Agent-based Micro-Storage Management
Jonathan Lukkien
11 juni 2013
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Jonathan Lukkien
Agent-based Micro-Storage Management
Overview
Introduction
Model
Game Theory Analysis
Adoptive storage strategy
Empirical results
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Jonathan Lukkien
Agent-based Micro-Storage Management
1. Introduction
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Jonathan Lukkien
Agent-based Micro-Storage Management
Quick recap
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Introduction
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Storage is vital for Smart Grid
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Peak-demand can get flattened
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Energy production with high variance in output can be used
Jonathan Lukkien
Agent-based Micro-Storage Management
Challenges
Introduction
Even with storage there are challenges:
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Everyone charging at once
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Batteries might cost a lot
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Storing energy might not be the best strategy
Jonathan Lukkien
Agent-based Micro-Storage Management
Multi-agent paradigm
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Smart meters empower agents
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More accurate prediction methods available
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Agents can solve our problem!
Jonathan Lukkien
Introduction
Agent-based Micro-Storage Management
Context
Introduction
According to the authors a lot of work done on the following:
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Individual homes optimizing storage
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Storage devices can ensure “following renewables”
But the research domain lacks non-homogeneous fleet research.
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Agent-based Micro-Storage Management
Current study focus
Introduction
The authors suggest the following to improve on the research
domain:
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A novel game-theoretic framework
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New agent-based storage strategies
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Agent-based learning strategies to predict optimal storage
capacity
Jonathan Lukkien
Agent-based Micro-Storage Management
2. Model
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Jonathan Lukkien
Agent-based Micro-Storage Management
Model schematic
Model
Three components make up the model:
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Agents
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Electricity Market
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Metrics
Jonathan Lukkien
Agent-based Micro-Storage Management
Model - Agents
Model
Characteristics of an agent are as follows:
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Load profile denoted as lia
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Storage capacity: ea
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Storage efficiency: αa
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running storage cost: ca
Jonathan Lukkien
Agent-based Micro-Storage Management
Model - Agents cont.
Model
Considering storage strategies we have the following important
issues:
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Maximum charging and discharging capacity: ba+ , ba−
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A storage profile to strategise: bai
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a−
bai = ba+
i − bi
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lia , ba+ and ba− are all small
Jonathan Lukkien
Agent-based Micro-Storage Management
Model - Market
Model
The market model is a black box, no layers! What we do have:
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Supply curve generated from historic supply curve
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Total electricity consumed per interval: qi = di + bi
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Market generates a price by inputting this qi in supply
function si
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Each agent pays according to lia + bai
Jonathan Lukkien
Agent-based Micro-Storage Management
Model - Market - Picture
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Agent-based Micro-Storage Management
Model
Model - Metrics
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Diversity Factor
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Load Factor
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Grid Carbon Content
Jonathan Lukkien
Model
Agent-based Micro-Storage Management
3. Game Theory Analysis
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Jonathan Lukkien
Agent-based Micro-Storage Management
Game Theory Analysis
Game Theory Analysis
Topics we’ll discuss:
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Rules of the game
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Nash equilibria
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Idealised scenarios
Jonathan Lukkien
Agent-based Micro-Storage Management
Rules of the game
Game Theory Analysis
First we do introduce some homogeneity:
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αa = α∀a
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ca = c∀a
Jonathan Lukkien
Agent-based Micro-Storage Management
Rules of the game cont.
Game Theory Analysis
The general rules:
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Agents are players
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Single 24 hour interval played
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Pay-off for an agent is -Total cost
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a+
a
Strategy space is −ba−
i ≤ bi ≤ bi
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Discharging has to take in to account storage efficiency
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Players can’t charge more than storage capacity
Jonathan Lukkien
Agent-based Micro-Storage Management
Nash equilibria
Game Theory Analysis
Nash equilibrium is a state where no single player has incentive
to change their behaviour.
In this paper they assume, because the changes in a strategy are
small, that the problem becomes a straightforward minimization
problem with the global generator costs having to be minimized.
Set of Nash equilibria is precisely the set of agent strategies
where ∀i ∈ I, bi = qid (pd ) − qic (pc ).
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Agent-based Micro-Storage Management
Idealised scenarios
Game Theory Analysis
If we have perfect efficiency and the cost for storing energy is
set to 0, what do you think will happen to the energy cost?
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Jonathan Lukkien
Agent-based Micro-Storage Management
Some drawbacks
Game Theory Analysis
Some remarks on using game theory:
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Agents act rationally, storage owners may not
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Perfect information is assumed, in reality this is probably
not the case
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Even with perfect information an agent might not realise
the perfect strategy
Jonathan Lukkien
Agent-based Micro-Storage Management
4. Adoptive storage strategy
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Jonathan Lukkien
Agent-based Micro-Storage Management
Day-Ahead Best-Response
Storage
Adoptive storage strategy
Every agent tries to predict market prices.
Subsequently they compute the optimal storage profile for every
time slot.
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Jonathan Lukkien
Agent-based Micro-Storage Management
Cost function
Adoptive storage strategy
P
a−
a a
a
arg minba ( i∈I pi (ba+
i − bi + li ) + c e with the following
constraints:
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Storage efficiency
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Not exceeding (dis)charging capacity in any i ∈ I
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Available energy constraints
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No reselling allowed
Jonathan Lukkien
Agent-based Micro-Storage Management
Learning
Adoptive storage strategy
Two passes over this problem to solve:
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set ea to ea (t + 1)
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change bai (t) to bai (t + 1)
Jonathan Lukkien
Agent-based Micro-Storage Management
5. Empirical results
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Jonathan Lukkien
Agent-based Micro-Storage Management
Calculated Nash equilibrium
results
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Jonathan Lukkien
Empirical results
Agent-based Micro-Storage Management
Adaptive storage evaluation
Empirical results
Authors
take these results to prove that they have set a benchmark for
any learning strategy in this system.
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Agent-based Micro-Storage Management
Social welfare
Empirical results
The social welfare point of view is illustrated in the following
figure:
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Jonathan Lukkien
Agent-based Micro-Storage Management
The paper goes on to say that financial incentives make the
system converge to 38% of the population having storage.
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Jonathan Lukkien
Agent-based Micro-Storage Management
Conclusion
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Empirical results
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We have seen a theoretical framework for agent strategies
in smart-grid
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An adaptive strategy to make this theoretical framework
practical
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An overall improvement to society when we make this
work!
Jonathan Lukkien
Agent-based Micro-Storage Management