A Synergetic Approach to the Modeling of Power Electronic Systems

We introduce the Synergetic approach, which brings great improvements in computer modeling and simulation of power electronic systems. Essentially, the process involves synthesis of control laws that result in collapse of (at least two) initially high-dimension models into a single model of lower-dimension. The technique requires creation of state space attractors, artificial manifolds, that reflect the desirable operating regimes of the dynamic system We explain the process and give example results. INTRODUCTION The synergetic approach, used in the Virtual Test Bed (VTB) project as a basis for synthesizing control laws for power systems, brings great improvements in the computer modeling of dynamic systems. Synergetic control theory helps in the modeling of power electronic systems in the following way: Properly synthesized synergetic control strategies inevitably decompose a system that is initially described by several high dimensional models into a hierarchical succession of asymptotically stable lower dimensional models. As a result, it is possible, for instance, to collapse several complicated components of a system model into a single component described by much simpler equations. In the modeling of controlled power electronic systems there are tasks and features that are essentially different from those handled by traditional electric circuit modeling and simulation tools. These differences arise from the fact that controlled systems are described not only by the systems of differential equations of the circuit elements, but also by the differential equations that describe the control laws of the system. Such control laws reflect the corresponding control strategies and directly influence the behavior of the collective system. The necessity of including the control laws into the power system object models leads to new tasks, which include the following: • Developing methods for understanding the parametric and structural robustness (insensitivity) of the objects and the control laws. As part of the modeling, it is necessary to address the question of how the simultaneous drift of either the object’s and/or the regulator's parameters influence the dynamic stability and the dynamic qualities of the power system. • Developing methods to determine the connective stability of the power system in general and of its parts (groups, zones, subsystems). As a result of modeling, we have to answer the question of how spontaneous commutations and new links influence the stability of the power system. PRINCIPLES OF SYNERGETIC CONTROL The Synergetic approach gives rise to a new ideological principle: even for a power system, control is a directed process of converting power, matter and information so as to ensure optimal functionality. This principle reveals the target orientation of control laws and deeply changes the emphasis of modeling by focusing attention on the result more than on the process. Control, as a measure of purposeful influence of a person on a power system and as a reflection of his aims and requirements, should weave together all the aspects of the system’s work as a whole. The same is true for its separate elements. In the VTB project, based on the synergetic concept of dynamic interaction among power, matter, and information, we have developed an applied theory for synthesizing vector regulators for nonlinear power systems. Synergetic Control Theory is a new direction in control science based on the principles of directed self-organization and the use of the natural nonlinear qualities of dynamic objects. The basic principles of synergetic control theory are as follows. 1. Artificial attractors – invariant manifolds – are formed in the state space of the object. On these attractors, we ensure organization of the desired dynamic and static qualities of the controlled objects. Formation of the attractors is the reflection of a directed self-organization process. 2. The dominant principle of synergetic synthesis methods is the principle of compressiondecompression of the phase flow of the controllable systems. 3. The developer’s requirements are presented in the form of a system of invariants (technical, power, electromagnetic, etc.) which describe the desired operating modes of the controlled objects. Attractors created in the state space of the object simplify the modeling process by ensuring a radical lowering of the dimensionality of the comprehensive nonlinear model that describes the dynamic characteristic s of the controlled subsystem and of the power system in general. As a result, it is possible to model the entire system though a single subsystem defined by the decomposed system of equations, the dimension of which can be found according to the following: m k n A * dim − = , where: A dim dimension of the decomposed system; n dimension of the initial system; m dimension of the control vector; and k number of sequentially used attractors. EXAMPLE APPLICATIONS Inverted Pendulum As a first example, consider the following equations that describe an inverted pendulum. Due to its distinctive features this model has became a sort of test problem for control theory methods − from classical linear methods based on PID regulators to the modern ones based on Fuzzy Neural Networks: