# Modeling and Simulation in Multibond Graphs Applied to Three-Phase Electrical Systems
## 1 Introduction
The energy management architecture model using a complete supervisory control and data acquisition system in a educational building was presented in [16]. An energy management system applied to isolated micro grids was proposed in [17], wherein they apply a PID controller which contains coordinate transformations from \((a,b,c)\) to \((d,q)\). When considering a renewable power system and its control, full modeling can be challenging because the system will have different energy domains. For example, if the system is the interconnection of thermoelectric, hydroelectric, wind turbines and photovoltaic panels as sources of generation, their transmission and distribution to electrical loads, then there are electrical, mechanical, thermal and hydraulic subsystems, subsystems for control as well as three-phase systems, due to which factors the bond graph is a system modeling methodology that can be applied to the systems formed by different energy domains. Likewise, the analysis and control of systems in the bond graph are direct and physically achievable. In addition, the modeling of systems with multiple phases or axes has been solved with multibond graphs which are vector bond graphs. The bond graph theory is based on an approach to modeling power transfer through ports called bonds. In this way, a structured approach to modeling dynamic systems is presented in the bond graph. The main characteristics of the bond graph can be stated below: (1) The bond graph allows the modeling of systems formed by different energy domains (electrical, mechanical, hydraulic, thermal, magnetic); (2) Through the causal information, the relationship between the elements of a system is known, determining mathematical models in transfer function or in state space, likewise, structural properties such as stability, controllability and observability can be directly obtained in the bond graph model without requiring its mathematical model; (3) Linear and nonlinear, invariant and time-varying systems with lumped distributed parameters can be modeled in a bond graph; and (4) Controllers can be designed in a bond graph environment. The modeling of robots, cars, projectiles or multi-axis systems often leads to complicated mathematical models. Even in bond graphs, these systems can result in models that cannot easily apply the methodology and its applications in the physical domain. Thus, the introduction of multibond graphs as an extension of bond graphs turns out to be a natural way to model multibody systems. In modeling with multibond graphs, single bonds are grouped into multibonds. Likewise, the generalized power variables of effort and flow in bond graphs are now vectors of effort and flow in multibond graphs whose matrix product determines power. Some papers on fundamentals and application with multibond graphs have been published, some of which are cited below: the basic concepts in the modeling with multibond graphs of physical systems are proposed in [18]. The causality assignment in vector bond graphs is introduced in [19]. The modeling of mechanical systems with multibond graphs was developed in [20]. The decomposition of multibody elements such as resistors, inertias, capacitors, transformers and gyrators into their equivalent in junctions, bonds and 1-port and 2-port elements was presented in [21]. Recently, some developments with multibond graphs have been published, and the representation of electrical circuits of phasors containing real and imaginary parts with two-dimensional multibond and steady state was proposed in [22]. The linearization of a class of nonlinear systems that can be modeled with multibond graphs was presented in [23]. The direct determination of the steady-state response for LTI systems modeled with multibond graphs with a derivative causality assignment to the storage elements was proposed in [24]. In this paper, the modeling of three-phase electrical systems in coordinates \((d,q,0)\) is presented.