Electric Machine Design

(a) Derive the expression of temperature gradient in conductors placed in slot if slot insulation is comparatively thick. [6] (b) An induction machine has a temperature rise of $25^{\circ }\text{C}$ and $40^{\circ }\text{C}$ after 1 hour and 2 hour respectively while operating at full load of $7.5\text{ kW}$. The constant losses are $80\%$ of full load copper loss. Determine how long the motor can be operated at twice the rated output without overheating.

a) Classify the transformer on the basis of construction, application, number of phase and cooling method. [4] b) For a $500\text{ kVA}$, $50\text{Hz}$, $6600/400$, single phase core type, oil immersed, natural cooled power transformer, the design parameters are: Constant for output voltage per turn $(K)=0.8$, Resistivity of copper $0.021\Omega {\text{-mm}}^2/\text{m}$, Maximum flux density in core $(B_m)=1.5{\text{ Wb/m}}^2$, Current density $=2.75{\text{ A/mm}}^2$, Core type = Cruciform, Window space factor $(k_w)=0.27$, Stacking factor $(K_i)=0.9$, Ratio of height to width of windows $(H_w/W_w)=2.5$, Ratio of yoke height to width $(H_y/D_y)=1$, Axial depth of LV winding $=402\text{ mm}$, Axial depth of Hv winding $=377.5\text{ mm}$, Inside diameter of LV winding $=310\text{ mm}$, Outside diameter of LV winding $=348\text{ mm}$, Inside diameter of HV winding $=360\text{ mm}$, Outside diameter of HV winding $=418\text{ mm}$, Calculate; (i) Dimension of core, window and yoke. (ii) Overall dimension of frame (iii) Perunit resistance and leakage reactance. (iv) Perunit regulation at $0.8\text{ pf}$ lagging Taking iron loss $=1460\text{ W}$, copper loss $=3865\text{ W}$ at full load, height of tank $=1.6\text{ m}$, length of tank $=1.05\text{ m}$, width of tank $=0.62\text{ m}$, find the necessary number of tubes and show its arrangement.

(a) Classify the insulating materials on the basis of their thermal stability. [5] (b) What are the fundamental requirements of high conducting materials? Classify and explain the electrical conducting materials in brief.

a) Write about the factors to be considered while estimating the length of air gap in induction machines. [6] b) A $15\text{ kW}$, $440\text{ V}$, $50\text{ Hz}$, $1480\text{ rpm}$, $3$-phase induction motor is built with an inner diameter of stator $25\text{ cm}$ and length $16\text{ cm}$. The specific loading is $23000\text{ ampere-conductors per meter}$. Estimate the following parameter for a $11\text{ kW}$, $460\text{ V}$, $6\text{ pole}$, $50\text{ Hz}$ delta connected induction motor, assuming same specific loadings as the previous motor with $84\%$ efficiency and power factor $85\%$ for each machine. Assume, current density $4{\text{ A/mm}}^2$, stator slot pitch is $15$ to $25\text{ mm}$, ratio of slot depth to width is $3$ and flux density in stator core is $1.2{\text{ Wb/m}}^2$. Calculate: (i) Main dimension (ii) No of stator slot (iii) No of stator conductor and area of stator slot (iv) Dimension of each stator slot (v) Minimum width of stator teeth

a) Explain the factors to be considered while selecting the number of poles in a DC machine. [8] b) Calculate the main dimensions of the machine for a $7.5\text{ kW}$, $4\text{ pole}$, $1000\text{ rpm}$ and $220\text{ V}$ DC shunt generator. Given that full load efficiency is $0.83$, maximum gap flux density is $0.9{\text{ Wb/m}}^2$, specific electrical loading is $30,000\text{ ampere conductor/meter}$ and field form factor is $0.7$. Assume that the maximum efficiency occurs at full load and the field current is $2.5\%$ of rated load current. The pole face is square.