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Computer application to load – flow study of the
 national 330kv transmission network
 (using newton – raphson technique)

                    1 James agajo 2 Sylvester Ehijie Ezewele  3 Awolo C. I.                         

                  Dept. of Electrical and Electronics Engineering                                 

          Federal Polytechnic, Auchi,
               Edo state  Nigeria                                                

                                    Phone: +2348053312732                                                                       

           agajojul@yahoo.com 
                                     
                                                Abstract
Computer application to Load – flow or power – flow
studies involves the determination of the bus
voltages and their phase angles, actute and reactive
powers of a system. The Newton – Raphson method
as it is used in this project [Load flow studies of the
National 330Kv transmission Network] is based on
Taylor’s series and partial derivatives. And the
Jacobian matrix are formulated using this Newton –
Raphson technique. However, the application of
MATLAB program based on the Newton Raphson
method is used in the computation of the voltages
and the sinusoidal wave form of the three phase
voltages of the 330Kv transmission network is also
analyzed.
Keywords:      Voltage ‘V’, phase angle ‘d’, active
power ‘P’, Reactive power ‘Q’.  
 
1.0    INTRODUCTION

Because of large territorial extension of a typical power system, it’s interconnection with neighboring systems and its layered structure, a modern power system can be considered to be composed of several subsystems. Earlier standpoint on power system operation and control was based on underlying assumption of centrality. But a rigidly centralized monitoring and control of a large power system poses many problems load flow analysis or some variation of it has got an extensive use in the operation of modern power system. For an online load flow study, it is necessary to update some of its input data continuously and the output results are also to be used on a real time basis.

For a large power system it means a continuous collection of real time data form various points dispersed in a vast time data from various points dispersed in a vast geographical area, a continuous updating of a large data base and a continuous delivery of its output results to a large number of remote points. All these factors may seriously affect the reliability, speed and practicability of a monitoring and control scheme [1].

If computations for different subsystems of an integrated system are done concurrently using a number of processors, load–flow study can be done in a shorter time. If distributed processing is done in real time, data is to be collected from local points only and a comparatively smaller data base is to be updated locally at regular intervals. Transmission of data over long distance to the central processing computer is reduced when MATLAB is employed. The eastern part of the Nigeria 330Kv grid network consists of Onitsha – Newhaven (96 Km) 330kv transmission line, Onitsha – Alaoji (138km) 330kv transmission line and Alaoji – Afam (25km) 330kv transmission line [4]. The eastern part of the network takes its source from Benin, through the Benin – Onitsha (137km) 330 transmission line this location all in Nigeria. The performance of the transmission line depends on its four parameters; series inductance and resistance, shunt conductance and capacitance. These four parameters are uniform only distributed alone the line.

In a realistic power system, there are large numbers of buses, though; each bus is connected to only a small number of the remaining buses.

In a large power system, there is sparsity due to presents of zero elements. This sparsity help in reducing the bus admittances matrix, that the numbers of elements are minimized. Also, computer memory requirement is minimized, since only non – zero elements are to be stored. This resulted in high-speed computation.

1.1           ECONOMIC IMPORTANCE

Load–flow studies are the essential and vital part of power system studies. Load flow studies are extremely important and essential for power system planning, designing, expansion design and for providing guidelines to power system engineers.

1.3             Importance Of Load – Flow Study In Power  System

Load–flow evaluations provides power flow and voltages for a specified capability of generators’ condensers and tap changing under load transformers as well as specified net interchange between individual operating systems.

1.4       Newton – Raphson Method as Applied to Load – Flow Studies

One of the methods applied to load – flow studies, which can easily be programmed and run in a digital computer is the Newton – Raphson techniques. The load – flow problem can be solved by using the Newton – Raphson technique. Among the numerous solution methods available for load flow studies, the Newton – Raphson technique is considered to be the most sophisticated and important. The Newton – Raphson technique is based on Taylor’s series and partial derivatives [3]. The method is recent, involves less number of iterations to reach convergence, takes less computer time, involves less computation cost and has convergence that is certain. The Newton – Raphson technique is very accurate, and it is independent of some factors like:

Swing bus selection
Transformer regulation and
Numbers of iterations.

The number of iterations needed in Newton – Raphson method is almost independent of the size of the power system.

Convergence can be achieved at a shorter time, if the first iteration is done through Gauss – Seidel technique and then use voltage value obtained for starting the Newton – Raphson iterations. These voltages obtained are used to evaluate active power (P) of every bus except the slack bus and also reactive power (Q) wherever reactive power is specified. The correction of bus voltage is determined by the difference between calculated and specified values. The process of iteration is continued till the difference in the specified and calculated values of the active power, reaction power and voltage magnitude are within the given permissible limit.

In Newton – Raphson technique, partial derivatives of second and higher order are neglected, this assumption requires the initial solution to be close to the final solution [2].

1.5       BUS CLASSIFICATION IN LOAD FLOW STUDIES

In load – flow studies, four quantities are associated with each bus, the four quantities are; active power (P), reactive power (Q), voltage magnitude /V/, and phase angle (d). In a load–flow problem, two of the four quantities are specified and the bus classification depends on the type of quantities specified at each bus. Base on the type of quantities specified, three types of buses are classified. They are;

1.5.1    Generation Bus

1.5.2  Slack or Swing Bus

The summary of the above discussion is given in the table below;

Table 1.1:           Bus classification

TYPE OF BUS

SPECIFIED QUANTITIES

UNKNOWN

Generation Bus

P,    /V/

Q,     d

Load Bus

P,     Q

/V/,  d

Slack Bus

/V/,  d

P,     Q

2.0    LOAD–FLOW EQUATIONS BASED ON NEWTON – RAPHSON  

        TECHNIQUE

Newton – Raphson method can be applied to load – flow problems in a number of ways. The most common is those that uses polar co – ordinates and rectangular coordinates. In practice, Newton – Raphson method using polar coordinates is used. This is because the use of polar form results in a smaller number of equations than the total numbers of equations involves in rectangular form [6]. In this project, only the polar coordinate form will be discussed.

2.1  NEWTON – RAPHSON TECHNIQUE USING POLAR  

       COORDINATES

When the bus voltages are expressed in polar form, Newton – Raphson technique can be applied to the load flow problem.

For any ith bus,

Vi  =  Vi ejdi   – -  – - – - – -  (2.1)

Taking the complex conjugate of equation 3.1, gives

Vi*  =  Vie-jdi   – - – - – - -   (2.2)

Vk  =  Vk  ejdk  – - – - – -  (2.3)

yik   =  yik e-jqik  – - – - -  (2.4)

Where d is the phase angle of the bus voltage and θik is admittance angle.

The complex conjugate of the power injected by the generating source is given as;

Si   =  Pi – j Qi  =  Vi    S    yik  Vk  – - – - -  (2.5)

Substituting the values of equations 3.2, 3.3, and 3.4 into equation 3.5 gives

Pi – j Qi  =     S   Vi Vk yik e-j(θik + dI – dk)  – - – - – (2.6)

Thus,

Pi  =     S     Vi Vk yik Cos (θik  +  di  + dk ) – - – - – (2.7)

And,

Q  =    S   Vi Vk yik Sin (θik + di – dk)  – - – - (2.8)

For n = 2, 3, 4 – - – - n and slack bus is bus 1

The off – diagonal elements are

pi  =  Vi Vk yik Sin (θik + di – dk) for  J1  – - – - – -  (2.9

dk

pi  =  Vi  yik Cos (θik + di – dk) for J2    – - -  – -  (2.10)

 

Qi  =  Vi  Vk yik Cos (θik + di – dk) for J3    – - -  – -  (2.11)

Qi  =  Vi  yik Sin (θik + di – dk) for J4    – - -  – -  (2.12)

The diagonal element are:

pi  =    S    Vi Vk yik Sin (θik + di – dk) for J1    – -  – -  (2.13)di

pi  =   2Vi yii  Cos θii +    S   Vk yik Cos (θik + di – dk) for J2  

Vi           – -  – -  (2.14)Qi  =    S    Vi Vk yik  Cos (θik + di – dk) for J3   – - -  -  (2.15)  

pi  =   2Vi yii  Sin θii +    S    Vk yik Sin (θik + di – dk) for J4, 

Vi     - – - – - -  -  (2.16)

         

2.2  APPLICATION OF NEWTON – RAPHSON METHOD TO LOAD FLOW STUDIES OF THE EASTERN PART OF THE NATIONAL 330KV TRANSMISSION NETWORK

The eastern part of the national 330kv transmission network consists of Onitsha, Newhaven, Alaoji and Afam. For the purpose of this study, Afam (22) is taken as slack bus and given code as Bus 1, Alaoji (18) is taken as Bus 2, Onitsha (17) as Bus 3 and Newhaven (14) as Bus 4. The bus data for the system is given as

Bus Code

Pa

Qa

/V/

d 

PL

QL

Bus Type

1

4.51

0.00

1.03

0.00

0.44

0.21

Swing

2

0.00

0.00

1.00

0.00

2.76

1.34

Load

3

0.00

0.00

1.00

0.00

1.52

0.73

Load

4

0.00

0.00

1.00

0.00

1.32

0.64

Load

 

 

 

 

 

Table 2.0         Bus DataThe line admittance is given in the table below:                                                              

Bus Number

X(PU)

R(PU)

Z = R + jx

y = 1/z

1 – 2

0.0035

0.0005

0.0005 + j0.0035

40 – j280

2 – 3

0.419

0.0049

0.0049 + j0.0419

2.8 – j24

3 – 4

0.0296

0.0034

0.0034 + j0.0419

1.9 – j25

 

 

 

 

Table 2.1         Line Data   The Mutual – Admittances are computed as follows

y12  = y21  =  -40 + j280

y23  =  y32 = -28 + j24

y34  =  y43  =  -1.9 + j25

The Self – Admittances are computed as follows

y11  =  40 – j280

y22  =  y12 + y23 = 40 – j280 + 2.8 – j24 = 42.8 – j304

y33  =  y23  +  y34
y44  =  1.9 – j25
From equation 4.8
Q02  =  -V    V1 V21 Sin (q21 + d   - d   ) – V   V23 Sin
(θ23 + d   - d  ) – (V  ) y22 Sin q22
= -1.0  x  1.03  x  283 Sin 98 – 1.0  x  1.0  x  37 Sin 139
-12  x  307 sin (-82)= -288.7 – 2.4.3  +  304  =  -9
D Q    =  2.76 – (-9)  =  11.76
Q    =  -V    V2 y32 sin (q32 + d   – d  ) – V   V4 y34 Sin
(q34  + d   – d  ) – (V   )2  y33 Sin  q33
= -1 x 1 x 37 Sin 139 – 1 x 1 x 25 Sin 95 – 12 x 49 Sin (-85)
= -24.3 – 25  +  48.8  =  0.5 Q    =  0.73 – (-0.5)  =  1.23
Q    =  -V    V3 y43 Sin (q43  + d   – d   ) – (V  )2  y44 Sin q44
= -1 x 1 x 25 Sin 95 – 12 x 25 Sin (-85)= -24.9  +  24.9  =  0
D Q    =  0.64  +  0  =  0.64
Therefore,

D V    = 0.00368 x 11.76 – 0.00373 x 1.23 + 0.00373 x 0.64 =  0.04

D V    =  -0.00373 x 11.76 + 0.0458 x 123 – 0.0458 x 0.64= 0.017

D V    =  000373 x 11.76 – 0.0458 x 1.23 + 0.0859 x 0.64

= 0.04

Hence,V    =  V    + D V    = 1.00 + 0.04  =  1.04 Pu

V    =  V    + D V     =  1.00 – 0.017  =  0.983 pu

V    =  V   + D V    =  1.00 + 0.04  =  1.04 pu

                                                                                                           

3.0  SYSTEM IMPLEMENTATION

Since we are determining the magnitude of voltages, partial derivatives of the reactive power with respect to voltage magnitude is considered when formulating the Jacobian’s – Matrix. This is so because the flow of reactive power (Q) is not much affected by the changes in the phase angle (d), but affected by the variation in magnitude of bus voltage (DV).

The elements of Jocobian’s matrix are formulated with latest voltages given and computed power (reactive). However, manual computation of load – flow done using Newton – Raphson method is very complex and it very easy and simple. This is shown in Appendix one, which is the MATLAB code that generates computed voltages. The MATLAB program for Newton – Raphson is simpler and contains few lines when compared with MATLAB program for Gauss – Seidel method.

The sinusoidal wave form of the three phase voltage of the 330Kv transmission network is analyzed in appendix two, using MATLAB subplot command.

The beauty of the work – done is the fast convergences of computed values.

Finally, the values obtained when MATLAB is used are in accordance with the once obtained using numerical analysis (Newton – Raphson Technique in polar coordinates to show the bus voltage angles). These values converge with the specified values from PHCN data book, see appendix.

4.0   CONCLUSION AND

Load – flow studies is extremely important and essential in power system analysis. It provides (1) guide line to power system engineers and acts as operating instructor to generating station and substation for relay settings, switching sequence, loading, tap – setting etc.

Informations obtained from load flow studies are used in analyzing the effect of temporary loss of generating station or transmission path on the power flow. Also it help in preparing software for on line operation, control and monitoring of power system.

When digital computers are employed in load – flow studies, it is important to use the Newton – Raphson method.

            RECOMMENDATIONS

i.          Accurate and effective load – flow studies should be done to provide required information for power system operation.

ii.         The initial solution for the values obtained should not be very for from the actual solution.

iii.        The Newton – Raphson method should be analyze by using computer program such as MATLAB.

REFERENCE

[1]        Gupta, J.B. A Course in Power Systems, Tenth Edition, S.K. Kataria & Sons, 2006.

[2]        Gupta, B.R. Power System Analysis and Design, Second Edition, Whereler Puplishing 1997.

[3]        Stevenso, William D, Elemement of Power System Analysis, Second Edition, Mchraw Hill Book    Company,     New York, 1962.

[4]        Anazia, E. Lecture Note on Power System analysis.

[5]        www. Weley. Com

[6]        Suml S. Rao, Switchgear Protection and Power Systems, Eleventh Edition, Khanna Publishers, 2004.

[7]        www. Synergetix. Com/tech/source book/material.

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Lutvak also cited the recent strategic adjustments by Facebook as regards their renewed focus on the 35 and up marketplace. “We could see that advertisers wanted to see an evolution in social networking towards more mature age groups”, said Lutvak.

Observers have lauded Facebook for attracting an increasing number of business and professional users and more consumers in the 35-plus age categories than is usual for networking sites, which often skew younger. All this should mean growing advertising revenue for the site.

Industry experts have also said a broader base of investors seems ready to embrace social networks, citing as evidence the networks’ rapid growth and funding rounds by venture firms and rich individuals. A recent case in point: the $40 million raised by Ning, an online service that allows consumers to create their own social network “for free in seconds,” according to its Web site. Netscape pioneer Marc Andreessen is one of its co-founders.

All of this bodes well for Lifesmine.com provided they continue to grow rapidly. The company is using a combination of Google pay par click advertising and consumer generated online publicity to add new subscribers. With general internet user trends pointing to continued growth of internet penetration by Baby Boomer, Lifesmine.com is poised to enjoy even more growth.

Robert Cefail

Editor-In-Chief

Press Direct International

Nowadays, many of us receive e-mail invitations to join social networking websites such as Facebook, LinkedIn, or MySpace. These services make it easy for members to send out invitation emails complete with response links, and it is in their best interests to do so – as more friends sign up, these sites register higher visits and page views, potentially leading to increased advertising income.

While only a few well-known social networking sites used to exist, this number has skyrocketed, resulting in many more invitations in your e-mail Inbox. Even if you know the sender and name of a social network to which you’ve been invited, before you click on an invitation response link, take a second and consider that not all invitation e-mails are what they seem. Some fraudulent “friends” and “social networks” could have drastic consequences to your security and privacy:

1) Make sure the invite link actually goes to the social network website and not somewhere else trying to “phish” for your personal information! It’s better to copy and paste URLs into your web browser instead of clicking invite links, as there are many sneaky tricks to hide the true web addresses in e-mail messages.

Even when you copy and paste URLs into a web browser, before actually visiting the websites, look in the browser’s address bar for any text such as “redirect” or “goto”. These may be signs of someone trying to redirect you to a nefarious website.

For example, imagine getting the following link inside an e-mail message for a hypothetical “Google Social Networking Service”:

http://translate.google.com/translate?u=stopbadware.org&hl=en&ie=UTF-8&sl=es&tl=en

Since the e-mail claims to be from “Google”, and the web address contains “google.com”, this will take you to a page on Google’s website, right? If you visit the above link you will go somewhere else…

This misdirection link was just an example and fairly easy to detect. Real spam e-mails use lots of other tricks for obfuscating (hiding) true web addresses. Instead of copying and pasting links, it may prove even safer to just visit website homepages directly, skipping invitation links, and then asking senders to be re-invited as their friend.

2) Do you know the person sending the invite? Do you know the name of the social networking site? If you’ve never heard of neither, there’s a high probability the site or the member is spamming. Sign up to the site and be placed on the user’s “friend” list and your mailbox may be subjected to all sorts of unsolicited e-mail.

Just as responding to junk e-mail alerts spambots that your e-mail address is active, responding to junk social networking requests does the same thing.

If you do know the friend but not the social networking site, what’s wrong with sending a quick e-mail to your friend and asking them if their invite was legitimate? If it was, no big deal, but if it wasn’t, you might have alerted your friend to a problem they need to fix on their end.

3) Nefarious websites may be breeding grounds for spyware distribution. Visit the website with the wrong browser and/or wrong software installed, and your computer may become infected.

Think your computer, even with antivirus and anti-spyware software installed, cannot be infected? These software packages may be installed on your system, and the wrong version combined with a 0-day exploit (a previously-unknown bug that has not been patched) can allow spyware / malware to be installed (this is not an exhaustive list):

Internet Explorer Macromedia Flash Mozilla Firefox Opera QuickTime for Windows RealPlayer Safari Shockwave Windows Media Player … And the list goes on.

4) When you access the social networking website, does it ask questions such as the following during the signup process?

* Social Security Number (a big NO-NO!)

* Name and password to another e-mail account so the site can notify all your contacts to join the social network (or nefarious sites can use your account to send e-mail spam to all your contacts UNDER YOUR NAME!)

* Mother’s Maiden Name (while legitimate networks may ask this for a “Security Question”, I would not provide it. This is one type of information miscreants can use to possibly get more information about yourself or sign up for credit or other offers in your name).

* Credit Card or Bank Account Number (unless it’s a LEGITIMATE SITE, you know it’s not a phishing site, and you’re signing up for subscription/premium services, NEVER, NEVER, NEVER PROVIDE THIS INFORMATION! This can cost you money, time, aggravation, and your credit rating.)

These are just four techniques nefarious social networks and/or members can use to violate your privacy, cost you time and money, and possibly harm your credit rating. While I’m not saying you should never join social networks, just be a little careful when you get invitations. Know who is sending you the invite and the legitimacy of the social network. Confirm the invite and visit the social network’s homepage directly. Plus, never provide too much information when signing up. Follow this advice to help increase your safety on the Internet while having fun joining your friends in social networks.

Make your social network earn money for you. Choose the right social network software to design your website, and provide the right kind of services to retain the users, helping them to invite their friends, in an attempt to build up large communities and groups. Provide them with enough opportunity to spend more and more time on your website, and slowly create that customer loyalty which is so very important in running a social networking website. The longer that the user remains on your website, they get more and more familiar with the name, and also get to know the products and the premium services that you offer. Your website starts to generate business as customer confidence builds up.
You would need to create a brand for big business coming your way. You would just need to see the kind of worldwide traffic visiting MySpace and Facebook, and spending considerable time in there. It is simply because the websites have been successful in creating a brand name for themselves, offering services that retain customers. The longer time that users hang around on your website, the more business opportunities are created for you. Your social networking software must be able to provide such facilities to the users, where the tools that you provide, help them to build their own identity amongst the groups and community that they join. Your website must be able to generate that interest in the users, making them spend more and more time in networking.
When you look at creating big business, your social network software must be able to generate interest in attracting advertisements from other well known websites. Last year, Google has paid nearly a billion US dollars to MySpace to put its advertisement on their site. Myspace also shared the revenue that was generated from the Google advertisements. That is big business. Your social networking website can earn money for you, when other business advertises on your site. But why should a running web business advertise on your website? Simple, since you have been able to create a huge database of the users. Obviously, advertising on your social networking website would prove to be advantageous.
Social networking helps to build up personal or professional set of relationships between individuals. It represents both, a collection of ties between people, and the strengthening of those ties as well. A website, which utilizes the right social network software, can provide a tool to measure of the loyalty that builds up by the continued presence of the users, and, at the same time, assists in determining how the information flows within the groups, building up and fostering the growing trust within.
There is good number of advantages in having your own social networking website. It has a great amount of value in internet marketing. It is also true that internet marketing could also be established without such a network, by getting involved in MLM with friends and relatives, purchasing email addresses and sending off flyer advertisements regarding your products, and many more. The marketing options become restricted than what it would be without a social networking website. For one, it is much easier to put together a large email address list by owning a social networking website. For such a website, you need to plan and have a marketing strategy, and with the deployment of the right social network software, much could be achieved.
In purchasing email lists, you need to remember, that the vast majority of the people in that email list is not interested in what business you have, no matter what it is. Most of your marketing email to the list would be considered as spamming, since there is no interest what-so-ever in what you have to offer. Even if you had tangible goods to offer for people to buy, there would not be any significant success in marketing your products, if you are restricted to email marketing using purchased email address listings.
So how would you benefit from having your own Private Social Network?
Here’s how:
-Build up your brand.
-Increase customer loyalty.
-Expand your customer base virally.
-Increase Traffic to your online content.
-Improve Communities.
-Up-sell Products & Services.
-Increase Market Differentiation.
-Boost Revenue.
-Reduce customer service costs.
-Retain customers.
If you are in a competitive business, where you need the attention of people, having your own social networking website is the only solution for you to build up customer loyalty and stand out more prominently in the marketplace. For such a website, you would need the right social networking software to provide you with the tools. As long as you can draw users on your website, more and more communities would develop, bringing in the customer loyalty that is so very much important for any business.