Introduction
Foundations
A Model-based Approach for the
Specification of a Virtual Power Plant
Operating in Open Context
Focus Theory
Running Example
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
Vasileios Koutsoumpas
Conclusion &
Future Work
The End
Fakultät für Informatik, Technische Universität München, Munich,
Germany
May 17, 2015
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Table of contents
Introduction
Introduction
Foundations
Focus Theory
Foundations
Focus Theory
Running Example
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Running Example
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
Conclusion &
Future Work
The End
Formal Specification
Conclusion & Future Work
The End
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Introduction
I
Open Context Systems (OCS)
I
I
I
I
I
I
I
I
Foundations
Focus Theory
Smart Cars, Smart Grids, Smart Homes, etc...
Virtual Power Plant (VPP)1
I
I
Introduction
Dynamic system boundary
Dynamic context awareness
Challenges
Limitations
Running Example
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
OCS involve Uncertainty
Uncertainty is an umbrella over terms (Accuracy,
Precision, Ambiguity, Vagueness, Predictability...)
Where is uncertainty located in a component?
Uncertain input, output, behavior
UI
#» #»
UB : I →O
Conclusion &
Future Work
The End
UO
1
Applying formal software engineering techniques to smart grids,
SE4SG-2012
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Research Problem
Introduction
Rapid Formal Methods(Bounded Top-Down)
(B)
Focus Theory
Running Example
impl
it 1
Informal
Requirements
Foundations
System
Specification
Modeling Theory
(C)
System Model
(A)
Informal
Requirements
Syntactic Interface
Semantic Interface
Composition
dec
deploy
Level of Fuziness
=
it 2
Informal
Requirements
+/-
Formal
Specification
simul
it N
FR
Simulation
Enviroment
Clasical Formal Methods(Top-Down)
Requirements
I
I
I
I
Formalization
Specification
Verification
Deployment
Conclusion &
Future Work
The End
PS1: Formalism for fuzzy specifications to model
explicitly uncertainty in component interactions
Equivalence model for quantitative reasoning
PS2: Formalism for qualitative specifications for
approximating component behaviors
Dynamic adaption to systems context
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Focus Theory
I
A formal theory for interactive systems
I
System structure: static hierarchy of components
Syntactic Interface: I B O
I
Component interactions through message exchange
Streams: finite
Focus Theory
Modeling Theory
(M ∞ )
I
or infinite
#»
#»
Semantic Interface : B : I → ℘(O)
I
Composition of subsystems: B1 ⊗ B2
I
Foundations
Running Example
I
(M ∗ )
Introduction
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
Conclusion &
Future Work
The End
i1 : T1
#»
#»
B : I →O
o : T3
i2 : T2
Figure: Focus Component
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Virtual Power Plant
Introduction
Natural
Enviroment
Foundations
Focus Theory
Running Example
Modeling Theory
t:T
w :W
Weather
Station
w :W
t:T
Virtual
Power Plant
Syntactic Interface
Semantic Interface
Composition
p:P
Consumer
Network
Formal
Specification
Conclusion &
Future Work
The End
Figure: Virtual Power Plant and its Context
I
Context-dependency
I
Time-Dependency
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Fuzzy Property
Definition (Fuzzy Property)
Introduction
A fuzzy property pe is a three-tuple hX , ξ, πξ i, where X is the
universe of discourse which can be referenced by pe, ξ is a
linguistic term which characterizes the property and
πξ : X → [0, 1] ∪ {⊥} is the membership function.
p1
p2
p3
x
0
5
10
µTroom (x)
0
0
0.1
p4
p5
p6
15
20
25
0.3
0.8
1
p7
p8
p9
30
35
40
0.6
0.1
0
Foundations
Focus Theory
Running Example
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
Conclusion &
Future Work
The End
1
πξ
T
5
10
15
20
25
30
35
40
45
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Fuzzy Port - Bindings
Definition (Fuzzy Port)
Introduction
A fuzzy port ΘT over a type T is a set of fuzzy properties
ΘT = {e
p ∈ P}, which satisfies the following two conditions:
- Each property type is a subset of T, formally:
∀e
p ∈ ΘT → pe.X ⊆ T
Foundations
Focus Theory
Running Example
Modeling Theory
(c1)
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
- Each property is uniquely characterized by its linguistic
term, formally:
Conclusion &
Future Work
The End
∀e
p1 , pe2 ∈ ΘT : pe1 6= pe2 → pe1 .ξ 6= pe2 .ξ
(c2)
Definition (Binding)
A binding B between a typed channel c : C and a fuzzy port
ΘT is a 2-tuple B = hc, ΘT i which satisfies following
connectivity property:
- C ⊆T
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Syntactic Interface
Syntactic Interface (IS I OS ) = I /O channels + fuzzy
IP/OP ports + I /O bindings
Introduction
Example (Syntactic Interface of the VPP)
Running Example
Foundations
Focus Theory
Modeling Theory
w :W
t:T
(A) − ΘW
sunny
1
cloudy
low
(B) − ΘT
Formal
Specification
average
high
low
1
0.6
0.4
0.6
0.4
0.2
0.2
0
0
0
10
20
30
40
50
60
weatherDescription %
70
80
90
100
(C ) − ΘP
average
high
0.8
Degree of membership
0.8
Degree of membership
Degree of membership
p:P
VPP
1
0.8
Syntactic Interface
Semantic Interface
Composition
Conclusion &
Future Work
The End
0.6
0.4
0.2
0
−10
0
10
20
Temperature °C
30
40
0
0.5
1
1.5
2
2.5
3
power kWh
3.5
4
4.5
5
Figure: Syntactic Interface Specification for the VPP
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Rule Base Specification
Given: IS I OS and µ = hi1 @t, ..., in @ti ∈ I1 × ... × In , the
semantics are determined by a rule base of the form:
Rro :
if i1 @t is
(1)
ξ1,r
.. and ... in @t is
(n)
ξn,r
Focus Theory
Modeling Theory
In case of multiple output channels: RS = {R O1 , ..., R Om }
in : In
Implication
Mod.
output(R )
{πξ1 ,...,ξn 1 , ...,
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
#»
#»
R : I → ℘(O)
i1 : I1
Foundations
Running Example
then o@(t + 1) is ξr , r = 1, .., k
Applicability
Mod.
{α1 , ..., αk }
Introduction
Conclusion &
Future Work
Defuzzyfication
Mod.
0
ocrisp
The End
o:O
output(Rk )
πξ1 ,...,ξn
}
Assembling
Mod.
output(R)
πξ1 ,...,ξn
Figure: Behavior interpretation of a rule based specification
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Mapping Strategies
Introduction
Foundations
Focus Theory
Running Example
Definition (Mapping Strategy)
A mapping strategy for a given property pe = hX , ξ, πξ i(total
or partial) is a high order function over a stream to a
membership function for that property, formally:
mapstrξ : Stream X , N ∪ {∞} → (πξ : X → [0, 1])
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
Conclusion &
Future Work
The End
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Composition
i20
i1
I
I1
i10
i2
R1
Introduction
Foundations
I2
Focus Theory
Running Example
R2
Modeling Theory
O2
o20
o1
O1
o10
o2
O
Figure: Parallel Composition with Feedback
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
Conclusion &
Future Work
The End
Given two subsystems S1 and S2 with I1 ∩ I2 = ∅ and
#»
#»
#»
#»
behavior functions R1 : I1 → ℘(O1 ) and R2 : I2 → ℘(O2 ),
the parallel composition is given by:
#»
#»
R1 ⊗ R2 : I → ℘(O)
where, I = I1 ∪ I2 , IPS = IPS1 ∪ IPS2 , O = O1 ∪ O2 , and
OPS = OPS1 ∪ OPS2 .
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VPP Specification
Introduction
Foundations
Focus Theory
Running Example
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Formal
Specification
Conclusion &
Future Work
The End
Figure: Virtual Power Plant Specification
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Conclusion & Future Work
Introduction
Foundations
Focus Theory
Running Example
Modeling Theory
I
Formalism for qualitative specifications within Focus
I
Framework for Uncertainty based on fuzzy logic
I
Limitations
Formal
Specification
I
Tooling
Conclusion &
Future Work
I
Case studies to evaluate the expressiveness and
effectiveness of the overall approach
The End
Syntactic Interface
Semantic Interface
Composition
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The End
Introduction
Foundations
Focus Theory
Running Example
Modeling Theory
Syntactic Interface
Semantic Interface
Composition
Thank you for your attention!
Formal
Specification
Conclusion &
Future Work
The End
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