THEORY EXAMINATION (SEM–VI) 2016-17 POWER SYSTEM ANALYSIS

POWER SYSTEM ANALYSIS (EEE601)

Section-wise Solved Answers & Notes

SECTION – A (10 × 2 = 20 Marks)

Short, direct answers

(a) Line and phase voltages in per-unit are equal

In per-unit system, base voltage is chosen such that

VL(base)=3VP(base)V_{L(base)}=\sqrt{3}V_{P(base)}VL(base)​=3​VP(base)​

Hence, when actual line and phase voltages are divided by their respective base values, per-unit values become equal.

(b) Relation between zero sequence current and neutral current

In=3I0I_n = 3I_0In​=3I0​

Neutral current is three times the zero-sequence current.

(c) Per-unit reactance conversion

Given:
Rated: 30 MVA, 11 kV, X = 20% = 0.2 pu                   New base: 50 MVA, 10 kV

Xnew=Xold×SnewSold×(VoldVnew)2X_{new} = X_{old}\times \frac{S_{new}}{S_{old}} \times \left(\frac{V_{old}}{V_{new}}\right)^2Xnew​=Xold​×Sold​Snew​​×(Vnew​Vold​​)2 Xnew=0.2×5030×(1110)2=0.403 puX_{new}=0.2\times\frac{50}{30}\times\left(\frac{11}{10}\right)^2 = \boxed{0.403\ pu}Xnew​=0.2×3050​×(1011​)2=0.403 pu​ 

(d) Short circuit capacity

It is the maximum fault MVA a system can deliver during short circuit.

Short circuit MVA=3VIfault\text{Short circuit MVA} = \sqrt{3}V I_{fault}Short circuit MVA=3​VIfault​ 

(e) Zero sequence network

Zero-sequence network consists of zero-sequence reactances of generators, transformers and lines, connected according to grounding and winding connections.

(f) Load flow analysis

It determines bus voltages, power flows, losses, and reactive power in a power system under steady-state condition.

(g) Transient stability

Ability of power system to maintain synchronism after a large disturbance like fault or sudden load change.

(h) Critical clearing time

Maximum time allowed to clear a fault without losing system stability.

(i) Causes of voltage surge

• Lightning strokes                              • Switching operations

(j) Bewley’s lattice diagram

Graphical method used to analyze travelling wave reflections and transmissions in transmission lines.

SECTION – B (Any 5 × 10 = 50 Marks)

(a) Impedance diagram on per-unit basis

Steps:                                                                   Select base MVA and base voltage

Convert all reactances to common base             Neglect resistance

Draw reactance-only diagram                             Purpose: Simplifies fault and stability analysis.

(b) Three-phase fault calculation

Steps:                                                                   Convert all impedances to per-unit

Draw reactance diagram                                      Find equivalent reactance

Calculate fault current                                          If=1XeqI_f = \frac{1}{X_{eq}}If​=Xeq​1​

Fault MVA:

=SbaseXeq= \frac{S_{base}}{X_{eq}}=Xeq​Sbase​​ 

(c) Zero sequence network for L-L fault

Zero-sequence network does not participate in line-to-line fault.

Sequence network connection:                           • Positive and negative sequence in parallel
• Zero sequence open                                         If=VZ1+Z2I_f = \frac{V}{Z_1+Z_2}If​=Z1​+Z2​V​ 

(d) Load flow bus classification                           • Slack Bus: Voltage & angle known
• PV Bus: Voltage & power known                     • PQ Bus: Power known

Gauss-Seidel Method:                                       • Assume voltages
• Calculate bus currents                                       • Update voltages
• Repeat till convergence                                     Acceleration factor improves speed.

(e) Critical clearing angle (Equal area criterion)

Given:

Pmax1=2.0, Pfault=0.5, Ppost=1.5P_{max1}=2.0,\ P_{fault}=0.5,\ P_{post}=1.5Pmax1​=2.0, Pfault​=0.5, Ppost​=1.5

Equal area criterion:           Areaacc=Areadec\text{Area}_{acc} = \text{Area}_{dec}Areaacc​=Areadec​

Graphically determine critical clearing angle δc.

(f) Step-by-step solution of swing equation

Swing equation:                d2δdt2=PaM\frac{d^2\delta}{dt^2}=\frac{P_a}{M}dt2d2δ​=MPa​​

At discontinuity:                Pa=Pm−PeP_a=P_m-P_ePa​=Pm​−Pe​

Numerical integration used for transient stability studies.

(g) Travelling waves

Characterized by:                                           • Surge impedance
• Velocity of propagation                               • Reflection & transmission

Wave equation:

∂2V∂x2=LC∂2V∂t2\frac{\partial^2 V}{\partial x^2}=LC\frac{\partial^2 V}{\partial t^2}∂x2∂2V​=LC∂t2∂2V​ 

(h) Effect of cable on surge

Given:                                     Z1=400Ω, Z2=50Ω, Vi=100kVZ_1=400\Omega,\ Z_2=50\Omega,\ V_i=100kVZ1​=400Ω, Z2​=50Ω, Vi​=100kV

Transmitted voltage:

Vt=Vi2Z2Z1+Z2V_t = V_i \frac{2Z_2}{Z_1+Z_2}Vt​=Vi​Z1​+Z2​2Z2​​ Vt=100×100450=22.2 kVV_t = 100\times\frac{100}{450} = \boxed{22.2\ kV}Vt​=100×450100​=22.2 kV​ 

SECTION – C (Any 2 × 15 = 30 Marks)

Q3 (a) Single line diagram & per-unit system

Single line diagram:                         Simplified representation of 3-phase system.

Per-unit system advantages:           • Eliminates transformer turns ratio
• Simplifies calculations                      • Reduces numerical errors

(b) Symmetrical components             Balanced star load:
Before fuse removal → only positive sequence

After two fuses removed →                   • Positive sequence
• Negative sequence                              • Zero sequence present

Q4 (a) Transient current in R-L circuit

At switching:                                          i=Imax(1−e−t/τ)i = I_{max}(1-e^{-t/\tau})i=Imax​(1−e−t/τ)

Maximum transient current:                  imax=2Isteadyi_{max}=2I_{steady}imax​=2Isteady​ 

(b) Formation of Y-bus matrix

Steps:                                                    • Self admittance = sum of connected admittances
• Mutual admittance = negative of line admittance             Y-bus is symmetrical matrix.

Q5

(a) Assumptions in stability studies

• Constant mechanical input                        • Neglect damping
• Constant voltage                                        • Classical generator model

(b) Equal area criterion

Used to determine transient stability of SMIB system by equating accelerating and decelerating areas.

(c) Protection against surges

• Lightning arresters                                      • Ground wires
• Surge absorbers                                          • Insulation coordination