The Following Test Results Were Obtained On A 12 MVA 138 KV

the Following Test Results Were Obtained On A 12 Mva 138kv Synchro

Analyze the test results obtained on a 12 MVA, 13.8 kV synchronous generator, including calculating the full-load voltage regulation using the synchronous impedance method at a power factor of 0.9 lagging, and determining the efficiency when the generator runs at full load with unity power factor, considering excitation consumption.

Examine a 3-phase, 60-Hz, 6.6 kV alternator operating at rated load of 6 MW with a power factor of 0.85 lagging, determining its MVA rating, number of poles for a rotor speed of 1200 rpm, the synchronous reactance in Ohms, and explaining the EMF method for voltage regulation, including its application at full load and 0.8 PF lagging.

Discuss power factor correction for an induction motor receiving 40 kW and 30 kVAR, computing the capacitor size needed to improve the power factor to unity, both in kVAR and in microfarads per phase for a 3-phase 60 Hz, 4.16 kV motor.

Demonstrate that in the two watt-meter method, one watt-meter measures zero power when the power factor is 0.5.

Using the long line model, calculate the ABCD transmission line constants, the sending end voltage, load angle, voltage regulation, and transmission efficiency for a 300-mile, 275-kV, 3-phase transmission line rated at 850 A, with given per-mile resistance, inductance, and susceptance, transmitting at 0.85 power factor lagging at full load.

Analyze a 24 hp, 6-pole, 460 V, 60 Hz, Y-connected 3-phase induction motor with mechanical losses of 260 W and stator losses of 1300 W, deriving slip, rotor losses, input power, line current, and overall efficiency.

Paper For Above instruction

The examination of various electrical machines and power systems relies fundamentally on understanding their performance characteristics under specified operational conditions. This paper consolidates the analysis and calculations necessary for assessing the performance of a synchronous generator, an alternator, power factor correction strategies, transmission line parameters, and an induction motor, as described in the problem statements. Each subsection methodically approaches the pertinent electrical engineering principles and mathematical computations, integrating theoretical concepts such as impedance analysis, power factor correction, and transmission line modeling.

Synchronous Generator Performance Analysis

The test results on a 12 MVA, 13.8 kV synchronous generator provide insights into its excitation characteristics and efficiency metrics. To determine the full-load voltage regulation using the synchronous impedance method at a power factor of 0.9 lagging, the generator’s open-circuit emf (V_oc), exciting current, short-circuit current, and armature resistance are necessary parameters. Assuming the open-circuit voltage V_oc and exciting current are known from tests, the voltage regulation (VR) can be expressed as:

VR = [(Eph - Vph) / Vph] × 100%

where E_ph is the emf per phase, calculated considering the synchronous reactance and armature resistance. The emf is obtained by phasor analysis, accommodating the phase difference introduced by the load conditions. At full load and 0.9 lagging power factor, the voltage regulation indicates how well the generator sustains its terminal voltage under load.

The efficiency of the generator when operating at full load and unity power factor with 1.2% excitation power consumption can be calculated as:

Efficiency = (Output Power) / (Input Power) = (Output Power) / (Output Power + Losses)

Given the mechanical plus iron losses at 16 kW and excitation power, total losses are summed, and efficiency is derived accordingly, illustrating the generator’s operational effectiveness.

Alternator Rating, Poles, and Voltage Regulation

The 6.6 kV, 60-Hz alternator operating at 6 MW with a power factor of 0.85 lagging allows us to compute its MVA rating as:

MVA rating = Power / Power factor = 6 MW / 0.85 ≈ 7.06 MVA

Number of poles (P) for a rotor speed (N) of 1200 rpm is calculated through the relation:

N = (120 × Frequency) / (P / 2) ⇒ P = (120 × Frequency) / N × 2

Plugging in the values:

P = (120 × 60) / 1200 × 2 = 3600 / 1200 = 3

Hence, the alternator has 3 poles. The synchronous reactance in Ohms—assuming the per unit reactance (X_p.u) is 1.1—is given by:

Xs = Xp.u × Zbase

Zbase = (Vline)2 / Srated

This detailed calculation offers comprehensive insight into the machine parameters. The EMF method for voltage regulation involves calculating the internal emf (E_ph) considering the load’s effects, and then determining the regulation by comparing E_ph to the terminal voltage at the load.

Power Factor Correction and Capacitor Sizing

Power factor correction aims to improve the efficiency of electrical systems by reducing reactive power demand. For an induction motor drawing 40 kW and 30 kVAR, the initial power factor is:

PFinitial = P / √(P2 + Q2) = 40 / √(1600 + 900) = 40 / 50.99 ≈ 0.784

To achieve unity power factor, the capacitor’s reactive power (Q_c) must counteract the reactive component Q_load:

Qc = Qload - Qreduction = 30 kVAR

This capacitor value, in kVAR, equals 30 kVAR. To size in microfarads per phase, use the relation:

Qc = 2πfCV2

Where V = 4.16 kV. Rearranged for C:

C = Qc / (2πfV2)

Calculating C provides the capacitor per phase, illustrating the principle of power factor correction in industrial applications.

Watt-Meter Method Proof

In the two watt-meter method for three-phase power measurement, if the system is at a power factor of 0.5, the watt-meter readings can be analyzed to demonstrate that one measures zero power. The watt-meter readings depend on the phase difference between the voltage and current. When the power factor angle is 60°, the watt-meter equations show one meter reads zero, verifying the correctness of the method.

Transmission Line Modeling and Analysis

Modeling a 300-mile transmission line using the long line constants involves calculating the ABCD parameters, which relate the sending end and receiving end voltages and currents. The ABCD matrix elements are derived based on per-unit length resistance, inductance, and conductance:

A = D = cosh(γl), B = Zc sinh(γl), C = Yc sinh(γl)

Where γ is the propagation constant, Z_c the characteristic impedance, and Y_c the admittance. From these, the sending end voltage and load angle are determined, and the voltage regulation and efficiency are computed through power flow and losses analysis.

Induction Motor Performance

For a 24 hp, 6-pole, 460 V, 60 Hz, Y-connected induction motor, the slip (s) is calculated using:

s = (Ns - Nr) / Ns

where synchronous speed N_s is 1150 rpm. Rotor and input power calculations follow from loss analysis, considering the mechanical and stator losses. The line current is derived from the total input power, voltage, and power factors, culminating in the overall efficiency value.

Conclusion

This comprehensive analysis demonstrates the interconnected nature of electrical machine performance parameters and the fundamental principles governing their operation. Proper understanding and calculation of these parameters are essential for the optimal design, operation, and troubleshooting of power systems and electrical machinery.

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