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 (CPSs). CPSs have computational and physical elements. System 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. CPSs revolutionize several domains including energy by transforming a traditional electric power grid into a smart grid. The existing electric power grid has components for generation, for transmission, and finally for distribution of electric power to large and small users. Power flows from generation components over transmission components to distribution components, servicing large commercial and public facilities as well as our homes. Growth in demand is responded to by augmenting the grid with additional generation, transmission, and distribution capacity. This enhanced capacity is costly and takes years to provision. Failure to accurately predict growth in demand or inaccurate estimates of grid performance can lead to excessive and unnecessary cost or inadequate capacity. Finally, awareness of the impact of less than optimal operation of the power grid and of the impact of continued use of fossil fuels for generation has increased.As a result, leadership and the public are increasingly interested in alternative approaches to meeting demand for electric power. In response to this interest, we see more and more a willingness to reshape our electric power “grid” as a “Smart Grid.” The proposed changes challenge traditional approaches to grid infrastructure and organization. The “smartness” of the Smart Grid consists in two distinct innovations. The first involves our integrating new technologies into the power grid and the second involves our radically changing the ways that grid elements relate to one another. A Smart Grid manages distributed generation and bidirectional power flow. In the Smart Grid, each new component could potentially affect the performance of many other elements of the grid and so we must have a means of expressing and evaluating proposed grid innovation.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.