Storing energy or Storing Consumption? It is not the same! Joachim Geske, Richard Green, Qixin Chen, Yi Wang 40th IAEE International Conference 18-21 June 2017, Singapore
Motivation Electricity systems with large share of intermittent renewables need flexibility May be provided by generation, or storage, or demand response Storage: potential to increase efficiency of electrical systems - especially in the context of integrating intermittent renewable technologies. Demand response: load shifting (demand response, DR) - immense potential (especially very short term 10 minutes for free)? can be enabled cheaply? Can we see this as storing consumption? 2
Motivation Shifting of single load (industrial processes) by several hours Time Here: Also shifting a series of small loads by a couple of minutes each (without spoiling) Time 3
Motivation Shifting of single load (industrial processes) by several hours Time Here: Also shifting a series of small load by a couple of minutes each (without spoiling) By shifting a series of loads also long term storage possible Storage potential huge - so are coordination requirements Unit commitment modelling impossible Time How is load shifted by rational agents? Is storing consumption equivalent to electricity storage? 4
Storing energy or storing consumption - It is not the same! To answer these questions: 1. Introduction We present DR model environment 2. COTS - We formulate a model of the cost of time shifting (COTS). 3. Nature of DR Storage - We show that rational DR can be interpreted as a sequence of time inhomogeneous capacity-constrained storages. 4. DR storage equilibrium - Finally we present examples of how this sequence of storages shifts load in a perfectly coordinated market system and we compare it to conventional energy storage. 5. Conclusion 5
1. Introduction DR Environment: Preferences: We assume that o there is a given preferred consumption schedule o there are device specific indifference threshold times (inertia of thermal storage, indifference) exploitable Technology, market environment: o there is a real time price signal o enabled devices are programmable by the consumer, responsive to price signals Question: How long should the usage of which device be postponed or pulled ahead, if this generates revenues? Sub-question: What are the costs of time shifting (COTS)? Model 6
2. COTS - Cost of time shifting We start by defining device groups: gather and order all enabled devices with respect to the shifting indifference (threshold) time. EE indifference threshold curve No delay cost Gradually ττ 6 ττ 5 increasing cost of delay ττ 4 ττ 3 ττ 2 DR enabled devices by threshold time ττ ii tt 0 period 1 tt 1 preferred start of using devices ττ 1 period 2 tt 7
2. COTS - Cost of time shifting Step 1 COTS by device group 4, 5 and 6. Action considered: shifting the whole block by ΔΔt Step 2 select the device groups, given a shifting volume S Solution: start with the highest threshold and add groups until shifting volume S is reached group 4, 5 and 6 are a good selection! EE ΔΔt ττ 6 S These devices incur a cost ττ 5 ττ 4 ττ 3 ττ 2 tt 0 period 1 tt 1 ττ 1 period 2 tt Step 3 determine aggregated COTS(ΔΔt,S) over all devices 8
2. COTS - Cost of time shifting Overall cost 1 device 1 device Bring forward Delay Cost per device Bring forward Delay 9
2. COTS - Cost of time shifting Overall cost 2 devices 2 devices 1 device 1 device Bring forward Delay Cost per device Bring forward Delay 10
2. COTS - Cost of time shifting 3 devices Overall cost 3 devices 2 devices 2 devices 1 device 1 device Bring forward Delay Cost per device Bring forward Delay 11
2. COTS - Cost of time shifting, move λ by t Integration with uniform distribution of device groups on [0,T]: (tt tt 0 0) CCCCCCCC λλ, tt tt 0 COTS = CCCCCCCC 2 2 tt tt 0 + λλ 2 λλ tt tt 0 1 λλ 2 2 2 0 3-D view: Contour view: 2 Share of shifted load tt tt 0 tt tt 0, tt tt 0 > 1 λλ tt tt 0 1 λλ A B C 2 2 B A 2 B C A Shifting to infinity: VVVVVVVV = lim tt CCCCCCCC λλ, tt /λλ Shifting time 12
3. Nature of DR Storage Shifting decision: How long tt tt 0 and how much ee of the energy consumption LL tt 0 planned for tt 0 should be shifted given price path pp tt? ee ee max tt,ee pp tt pp tt 0 CCCCCCCC, tt tt LL tt 0 LL tt 0 0 0 ee LL tt 0 Very difficult problem (nonlinear, mixed integer)! To approximate interpret CCCCCCCC as penalty function formulation for this constrained optimization problem: ee max tt,ee pp tt pp tt 0 LL tt 0 ss. tt. : tt tt 0 1 ee LL tt 0 0 ee LL tt 0 shifting can be approximated by a series of time inhomogeneous load restricted storages Including two dynamic components in the capacity constraint! 13
4. DR storage equilibrium What is the impact of these dynamic constraints if we consider an overlapping series of these storages in a perfectly coordinated market environment? Equilibrium model utility-maximizing representative consumer Fossil generation: technologies with capacity and variable cost Resource constraint: generation exceeds demand + shifted load DR as described, one storage per period Optimizer selects if storage blocks are used for storage: long term storage with little capacity or short term storage with huge capacity (mixed integer Program) and the shifting direction. Scenario: in sine-wave-form (peak twice the min load) All load is capable of shifting 14
4. DR storage equilibrium common pattern Demand Response Conventional Storage 15
4. DR storage equilibrium common pattern Demand Response Conventional Storage 16
4. DR storage equilibrium common pattern Demand Response Conventional Storage 17
4. DR storage equilibrium Sensitivity: If load min decreases the valley is not filled at all 18
5. Conclusion Storing energy or storing consumption: It s not the same! 1. Micro foundation of DR 2. DR can be interpreted as dynamic, time inhomogeneous storage 3. In Equilibrium: DR shaves peak, causes a land slide and fills a valley incompletely 4. DR might steepen the load gradient stresses the system 5. Complementary interaction with conventional storage is likely: as little conventional storage might fill the valley completely, if DR is cheap. To do: 1. Is there a simple (time homogenous) approximative storage model for DR? stochastic analysis 2. Necessary application of potent solvers (CPLEX), realistic time resolution 3. Renewable impulses 19
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2. COTS - Cost of time shifting Moment cost of time shifting per device group cc ωω, tt tt 0 = CCCCCCCC tt tt 0 ωω 0 eeeeeeee Optimal decision: select device group ωω with high threshold first to fulfil savings target λλ Cost of load shifting CCOOOOOO λλ, tt tt 0 λλ = ωω ωω tt = tt 0 ff ωω dddd ff ωω uniform distribution of device groups on [0,T]: (tt tt 0 0) ωω ωω λλ ee ββββ ff ωω cc ωω, ττ dddd dddd CCCCCCCC λλ, tt tt 0 = CCCCCCCC 2 2 tt tt 0 + λλ 2 λλ tt tt 0 1 λλ 2 2 2 0 2 tt tt 0 tt tt 0, tt tt 0 > 1 λλ tt tt 0 1 λλ 2 2 2 21
4. DR storage equilibrium Minimize Total Generation Cost Resource constraint Generation capacity constraint min cc ffffff xx + cc vvvvvv xx tt tt xx tt0 + ss DDDD DDDD tt,tt0 LL tt0 + ss tt0,tt tt tt xx xx tt0 0 DR storage capacity tt tt 0 DDDD 1 ss tt 0,tt DDDD LL tt0 Block storage logic (only exactly one target period) No storage cycles - one way storage 22