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The Algebra of Systems and System Interactions with an application to Smart Grid



Charif Mahmoudi, Hasnae Bilil, Edward R. Griffor


Systems are integrations of devices or component elements and even other systems. The notion of a system comprehends engineered and biological or mechanical or physical systems. Examples include information and dynamical systems as well as integrations of the two, sometimes called cyber-physical systems (CPS). Cyber-physical systems have computational and physical elements. Systems integration allows us to build more complex or compound systems from given ones. In such systems, computers and measurement devices are combined to deliver functions that may impact or influence the physical elements. Feedback loops are used where physical elements influence in turn computational elements and vice versa. Applications of CPSs have an economic and societal potential that goes beyond what has been realized. CPS revolutionize several domains including energy by transforming a traditional electric power grid into smart grid. In this chapter we will focus on CPS, rather than general systems, for the sake of clarity and we propose a language for expressing the elements of a CPS and an operation of ‘composing’ CPS elements that we will show is a simple algebra that is capable of helping planners and engineers design and test the CPSs of the future. That will enable planners and engineers to design, and ultimately simulate, the composition and the integration of CPSs such as grid system. This ‘CPS algebra’ is based on a formal language that offers the expressive power needed to capture the observable behavior of CPS components, allows the composition of existing CPSs, and supports a methodology for the study of critical properties of the CPS such as safety and security, properties that are especially important for critical infrastructure such as the electric power grid. We will give examples of the resulting smart grid algebra, using a model of smart grid simplified for our purposes here.
Handbook of System Safety and Security, 1st Edition
Publisher Info
Elsevier Inc, Rockville, MD


Algebra , Cyber-Physical systems, Smart Grid


Mahmoudi, C. , Bilil, H. and Griffor, E. (2016), The Algebra of Systems and System Interactions with an application to Smart Grid, Handbook of System Safety and Security, 1st Edition, Elsevier Inc, Rockville, MD, [online], (Accessed May 24, 2024)


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Created October 14, 2016, Updated November 10, 2018