy within neighbourhood � in each neighbourhood N i at time t � renewable energy R i p t q “ m i ¨ r i p t q � consumption/demand m i ÿ L i p t q “ l ij p t q j “ 1 � use of local renewable energy E i p t q “ min p L i p t q , R i p t qq � local excess demand D i p t q “ L i p t q ´ E i p t q � local excess renewable energy X i p t q “ R i p t q ´ E i p t q 7 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Quantifying residential smart grids www.quanticol.eu � p D i p t q ą 0 q ñ p X i p t q “ 0 q and p X i p t q ą 0 q ñ p D i p t q “ 0 q each neighbourhood either has surplus renewable energy or excess demand but not both � assume redistribution of surplus energy to N i : F i p t q � use of shared renewable energy S i p t q “ min p D i p t q , F i p t qq � use of grid energy G i p t q “ D i p t q ´ S i p t q � wastage of renewable energy W i p t q “ F i p t q ´ S i p t q assume maximal allocation within neighbourhood, wastage is energy which cannot be used by any house in neighbourhood 8 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Redistribution policies www.quanticol.eu � requires definition of adjacent neighbourhoods: von Neumann (four compass points), Moore (eight compass points) � how to divide up surplus energy from a neighbourhood between adjacent neighbourhoods � equally � proportional to excess demand � relative to wind speed, proportional to excess demand only to those neighbourhoods with lower wind speeds � policy determines amount of energy moving in each direction, based on local information only � how much energy to give to each neighbourhood in a direction � sufficient to cover excess demand � sufficient to cover some proportion of excess demand 9 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Allocation in one direction www.quanticol.eu � general form, assuming direction is from 1 to n unallocated energy “moving” in direction Y at N i U Yi T Yi energy allocated to N i from direction Y energy from N i for direction Y (some fraction of X i ) T iY A Yi excess demand that may be satisfied from direction Y (some fraction of D i ) # 0 i “ 1 U Yi p t q “ U Y p i ´ 1 q p t q ´ T Y p i ´ 1 q p t q ` T p i ´ 1 q Y p t q otherwise # U Yn p t q i “ n T Yi p t q “ min p U Yi p t q , A Yi p t qq otherwise ÿ F i p t q “ T Yi p t q Y 10 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Allocation in one direction www.quanticol.eu U Y p i ´ 1 q U Y p i ` 1 q U Yi T p i ´ 1 q Y T Y p i ´ 1 q T iY T Yi X i ´ 1 D i ´ 1 X i D i N i ´ 1 N i Y 11 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Model parameters www.quanticol.eu � 7 neighbourhoods in a row (also 4 ˆ 4 grid) � each neighbourhood has 4 houses � electricity cost: peak 0.272 £ /kWh, mid-peak 0.194 £ /kWh, off-peak is 0.107 £ /kWh [Oviedo et al , 2012] � appliance consumption: washing machine 0.82 kWh for one hour, dishwasher 2.46 kWh for 1.5 hours, probability distribution of starting time [Oviedo et al , 2012] � background consumption: daytime 0.3 kWh, evening 0.5 kwH, nighttime 0.1kWh [Yao and Steemers, 2005] 12 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Model parameters www.quanticol.eu � 80% probability of wind strong enough to drive a turbine in the UK [Sinden, 2007] � 25% to 35% generation capability of a wind turbine rated at x kWh in the UK [Sinden, 2007] � stochastic wind pattern consists of � wind strength: constant value w str , varying in intensity by neighbourhood � wind presence: exponentially distributed with rate 1/ w pres � wind absence: exponentially distributed with rate 1/ w abs � defines a Markov modulated Poisson process � fix w pres and vary w abs for a range of wind probabilities from 50% (1.2 and 1.2) to 80% (1.2 and 0.3) 13 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Scenario: one wind www.quanticol.eu N 1 N 2 N 3 N 4 N 5 N 6 N 7 1.00 1.00 0.50 0.50 0.25 0.25 0.25 14 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Scenario: two winds www.quanticol.eu N 1 N 2 N 3 N 4 N 5 N 6 N 7 1.00 0.50 0.25 0.25 0.50 1.00 15 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Comparison www.quanticol.eu � scenario comparison one wind two winds � sharing in one wind scenario � increases usage of renewables from 55% to 70% � decrease wastage of renewables from 57% to 27% 16 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Heat map www.quanticol.eu � range for w str : 0.2, 0.4, 0.6, 0.8, 1.0 � range for w abs : 0.3, 0.6, 0.9, 1.2 � w pres : 1.2 17 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Comparison across neighbourhoods www.quanticol.eu Local renewable usage N1 N2 N3 N4 N5 N6 N7 1.00 1.00 0.50 0.50 0.25 0.25 0.25 Wind intensity 18 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Comparison across neighbourhoods www.quanticol.eu Shared renewables usage N1 N2 N3 N4 N5 N6 N7 1.00 1.00 0.50 0.50 0.25 0.25 0.25 Wind intensity 19 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Comparison across neighbourhoods www.quanticol.eu Grid usage N1 N2 N3 N4 N5 N6 N7 1.00 1.00 0.50 0.50 0.25 0.25 0.25 Wind intensity 20 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Comparison across neighbourhoods www.quanticol.eu Cost N1 N2 N3 N4 N5 N6 N7 1.00 1.00 0.50 0.50 0.25 0.25 0.25 Wind intensity 21 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Comparison across neighbourhoods www.quanticol.eu Wastage N1 N2 N3 N4 N5 N6 N7 1.00 1.00 0.50 0.50 0.25 0.25 0.25 Wind intensity 22 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Policies considered www.quanticol.eu � dividing up surplus between adjacent neighbourhoods eq Split equally dm Split proportionally by demand dw Split weighted by demand da Direction of highest demand receives all surplus wn Split proportionally by demand among adjacent neighbourhoods that have lower wind speed � allocation to neighbourhoods as surplus moves 100 100% of excess demand allocated inc Proportion of excess demand allocated increases in the direction of supply wnd Proportion of excess demand allocated is inversely proportional to wind speed � policies considered eq100, dm100, dminc, dmwnd, dw100, da100, wn100 23 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Policies: one wind www.quanticol.eu Proportion renewables “ Local and shared renewable usage Total usage 24 / 30

quan�col . ........ . . . ... ... ... ... ... ... ... Policies: one wind www.quanticol.eu Renewables not used Proportion wastage of renewables “ Total renewables generated 25 / 30