INVESTIGATION ON SIX-PHASE SELF-EXCITED INDUCTION GENERATOR

Abstract

Multi-phase /high phase number (more than 3Φ) systems are potential alternative to their three phase counterpart systems in respect of various beneficial advantages for high power electric applications. The affectionate utilization of renewable /non-conventional energy resources in fuel redemption had a need of low cost and appropriate generating systems in enlivening the small /large scale industrial applications and variety of future energy demands. Stand-alone /isolated induction generators are attractive substitutes having numerous relative advantages over the well-known synchronous generators in electric power generation in conjunction with non-conventional energy resources. The cost effective utilization of advantageous features during isolated mode in induction generator technology had opportunity to supplement the electric power from different site resources to underprivileged far-flung and remote areas. So, investigation on six-phase self-excited induction generator (SP-SEIG) has taken place during past decades for exploiting the propitious features of multiphase machines conjointly stand-alone self-excited induction generators (SEIG) in the area of non-conventional energy generation for being a viable alternative over other generating systems. Apart from literature, which interpret correlations among the machine parameters and variety of variables in multi-phase (six-phase) isolated mode of SEIG, further, efforts are made to draw special attention to highlight other potential issues related to the use of SP-SEIG (when both 3-Φ sets are designed with 30° displacement and their neutrals are isolated) in aspect of present and future development. As compared to existing new methodology, conventional techniques used during last several decades focus on modelling and analysis of SP-SEIG to analyze the steady state and dynamic performance of simple and compensated SP-SEIG during balanced /unbalanced conditions. Steady-state study is needed for ensuring good quality power and assessing the suitability of different configurations of SEIG. Transient behaviour during dynamic analysis provides the knowledge about the suitability of capacitor ratings, machine winding, and its insulation level for protection purpose. Small signal stability analysis is requisite to deliberate the stability of proposed system when each machine variable goes through small disturbances from its reference value by using popular techniques. An appropriate controller design and analysis is also carried out on simple SP-SEIG during consumer load variations for ensuring good quality power delivery in small reasonable generating system by a new technique. In steady state analysis, a simple technique along with machine data is contemplated to predict the saturated magnetizing reactance ‘Xm’ and per-unit frequency ‘F’. The steady state performance deals with a mathematical matrix model of simple and compensated six-phase self-excited (isolated) induction generator (SP-SEIG) using loop impedance method, based on graph theory from its per unit representation of per-phase generalized equivalent circuit, to ii study the comparative steady-state behaviour of different configurations. The machine voltage regulation are enhanced by employing supplementary series capacitors within short-shunt and long-shunt configurations in self-excited induction generator ‘SEIG’. The resultant matrix model is simple and flexible for various future modifications. The optimization of ‘Xm’ and ‘F’ variables of generalized matrix model are performed by using Newton-Raphson ‘NR’ routine based analytical technique for a variety of loading conditions and in different operating modes of fundamental configurations. Further, the computation of optimized ‘Xm’ and ‘F’ value participates in the estimation of various machine performance parameters. Steady state study is also needed for initializing the dynamic and transient simulation. During dynamic analysis, a popular two axis (dq0) model of a saturated simple and compensated multi-phase (six-phase) self-excited induction generator (SP-SEIG) is constructed by park’s transformation using mixed (stator current and magnetizing flux) state variables. The model is characterized with very simple system matrix in which only four elements could be dependent on saturation, when considered. Mixed stator current and airgap flux state space model possesses the advantage of having variable speed operation under variable magnetizing flux level in the machine. Under variable speed operating conditions, flux level in the machine needs to be modelled accordingly that accounts for the main flux saturation. This mixed stator current and air-gap flux as a state-space variables model preserves the information about both stator and rotor parameters. On the other perspective, considerably simpler than d-q axis winding current model and has simple matrix. This saturated machine model is mostly applied in air-gap flux field oriented vector control strategy. In transient behaviour analysis, performance equations in dynamic model utilize the steady state magnetizing inductance ‘Lm’ along with dynamic inductance ‘L’ rather than saturated magnetizing inductance ‘Lm’ and its derivative. During analysis, the effects of common mutual leakage inductance between two three-phase winding sets and cross saturation coupling between d- and q- axis of stator have not been considered. Differential equations has been computed with an explicit MATLAB algorithm for the implementation of 4th order Runge-Kutta ‘RK4’ subroutine. Proper values of shunt capacitor avoid the excessive voltage at the terminals of SP-SEIG under loading condition. A careful value selection of the combination, i.e. shunt and series capacitors also eliminates the enormous terminal voltage when switching the load, and can maintain the no-load voltage because of extra reactive power supplied by the series capacitors. The involvement of series capacitors satisfy the requirement of voltage regulation when load is suddenly switched on after few second and retains the no-load terminal voltage as per self-regulating nature. The stability investigation in this thesis reveals that the eigenvalues are dependent upon the machine parameters and variables. The most critical parameter is the variation in iii magnetizing inductance ‘Lm’, which focuses on stabilization of SP-SEIG. Firstly, Taylor series is applied to linearize the nonlinear equations of the machine; secondly, Eigenvalue basic criterion is used to find out the machine eigenvalues about small deviation using a group of higher order equations from the linearized SP-SEIG model during balanced operating condition. Lastly, the nature and magnitude of eigenvalues are correlated with the machine parameters and variables under no load and different loading conditions which provide a ground in the study of machine stability. So, the eigenvalue behaviour of a six-phase selfexcited induction generator is varied in accordance with small deviations of machine parameters and variables for determining its small signal stability analysis. Further, two transfer functions between the mechanical input torque and small changes in active power and reactive power have also been established to identify the machine stability by graphical means. Generator terminal voltage and frequency are also markedly affected by the excitation capacitor, connected load and rotor speed at renewable energy plants in remote sites or developing countries. On faults due to abrupt reduction in torque during short circuits, machine speed may accelerate and tends towards terminal voltage collapse with the immediate increase in reactive power of self-excited induction generator. So, there is need of control in extreme values of generator terminal voltage and frequency during variations in machine load characteristics or prime mover speed, and also need of speed control during faults in system. For enhancement in voltage and frequency regulation of SEIG, there are others different power electronics aid controllers. Power electronics aid controller are efficient, fast and up-todate which facilitates a new birth and growth in to previous terminal voltage and generated frequency ‘Voltage and Frequency’ control schemes of self-excited induction generator during various operating conditions and /or in variable speed applications of SEIG when there is no governor control in small energy generating plants. Before, voltage and frequency control of 3- phase isolated induction generator was in consideration for researcher, here attempt is control of voltage and frequency of 6-phase isolated induction generator i.e. SP-SEIG. Various isolated /capacitor-excited induction generator control techniques are in practice today. The most simple and popular control technique is by generating variable frequency supply which has constant voltage to frequency ratio. The constant ‘voltage to frequency ratio’ technique is popularly known as V/F control scheme, in which voltage is proportional to system frequency for keeping flux remains constant in control process. Similarly, a constant ‘voltage and frequency’ or ‘V and F’ or ‘volt and hertz’ new strategy controller and its scheme should be designed and formulated, respectively, for the sake of maintaining desired power quality, in spite of variations in consumer loads. Simplified and moderate Simulink model for voltage and frequency control of isolated six-phase induction generator can keep the terminal voltage and generated frequency remain constant so that generator output power remains constant. iv Complete Simulink model has SP-SEIG, controller and its control scheme, and static load arrangement which retains the voltage and frequency almost fixed with marginal drop in machine speed during variations in consumer energy demands. A new control strategy in voltage and frequency controller of SP-SEIG supplying static load is described with two closed control loops. V and F (volts and Hz) controller consists of current controlled voltage source inverter (CC-VSI) and a high frequency DC chopper. Both keeps the generated voltage and frequency constant against changes in load characteristics. Simulation outputs depict the constant generated voltage and frequency with change in load characteristics. In this way, proposed controller behaves as frequency and voltage regulator. Simplified Simulink model possess control scheme which generates gate drive signals to IGBTs switches of VSI and chopper switches. Simulink model of voltage fed controller ‘VFC’ has two PI controllers, first is to regulate AC terminal voltage (Vt) and second is for regulating DC bus voltage of VSI. First, a mathematical model of SP-SEIG supplying static load is derived under transient and dynamic conditions. Then, model of D.C. side of inverter along with current controlled voltage source inverter is developed for the control purpose of SP-SEIG. Having two PI controllers in Simulink model, it has complex functionality which is overlooked by its reliable and goal accomplished output performance. An Outlook on whole research work involves change of variables approach revolutionized by R.H.Park in late 1920s. Park’s theory has served as the advantageous theoretical foundations for the equations of transformation in arbitrary reference frame (proposed reference frame is stationary) in the analysis of SP-SEIG. Steady-state modelling using loop impedance and graph network theory; Steady-state analysis using NR numerical technique; Dynamic modelling using mixed variable approach; Transient analysis using conventional RK4 algorithm; Stability analysis by using an eigenvalue criterion in addition to standard (Rootlocus) graphical tool, and, V and F control of SP-SEIG is carried out by using a new strategy. Although, NR numerical technique and RK4 algorithm are not seeding well in the computational analysis, yet not obsoleted being simple, fast and effective if initial guesses are perfectly chosen. Thesis task presents an opportunity to focus on following performances of SP-SEIG under balanced or unbalanced and resistive ‘R’ or resistive-inductive ‘R-L’ static loads to analyze the performance parameters of simple-shunt and compensated SP-SEIG.  The steady state analytical machine performance results obtained by the proposed schemes are compared. Steady state initial values of few machine variables have been used for dynamic and transient analysis. v  Analytical dynamic and transient performance results are found for the R and RL loading on the machine system. In both the cases (R and R-L loading), the voltage drops are unequal and marked when variation from no load to full load.  Stability is also an important factor being considered to investigate the effect of given values of excitation capacitance, speed and loads. Root-locus graphical tool create an opportunity to observe the behaviour of characteristic roots (or eigenvalues or latent roots) in the s-plane.  Besides the assistance of isolated /capacitor excited induction generator, it has two crucial deficiencies for need of extra reactive power during faults and loss of excitation during abrupt change in machine load or prime mover speed. Capacitor excitation survives when there is almost constant system load or prime mover speed. So, a new controller scheme is employed for constant ‘volt and hertz’ or rotor speed for only one particular R loading to demonstrate an introspective spotlight on new strategy being applied in to the Matlab Simulink model of voltage and frequency controller of SP-SEIG.