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?

Motivation Load Load Load Load Load Load Load Shifting of single load (industrial processes) by several hours Load Load Time Here: Also shifting a series of small loads by a couple of minutes each (without spoiling) Load Load Load Load Load Time

Motivation Load Load Load Load Load Load Load Load Load Load Shifting of single load (industrial processes) by several hours Load Load 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 Load Load Load Load Load Load Load Load Time How is load shifted by rational agents? Is storing consumption equivalent to electricity storage?

Storing energy or storing consumption - It is not the same! To answer these questions: Introduction – We present DR model environment COTS - We formulate a model of the cost of time shifting (COTS). Nature of DR Storage - We show that rational DR can be interpreted as a sequence of time inhomogeneous capacity-constrained storages. 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. Conclusion Verbesserung: Konsum der mehr als eine Periode dauert steht zum shifting in der nächsten Periode nicht zur Verfügung.

1. Introduction DR Environment: Preferences: We assume that there is a given preferred consumption schedule there are device specific indifference threshold times (inertia of thermal storage, indifference) – exploitable Technology, market environment: there is a real time price signal 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 Assumption: der Konsum dauert höchstens eine Periode, danach kann wieder neu entschieden werden.

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. indifference threshold curve 𝐸 No delay cost 𝜏 6 𝜏 5 𝜏 4 𝜏 3 𝜏 1 𝜏 2 Indifference threshold is identity function The devices do not neccessarily have the same operating time Gradually increasing cost of delay DR enabled devices by threshold time 𝜏 𝑖 𝑡 period 2 𝑡 0 period 1 𝑡 1 preferred start of using devices

2. COTS - Cost of time shifting Step 1 – COTS by device group 4, 5 and 6. Action considered: shifting the whole block by 𝜟t 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! 𝐸 𝜟t S 𝜏 6 𝜏 4 𝜏 5 Indifference threshold is identity function The devices do not neccessarily have the same operating time These devices incur a cost 𝜏 3 𝜏 1 𝜏 2 𝑡 period 2 𝑡 0 period 1 𝑡 1 Step 3 – determine aggregated COTS(𝜟t,S) over all devices

2. COTS - Cost of time shifting Overall cost 1 device 1 device Bring forward Delay Cost per device Bring forward Delay

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

2. COTS - Cost of time shifting Overall cost 3 devices 3 devices 2 devices 2 devices 1 device 1 device Bring forward Delay Cost per device Bring forward Delay

2. COTS - Cost of time shifting, move l by t Integration with uniform distribution of device groups on [0,T]: (𝑡− 𝑡 0 ≥0) 𝐶𝑂𝑇𝑆 𝜆,𝑡 |𝑡 0 = 𝐶𝑂𝑇𝑆 2 2 𝑡− 𝑡 0 +𝑇 𝜆−2 𝜆 2 𝑇 𝑡− 𝑡 0 −𝑇 1−𝜆 2 𝑇 2 𝑇 0 2 𝑇 𝑡− 𝑡 0 ≥𝑇 2 𝑇 𝑇≥𝑡− 𝑡 0 , 𝑡− 𝑡 0 𝑇 >1−𝜆 2 𝑇 𝑡− 𝑡 0 𝑇 ≤1−𝜆 2 𝑇 A B C Share of shifted load Shifting time COTS 3-D view: Contour view: Shifting time Share of shifted load A A B B C Shifting to infinity: 𝑉𝑜𝐿𝐿= lim 𝑡→∞ 𝐶𝑂𝑇𝑆 𝜆,𝑡 /𝜆

3. Nature of DR Storage Shifting decision: How long 𝑡− 𝑡 0 and how much 𝑒 of the energy consumption 𝐿 𝑡 0 planned for 𝑡 0 should be shifted given price path 𝑝 𝑡 ? max 𝑡,𝑒 𝑝 𝑡 −𝑝 𝑡 0 𝑒 𝐿 𝑡 0 −𝐶𝑂𝑇𝑆 𝑒 𝐿 𝑡 0 ,𝑡− 𝑡 0 0≤𝑒≤𝐿 𝑡 0 Very difficult problem (nonlinear, mixed integer)! To approximate interpret 𝐶𝑂𝑇𝑆 as penalty function formulation for this constrained optimization problem: max 𝑡,𝑒 𝑝 𝑡 −𝑝 𝑡 0 𝑒 𝐿 𝑡 0 𝑠.𝑡.: 𝑡− 𝑡 0 𝑇 ≤1− 𝑒 𝐿 𝑡 0 0≤𝑒≤𝐿 𝑡 0 Load shifting can be approximated by a series of time inhomogeneous load restricted storages Including two dynamic components in the capacity constraint!

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: Load in sine-wave-form (peak twice the min load) All load is capable of shifting

4. DR storage equilibrium – common pattern Load Demand Response At the peak 2 fridges may shift. Then load falls and there is only one fridge that can take over. So one (net) fridge needs to be activated even though the valley is not yet reached – landslide. Conventional Storage

4. DR storage equilibrium – common pattern Load Demand Response At the peak 2 fridges may shift. Then load falls and there is only one fridge that can take over. So one (net) fridge needs to be activated even though the valley is not yet reached – landslide. Conventional Storage

4. DR storage equilibrium – common pattern Load Demand Response At the peak 2 fridges may shift. Then load falls and there is only one fridge that can take over. So one (net) fridge needs to be activated even though the valley is not yet reached – landslide. Conventional Storage

4. DR storage equilibrium Sensitivity: If load min decreases – the valley is not filled at all 16/3 13/3 17/2

Storing energy or storing consumption: It‘s not the same! 5. Conclusion Storing energy or storing consumption: It‘s not the same! Micro foundation of DR DR can be interpreted as dynamic, time inhomogeneous storage In Equilibrium: DR shaves peak, causes a land slide and fills a valley incompletely DR might steepen the load gradient  stresses the system Complementary interaction with conventional storage is likely: as little conventional storage might fill the valley completely, if DR is cheap. To do: Is there a simple (time homogenous) approximative storage model for DR?  stochastic analysis Necessary application of potent solvers (CPLEX), realistic time resolution Renewable impulses