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?
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Motivation
Shifting of single load (industrial processes) by several hours
Load
Time
Here: Also shifting a series of small loads by a couple of minutes each (without spoiling)
Load
Load
Load
Load
Time
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Motivation
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)
Load
Load
Load
Load
Load
Load
Load
Load
 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?
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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
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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
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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
𝜏6
Gradually
𝜏5
increasing
𝜏4
cost of
𝜏3
delay
𝜏2
DR enabled devices by
threshold time 𝜏𝑖
𝜏1
𝑡0
period 1
𝑡1
𝑡
period 2
preferred start
of using devices
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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
𝜏6
These devices
𝜏5
incur a cost
𝜏4
𝜏3
𝜏2
𝜏1
𝑡0
period 1
𝑡1
𝑡
period 2
 Step 3 – determine aggregated COTS(𝜟t,S) over all devices
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2. COTS - Cost of time shifting
Overall cost
1 device
1 device
Bring forward
Delay
Cost per device
Bring forward
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Delay
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2. COTS - Cost of time shifting
Overall cost
2 devices
2 devices
1 device
1 device
Bring forward
Delay
Cost per device
Bring forward
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Delay
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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
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Delay
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2. COTS - Cost of time shifting, move l by t
Integration with uniform distribution of device groups on [0,T]: (𝑡 − 𝑡0 ≥ 0)
2
2 𝑡 − 𝑡0 + 𝑇 𝜆 − 2 𝜆
𝑡 − 𝑡0 − 𝑇 1 − 𝜆
𝑇
2
𝑇
3-D view:
COTS
2
0
𝑇
2
𝑡 − 𝑡0 ≥ 𝑇
𝑇
Contour view:
 Shifting to infinity: 𝑉𝑜𝐿𝐿 = lim𝑡→∞ 𝐶𝑂𝑇𝑆 𝜆, 𝑡 /𝜆
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𝑇
2
𝑡 − 𝑡0
𝑇 ≥ 𝑡 − 𝑡0 ,
>1−𝜆
B
𝑇
𝑇
2
𝑡 − 𝑡0
C
≤1−𝜆
𝑇
𝑇
Share of shifted load
𝐶𝑂𝑇𝑆 𝜆, 𝑡|𝑡0
𝐶𝑂𝑇𝑆
=
2
2
A
A
B
B
C
Shifting time
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3. Nature of DR Storage
Shifting decision: How long 𝑡 − 𝑡0 and how much 𝑒 of the energy
consumption 𝐿 𝑡0 planned for 𝑡0 should be shifted given price path
𝑝 𝑡 ?
𝑒
𝑒
max𝑡,𝑒 𝑝 𝑡 − 𝑝 𝑡0
− 𝐶𝑂𝑇𝑆
, 𝑡 − 𝑡0
𝐿 𝑡0
𝐿 𝑡0




0 ≤ 𝑒 ≤ 𝐿 𝑡0
Very difficult problem (nonlinear, mixed integer)!
To approximate interpret 𝐶𝑂𝑇𝑆 as penalty function formulation for
this constrained optimization problem:
𝑒
max𝑡,𝑒 𝑝 𝑡 − 𝑝 𝑡0
𝐿 𝑡0
𝑡 − 𝑡0
𝑒
𝑠. 𝑡. :
≤1−
𝑇
𝐿 𝑡0
0 ≤ 𝑒 ≤ 𝐿 𝑡0
Load shifting can be approximated by a series of time
inhomogeneous load restricted storages
Including two dynamic components in the capacity constraint!
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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
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4. DR storage equilibrium – common pattern
Load
Demand
Response
Conventional
Storage
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4. DR storage equilibrium – common pattern
Load
Demand
Response
Conventional
Storage
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4. DR storage equilibrium – common pattern
Load
Demand
Response
Conventional
Storage
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4. DR storage equilibrium
Sensitivity: If load min decreases – the valley is not filled at all
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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
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