Model and Performance of Single-Phase Induction Generators - Thesis Example

This paper investigates and analyzes the steady and performance of single phase induction generator. It uses analysis mathematical models and equivalent circuits to give more detailed explanation about the steady state and performance of this generator. Introduction Engineers have been thinking on how to replace the traditional methods of energy production which are not friendly to the environment and seem obsolete. The unavailability of power in a remote and not easily accessible areas and the issues of power black out that result in need for standby power source also motivated engineers to research on advanced techniques that may bring the mentioned problems to halt. The single phase induction generator has become one of the devices in consideration to achieve this goal it was explored with a view of bringing cost effective small power generator acceptable to the users. The induction generator is considered more advantageous as compared to the synchronous generator. It has the following advantages: rugged in construction, low maintenance and operational cost, self protection against fault, good dynamic fault, capable of generating power at varying speed and do not need brushes and commentators. The self excited induction motor uses turbines (steam, water and wind) as the prime mover to produce power. The prime mover rotates the rotor windings thereby causing it to cut the magnetic flux induced by the excitation windings connected to an external power source. The end of stator main windings is taken and connected to the required load. The induction generator only operates when there is the slip that is the rotor should rotate at a speed greater than synchronous speed of the stator magnetic flux. Analysis The self excited single phase induction generator structure consist of the rotor (rotor windings) and stator (has both the main and exciting windings).The rotor shaft is connected to the prime mover while one end terminals of stator main windings has provision for load connection. The main winding has a series connected capacitor that regulates voltage output and provide power of the connected load. With no load connected to the main winding the generator after self-excitation run at desired speed and produces certain no-load voltage which can only be changed by varying the self-excitation capacitor accordingly. Connection of the load leads to drastic drop of terminal voltage due to increased reactive power VAR. To maintain the terminal voltage, capacitor value in the series with the load is increased to counter for the reactive power. When doing the analysis of this generator, there are several assumptions that are made to improve the design of this machine. These assumptions include; all parameters are considered constant with the level of saturation except magnetizing reactance. The magnetomotive force (mmf) space harmonics and time harmonics in the induced voltage and current waveform can be ignored. There is equal leakage reactance for both stator and rotor windings, the magnetizing reactance relating to backward field is eliminated and the machine is considered lossless. The parameters that are considered most important and sensitive to design and modification of the machine are resistances and leakage reactance. The circuit above is an equivalent circuit of the self excited single phase induction generator. It represents single phase induction generator based on the double field theory. From the circuit, the generator is represented in resistances and inductive reactance of both the main winding and auxiliary (exciting) winding. The subscript sm indicates that the parameter is of main winding of the stator while the subscript sm indicates that the parameter is of auxiliary winding of the stator. F represents the per unit frequency of the generator, U represent per unit speed of the generator and a represent turn ratio between the auxiliary (excitation) winding and stator main winding. The rotor resistances and inductive reactance are referred to the stator for easy analysis. From the circuit, the main winding and auxiliary winding impedances can be realized. ZImL = Rsm/F + jXSm + RL/F + JxL - jXCSm/F2…………………..1 Z 2al = Rsa/2Fa2 + jXsa/2a2 - Jxcca/2F2a2 - Z1Ml/2………………..2 Z+ = (jXmm (Rmm/(F-U) + jXmm )) /( (Rm / (F-U) + j(xmm + Xmm)) Z- = ( jXmm ( (Rmm / (F + U ) + jXmm)) / (Rm / (F + U)+j(Xmm + Xm)) The above equivalent circuit can be simplified by combining the parameters as shown by the equations above to give the equivalent circuit as shown below. For self excitation condition to exist, the summation of current in the node zero must be zero. 1 / (ZImL+Z+) =( 1 / (ZImL + Z-)+1/ZIl)…………………..3 With the known magnetization curve from the measurements, the value of per unit frequency (F) and main winding reactance are chosen wisely to be to solve the unknowns from the equation 3 above. The main winding reactance (Xmm) is a function of the magnetizing current Xmm(Imm).The simplified equivalent circuit can be solved by determining the two currents (Im+ and Im-) The computation can be further simplified by considering Z- as Z- = (Rrm/F + U) + jXm Considering all parameters constant except Xmm , we can express Z+ as a subject of all other parameters and it is shown bellow. Z+ = (Zim +Z-) * ZL / (ZimL + Z- + ZL) - ZimL………………..4 All the parameters (impedances) on the left side of the equation above are dependent on per unit frequency, if all the following parameters are given: speed n, auxiliary winding capacitance Ccm , main winding capacitance Csm ,load reactance XL. Z+ = f (F) for the given value of speed n, capacitors and load, can be simply be calculated for the row values of F. The relationship can be represented as shown below. Z+ (F, Xmm ) =( jXmm (Rmm /(F + U) + jX sm)) / ( j(Xrm + Xcm) + (Rmm / ( F – U)))………5 Plotting the air gap voltage against the main winding current in a graph, the realized main winding reactance is compared with the air gap voltage. Plotting the air gap voltage against the main winding reactance the graph of air gap voltage is realized. The graph is as shown below. The per unit frequency as a function of main winding reactance Xmm(F) can be determined By use of imaginary part of the equation 5.The value of F is determined from the graph of air gap voltage against the reactance of the main winding which is the used in determining the magnetizing current of the main winding. Imm = Vg+ / Xmm From the simplified equivalent circuit, determination of the two current can be used to calculate the steady state characteristics when the parameters (per unit frequency F, magnetizing reactance Xmm and air gap voltage Vg+ ) are known. Im+ (F) = Vg+/F* 1 / (ZimL+ ( ZAl*ZImL)/ZAl + ZImL)) Im-(F) = Im+(F) * ZaL / (Z- + ZImL) The load current is calculated by summing the two currents Im = Im+ + Im- The auxiliary current is determined as Is = j(Im+ -Im+) The output power is POut = Im2*RL The rotor current given by the equation Ir+ = -Im +* jXmm / (Rrm / (F-U) + j(Xrm + Xmm)) The total input active power from the shaft is Pinput 2I2r+*( Rrm*U) / (F-U) -2I2m- *RrmU / (F+U) As the speed is varying, the slip will be changing. To yield realistic result, the load resistance should be changed with the slip from the beginning. The function Xmm(Vg+) is presented in a table for different values . The function Xmm (F) is also presented in the table. The value of the Xmm is the checked from the table. Failure to find it from the given data means that the either the load impedance or the capacitors for a particular frequency and speed is not within the existence domain. This will call foe modification of load impedance or the capacitor to fit in the required domain. The algorithm was synthesized as shown in the figure above to generate the values for different parameters. The magnetizing curve Vg+( Im) is obtained experimentally in the synchronous bare rotor test Before the rotor cage was located in the rotor slot. The IG was driven at the synchronism, n=3000rpm (f = 50Hz) and the a.c fed from the variac in the main winding only with auxiliary winding open. It could alternatively be calculated at standstill with the d.c excitation via FEM. In this case, the auxiliary winding is also open. From the test it was realized that the larger the speed the larger the load voltage, the lower the speed the greater the current for given the load. It was shown that the voltage waveform is rather sinusoidal up to rated value. The no load voltage increases with capacitance of the auxiliary winding. The voltage regulation is very satisfactory from 230V to 245V. From the experiment the results of various parameters when plotted give the following graphs. The graph show the relationship between different parameters as was obtained from the experiment. Works Cited Karady, George G., and Keith E. Holbert. Electrical energy conversion and transport an interactive computer-based approach. Hoboken, N.J.: Wiley, 2005. Print. Lai, Loi Lei, and Tze Fun Chan. Distributed generation: induction and permanent magnet generators. Chichester, England: IEEE/Wiley, 2007. Print. Read More