Formal verification of Signal programs: Application to a power transformer station controller

Abstract

We present a methodology for the veri cation of reactive systems, and its application to a case study. Systems are speci ed using the synchronous data ow language Signal. As this language is based on an equational approach (i.e. Signal programs are constraint equations between signals), it is natural to translate its Boolean part into a system of polynomial equations over three values denoting true, false and absent. Using operations in algebraic geometry on the polynomials, it is possible to check properties concerning the system, such as liveness, invariance, reachability and attractivity. We apply this method to the veri cation of the automatic circuit breaking control system of an electric power transformer station. This system handles the reaction to electrical defects on high voltage lines.

Incremental design of a Power transformer station controller using a controller synthesis methodology

“…We chose to specify each local controller in SIGNAL because they merge logical and numerical aspects. Here, we give only a brief description of the behavior of the different cells (more details can be found in [6], [7]). The other part concerns more general requirements to be checked by the global controller of the power transformer station.…”

“…The specification of a large part of these local controllers has been performed using the SIGNAL synchronous language [6] and verified using our formal calculus system, named SIGALI [7].…”

“…The transformer station network we are considering contains four departure, two arrival, and one link circuitbreakers, as well as the cells that control each circuitbreaker [7]. The process, Physical_Model in Fig.…”

“…To model its behavior, a SIGNAL process is translated into a system of polynomial equations over Z Z= 3Z Z [7]. The three possible states of a Boolean signal X (i.e., present and true, present and false, or absent) are coded in a signal variable x by present and true 3 1, present and false 3 À1, and absent 3 0.…”

Polyhedral Analysis for Synchronous Languages

“…model checking). For instance, model checking has been used at an industrial scale to Signal programs to check properties such as liveness, invariance and reachability [5]. Whereas model checking efficiently decides properties of finite state systems, the use of techniques from static analysis enables to prove properties about infinite state systems such as properties on the linear relations between numerical quantities in the system.…”