A Model-based Approach for the Specification of a Virtual Power Plant Operating in Open Context

Transcription

1 A Model-based Approach for the of a Virtual Power Plant Operating in Open Context Vasileios Koutsoumpas Fakultät für Informatik, Technische Universität München, Munich, Germany May 17, / 15

2 Table of contents 2 / 15

3 Open Context Systems (OCS) Dynamic system boundary Dynamic context awareness Smart Cars, Smart Grids, Smart Homes, etc... Virtual Power Plant (VPP) 1 Challenges Limitations 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 UO 1 Applying formal software engineering techniques to smart grids, SE4SG / 15

4 Research Problem Level of Fuziness Informal Requirements Informal Requirements Informal Requirements (A) it 1 it 2 it N FR Rapid Methods(Bounded Top-Down) (B) System impl System Model simul Clasical Methods(Top-Down) Requirements ization Verification Deployment = (C) +/- Simulation dec deploy Enviroment PS1: ism for fuzzy specifications to model explicitly uncertainty in component interactions Equivalence model for quantitative reasoning PS2: ism for qualitative specifications for approximating component behaviors Dynamic adaption to systems context 4 / 15

5 A formal theory for interactive systems System structure: static hierarchy of components : I O Component interactions through message exchange Streams: finite (M ) or infinite (M ) : B : #» I ( O) #» of subsystems: B 1 B 2 i 1 : T 1 i 2 : T 2 B : #» I #» O o : T 3 Figure: Focus Component 5 / 15

6 Virtual Power Plant Weather Station w : W t : T Natural Enviroment w : W t : T Virtual Power Plant p : P Consumer Network Figure: Virtual Power Plant and its Context Context-dependency Time-Dependency 6 / 15

7 Fuzzy Property Definition (Fuzzy Property) A fuzzy property p is a three-tuple X, ξ, π ξ, where X is the universe of discourse which can be referenced by p, ξ is a linguistic term which characterizes the property and π ξ : X [0, 1] { } is the membership function. p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 x µ Troom (x) π ξ T 7 / 15

8 Fuzzy Port - Bindings Definition (Fuzzy Port) A fuzzy port Θ T over a type T is a set of fuzzy properties Θ T = { p P}, which satisfies the following two conditions: - Each property type is a subset of T, formally: p Θ T p.x T (c1) - Each property is uniquely characterized by its linguistic term, formally: p 1, p 2 Θ T : p 1 p 2 p 1.ξ p 2.ξ (c2) Definition (Binding) A binding B between a typed channel c : C and a fuzzy port Θ T is a 2-tuple B = c, Θ T which satisfies following connectivity property: - C T 8 / 15

9 (I S O S ) = I /O channels + fuzzy IP/OP ports + I /O bindings Example ( of the VPP) w : W t : T VPP p : P sunny (A) Θ W (B) Θ T (C) Θ P cloudy low average high low average high Degree of membership Degree of membership Degree of membership weatherdescription % Temperature C power kwh Figure: for the VPP 9 / 15

10 Rule Base Given: I S O S and µ = i i I 1... I n, the semantics are determined by a rule base of the form: Rr o : if i is ξ (1) 1,r.. and... i is ξ n,r (n) then o@(t + 1) is ξ r, r = 1,.., k In case of multiple output channels: R S = {R O 1,..., R Om } i 1 : I 1 i n : I n Applicability Mod. {α 1,..., α k } Implication Mod. {π output(r1),..., ξ1,...,ξn π output(rk) } ξ1,...,ξn R : #» I ( #» O) Defuzzyfication Mod. o crisp Assembling Mod. π output(r) ξ1,...,ξn o : O Figure: Behavior interpretation of a rule based specification 10 / 15

11 Mapping Strategies Definition (Mapping Strategy) A mapping strategy for a given property p = X, ξ, π ξ (total or partial) is a high order function over a stream to a membership function for that property, formally: mapstr ξ : Stream X, N { } (π ξ : X [0, 1]) 11 / 15

12 i1 I i 2 I 1 i 2 i 1 I 2 o1 R 1 R 2 o O 2 o 1 1 O 2 O o 2 Figure: Parallel with Feedback Given two subsystems S 1 and S 2 with I 1 I 2 = and behavior functions R 1 : I #» 1 ( O #» 1 ) and R 2 : I #» 2 ( O #» 2 ), the parallel composition is given by: R 1 R 2 : #» I ( #» O) where, I = I 1 I 2, IP S = IP S1 IP S2, O = O 1 O 2, and OP S = OP S1 OP S2. 12 / 15

13 VPP Figure: Virtual Power Plant 13 / 15

14 ism for qualitative specifications within Focus Framework for Uncertainty based on fuzzy logic Limitations Tooling Case studies to evaluate the expressiveness and effectiveness of the overall approach 14 / 15

15 Thank you for your attention! 15 / 15