O. Wasynczuk

Dynamic Behavior of a Class of Photovoltaic Power Systems

An important consideration in the operation of grid connected photovoltaic power systems is a means of adjusting the photovoltaic array voltage so that maximum output power is achieved for the given atmospheric conditions. The dynamic behiavior of a specific photovoltaic power system which utilizes the well known perturb and observe method of power tracking is examined. Using measured insolation data, it is demonstrated that the perturb and observe method of control migrates considerably from peak power whenever the insolation varies randomly as a result of cloud cover. An alternate method of power tracking is also examined. It is shown that the photovoltaic power system, utilizing the proposed method of power tracking, is able to track accurately peak power conditions during periods of randomly varying insolation.

Dynamic Behavior of a Class of Wind Turbine Generators during Random Wind Fluctuations

Common in the design of wind turbine generators of the multi-megawatt size is a soft shaft in the low speed part of the drive train. The presence of the soft shaft gives rise to a low frequency torsional mode involving an oscillation where the hub and blades swing relative to the generator. It is shown that normal wind variations can excite this mode resulting in large oscillatory fluctuations in the drive train torques as well as in the generated electric power. Methods of improving the dynamic performance are examined.

Modeling and Dynamic Performance of a Line-Commutated Photovoltaic Inverter System

Interest in utility-interactive photovoltaic (PV) inverter systems has increased over the past decade and numerous central-station PV systems have been installed. It is anticipated that as PV system costs decrease, residential systems will be installed in increased numbers. Although a substantial amount of literature is available concerning the design, protection, safety, economics, and operating experience of residential and central-station PV systems, little information is available regarding their dynamic electrical characteristics and the computer modeling of these systems. Moreover, most of the available literature concerning modeling and/or dynamic performance focuses either upon the long-term dynamic behavior as it affects power system scheduling or upon the steady-state harmonic characteristics. In recent work, highly detailed computer models of a representative set of PV systems have been developed and several of these models have been verified by comparison with system measurements [1, 2]. However, the models described in [1, 2] are more complex than necessary for large-scale power system studies in which the fast switching transients associated with the dc-to-ac inverter are of little concern and only the slower cycle-to-cycle behavior of the PV system is of interest. In fact, it is not possible to incorporate these detailed models into conventional transient stability programs due, in part, to the very small time-step requirements associated with these models. In this paper, a three-phase line-commutated utility-interactive photovoltaic inverter system is investigated. A schematic diagram of the selected PV inverter system is depicted in Fig. 1.

Damping Subsynchronous Resonance Using Reactive Power Control

The IEEE benchmark system is used to demonstrate a method of damping subsynchronous resonance using a set of phase controlled reactors connected to the machine terminals. It is possible to prevent one mode of instability by modulating the reactive power consumed by the reactors in proportion to the change in generator speed. However, it is shown that this previously Suggested method of control is ineffective in damping all possible modes of instability of the benchmark system due to subsynchronous resonance. Methods of control are established which can be used to damp all critical modes of instability using a set of phase controlled reactors

Theory and Comparison of Reduced Order Models of Induction Machines

Three methods of deriving linearized, reduced order models of induction machines are presented and compared. The first is the familiar method of neglecting stator transients (p¿terms). Although the development of the second method is similar to the first, it yields a model with substantially different dynamic characteristics. In the third method, only the fast components of the stator flux linkages are neglected in the solution of the slower rotor variables rather than neglecting the rate of change of stator flux linkages (p¿terms). This refinement markedly improves the accuracy of the resulting reduced order model. The improvement is demonstrated by comparison of the response characteristics predicted by the three reduced models with that predicted by the complete or detailed model.

Analysis of a Permanent Magnet Synchronous Machine Supplied from a 180° Inverter with Phase Control

Reference frame theory is used to establish the equations which describe the steady-state and dynamic behavior of an electric drive system consisting of a permanent magnet synchronous machine supplied from an inverter operating in the 180° conduction mode and with provisions to shift the phase of the stator voltages relative to the rotor position. An expression for the phase-shift angle which yields maximum torque is derived. It is shown that a comparison of the stator time constant and the no-load rotor speed without phase shift, can be used to anticipate the increase in average torque achievable by phase shifting. It is also shown that advancing the phase of the stator voltages advances the phase of the fundamental component of the stator phase currents relative to the phase voltages. A method of calculating the steady-state harmonic currents and torque is also given. The information given in this paper should serve as a guide for the operation of brushless dc motors and the design of speed or position controls that employ phase shifting techniques along with or instead of pulse width modulation.

Analysis and Modeling of a Single-Phase Brushless DC Motor Drive System

Brushless dc motors are becoming widely used in low-power applications such as blower motors, computer disk-drive spindle motors, and in copiers and laser printers. For these applications, the brushless dc motor offers the following advantages: small size, reliability, no carbon dust from brushes, precise speed control, and potentially high efficiency. The most commonly used brushless dc motors are twoor three-phase permanent-magnet ac machines driven by a dc-to-ac inverter. The three-phase machine combined with a six-pulse full-bridge inverter often represents the best trade-off of machine iron and copper utilization with the cost of the inverter. Because of the prevalence of two-and three-phase devices, they are the brushless dc motors which have been analyzed the most extensively. On the other hand, there has been little investigation into the operation of the single-phase brushless dc motor. Single-phase motors, in general, suffer from slower starting characteristics, less efficient utilization of machine iron and copper, and higher losses. Therefore, single-phase motors are limited to low-power applications where rapid response and high efficiency are not required. The primary advantage of single-phase devices is the simplified source requirements. For example, a single-phase brushless dc motor requires only one-third the number of transistors and position sensors needed by a three-phase motor and can be powered by a single dc voltage source. Thus, in applications where cost is of greater importance than performance, the single-phase motor may be a superior alternative to a two-or three-phase motor.

Solution of State Equations in Terms of Separated Modes with Applications to Synchronous Machines

Using a special linear transformation, a linear time invariant state model can be changed into a new form defined as the separated mode model. As this transformation is repeated, the state model tends to be separated into two decoupled or independent parts. Each of them is a lower dimensional state model. The solutions of the two are the fast and slow components of the original state model respectively. Applying this approach to induction and synchronous machines, new linearized reduced order models are obtained. Computation results have shown that the new models have lower dimension and higher accuracy than the common one which neglects stator transients (p¿ terms).

A Finite Element based State Model of Solid Rotor Synchronous Machines

In this work, a state model which portrays the dynamic electromagnetic characteristics of a synchronous machine is derived based upon the first order finite element method. The method of finite elements is used to determine the axial component of magnetic vector potential throughout the cross section of the machine. Algebraic relationships between the winding voltages and the magnetic vector potentials are derived. These are used to establish a state model which admits winding voltages as inputs. The resulting model consists of a set of first order, ordinary differential equations which predict vector potentials at grid nodes along with the winding currents as time proceeds following arbitrary disturbances in stator or rotor voltages. As an initial verification step, this method has been applied in two linear examples. The first involves a simplified geometric representation of the synchronous machine for which an analytical solution of the defining field equations can be obtained. The second involves a more detailed geometry which includes stator and rotor slots. Numerical solutions are shown to be in excellent agreement with analytical solutions for the simplified structure. In the detailed geometry, numerical solutions are shown to compare favorably with the classical equivalent circuit representation.

A Refined Method of Deriving Reduced Order Models of Induction Machines

A refined method of deriving non-linear, reduced order models of induction machines is presented and evaluated. This method differs from the classical method of neglecting stator transients (p? terms) in that only the fast components of the stator flux linkages are neglected when solving for the slower rotor variables. The accuracy of the refined model is assessed by comparing its transient characteristics with those of a detailed model and the standard reduced order model obtain by neglecting the stator transients. It is shown that the refined model more closely approximates the lower frequency characteristics of the induction machine following both large and small disturbances than the standard reduced order model.