1. 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

2. 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?

3. 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

4. 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?

5. 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.

6. 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.

7. 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

8. 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

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

10. 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

11. 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

12. 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 𝑡− 𝑡 0 +𝑇 𝜆−2 𝜆 𝑇 𝑡− 𝑡 0 −𝑇 1−𝜆 2 𝑇 𝑇 𝑇 𝑡− 𝑡 0 ≥𝑇 𝑇 𝑇≥𝑡− 𝑡 0 , 𝑡− 𝑡 0 𝑇 >1−𝜆 𝑇 𝑡− 𝑡 0 𝑇 ≤1−𝜆 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

13. 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!

14. 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

15. 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

16. 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

17. 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

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

19. 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