# Interpreted Petri Nets Applied to Autonomous Components within Electric Power Systems
## 3 Modeling Autonomous Components within Power and Energy Systems with Interpreted Petri Nets  
The proposed methodology for modeling the autonomous components within power and energy systems is briefly illustrated in Figure 3 and includes six steps. The schema graphically shows the proposed flow and is strongly connected with Algorithm 1. First, output signals corresponding to system states should be specified. They are used to indicate the current system states (e.g., operation mode or progress in algorithm realization). Then, input signals corresponding to conditions should be defined. They are used as triggers between system states and indirectly influence the property of determinism (q.v. Definitions 6 and 7), which will be shown subsequently. Next, the structure of an interpreted Petri net can be created. It is used as a basis specification, which is supplemented by the defined input and output signals. It influences directly the properties of liveness, safety, and reversibility (q.v. Definitions 2-4). Output signals are assigned to places and used for activating appropriate signals related to the current status of algorithm realization. Figure 2: A sample Petri net (**a**), an interpreted Petri net (**b**), and signals description (**c**). In other words, the particular output signal assigned to a place is active as long as that place contains a token. Input signals are assigned to transitions and used as conditions for their particular firing, and they indirectly influence the property of determinism (q.v. Definitions 6 and 7). If the guard of a transition is fulfilled and its input place(s) contain(s) a token, the transition may be fired. Finally, we obtain the interpreted Petri net, which can be analyzed and formally verified, focusing especially on such properties as liveness, safety, reversibility, and determinism, which can be treated as performance indicators. Formally, construction of an interpreted Petri net for autonomous components within power systems, focusing in particular on the control aspects, can be realized following Algorithm 1. The starting point is an informal specification, while the result is a properly formed interpreted Petri net. The algorithm realizes steps 1-5 of the proposed modeling methodology, formally defining step 1 (line 1), step 2 (lines 2-5), step 3 (lines 6-8), step 4 (lines 9-11), and finally, step 5 (lines 12-16). As a result, an interpreted Petri net is returned (line 17) that can be analyzed and verified (step 6). The structure of the constructed interpreted Petri net (the result of step 3) directly influences the properties of liveness, safety, and reversibility (q.v. Definitions 2, 3 and 5). In order to achieve a live net, no deadlock can occur. In order to achieve a safe net, all places may contain at most one token. In order to achieve a reversible net, the initial marking has to be reachable from any other marking. The property of determinism is directly influenced by the structure and input signals which are assigned to transitions. If two transitions with a common input place have non-exclusive conditions, it is not known which of them will be realized if both conditions are true (illustrated in Figure 4a: if \(x1=1\) and \(x2=1\), either transition \(t1\) or \(t2\) will fire). Figure 3: The schema of the proposed modeling methodology.