Power Flow Study: Mathematical Analysis Of Electric Power Flow In A System

Objectives

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

• To determine the category of buses to be used.
• To develop a model of a power system using Systems toolbox and perform load flow studies of the system.

In this lab work the following tasks were performed:  

1. Identification of bus type of each of the buses to be used in the power system  
2. Conversion of transmission line impedance
3. Calculation of resistance and inductance of each of the transmission line
4. Construction of a Power System model of the system under consideration.
5. Load flow analysis.  
6. Generation of load flow report of the system  

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:

P_base=Q_base=S_base=100 MVA

P_act= S_base* P_pu    Q_act= S_base* Q_pu  ……………………………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

S_base=100MVA

V_base=15kV

         Z_act=Z_base*Z_pu

             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     

Types of Buses in Power System

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 Z_f¯ to the three phases, as shown in Figure below. If Z_f¯ = 0 the fault is known as a solid or a bolted fault. These errors can be of two categories:

Actual Power Values

 (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 Z_f¯ = 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:

1. Incorporate computer monitoring software for fault detection
2. More work to be carried out on the analysis so that it can reflect the post fault security of a system.
3. High-tech method on interfacing of fault recognition application and protection methods e.g. circuit breakers needs to be considered to increase the switching speed of our protective devices. 4. There is need to emphasis on the significance of the fibre optics know-how to fault studies so as to have our fault analysis soft wares fixed in the communication link for well-organized customer notification services on fault occurrences.

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).