Calculation of Inertia and reactance of a Synchronous generator

Submitted by:Shasank Mallela (23823)Jamshid Ummattam Kuzhiyil (23562)Chakradhar Naidu (23648)Sharath Chandra Kasoju (23645)

HS Ravenburg-WeingartenCalculation of Inertia and reactance of a Synchronous generatorScientific Project

Submitted to:Prof. Gerd Thieleke

Contents1.Introduction22.Synchronous Generators33.Calculation of Synchronous reactance64.Moment Of Inertia105.References22

1. IntroductionAs part of this scientific project, we are measuring the Moment of Inertia and Reactance parameters of a synchronous generator.The inertia is a parameter of rotating electrical machinery often required by customers as guaranteed data. Besides, it is commonly used by power systems analysts who use it as input data for simulation programs. It has the advantage of conferring simplicity to the motion equation for calculation of torque. We are using a Liebherr synchronous generator for which the inertia value is not provided by the manufacturer. The experiment includes the calculation of Inertia theoretically and practically. Theoretical calculations are derived from the generator plan whereas practical value is obtained by running the machine.The ability to predict the reactance of a generator is of prime importance. The reactance has a significant impact on the magnitude of the fault currents generated within the machine during an event such as a 3 phase short-circuit. Power system designers routinely use the generator reactance as a key parameter to aid in the design of the complete power generation system.Generator reactances are used for two distinctly different purposes. One use is to calculate the flow of symmetrical short circuit current in coordination studies. A second use for generator reactances is in specifications that limit the sub-transient reactance in order to limit the voltage distortion induced by non-linear loads.

2. Synchronous GeneratorsIn a synchronous generator, a DC current is applied to the rotor winding producing a rotor magnetic field. The rotor is then turned by external means producing a rotating magnetic field, which induces a 3-phase voltage within the stator winding. Field windings are the windings producing the main magnetic field (rotor windings for synchronous machines); armature windings are the windings where the main voltage is induced (stator windings for synchronous machines). The frequency of the resulting voltage and current is synchronized with rotor mechanical speed. Resulting stator currents also produce a rotating mmf that, under steady-state operation, rotates at the same speed as rotor with an angular separation (depending on electrical output torque Te (or power P). This project involves a Liebherr Typ GD 720 S 34 Synchronous generator with the following details.

Generator Ratings as given by the manufacturer:Liebherr

Typ GD 720 S 34

SY- GENNr. G04470

380V 15.2A

10 KVA Cos 1.0

1500 U/mim 50Hz

Err = 180V 1.72 A

GEG-Err = 24 V 0.74 A

The generator rotor is rotated by means of a pelton turbine which provides the mechanical energy which is converted in to the generated electrical energy. The basic requirement of generator operation is that they must remain in synchronism.TURBINE: The turbine exerts a torque in one direction which causes the shaft to rotate. The torque is called the mechanical torque Tm.GENERATOR: The generator exerts a torque in the direction opposite to the mechanical torque whichretardsthemotioncausedbythemechanicaltorque. The torque is electromagnetic called Te.If the machine is in synchronism thenTm = TeIn this steady state, the electrical torque is equal to the mechanical torque, and hence the accelerating power will be zero. During this period the rotor will move atsynchronous speedwsin rad/s.If it is not equal then it leads to accelerating torque because of the difference Tm- Te and it is indicated by Ta. The accelerating torque can be positive or negative depending on the direction of acceleration.The electrical rated torque is calculated from the following equationTe = The above equation is related to torque and powerIf we consider the position of the rotor angle of that from the generator reference frame the Angular acceleration is given from the following Equation. Let us consider a three-phase synchronous alternator that is driven by a prime mover. The equation of motion of the machine rotor is given by

whereJis the total moment of inertia of the rotor mass in kgm2

Tmis the mechanical torque supplied by the prime mover in N-m

Teis the electrical torque output of the alternator in N-m

is the angular position of the rotor in rad

This is where moment of inertia comes in to picture which is required for the calculation of accelerating torque.

3. Calculation of Synchronous reactance

AIM: - To measure direct axis synchronous reactance of synchronous machine.

THEORY:- Direct axis synchronous reactance and quadrature axis synchronous reactance are the steady state reactance of the synchronous machine. These reactances can be measured by Performing open circuit, short circuit tests and the slip test on synchronous machine.It may be noted that the direct- and quadrature-axis synchronous reactances of a round-rotor (non-salient pole) machine have same values.The machine we are using is a non-salient pole machine, hence we calculated only the d-axis reactance.

Direct-axis synchronous reactances (Xd ):- The direct axis synchronous reactance of synchronous machine in per unit is equal to the ratio of field current. Ifsc at rated armature current from the short circuit test, to the field current, Ifo at rated voltage on the air gap line. Direct axis synchronous reactance (Xd) = Ifsc /Ifoc per unit This direct-axis reactance can be found out by performing open circuit and short test on alternator.

1. The Open-Circuit Test :-

The open-circuit test, or the no-load test, is performed by

1) Generator is rotated at the rated speed. 2) No load is connected at the terminals.3) Field current is increased from 0 to maximum.4) Record values of the terminal voltage and field current value.

Circuit diagram to perform open-circuit test. With the terminals open, IA=0, so EA = V. It is thus possible to construct a plot of EA or VT vs IF graph. This plot is called open-circuit characteristic (OCC) of a generator. With this characteristic, it is possible to find the internal generated voltage of the generator for any given field current.

Open-circuit characteristic (OCC) of a generator The OCC follows a straight-line relation as long as the magnetic circuit of the synchronous generator does not saturate. Since, in the linear region, most of the applied mmf is consumed by the air-gap, the straight line is appropriately called the air-gap line.

2. The Short-Circuit Test The short-circuit test provides information about the current capabilities of a synchronous generator. It is performed by 1) Generator is rotated at rated speed. 2) Adjust field current to 0. 3) Short circuit the terminals. 4) Measure armature current or line current as the field current is increased. SCC is essentially a straight line. To understand why this characteristic is a straight line, look at the equivalent circuit below when the terminals are short circuited.

Circuit diagram to perform short-circuit test. When the terminals are short circuited, the armature current IA is: And its magnitude is:

From both tests, here we can find the internal machine impedance (EA from OCC, IA from SCC):

Since Xs >> RA , the equation reduces to:

After doing the above tests we got the data as shown in the following pages.

4. Moment Of InertiaMoment of inertia is basically rotational inertia.It's the resistance to rotational acceleration/deceleration of a mass. Inertia has effect on the cost of machine as for achieving higher inertia value, the cost of machine will increase. We are calculating here the moment of inertia of the combined generator-turbine set. The experiment involves calculation of the theoretical and practical values of inertia and compares them for convergence.Theoretical calculation:Theoretical value is obtained from the generator plan provided. A general outline of the plan is shown below.

RotorPart 1:

Moment of inertia with respect to center axisJ1 = M1R12J1 = V1R12 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V1 Volume = R12l1M1 Mass

J1 = (3.8)46.257.81000 kgm2

J1 = 0.001597 kgm2

Part 2:

Moment of inertia with respect to center axisJ2 = M2R22J2 = V2R22 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V2 Volume = R22l2M2 Mass

J2 = (0.035)40.1957.81000 kgm2

J2 = 3.58510-3 kgm2

Part 3:

Moment of inertia with respect to center axisJ3 = M3R32J3 = V3R32 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V3 Volume = R32l3M3 Mass

J3 = (0.03)40.1157.81000 kgm2

J3 = 1.14110-3 kgm2

Part 4:

Moment of inertia with respect to center axisJ4 = M4R42J4 = V4R42 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V4 Volume = R42l4M4 Mass

J4 = (0.028)40.0667.81000 kgm2

J4 = 0.000497 kgm2

Part 5:

Moment of inertia with respect to center axisJ5 = M5R52J5 = V5R52 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V5 Volume = R52l5M5 Mass

J5 = (0.027)40.0917.81000 kgm2

J5 = 5.92510-5 kgm2

Part 6:

Moment of inertia with respect to center axisJ6 = M6R62J6 = V6R62 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V6 Volume = R62l6M6 Mass

J6 = (0.021)40.027.81000 kgm2

J6 = 4.76510-5 kgm2

Part 7:

Moment of inertia with respect to center axisJ7 = M7R72J7 = V7R72 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V7 Volume = R72l7M7 Mass

J7 = (0.0325)40.10257.81000 kgm2

J7 = 1.410-4 kgm2

Part 8:

Moment of inertia with respect to center axisJ8 = M8R82J8 = V8R82 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V8 Volume = R82l28M8 Mass

J8 = (0.02725)40.1267.81000 kgm2

J8 = 8.45*10-4 kgm2

Part 9:

Moment of inertia with respect to center axisJ9 = M9R92J9 = V9R92 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V9 Volume = R92l9M9 Mass

J9 = (0.025)40.0427.81000 kgm2

J9 = 2.03410-4 kgm2

Part 10:

Moment of inertia with respect to center axisJ10 = M10R102J10 = V10R102 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V10 Volume = R102l10M10 Mass

J10 = (0.024)40.0827.81000 kgm2

J10 = 3.31310-4 kgm2

Part 11:

Moment of inertia with respect to center axisJ11 = M11R112J11 = V11R112 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V11 Volume = R112l11M11 Mass

J11 = (0.0125)40.0547.81000 kgm2

J11 = 210-5 kgm2

Part 12:Moment of inertia of part 12 (neglecting the small hole and considered it as a uniform cylinder)J12 = M12R122J12 = V12R122 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V12 Volume = R122l12M12 Mass

J13 = (0.019)40.0867.81000 kgm2

J13 = 1.2610-4 kgm2

Part 13:

Moment of inertia with respect to center axisJ13 = M13R132J13 = V13R132 Where: Density of the material (assume to be steel alloy = 7.8 g/cm3 = 7.8*1000 kg/m3)V13 Volume = R132l13M13 Mass

J13 = (0.01535)40.057.81000 kgm2

J13 = 3.3110-5 kgm2

Part 14:

Moment of Inertia of the rotor winding around the axis

J14 = M14 (Ra2 + Rb2)

J14 = l (Ra2 + Rb2)

Density assumed as = 80 % Cu + 20% Steel

= .8 8900 + .2 7800

= 8680 Kg/m3

J14 = 8680 Kg/m3 (.258) ((.105)4 (.035)4)

J14 = 0.422 Kg m2

Turbine

Part 1:

I1 = M (a2+b2)I1 =(0.042+0.0192) h (R2-r2)I1 = 2.5210-3kgm2

Part 2:I2 = M (a2+b2)I2 = (0.2152) (0.0522-0.042)I2 = 2.9010-3Kgm2

Part 3: I3 = M (a2+b2)I3 = M (0.071+0.0522)I3 = 8.8610-3Kgm2

Total moment of inertia of the whole system is given by Inertia = turbine inertia + motor inertiaInertia = 0.4454 kg m2

Practical Calculation:The speed vs time characteristics of the generator is as shown below.

Rated electrical torque is given by Te = Pw 9.554 / nTe = 36.78 Nm (where power = 5776 W, n = 1500 rpm)As per the theoretical calculation assumption of the mechanical torque of a synchronous motorTe TmThe accelerating torque is approximated to nearly 99.99%The accelerating Torque = 0.24 NmTa = J. (2 / 60). dn /dtTherefore inertia of the system is calculated from the following equation J = td = J = 0.63 kg m2

Comparison Of Inertia values:-Theoretical valuePractical value

0.4454 kgm20.63 kgm2

5. References

Synchronous Generators by Dr. Suad Ibrahim Shahl Synchronous machine parameters estimation by Paladin Grid Inertia and Frequency Control in Power Systems with High Penetration of Renewables by Pieter Tielens, Dirk Van Hertem