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Shortcut from electrical networks to Petri nets
Marcel Chevalier, Laurent Buchsbaum, Nicolas Argaud
To cite this version:
Marcel Chevalier, Laurent Buchsbaum, Nicolas Argaud. Shortcut from electrical networks to Petri
nets. QUALITA’ 2015, Mar 2015, Nancy, France. �hal-01149783�
Shortcut from electrical networks to Petri nets
Marcel Chevalier / Laurent Buchsbaum Analytics for Solutions / Global Solutions
Schneider Electric Grenoble, France F-38050
Marcel.Chevalier@Schneider-Electric.com, Laurent.Buchsbaum@Schneider-Electric.com
Nicolas ARGAUD Master MSID
Université de Pau et des Pays de l’Adour Pau, France F-64000
N.Argaud@LaPoste.net
Abstract—In this paper, we present a methodology to automatically derive a Petri net from a single-line electrical network. This Petri net is used to simulate the behavior of the electrical network on a given time interval, operation which we can iterate, enabling us to compute some dependability characteristics on the network (typically, the unavailability of different elements in the electrical network, and their contribution to the overall network unavailability).
Index Terms—Petri net, electrical network, dependability.
I. INTRODUCTION
In an industrial environment, the managers of electrical networks can face different situations, such as modernization plans for the electrical network infrastructure, or a management of several plants dispatched on different continents, while taking into account local habits.
Moreover, needs for maintainability and exploitation optimization are always increasing, together with cost reduction linked to electrical network distribution management.
Finally, people are more and more interested in minimizing the risks for production loss, due to electrical outage.
The work we introduce in this paper is part of the MP4 methodology [1] [2], which allows studying deeply an electrical network distribution infrastructure, in a 4-step scheme:
- Specification of needs for electrical energy, and assessment of actual capacity of the considered plant;
- Assessment of the equipments and the robustness of the electrical network, by identification of the stress for each device, and modeling of the electrical power availability;
- Computation of a criticality index for each device, part of the electrical network;
- Identification of the Service policy best suited for the electrical installation, including the list of critical points for personal safety, and the action plans to improve the current performance of the electrical network.
II. DEPENDABILITY ASSESSMENT
In the second phase described here above, we use a tool able to derive a mathematical model of the electrical network,
in order to study the dependability characteristics of the electrical installation.
As an example, let us consider the following electrical network (fig. 1):
Figure 1: example of electrical network
This picture describes the different ways the red busbar at the bottom can be fed with electrical energy, these different ways being highlighted by orange lightning, as showed on the zoom hereafter:
Figure 2: zoom on electrical network
The busbar located immediately above-left of the red busbar, presents a k-out-of-n redundancy. Specifically, this busbar if fed by 8 different energy lines, but it is declared to be operational as soon as 6 of them are able to carry the electrical energy to it. We say that this is a 6oo8 redundancy, meaning 6 out of 8 lines are sufficient to feed the busbar with electrical energy.
The busbar located immediately above-right of the red busbar, presents also a redundancy, but here, we have a 2oo2 redundancy, that is to say that we will consider the busbar energized whenever the 2 electrical lines above it will provide energy.
This type of redundancy is automatically handled in the tool, which provides automatically the corresponding fault tree for the electrical network [3] [4]. As an example, this is the fault tree automatically derived from a real example:
Figure 3: fault tree generated automatically This step allows easily computing a forecasted unavailability for the energy on the final red busbar.
If we iterate the computation for each critical point in the electrical network, we can compute the contribution of each device to the unavailability, and classify them according to their contribution. Here after, we present an example of such a classification:
Figure 4: contributions to the system availability Together with the results of the stress analysis, and combined with a matrix approach, we are able to derive the optimal maintenance policy for all the equipments in the electrical networks.
III. LIMITATIONS OF FAULT-TREE METHOD
Up to 2014, this automatic computation step has been based of the Fault Tree methodology, but this technique presents some limitations:
- As it makes a picture of the installation, it assumes the installation will not change its structure, whereas a real electrical network may experience some new configurations in case electrical links are broken, and we must transfer the energy using another way;
- When used in high-reliability domains such as hospitals, electrical networks often embed batteries to be able to supply immediately electrical energy when experiencing electrical outages. But these batteries have limited capacity in time, which are difficult to model with fault trees.
When trying to overcome these limitations, we have tested the Petri nets methodology. We present here after this experiment.
IV. THE PETRI NET APPROACH
Rather than transforming the electrical network into a fault tree, we have tried to transform the electrical network into a Petri net, in order to be able to simulate its behavior on a given time interval, and iterate this step a given number of stories, to allow computing statistical results on the electrical network.
This has been done through:
- The construction of an electrical components library (batteries, busbars, circuit breakers, cables, electrical supplies);
- The implementation of an algorithm able to build automatically a Petri net, corresponding to a given electrical network;
- Some statistical studies on the obtained results.
A. Example of electrical network
Let us consider a network made with a Supply source (the grid), a transformer (T1), a first busbar (JdB1), a second one (Util), a circuit breaker (D1) normally closed in normal situations, and a specific load (CP1), as described in the picture here after.
Figure 5: second example of electrical network In this network, we assume we are interested in the mean total time of unavailability of the “Util” busbar, and in the contribution of each equipment to this unavailability.
B. Electrical components
We have considered three different types of components:
- The sources, including the grid, generators, batteries and capacitors;
- The links, including cables and busbars;
- The devices, including transformers, circuit breakers, fusibles, sectioning devices, switches, fusible-switches, contactors and loads.
For each of these components, we have developed its corresponding Petri net, which takes into account all the states the product may experience (operation, failure, destruction, short-circuit [transient state], short and long outage [for sources], unwanted closure or opening [for circuit breakers]).
As an example, we present in the picture here after the modeling of the different states for a cable [in French];
Figure 6: Petri net modeling of a cable
Thus, most of the time, the token is located in the first place, at the top of the picture, indicating that the cable is operating correctly. But when a failure happens, this token is transferred to one of the three intermediary states (numbered
“2” to “4”), depending on the type of the failure, which will result either in a simple failure (place #2), the total destruction of the cable (place #3), or an internal short circuit (place #4).
Finally, when repaired, it will go back to place #1, here above duplicated for easier readability.
C. Connection of components
To model the electrical network, the tool picks in the component library the Petri net corresponding to the elements of the network, with their internal variables indicating their state at a given time.
Then, it studies which component is linked to another component, and for these two components, applying usual rules in electrical engineering, it merges their internal variables, whenever relevant.
An example of such merging is described in the picture here after, representing a little part of an electrical network, made with a source of energy (S1), a circuit breaker (D1) and a cable (C1), all of three connected in line. The left side of the picture shows all the variables associated with the three elements S1, D1 and C1. To connect these devices, we have to merge some downstream variables of a product, with some upstream variables of another product, to represent the real electrical connections; the right side of the picture shows how the corresponding variables have been merged to fulfill the electrical engineering rules. We can notice that some variables have been kept alone: this derives from the different types of elements, which can experience different states in their operating life, and may generate some particular events outside this little part of the electrical network.
Figure 7: merging of variables in the Petri net At the end of this process, we get the complete representation of the electrical network in a Petri net form, allowing to simulate it within a given time interval.
V. PLAYING THE PETRI NET
To simulate the Petri net, we must indicate the statistical distribution we assume for the different states and for all elements in the network.
Basically, and in accordance with wide-agreed rules, we have focused on three main distributions:
- Dirac distribution, relevant for modeling fixed delays, such as a battery autonomy;
- Exponential distribution, relevant for failures and repairs, and for circuit breaker operating delays;
- Weibull distribution, relevant to model the survival time of components, in case of over-intensity.
These statistical distributions and the corresponding parameter values have been described directly in the tool, simplifying the work for modeling, but can easily be changed in case of evolution.
Then, we have to define the time window in which we will simulate the Petri net, for example 20 years, if relevant for the electrical installation we are studying. Finally, and in order to compute statistics, we will define a number of stories, i.e. the number of simulations we will perform for the network, to be able to experience virtually the greatest number of foreseeable situations [5] [6] [7] [8].
As an example, we have considered the network described in section IV-A, which we have simulated on a 400 000 hours period (equivalent to 45 years of operation), and a thousand times. This has resulted in the corresponding figures:
Figure 8: component contributions to unavailability
What we see here is that on a 400 000 hours basic period, we can forecast around 70 hours of unavailability. Moreover, we can easily identify that two main elements contribute to this unavailability, and derive the corresponding maintenance plans, given the complementary elements for maintenance (price of spare parts, criticality of failure, etc.)
These results complete those obtained by the fault tree approach, which provides the minimal cutsets of the system, highlighting the weaknesses of the electrical network. Because the Petri net model takes into account some particular behaviors of the network, the corresponding quantitative results will be closer to what is expected as unavailability value for the electrical network in operational conditions.
Concerning the computation time, the above cited simulation has been conducted in the GRIF / MOCA-RP software [9] within a 2-minutes timescale. For more complicated electrical networks, the computation time may be much greater: this is why we are still working on the optimization of the electrical network transcription in Petri nets.
At the end of this process, we expect to deliver this software program to the operational teams, dedicated to the analysis of electrical networks. We therefore plan to improve the quantitative approach of our operational colleagues, who have already conducted more than 400 evaluations for more than 200 industrial sites, in food and beverages, automotive, building, oil and gas, mining, health or infrastructure domains.
VI. RESULTS AND CONCLUSION
The work presented in this paper is the first step to build an automated environment to model electrical networks behavior with Petri nets, but it currently allows to model simple networks, derive their unavailability, and compare this result with the one obtained with fault tree method, providing elements of reflection for improving maintainability of the network.
With an extra work on robustness, we plan to include it in the day-to-day work of service engineers, whose methodology has been deployed on 450 different plants, representing 450 electrical network assessments in many industries, including food and beverages, automotive, building, oil and gas, mines, health care or infrastructures. It has allowed reducing the risks for people safety, together with the financial risks linked with critical electrical installation outages.
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