# Power System Analysis Control

# Part 1:

- The calculation of the following is conducted assuming positive sequence operation.

i. Propagation constant ?=?+j?

Where ? is the attenuation constant and ? is the phase constant

The series impedance 0.0172 + j0.3 and the shunt admittance

?=? Z*Y

?=

?= 0.0011234185 km^{-1} ?=88.359317115

ii. The impedance of the 314 km transmission line is

? ?=

?

- 1.640680 ?

= 267.3709431-7.658341 ?

iii. ABCD parameters are the generalized constants for circuits that are used to model the transmission lines. These types of parameters are mainly used in the two-port network that represents a transmission line (Papadopoulos *et al. *2016).

**Figure 1: ABCD parameters for a radial transmission line**

(Source: Parihar, M., Bhaskar, M. K., & Jain, 2017)

?l= (0.0011234185 * 314) = 0.352753409

A=cos h ? l= 1.210284281

B= Z_{c}sin h?l= 96.39044565 ohm

C= sinh ? l = 0.364252168 Siemens

D = cos h ? l = 0.352753409

iv. The values for exact pi equivalent circuit model parameters would be (HVDC, 2019)

= 3.00577055 E - 01 and

Z’ = Z_{c}*sin h*?*l

= 96.39044565 ohm

b) Z parameters and Y parameters of the pi-equivalent circuit (ECE, 2019),

Value for exact-pi equivalent Z_{LL}= 9.851050581 E + 01 and the value of exact-pi equivalent Y_{LL}= 9.540916879 E + 01

**Figure 1: Graph of the electrical load**

(Source: Created by researcher)

# Part 2:

- The following parameters are calculated using relevant individual values

i. SIL or the Surge Impedance Loading is a situation when a balance of natural power balance takes place. The ratio of voltage to current is known as the Impedance and that the root of the ratio between Inductance and Capacitance is known as surge impedance (Paganotti *et al.*2017). Therefore,

ii. The delivery of theoretical maximum power is 1879.454 for the 314 km long transmission line.

b) If the line is operated at 500kV nominal voltage and that the receiving end and sending end voltages are kept at the same the Surge Impedance Loading for the line would be V^{2}/Z, where Z represents the surge impedance and V represents the nominal voltage.

Therefore,

# Part 3:

- ?=?
_{max, }where ? is the power angle. Therefore, ?_{max}=32/0.95=33.68421

The Surge Impedance Loading for receiving end voltage of 0.95pu will be

b) The practical loadability of the transmission line during the nominal voltage of 500 kV will be 1894.655 MW

# Part 4:

i. The sending end line voltage is related to the current constraint parameter in the specified attributes of voltage and is highly related to the power angle (Beerten, D'Arco & Suul, 2015). As per the calculations,

Z=R+jX

If the shunt capacitance and shunt conductance are omitted the current flowing through the circuit could be easily managed by taking

I_{S }= I_{r}= I

Power per phase = (1/3) × (total power)

Per phase reactive volt-amperes = (1/3) × (total reactive volt-amperes)

The phase voltage for a balanced 3-phase, transmission line conned in star configuration is the product of inverse square root of three to the line voltage.

Therefore, the line-to-line voltage is

= (1/3) × (760)

= 253.33 kV and 88.35931712 degrees.

ii. When the load is not present and the current is zero and assuming the sending end voltage 760 kV, the no-load receiving end voltage will be:

= 240.666 kV and the degrees would be zero due to the presence of no load.

From this, it can be stated that as the length of the line increases the rise in receiving end voltage during no-load condition tends to be more predominant.

iii. Therefore, the voltage regulation is equal to ( 760 - 720 / 760) * 100

= (40 / 760) * 100

= 5.263%

# Part 5:

- The value of Y’
_{new}is given by

Y’_{new }= G’ + j (1-(?_{shunt} / 100_{t}))

i. By taking the Z’_{new} = Z’ and Y’_{new} as the updated values, the values of shunt reactive compensation for A is 9.5644 E -01 and that for the shunt reactive compensation B is 8.5315 E +01.

ii. During the supply of full load current and the receiving end, voltage is 0.95 per unit, the receiving end voltage is found to be 722 kV at unity power factor.

Therefore, the sending end line to line voltage is,

= ((1/3) × (722)) + Z

= 240.66 + 0.30049266

= 240.96649266 kV and the degrees would lead by 86.71863423.

iii. The no-load voltage for the same circuit would be

= ((1/3) × (722)) + 1/Z

= 237.666 + 1/0.30049266

= 237.99387 kV and the degrees would be zero due to the presence of no-load.

iv. The voltage regulation for the transmission line with the presence of shunt compensation would be (Oleka, Ndubisi & Ijemaru, 2017),

= ( (735 - 760) / 760 ) * 100%

= ( 0.03289 ) * 100%

= 3.289%

v. When the reactors are switched off at high load and switched on at light load and Assuming the sending end voltage is regulated at this voltage magnitude and is maintained constant, the receiving end voltage under no-load operation will be,

= (760 - 10) kV

= 750 kV and the degrees would be 88.35931712

vi. The voltage regulation so calculated for the transmission line as a percentage for the transmission line operating with switched shunt reactive compensation would be

= ( (740 - 760) / 760 ) * 100%

= ( 0.0263 ) * 100%

= 2.63%.

b) If the transmission line is operated at 500 kV as the nominal voltage, the voltage regulation for the transmission line would be

= ( (490 - 500) / 500 ) * 100%

= ( 10 / 500 ) * 100%

= 0.02 * 100 %

= 2%

According to the comparison between the Voltage Regulation with the switched shunt reactive compensation and that with the Voltage Regulation of nominal voltage of 500 kV the regulation in the voltage drops by a percentage of 0.666.

**Figure 2: Electrical load**

(Source: Created by researcher)

# Part 6:

- To improve the loadability of the transmission line, it has been supplemented with the series capacitive compensation. This process has been performed through the installation of two capacitors at both the ends of the transmission line (Natarajan, 2018). This helps the inductance created by the transmission line to lower at a minimum level.

i. The impedance Z_{cap} associated with each of the capacitive element would be zero for the real part, however, the imaginary part would be -1.2938E+01. This helps to reflect the phase angle and the phase magnitude.

ii. The equivalent parameters of A and B are A_{eq} and B_{eq} respectively that can be obtained through

A_{eq} = A + C Z_{cap}

B_{eq} = A + C Z^{2 }+ (A + D ) Z_{cap} **+ **B

Accordingly, the values for the A equivalent is 8.5645E+03 for the real part and 0.00 for the imaginary part. On the other hand, the values for the B equivalent are 6.2545 E +01 and 0.00 for the imaginary part.

iii. The theoretical maximum power delivered by the transmission system would be 7.4354E+03 MW.

iv. To transfer the real power across the transmission line there needs to be an angle (delta) between the voltages at each end of the line. The theoretical maximum power is transferred at a normal angle, which is at 90 degrees. The difference between the theoretical maximum powers is 3.74 E+03 %

v. Practical line loadability at 0.95 pu is 740.666 kV.

vi. The difference is 6.7876E+01 for real part and 1 for the imaginary part.

b) The SIL value is the same for the previous value.

# Reference List:

Beerten, J., D'Arco, S., & Suul, J. A. (2015). Cable model order reduction for HVDC systems interoperability analysis. Retrieved from: https://lirias.kuleuven.be/retrieve/346436

ECE (2019), *Line Capability Curve*. Retrieved from: http://www.ece.ualberta.ca/~apic/papers/Vstability_and_Dynamics/LineCapabilityCurve.pdf

HVDC (2019),* PI-Section Equivalent Circuits.* Retrieved from: https://hvdc.ca/webhelp/EMTDC/Transmission_Lines/PI-Section_Equivalent_Circuits.htm

Natarajan, R. (2018). *Power system capacitors*. Florida: CRC Press. Retrieved from: https://pdfs.semanticscholar.org/6b60/b6b01495627f85e7d2e7c8c374da3e8e7c9c.pdf

Oleka, E. U., Ndubisi, S. N., & Ijemaru, G. K. (2016). Electric power transmission enhancement: A case of nigerian electric power grid. *American Journal of Electrical and Electronic Engineering*, *4*(1), 33-39. Retrieved from: https://www.researchgate.net/profile/Gerald_Ijemaru/publication/303587234_Electric_Power_Transmission_Enhancement_A_Case_of_Nigerian_Electric_Power_Grid/links/5749570908ae5bf2e63f00bc/Electric-Power-Transmission-Enhancement-A-Case-of-Nigerian-Electric-Power-Grid.pdf

Paganotti, A. L., Afonso, M. M., Schroeder, M. A. O., Alipio, R. S., & Gonçalves, E. N. (2017, September). A non conventional configuration of transmission lines conductors achieved by an enhanced differential evolution optimization method. In *2017 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (ISEF) Book of Abstracts* (pp. 1-2). IEEE. Retrieved from: https://www.researchgate.net/profile/O_Schroeder/publication/321233941_A_non_conventional_configuration_of_transmission_lines_conductors_achieved_by_an_enhanced_differential_evolution_optimization_method/links/5ac4aeb5a6fdcc1a5bd06628/A-non-conventional-configuration-of-transmission-lines-conductors-achieved-by-an-enhanced-differential-evolution-optimization-method.pdf

Papadopoulos, T. A., Chrysochos, A. I., Doukas, D. I., Papagiannis, G. K., & Labridis, D. P. (2016). Induced voltages and currents: Overview and evaluation of simulation models and methodologies. Retrieved from: https://www.researchgate.net/profile/Dimitrios_Doukas3/publication/308419150_Induced_Voltages_and_Currents_Overview_and_Evaluation_of_Simulation_Models_and_Methodologies/links/57f7b22d08ae8da3ce590d1e/Induced-Voltages-and-Currents-Overview-and-Evaluation-of-Simulation-Models-and-Methodologies.pdf

Parihar, M., Bhaskar, M. K., & Jain, D. (2017, March). Long Transmission Line Performance and Model Analysis. In *National Conference on New Advances in Communications, Networking and Cryptography (NACNC)* (pp. 28-29). Retrieved from: https://www.researchgate.net/profile/Manish_Parihar2/publication/321965442_LONG_TRANSMISSION_LINE_PERFORMANCE_AND_MODEL_ANALYSIS_NACNC-2017_confrence/links/5a3b700f0f7e9bbef9fec97b/LONG-TRANSMISSION-LINE-PERFORMANCE-AND-MODEL-ANALYSIS-NACNC-2017-confrence.pdf