Power flow study talk about the mathematical analysis of the flow of electric power in a power system [2]. This study plays a vital role in deducing the best operational point of the system and in development of the future expansion of a grid system. We are required to design a power plant that will supply Sydney, Wollongong, Newcastle, Canberra, and Orange. The Assumption made here is the power plant is situated in Sydney & Wollongong. It is assumed that Newcastle, Canberra, and Orange do not have a power generation facility of its own, and it obtains its power from a sub-transmission line. The total power that needs to be generated ought to be 640MVA or slightly higher [1].
Objectives
In this lab work the following tasks were performed:
The types of buses in power system are as follows;
Bus 1-Swing bus
Bus 2-Generator bus
Bus 3-Generator bus
Bus 4-Generator bus
To convert the pu unit values of the system the following formulas are applied:
Pbase=Qbase=Sbase=100 MVA
Pact= Sbase* Ppu Qact= Sbase* Qpu ……………………………equation 1
Bus 1 Power demand
Bus 2
Power demand
Generation
Bus 3
Power demand
Generation
Bus 4
Power demand.
Generation
The actual power values are as shown in table 1 below:
Bus # |
Real Power Demand in MW |
Reactive Power Demand in MVAR |
Real Power Generation MW |
Reactive Power Generation MVAR |
1 |
100 |
50 |
? |
? |
2 |
0 |
40 |
400 |
? |
3 |
200 |
100 |
0 |
? |
4 |
200 |
100 |
0 |
? |
TABLE1: Actual values of the bus power data.
Impedance
Sbase=100MVA
Vbase=15kV
Zact=Zbase*Zpu
The actual impedance of the transmission lines will be given by:
Transmission Line |
Reactance (ohms) |
Line 12 |
0.3375 |
Line 13 |
0.45 |
Line 14 |
0.225 |
Line 23 |
0.225 |
Line 34 |
0.3375 |
TABLE 2: reactance in ohms
Determination of the resistances and inductances of the transmission lines.
From the information given that the transmission lines are lossless therefore their resistances are zero [4]. The inductances of the lines can determined from the reactance as follows:
X=2*∏*f*L
Therefore:
The inductances were tabulated as shown below:
Transmission Line |
Inductances (mH) |
Line 12 |
1.0743 |
Line 13 |
1.4324 |
Line 14 |
0.7162 |
Line 23 |
0.7162 |
Line 34 |
1.0743 |
Table 3: the inductances of the respective transmission lines.
The construction of the power system model in simpower system is attached to this report as an .slx file and the report as a .rep file. The summary of the report is as follows:
The Load Flow converged in 3 iterations!
Summary for sub network No 1
Total generation: P= 500.00 MW Q= 412.78 Mvar
Total PQ load: P= 0.00 MW Q= 0.00 Mvar
Total Zshunt load: P= 500.00 MW Q= 290.00 Mvar
Total ASM load: P= 0.00 MW Q= 0.00 Mvar
Total losses: P= 0.00 MW Q= 122.78 Mvar
1: BUS_1
V= 1.000 pu/15kV 0.000; Swing bus
Generation: P= 100.00 MW Q=75.66 Mvar
PQ_load: P= 0.00 MW Q= 0.00 Mvar
Z_shunt: P= 100.00 MW Q= 50.00 Mvar
–> BUS_2: P= -147.91 MW Q= 16.62 Mvar
–> BUS_3: P= 15.55 MW Q= 0.24 Mvar
–> BUS_4: P= 132.36 MW Q= 8.80 Mvar
2: BUS_2
V= 1.000 pu/15kV 12.820
Generation: P= 400.00 MW Q= 88.91 Mvar
PQ_load: P= 0.00 MW Q= 0.00 Mvar
Z_shunt: P= 0.00 MW Q= 40.00 Mvar
–> BUS_1: P= 147.91 MW Q= 16.62 Mvar
–> BUS_3: P= 252.09 MW Q= 32.30 Mvar
3: BUS_3
V= 1.000 pu/15kV -1.780
Generation: P= 0.00 MW Q= 135.98 Mvar
PQ_load: P= 0.00 MW Q= 0.00 Mvar
Z_shunt: P= 200.00 MW Q= 100.00 Mvar
–> BUS_1: P= -15.55 MW Q= 0.24 Mvar
–> BUS_2: P= -252.09 MW Q= 32.30 Mvar
–> BUS_4: P= 67.64 MW Q= 3.44 Mvar
4: BUS_4
V= 1.000 pu/15kV -7.610
Generation: P= 0.00 MW Q= 112.24 Mvar
PQ_load: P= 0.00 MW Q= 0.00 Mvar
Z_shunt: P= 200.00 MW Q= 100.00 Mvar
–> BUS_1: P= -132.36 MW Q= 8.80 Mvar
–> BUS_3: P= -67.64 MW Q= 3.44 Mvar
It was deduced that bus 1supplied reactive power to all the other three buses to meet their demands and the losses of the transmission lines [6]. Bus 1 also supplied real power to bus 3 and 4 while receiving real power from bus 2. Bus 2 supplied both reactive and real power to bus 1 and bus 3. Bus 3 received real power from bus 1 and bus 2 while supplying reactive power to bus 4. In addition, bus 3 supplied reactive power to the other buses. Bus 4 received real power from bus 1 and bus 3 while supplying reactive power to the two buses. The actual amount of the power supplied and received from the buses are given the report generated from power system model. From the analysis, this is the most economical power system that is required to be stationed in Sydney & Wollongong for the supply of power to all other areas of interest
Finally, the system maintained a flat voltage profile [7]. The voltage magnitude was maintained at 1 pu/15 kv across all the buses. However the phase angles of the voltages varied in each bus. The phase angle of the voltages in bus 1, bus 2, bus 3 and bus 4 were 00, 12.820,-1.780 and -7.610. The angles variations depicted the direction of flow of both reactive and real power.
Conclusion
From the load analysis we can conclude that the power was balanced throughout the power system. The total generation of the power system was 648.4 MVA with a total losses of 122.78 MVAR due to inductances of the transmission line.
Under usual circumstances, a power system works under stable circumstances with all equipment carrying standard load currents and the bus voltages within the agreed limits. This state can be interrupted owing to an error in the system [5]. An error in a circuit is a bomb that hinders with the standard flow of current. A short circuit error arises when the lagging of the system fails ensuing in low impedance path either between phases or phase(s) to ground. This leads to extremely high currents to flow in the circuit, necessitating the operation of shielding equipment to avert damage to equipment [6]. The short circuit errors can be classified as: Symmetrical faults or unsymmetrical faults
A three phase symmetrical fault is triggered by use of three equal fault impedances Zf¯ to the three phases, as shown in Figure below. If Zf¯ = 0 the fault is known as a solid or a bolted fault. These errors can be of two categories:
(a) Line to line to line to ground fault (LLLG fault) or
(b) Line to line to line fault (LLL fault).
As the three phases are similarly affected, the system remains balanced. That is the reason why, this fault is known as a symmetrical or a balanced error and the error analysis is carried out per phase basis [8]. The behavior of LLLG fault and LLL fault is identical due to the balanced nature of the fault. This is a very severe error that can happen in a system and if Zf¯ = 0, this is generally the most severe error that can happen in a system. By chance, such errors transpire intermittently and only around 5% of the system errors are three phase faults. Figure 4.39: Symmetrical Fault
Errors in which the balanced state-run of the network is distressed are known as unsymmetrical or unbalanced errors [10]. The most common category of unbalanced fault in a system is a single line to ground fault (LG fault). Almost 65 to 80% of errors in a system are LG faults. The other forms of unbalanced faults are line to line faults (LL faults) and double line to ground faults (LLG faults). About 16 to 26% faults are LLG faults and 6to 16% are LL faults. These faults are shown in Figure below. Unsymmetrical Fault Most of the errors transpire on transmission lines as they are uncovered to external components. Lightening strokes may cause line insulators to flashover, high velocity winds may cause tower failure, ice loading and wind may result in mechanical failure of line or insulator and tree branches may cause short circuit. Much less common are the errors on cables, circuit breakers, generators, motors and transformers. Fault analysis is necessary for selecting proper circuit breaker rating and for relay settings and coordination. The symmetrical faults are analyzed on per phase basis while the unsymmetrical faults are analyzed using symmetrical components. Further, the Z¯BUS matrix is very useful for short circuit studies.
The power producing companies and power transmission and distribution companies should create a fully – fledged faults analysis section in their organizations to establish and implement up-to-date high-tech techniques of electrical power systems fault analysis that would offer more precise data that can be used to size and set shielding devices sufficiently.
For purposes of future work, the following should be given due attention:
Reference
[1] Das, J. C. (2016). Power System Analysis: Short-Circuit Load Flow and Harmonics, Second Edition. Baton Rouge: CRC Press.
[2] Degeneff, R. C., & Hesse, M. H. (2012). Principles of power engineering analysis. Boca Raton, FL: CRC Press.
[3] Glover, J. D., & Sarma, M. S. (2012). Power system analysis and design. Pacific Grove, CA: Wadsworth/Thomson Learning.
[4] Go?nen, T. (2013). Modern power system analysis.
[5] KARRIS, S. T., & KARRIS, S. T. (2009). Circuit analysis I: with MATLAB computing and Simulink/SimPowerSystems modeling. Fremont, Calif, Orchard Publications. https://www.books24x7.com/marc.asp?bookid=30671.
[6] Kothari, D. P., & Nagrath, I. J. (2008). Modern power system analysis. Boston: McGraw-Hill Higher Education.
[7] Kumar, N., & Kumar, S. (2010). Power system analysis. New Delhi: Asian Books
[8] LI, S. (2010). Power flow in railway electrification power system.
[9] Nagsarkar, T. K., & Sukhija, M. S. (2007). Power system analysis.
[10] National Renewable Energy Laboratory (U.S.), & United States. (2011). Symmetrical and Unsymmetrical Fault Currents of a Wind Power Plant: Preprint. Golden, Colo: National Renewable Energy Laboratory (U.S).
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