Modeling of electromechanical systems
Introduction
Power balance is a basis for stable operation of power system , which is frequently disturbed by some factors such as faults and intermittent power generations. These threatening behaviors may lead to oscillation between the generating units and the interconnected systems, and even worse, which probably cause serious large-scale blackout in power system. Currently, one of the principal methods solving the power imbalance is to reserve adequate spare capacity for the system, which not only increases the investment, but also reduces the utilization of electrical equipments. With the development of energy storage (ES) technologies, a new way of utilizing energy storage technology to solve the power imbalance has been paid more and more attentions. From state-of-the-art technologies of ES, a great variety of the technologies have been developed. However, from a viewpoint of power system operation, the technologies of ES at least need to have the following features: large capacity, fast power response speed, high efficiency, long service life, low operation cost and environmental friendship, and so forth. In terms of these requests, most of ES technologies are still immature except pumped-storage. A new method utilizing spiral springs as ES medium is proposed in reference , which is called mechanical elastic energy storage (MEES); some of the basic characteristics for the technology are discussed in . Due to the benefits of small size, low loss, and high efficiency, permanent magnet synchronous motor (PMSM) is chosen as the servomotor for the MEES system. Thus, the MEES system, which is integrated by the mechanical device (spiral springs and the correspondingly coating shell), the electrical installation (PMSM), and relevant control information elements, is a typically complex nonlinear system of electromechanical coupling. Parameter coupling, which is induced between electromagnetic parameters of PMSM and mechanical parameters of spiral springs, may affect the dynamic performance of the system. The preexisting studies have shown that revealing the law of electromechanical interaction from the point of view of energy is an effective solution to research dynamic characteristics of complex electromechanical system. Lagrange-Maxwell equation of flywheel energy storage is deduced in reference by calculation of integral of magnetic density in the area of magnetic field.
The modeling and control of complex dynamic systems are the rapidly emerging researching topics [16], especially for the nonlinearities in the systems . The paper concentrates on modeling and decoupling control of complex PMSM based MEES system in detail. The mechanical device is taken into account in the analysis of electromechanical coupling, which can make the research become closer to the reality. Especially for the mechanical spiral springs with a big quality and large inertia, neglecting their influence will make the results inaccurate, even unavailable. The overall aim of the paper is to model and control the complex electromechanical system based on the characteristics of mechanical spiral springs in order to improve the operating stability of the system; in particular, the main innovative points of the research are represented as follows:(a)previous researches mainly focus on the motor ontology for the electromechanical issue; the difference in the research is to consider the mechanical device as a node in generalized coordinate system; the terse nonlinear dynamic model for a complex electromechanical system is deduced and constructed through Lagrange-Maxwell energy method by the principle of electromechanical coupling.(b)the generalized coordinates of MEES system are determined. The functions of the kinetic energy, magnetic energy, the potential energy, and the energy dissipation of the whole system are obtained, and the differential equations with electromechanical parameters of MEES system are established by applying the extended Lagrange-Maxwell equation.(c)the theory of direct feedback linearization (DFL) is applied to decouple the nonlinear model and convert the developed model for MEES system from nonlinear to linear. An optimal linear controller is designed to accomplish the speed tracking control for the linearized model.
The paper is organized as the following: it starts with introductions to the ES technologies and the electromechanical characteristics of MEES system in Section 1. The constitution and operating principles of the MEES system are described in Section 2. Mathematical modeling of electromechanical coupling for the complex MEES system is deduced in Section 3. In Section 4, DFL based decoupling control of the dynamic model is proposed, and an optimal linear controller is designed to accomplish the speed tracking control for the linearized model. Section 5 gives the results of numerical simulation. Finally, the conclusions are summarized in Section 6.
Preliminaries and Problem Description
Constitution of MEES System
In order to give the readers a better understanding of the operating principle of the research object, the composition scheme of MEES system served by PMSM and bidirectional converters is described in Figure 1.
Figure 1
The composition scheme of MEES system served by PMSM and bidirectional converters.
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PMSM based MEES system consists of several elements: ES box (multiple spiral springs wrapped up in it), gear box, PMSM, bidirectional converters, breaker, and controller. Therefore, the electromechanical coupling is caused by the interaction between electromagnetic parameters of PMSM and mechanical parameters of spiral springs. A MEES power station can be built by getting tens or even more units together. Through a central controller, the units in the power station can be controlled orderly to realize the goal of large-scale energy storage and power generation. It is important to note that a linkage form structure for ES box is proposed in order to increase the energy storage capacity; for details see [13].
Operating Principle of MEES System
The basic operation principle of the MEES system is concerned with two processes: energy storage and power generation. The load or drive source of MEES system in energy storage or power generation is spiral springs in ES box. In the process of energy storage, PMSM, which is driven by power grid, tightens the springs through gear box. Then, the electric energy is stored in the form of elastic deformation energy. Once the unit receives a signal of releasing energy, the tightened springs start to release energy and drive the motor to generate electricity.