Power and Energy System Modeling Based on Modified Tellegen Principle

The chapter deals with a problem of power and energy modeling of dynamic systems and their numerical solutions. The proposed approach is based on modified Tellegen’s theorem well known from electrical circuits solving. The new of this approach is that it is based on the power calculation for different linear and nonlinear physical systems. It is supposed that system is described by state space equations and from these equations the power and energy are calculated. The results can be used for electrical circuits, but also for other real physical system e.g. mechanical systems, heat transfer etc. which are described by state space equations. Thus, mathematically as well as physically correct results are received. Certain known and often used system representation structures are used and their transformations. The theory is supported by solved examples. The mathematical origin, derivation and results of simulations are given in this chapter. It is important mark here a close relationship between first and second Kirchhoff’s laws ensuring physical rightness and link to Tellegen’s theorem. It is also important to note that inner product incorporate instantaneous power dissipated on resistors and instantaneous power on inductors and capacitors. At last, let’s note that Tellegen’s principle can be used not only to electrical circuits but as well any model of a physical correct system with lumped parameters. Therefore if the system is described accurately by state space equations, currents and voltages can be substituted by state space variables and it’s derivations. In the chapter, the nonlinear differential equations of linear and nonlinear systems are numerically solved and optimization methods are used in some circumstances. The examples in chapter include also solution of chaotic systems. It is important to note that solution in this chapter is based on power and energy and therefore can be useful also for modeling some devices used in renewable power systems e.g. batteries, capacitors and ultracapacitors, photovoltaic panels etc.