Department of Electrical Engineering and Computer Science

EEL6208 Advanced Electric Machinery

Homework Set No. 3

Problem 1.

We have designed a round rotor synchronous generator in course Topic 12 example.You can run the code sgDesign.m and find out the geometry of the machine. For this generator:(1) Calculate the self and mutual inductances based on the formulas derived in class;

(2) Find the synchronous reactance at steady state;

(3) Estimate the armature winding resistance and field winding resistance ;(4) Calculate and plot the OCC curve (only the air-gap line).

You can add these parts to the design code.

Problem 2. A 12.6 kV (line to line or terminal voltage), 150 MW (real power), 60 Hz, Y connected, 0.85 power factor lagging, four pole synchronous generator has the OCC curve (ET vs If) and SCC curve (IL,sc vs If) shown in the figure. Armature and field resistances is are listed in the figure. (1) Find the rated current.(2) Find the mechanical speed of the generator.(3) Input the OCC and SCC curves into MatLab and then use them to calculate the

approximate synchronous reactance . Plot versus . What’s the unsaturated

synchronous reactance ?(4) Find short circuit current ratio (SCR).

Use the for in the following calculations: (5) If the generator is now operating at full load, how much field current and field voltage

is required to keep the terminal voltage VT equal to 12.6 kV?

(6) Suppose that the generator is connected to a 50MW load at 0.8 PF leading, how much field current and field voltage would be required to keep VT at 12.6 kV?

(7) How much field current is needed to keep open circuit terminal voltage at 12.6 kV? Keep the field current and operate the machine at 150 MW, 0.85 PF lagging load. What’s the terminal voltage? Calculate voltage regulation.

Problem 3.

Design a 3 phase round rotor turboalternator satisfy the following specs:

150 MW (real power), Y connected, 12.6 kV (terminal voltage), 60 Hz4 pole , 0.85 pf laggingMaximum allowable rotor peripheral speed 250 m/s for 20% over speed run.Directly cooled stator (water)Directly cooled rotor (hydrogen) Vfmax = 500 V60 slots, 14/15 pitch, skew 1 slotNumber of parallel circuits C = 12Working temperature 25oC

List your geometry details. Also answer questions listed in Problem 1.

Problem 4.

We have studied 3 phase rectifier in Topic 15d. For a 5 phase rectifier, find the relationship between phase voltage and output DC voltage.

Confirm your results using SimuLink.

Problem 5.

Using embedded MatLab to build a model for a 200 KW synchronous generator system which consists of a main machine and an exciter. Assume the generator speed is 12 krpm (fixed). The DC bus voltage after rectification should be regulated to be 270 V DC through a controller. After building the model, plot figures like those in my Topic 16b notes. Neglect damper when you build models (see Topic 12b notes). Key parameters are: For the main machine (10 pole):

R s=0.008ΩR f=0 .2ΩLls=8 .5μH

Lmd=90 μHLmq=40 μHLlf=0 .65 mHLmf=7mHLsf=0 .6 mH

For the exciter (6 pole):

R s=0. 035ΩR f=0 .012ΩLls=7 .5 μH

Lmd=80μHLmq=35μHLlf=10μHLmf=0 .1 mHLsf=75μH

Problem 6.

Use MatLab symbolic toolbox to derive equations in notes “12 a dq Theory for Synchronous Machine with Damper”.