Analysis of Petri Nets and Transition Systems

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459

Bounded Petri Net Synthesis from Modal Transition Systems is Undecidable

In this paper, the synthesis of bounded Petri nets from deterministic modal transition systems is shown to be undecidable. The proof is built from three components. First, it is shown that the problem of synthesising bounded Petri nets satisfying a given formula of the conjunctive nu-calculus (a suitable fragment of the mu-calculus) is undecidable. Then, an equivalence between deterministic modal transition systems and a language-based formalism called modal specifications is developed. Finally, the claim follows from a known equivalence between the conjunctive nu-calculus and modal specifications

k-Bounded Petri Net Synthesis from Modal Transition Systems

We present a goal-oriented algorithm that can synthesise k-bounded Petri nets (k in N^+) from hyper modal transition systems (hMTS), an extension of labelled transition systems with optional and required behaviour. The algorithm builds a potential reachability graph of a Petri net from scratch, extending it stepwise with required behaviour from the given MTS and over-approximating the result to a new valid reachability graph. Termination occurs if either the MTS yields no additional requirements or the resulting net of the second step shows a conflict with the behaviour allowed by the MTS, making it non-sythesisable

Business case analysis of hybrid systems consisting of battery storage and power-to-heat on the German energy market

Declining prices on frequency containment reserve (FCR) markets endanger the profitability of battery energy storage systems (BESS). BESS combined with power-to-heat units could improve the economics both by supplying higher power rates on FCR markets and by converting excessive power into heat. Two cases were investigated with a techno-economic model using primary operation and market data of 2018/2019. The system amortises after 12 years with a net present value of two million € operating on the FCR market. No improvement was realized by additional arbitrage trading. Taxes, levies and charges frameworks are crucial for the economic success of hybrid systems

Incremental Process Discovery using Petri Net Synthesis

International audienceProcess discovery aims at constructing a model from a set of observations given by execution traces (a log). Petri nets are a preferred target model in that they produce a compact description of the system by exhibiting its concurrency. This article presents a process discovery algorithm using Petri net synthesis, based on the notion of region introduced by A. Ehrenfeucht and G. Rozenberg and using techniques from linear algebra. The algorithm proceeds in three successive phases which make it possible to find a compromise between the ability to infer behaviours of the system from the set of observations while ensuring a parsimonious model, in terms of fitness, precision and simplicity. All used algorithms are incremental which means that one can modify the produced model when new observations are reported without reconstructing the model from scratch

Incremental Process Discovery using Petri Net Synthesis

International audienceProcess discovery aims at constructing a model from a set of observations given by execution traces (a log). Petri nets are a preferred target model in that they produce a compact description of the system by exhibiting its concurrency. This article presents a process discovery algorithm using Petri net synthesis, based on the notion of region introduced by A. Ehrenfeucht and G. Rozenberg and using techniques from linear algebra. The algorithm proceeds in three successive phases which make it possible to find a compromise between the ability to infer behaviours of the system from the set of observations while ensuring a parsimonious model, in terms of fitness, precision and simplicity. All used algorithms are incremental which means that one can modify the produced model when new observations are reported without reconstructing the model from scratch

Bounded choice-free Petri net synthesis: algorithmic issues

This paper describes a synthesis procedure dedicated to the construction of choice-free Petri nets from finite persistent transition systems, whenever possible. Taking advantage of the properties of choice-free Petri nets, a two-step approach is proposed. A pre-synthesis step checks necessary structural properties of the transition system and constructs some data structures needed for the second step. Then, a minimised set of simplified systems of linear inequalities is distilled from a general region-theoretic approach. This leads to a substantial narrowing of the sets of states for which linear inequalities must be solved, and allows an early detection of failures, supported by constructive error messages. The performance of the resulting algorithm is measured and compared numerically with existing synthesis tools.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

A graph-theoretical characterisation of state separation

Region theory, as initiated by Ehrenfeucht and Rozenberg, allows the characterisation of the class of Petri net synthesisable finite labelled transition systems. Regions are substructures of a transition system which come in two varieties: ones solving event/state separation problems, and ones solving state separation problems. Linear inequation systems can be used in order to check the solvability of these separation problems. In the present paper, the class of finite labelled transition systems in which all state separation problems are solvable shall be characterised graph-theoretically, rather than linear-algebraically.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

Optimised capacity and operating strategy for providing frequency containment reserve with batteries and power-to-heat

Batteries provide growing amounts of Frequency Containment Reserve (FCR) in the German electricity market. We examine the ideal battery capacity as well as the state of charge (SoC) setpoint for provision of FCR following a profit maximisation approach. While a lot of research neglects taxes, their huge influence on the results is considered. In addition to stand-alone battery systems, we also consider hybrid systems, combining a battery storage with a Power-to-Heat (PtH) module. The hybrid system has two variants: in one variant energy is sold when the battery is fully charged, while in the other one the PtH module is used. Based on historical frequency and market data for one year, the performance of the different system variants is evaluated via a simulation. 2048 different combinations of battery capacity and SoC setpoint are examined. The performance of each configuration is evaluated with the net present value (NPV) method, allowing an economic comparison. The results show a financial advantage for the hybrid systems which sell energy when the battery is fully charged. The system configuration with the best NPV is a hybrid system with a battery capacity of 480 kWh and an SoC setpoint of 98%. The best battery capacity of all considered variants has a lower capacity to power ratio than the usual ratio of 1 MWh to 1 MW, assumed in most other studies. Non-optimal battery capacities have a stronger negative effect on the economic efficiency of the systems than non-optimal SoC setpoints. The results emphasise that the battery capacity is a critical investment decision