28-02-2010, 11:58 PM
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ABSTRACT
In recent years, digital computer is becoming most appropriate tool to solve any engineering problem. In last two decades number of programs have been developed for computers in solving power system problems. Many of these programs deal with system load flow, short circuit currents, stability, and for control of power systems. The higher percentage of proper utility of computers in distribution systems saves engineering time and investment.
All the time the distribution engineer encounters the routine problems of voltage, reactive power, short circuit current which are monotonous and time consuming. The proper use of digital computer release distribution engineer from his tedious, repetitive calculations, allowing him to use that time more effectively for distribution system planning.
One can solve his individual problems on computers of small and medium size. Generally the problems are sequential and follow fixed mathematical relationships and they can be successfully programmed. The nature of problem accuracy and saving in time are the main governing factors in computer programs.
In the present work, emphasis is laid on developing digital computer program for load flow calculations of distribution networks.
Load flow techniques are widely used in the planning and daily operation of power systems including that of the online monitoring of distribution system operation.
This dissertation work presented an innovative technique for load flow calculations of distribution networks called dist flow method. In this method, a method of reducing radial network into a single line equivalent has been developed which simplifies lengthy calculations of reduced network. The reduced network also enables the fast computation of load flow solutions of distribution networks.
Presented By
By
S. MAHABOOB BASHA
(05063A2011)
INTRODUCTION
In India, the distribution systems losses is about 12% of the generation, which is high when compared to developed countries. In attempting to reduce distribution system losses, a thorough knowledge of distribution system losses, a thorough knowledge of distribution system loss calculation has to be understood.
Presently computers are widely used to solve utility engineering problems. New programs are being developed for load flow stability, short circuit, and for control of power systems. Considering the utility investment in the distribution system, new tools are essential to save engineering time and to reduce investment. In solving distribution problems, tedious hand calculations can be avoided with the help of new algorithms and preferably with small computing systems.
A power system is an inter connected system composed of generating stations, which convert fuel energy into electricity. Substations that distribute electrical power to loads (consumers) and transmission lines that tie the generating stations and distribution substations together. According to voltage levels an electric power system can be viewed as consisting of generating system, a transmission system and a distribution system.
The distribution system is generally categorized into two subdivisions.
1. Primary Distribution
Which carries load at higher than utilization voltages from the substation (or other source) to the point where the voltage is to be stepped down to the value at which the energy is utilized by the consumer.
2. Secondary Distribution
Which includes the part of the system operation at utilization voltage, upto the meter at the consumer's premises.
Primary distribution system include the following basic types.
i. Radial system and
ii. Loop systems.
Chapter 2 explains in detail about the innovative technique for load flow calculations reactive power analysis of distribution networks. A method for reducing a radial network into a single line equivalent, known as Dist flow method has been developed by G.B. Jasmon and L.H.C.C. Lee which simplifies lengthy calculations of an unreduced network. This reduced network also enables the fast computation of load flow solutions of distribution networks. The conditions for voltage collapse to occur are easily derived form the single line equivalent.
The complete simplification of equations involved are given in Chapter 2.
Application of this Dist flow method for two test systems is explained using software programme in Chapter 4 and the results thus obtained are given in Chapter 5.
1.1 DISTRIBUTION SYSTEMS
1.1.1 Introduction
An electric distribution system, or distribution plant as it sometimes called, is all of that part of an electric power system between the bulk power source or sources and the consumer's service switches. The bulk power sources are located in or near the load area to be served by the distribution system and may be either generating stations or power substations supplied over transmission lines. Distribution system can, in general, be divided into six parts, namely, subtransmission circuits, distribution substations, distribution transformers, secondary circuits (or) secondaries, and consumer's services connections and meters (or) consumer's services.
The subtransmission circuits extend from the bulk power source or sources to the various distribution substations located in the load area. They may be radial circuits connected to a bulk power source at only one end or loop and ring circuits connected to one or more bulk power sources at both ends. The subtransmission circuits consist of underground cable, aerial cable, or overhead open-wire conductors carried on poles, or some combination of them. The subtransmission voltage is usually between 11 and 33 kv, inclusive.
Each distribution substation normally serves its own load area, which is a subdivision of the area served by the distribution system. At the distribution system substation the subtransmission voltage is reduced for general distribution throughout the area. The substation consists of one or more power-transformer banks together with the necessary voltage regulating equipment, buses, and switch gear.
The area served by the distribution substation is also subdivided and each subdivision is supplied by a distribution or primary feeder. The 3- primary feeder is usually run out from the low voltage bus of the substation to its load centre where it branches into three phase subfeeders and 1- laterals. The primary feeders and laterals may be either cable (or) open wire circuits.
The distribution plant occupies an important place in any electric power system. Briefly, its function is to take electric power from the bulk power source or sources and distribute to deliver it to the consumers. The effectiveness with which a distribution system fulfills this function is measured in terms of voltage regulation, service continuity, flexibility, efficiency and cost.
1.2 Types of Distribution Systems
1.2.1 The Radial System
The radial type of distribution system, a simple form. It is used extensively to serve the light and medium density load areas where the primary and secondary circuits are usually carried over head on poles. The distribution substation or substations can be supplied from the bulk power source over radial or loop subtransmission circuits or over a subtransmission grid or network. The radial system gets its name from the fact that the primary feeders radiate from the distribution substations and branch into subfeeders and laterals which extend into all parts of the area served. The distribution transformers are connected to the primary feeders, subfeeders, and laterals, usually through fused cutouts, and supply the radial secondary circuits to which the consumer's services are connected.
Fundamentally the advantages of the radial distribution system are simplicity and low first cost. These result from a straight forward circuits arrangement where a single (or) radial path is provided from the distribution substation, and sometimes from the bulk power source, to the consumer. With such a circuit arrangement the amount of switching equipment is small and the protective relaying is simple. Although simplicity and low first cost account for the wide spread by of the radial system they are not present in all forms of the system.
The lack of continuity of service is the principal defect of the radial system of distribution. Attempts to over come this defect have resulted in many forms and arrangements of the radial system. Frequently the system is radial only from the distribution substations to the distribution transformers. Because of the many system arrangements encountered is some times difficult to determine in what major type of a system should be classified. To aid in such classification and to allow more readily the discussion of radial systems, it should be remembered that a radial system is a system having a single path over which current may flow for a part or all of the way from the distribution substation or substations to the primary of any distribution transformer.
1.2.2. The Loop System
The loop type of distribution system is used most frequently to supply bulk loads such as small industrial plants and medium (or) large commercial buildings, where continuity of service is of considerable importance. The subtransmission circuits of the loop system should be parallel (or) loop circuits or a subtransmission grid. These subtransmission circuits should supply a distribution substation (or) substations. The reason for this is that as much or more reliability should be built into the system from the low-voltage bus of the distribution substation back to the bulk power source (or) sources as is provided by the loop primary feeders. The use in a loop system of a radial subtransmission circuit or circuits and a distribution substation (or) substations, which may not provide good service continuity, does not give a well coordinated system. This is because a fault on a subtransmission circuit or in a distribution substation transformer results in a interruption of service to the loads supplied over the more reliable loop primary feeders. The subtransmission circuits and distribution substations are often common to both radial and loop type distribution systems.
MODELING OF DISTRIBUTION SYSTEMS
2.1. Load Flow Analysis
Distribution system has not received much attention unlike load flow analysis of transmission systems. However, some work has been carried out on load flow analysis of a distribution network but the choice of a solution method for a practical system is often difficult. Generally distribution networks are radial and the R/X ratio is very high. Because of this, distribution networks are ill-conditioned and conventional Newton Raphson (NR) and fast decouple load flow (FDLF) method are inefficient at solving such networks.
Baran and Wu [1], obtained the load flow solution in a distribution system by the iterative solution of three fundamental equations representing real power, reactive power and voltage magnitude. These three equations are very useful, since they deal to the use in real physical systems than in other traditionally known forms, in this dissertation work, equations, have been further developed in which the loss terms in two of the fundamental equations are grouped and represented in a single line equivalent. Present work extends the single line equivalent network to be used for load flow calculations and for deriving the condition for voltage collapse to occur. Due to simplicity of the single line equivalent technique, stability analysis based on this equivalence is much simplified making it most suitable for use in real time distribution system monitoring. A further special feature of the method illustrated in this work is that all voltage terms are eliminated from the equations for solving the load flows there by simplifying the equations for iterative solution.
In India, all the 11 KV rural distribution feeders are radial and too long. The voltages at the far end of many such feeders are very low with very high voltage regulation more preferable. Another advantage of the distflow method is that it requires less computer memory. Convergence is always guaranteed for any type of practical radial distribution network with a realistic R/X ratio while using the distflow method. Loads in the present formulation have been represented as constant power. However, the dist flow method can easily include composite load modelling. Several practical rural radial distribution feeders in India have been successfully solved using the dist flow method. The data of various radial systems can be obtained using the On line production of load data in substations [10] system described by Schrock and K.C.Kwong[10].
2.2. On Line Production of Load Data in Substations
The acquisition of statistical data on a power system is a necessary part in its operation and planning. The essential information, such as average daily load curve and maximum demand is often derived by a combination of pulse summation and computer analysis. A microprocessor based system has been developed which captures and analyses voltages and currents on feeders and produces a set of reduced data which fully describes the recent load pattern locally in the substation. Such a system is described by F.S.Schroder and K.C.Kwong.
The load on a power system is characterised by the fact that it is determined by the consumer and not the electricity authority. Consequently, it must be metered firstly so that it can be controlled and secondly so that a record is kept for later analysis. A microprocessor systems is chosen so that the load data could be fully analysed locally in the substation and only the minimum amount of data consistent with the provision of all the necessary
information to describe what loads have occured is outputed. A number of such statistical metering schemes are available commercially. In the system developed by the author[10] the statistical data is on-line and could be displayed on the screen of a Video Display Unit or on a printer at any time. This data is also in a much condensed format and is immediately usable for planning and system operation purposes from the hard-copy printer output. Alternatively the data could be transferred onto a cassette tape for archive and
for further analysis.
The system as developed is aimed for the acquisition of statistical data in a medium size substation. It caters for the measurement of both balanced and unbalanced feeder loads using a flexible combination of input channels.
The data returned by the data acquisition system can be accessed for functions such as
detection of power failures (when the voltage drops to below 20% of the rated value).
measurement of time when the voltage value falls outside the +6% limits.
detection of maximum demands and their times of occurrence. to predict the voltage collapse (point of occurrence).
This system is a joint effort between the South East Queensland Electricity Board & The Capricornia Institute of Advanced Education.
2.3 Methodology
Distflow Method
2.3.1. Mathematical formulation of Techniques
Governing equations of a single-line system.
Before proceeding to the actual system we first derive the equations that characterize the behaviour of a single-line system.
Consider the single line in fig. 1 which has the following parameters.
Where
P : Injection of real power
Q : Injection of reactive power
r : Resistance of the line
x : Reactance of the line
PL : Real load
QL : Reactive load
V : Voltage magnitude
From fig. (1) the real and reactive power equations have been derived as
P = resistive loss in the line + real load
i.e. P = I2r+PL
the current through the line, I in terms of P and Q is
I2 =
Therefore the equation becomes
P = ¦ (1)
Similarly the reactive power
Q = ¦ (2)
From equations (1 and 2), we can eliminate the terms.
From equation (1)
P =
¦ (3)
and from the equation (2)
Q =
¦ (4)
From equations (3) and (4) the resultant equation can be written as
= r(Q-QL)
By rearranging¦5
= r(Q-QL)
(Q-QL) =
Q =
Squaring on both sides,
Now this Q2 substitute in equation (1)
The voltage at the sending end is the reference voltage and its magnitude is kept constant, and in this case V2=1.
Therefore the equation becomes
From this equation a quadratic equation in terms of P is obtained as follows:
Finally we get,
From the above equation, the expression for P can be obtained as
¦ (6)
Similarly for the reactive power Q,
Rearranging the equation (5) and eliminating P in equation (2)
P =
Squaring on both sides,
Substitute this value of P in equation (2)
=
Q =
The above equation can be written as
(Since V2=1).
Therefore the equation becomes,
+
This is the quadratic equation interms of Q.
From the above equation, the expression fro reactive power Q can be obtained as
¦ (7)
2.3.2. Power Flow Equations:
Consider the radial network
Fig. 4: Online Diagram of a radial Network
We represent the line with impedance and loads as constant power sinks power flow in a radial distribution network can be described by a set of recursive equations that are structurally rich and conductive for computationally efficient solutions. Those power flow equations are called DISTFLOW Branch equations, that use the real power, reactive power and voltage magnitude at the sending end of a branch i.e., Pi, Qi, Vi respectively to express the same quantities at the receiving end of the branch as follows:
= - ¦ (8)
= - ¦ (9)
= ¦ (10)
Hence if P1, Q1, V1 at the first node of the network is known or estimated, then the same quantities at the other nodes can be calculated by applying the above branch equations successively. We shall refer to this procedure as a FORWARD UP DATE.
Dist flow branch equations can be written backward too, i.e., by using the real power, reactive power and the voltage magnitude at the receiving end of a branch Pi, Qi, Vi to express the same quantities at the sending end of the branch. The result is the following recursive equations, called the BACKWARD branch equations.
= ¦ (11)
= ¦ (12)
= ¦ (13)
Where =
=
The procedure is referred as BACKWARD UPDATE. Similar to forward update, a Back ward update can be defined.
Start updating from the last node of the network assuming the variables at that point are given and proceed backward calculating the same quantities at the other nodes by applying (11), (12) and (13) successfully. Updating process ends at the first node (i.e., at node 1) and will provide the new estimate of the power injections into the network P1 and Q1.
Note that by applying backward and forward update schemes successively one can get a power flow solution.
2.3.3. Reduction of Real Network to a Single Line Equivalent
In this section we will show how a given power distribution network can be reduced to a single line equivalent.
The real and reactive power flows in any line are given by
= -
= -
The real and reactive loss terms in the above equations are
= ¦ (14)
= ¦ (15)
Using equation (2.14) the ratio of real losses (LPi) between branch i and proceeding branch i+1 can be computed as,
=
= ¦ (16)
By considering the current flow in the branch i,
=
From the above equation the voltage ratio between branches i and i+1 is
= ¦ (17)
equation (2.17) can be submitted in equation (2.16) to get the ratio of real losses
=
=
Similarly for the ratio of reactive losses
= .
=
= ¦ (19)
For a given distribution network the total injected real and reactive powers are:
P = ¦ (20)
Q = ¦ (21)
From the equation (18) and (19) it can be seen that the losses in the distribution network are ratios of the losses in the preceding branch of the network.
Hence
P = ¦ (22)
Q = ¦ (23)
Since (V2 = 1)
Where
req is the equivalent resistance of the single line
and xeq is the equivalent reactance of the single line
Hence we have now reduced the real distribution network consisting of many branches into a system with only one line.
The values of req and xeq can be obtained by
= ¦ (24)
xeq = ¦ (25)
Where
TLP = LPi is the total real power losses in the system with a power injection of .
TLQ = LQi is the total reactive power losses in the system with a power injection of .
Power Factor: Power factor is defined as Ratio of active power (in KW) to the apparent power (in KVA).
(26)
Where p “ is active power.
q “ is reactive power
REACTIVE POWER COMPENSATION
INTRODUCTION
Shunt and series reactive compensation using capacitors has been 3 widely recognized and powerful method to combat the problems of voltage drops, power losses, and voltage flicker in power distribution networks. The importance of compensation schemes has gone up in recent years due to the increased awareness on energy conservation and quality of supply on the part of the Power Utility as well as power consumers. This article (in two parts) amplifies on the advantages that accrue from using shunt and series capacitor compensation. It also tries to answer the twin questions of how much to compensate and where to locate the compensation capacitors.
3.1 SHUNT CAPACITOR COMPENSATION IN DISTRIBUTION SYSTEMS:
Fig. 1 represents an a.c. generator supplying a load through a line of series impedance (R+jX) ohms, fig. 2(a) shows the phasor diagram when the line is delivering a complex power of (P+jQ) VA and Fig. 2 -(b) shows the phasor diagram when the line is delivering a complex power of (P+jO) VA i.e. with the load fully compensated. A thorough examination of these phasor diagrams will reveal the following facts. which is higher by a factor of compared to the minimum power loss attainable in the system.
2. The loading on generator, transformers, line etc is decided by the current flow. The higher current flow in the case of uncompensated load necessitated by the reactive demand results in a tie up of capacity in this equipment by a factor of i.e. compensating the load to UPF will release a capacity of (load VA rating X Cos) in all these equipment.
3. The sending-end voltage to be maintained for a specified receiving-end voltage is higher in the case of uncompensated load. The line has bad regulation with uncompensated load.
4. The sending-end power factor is less in the case of an uncompensated one. This due to the higher reactive absorption taking place in the line reactance.
5. The excitation requirements on the generator is severe in the case of uncompensated load. Under this condition, the generator is required to maintain a higher terminal voltage with a greater current flowing in the armature at a lower lagging power factor compared to the situation with the same load fully compensated. It is entirely possible that the required excitation is much beyond the maximum excitation current capacity of the machine and in that case further voltage drop at receiving-end will take place due to the inability of the generator to maintain the required sending-end voltage. It is also clear that the increased excitation requirement results in considerable increase in losses in the excitation system.
It is abundantly cleat from the above that compensating a lagging load by using shunt capacitors will result in
i. Lesser power loss everywhere upto the location of capacitor and hence a more efficient system
ii. Releasing of tied-up capacity in all the system equipments thereby enabling a postponement of the capital intensive capacity enhancement programmes to a later date.
iii. Increased life of eqipments due to optimum loading on them
iv. Lesser voltage drops in the system and better regulation
v. Less strain on the excitation system of generators and lesser excitation losses.
vi. Increase in the ability of the generators to meet the system peak demand thanks to the released capacity and lesser power losses.
Shunt capacitive compensation delivers maximum benefit when employed right across the load. And employing compensation in HT & LT distribution network is the closest one can get to the load in a power network. However, various considerations like ease of operation end control, economy achievable by lumping shunt compensation at EHV stations etc will tend to shift a portion of shunt compensation to EHV & HV substations. Power utilities in most countries employ about 60% capacitors on feeders, 30% capacitors on the substation buses and the remaining 10% on the transmission system. Application of capacitors on the LT side is not usually resorted to by the utilities.
Just as a lagging system power factor is detrimental to the system on various counts, a leading system pf is also undesirable. It tends to result in over-voltages, higher losses, lesser capacity utilisation, and reduced stability margin in the generators. The reduced stability margin makes a leading power factor operation of the system much more undesirable than the lagging p.f operation. This fact has to be given due to consideration in designing shunt compensation in view of changing reactive load levels in a power network.
Shunt compensation is successful in reducing voltage drop and power loss problems in the network under steady load conditions. But the voltage dips produced by DOL starting of large motors, motors driving sharply fluctuating or periodically varying loads, arc furnaces, welding units etc can not be improved by shunt capacitors since it would require a rapidly varying compensation level. The voltage dips, especially in the case of a low short circuit capacity system can result in annoying lamp-flicker, dropping out of motor contactors due to U/V pick up, stalling of loaded motors etc and fixed or switched shunt capacitors are powerless against these voltage dips. But Thyristor controlled Static Var compensators with a fast response will be able to alleviate the voltage dip problem effectively.
3.2. SERIES CAPACITOR COMPENSATION IN DISTRIBUTION SYSTEMS:
Shunt compensation essentially reduces the current flow everywhere upto the point where capacitors are located and all other advantages follow from this fact. But series compensation acts directly on the series reactance of the line. It reduces the transfer reactance between supply point and the load and thereby reduces the voltage drop. Series capacitor can be thought of as a voltage regulator, which adds a voltage proportional to the load current and there by improves the load voltage.
Series compensation is employed in EHV lines to 1) improve the power transfer capability 2) improve voltage regulation 3) improve the load sharing between parallel lines. Economic factors along with the possible occurrence of sub-synchronous resonance in the system will decide the extent of compensation employed.
Series capacitors, with their inherent ability to add a voltage proportional to load current, will be the ideal solution for handling the voltage dip problem brought about by motor starting, arc furnaces, welders etc. And, usually the application of series compensation in distribution system is limited to this due to the complex protection required for the capacitors and the consequent high cost. Also, some problems like self-excitation of motors during starting, ferroresonance, steady hunting of synchronous motors etc discourages wide spread use of series compensation in distribution systems.
3.3. SHUNT CAPACITOR INSTALLATION TYPES:
The capacitor installation types and types of control for switched capacitor are best understood by considering a long feeder supplying a concentrated load at feeder end. This is usually a valid approximation for some of the city feeders, which emanate from substations, located 4 to 8 Kms away from the heart of the city. Ref Figs 3 & 4.
Absolute minimum power loss in this case will result when the concentrated load is compensated to up by locating capacitors across the load or nearby on the feeder. But the optimum value of compensation can be arrived at only by considering a cost benefit analysis.
The reactive demand of the load varies over a day and a typical reactive demand curve for a day is given in fig. 5.
It is evident from fig.5 that it will require a continuously variable capacitor to keep the compensation at economically optimum level throughout the day. However, this can only be approximated by switched capacitor banks. Usually one fixed capacitor and two or three switched units will be employed to match the compensation to the reactive demand of the load over a day. The value of fixed capacitor is decided by minimum reactive demand as shown in Fig 5.
Automatic control of switching is required for capacitors located at the load end or on the feeder. Automatic switching is done usually by a time switch or voltage controlled switch as shown in Fig 5. The time switch is used to switch on the capacitor bank required to meet the day time reactive load and another capacitor bank switched on by a low voltage signal during evening peak along with the other two banks will maintain the required compensation during night peak hours.
3.4 ECONOMIC JUSTIFICATION FOR USE OF CAPACITORS:
The increase in benefits for 1 kVAR of additional compensation decrease rapidly as the system power factor reaches close to unity. This fact prompts an economic analysis to arrive at the optimum compensation level. Different economic criteria can be used for this purpose. The annual financial benefit obtained by using capacitors can be compared against the annual equivalent of the total cost involved in the capacitor installation. The decision also can be based on the number of years it will take to recover the cost involved in the Capacitor installation. A more sophisticated method would be able to calculate the present value of future benefits and compare it against the present cost of capacitor installation.
When reactive power is provided only by generators, each system component (generators, transformers, transmission and distribution lines, switch gear and protective equipment etc) has to be increased in size accordingly. Capacitors reduce losses and loading in all these equipments, thereby effecting savings through powerless reduction and increase in generator, line and substation capacity for additional load. Depending on the initial power factor, capacitor installations can release at least 30% additional capacity in generators, lines and transformers. Also they can increase the distribution feeder load capability by about 30% in the case of feeders which were limited by voltage drop considerations earlier. Improvement in system voltage profile will usually result in increased power consumption thereby enhancing the revenue from energy sales.
Thus, the following benefits are to be considered in an economic analysis of compensation requirements.
i. Benefits due to released generation capacity.
ii. Benefits due to released transmission capacity.
iii. Benefits due to released distribution substation capacity.
iv: Benefits due to reduced energy loss.
v. Benefits due to reduced voltage drop.
vi. Benefits due to released feeder capacity.
vii. Financial Benefits due to voltage improvement.
Which are the benefits to be considered in capacitor application in distribution system Capacitors in distribution system will indeed release generation and transmission capacities. But when an individual distribution feeder compensation is in question, the value of released capacities in generation and transmission system are likely to be too small to warrant inclusion in economic analysis. Moreover, due to the tighty inter-connected nature of the system, the exact benefit due to capacity release in these areas is quite difficult to compute. Capacity release in generation and transmission system is probably more relevant in compensation studies at transmission and sub- transmission levels and hence are left out from the economic analysis of capacitor application in distribution systems.
3.4.1. Benefits due to released distribution substation capacity:
The released distribution substation capacity due to installation of capacitors which deliver Qc MVARs of compensation at peak load conditions may be shown to be equal to
In general and when
Sc = Released station capacity beyond maximum station capacity at original power factor
SC = Station Capacity
Cos = The P.F at the station before compensation :
The annual benefit due to the released station capacity = where C= Cost of station & associated apparatus per MVA
3.4.2. Benefits due to reduced energy losses:
Annual energy losses are reduced as a result of decreasing copper loss due to installation of capacitors. Information on type of capacitor installation, location of installation nature of feeder loading etc. are needed to calculate this. The calculation can proceed as follows.
Let a current flow through a resistance R. The power loss is (Ij2+ I22)R- The power loss due to reactive component is I22 R. Compensating the feeder will result in a change only in I2. Hence the new power loss will be (I22+(I2-IC) 2) R where Ic is the compensating current. Hence the decrease in power loss due to compensating part of reactive current is (2 I2Ic-Ic2) R.
Now, if I2 is varying (it will be varying according to reactive demand curve) the average decrease in power loss over a period of T hours will be equal to (2 I2Ic FR-Ic2) R where I2 stands for peak reactive current during T hours through the feeder section of resistance R, Ic is compensation current flowing through the same section for the same period and FR is reactive load factor for T hours in the same section. Thus total energy savings in this section of feeder for T hours will be 3(2I2IcFR-Ic2) RT.
One day can be divided in to many such periods depending on the number of fixed and switched capacitors and the sequence of operation of switched capacitors. Also, the feeder can be modelled by uniformly distributed load or discrete loading and total energy savings can be found out for each period over the entire period by mathematical integration or discrete summation. The daily and hence the annual energy savings for the entire feeder can be worked by an aggregation over the time periods.
Let E this value if total energy savings per year. Annual benefits due to conserved energy will be E cost of energy.
3.4.3. Benefits due to released feeder capacity :
In general feeder capacity is restricted by voltage regulation considerations rather than thermal limits. Shunt compensation improves voltage regulation and there by enhances feeder capacity. This additional feeder capacity can be calculated as where Qc is compensation (MVAR) employed, X and R are feeder reactance & resistance respectively and Cos is the P.F before compensation. The annual benefits due to this will be SF X C x i where C is the cost of the installed feeder per MVA and / is the annual fixed charge rate applicable.
3.4.4. Financial benefits due to voltage improvement :
Energy consumption increases with improved voltage. Exact value of the increased consumption can be worked out from a knowledge of elasticity of loads of the concerned feeders with respect to voltage, Let it be EC. Annual revenue increase due to this will be Ecx cost of energy.
3.4.5. Annual equivalent of total cost of the installed capacitor banks.
This will be equal to QcxCxi where Qc is total capacitive MVAR to be installed, C is cost of capacitors per MVAR and / is the annual fixed charge applicable.
The total annual benefits should be compared against the annual equivalent of total cost of capacitors to arrive at optimum compensation levels.
3.5. SELECTION OF CAPACITOR RATINGS:
In this project the rule of A.P.E.R.C. (Andhra Pradesh Electrical Regulatory Commission) for connecting capacitors is used at all loads.
According to A.P.E.R.C. rule for every 5HP load a capacitor of rating 2 KVAR must be connected at loads (i.e. 0.536 KVAR for 1 KW).
CASE STUDY OF DIST FLOW METHOD
4.1 FLOW CHART
4.2 ALGORITHM FOR DIST FLOW METHOD
1. Start the initial iteration by using the total real loads and reactive loads as the initial power injection.
2. Sum all the real and reactive losses and find the equivalent resistance (req) and reactance (Xeq) for a single “ line system equations (2.24) and (2.25).
3. Calculate the new power injection by using equations (2.6) and (2.7). If Pi+1 “ Pi < e, where ˜e™ is a set tolerance of 0.0001, then go to step 5, other wise go to step 4.
4. Iterate with new power injection from step 3, then go to step 2.
5. Calculate other parameters required, eg voltages, p.f. The voltage can be calculated from the losses and power injections in the individual lines from equations (2.8), (2.9), (2.10) and (2.26).
4.3. SYSTEM DATA & NETWORKS
CASE STUDY “ 1 (DATA & FIGURE)
Single line diagram of a 33 bus Network having a base voltage of 11 KV and base MVA of 10.00
CASE STUDY “ 2 (DATA & FIGURE)
Single line diagram of a 12 bus Network having a base voltage of 11 KV and base MVA of 10.00
INPUT DATA OF A 33 BUS SYSTEM HAVING A BASE VOLTAGE OF 11KV AND BASE MVA OF 10.00
Branch No. Sending Node Receiving Node Resistance in Ohms Reactance in Ohm Active Power in KW Reactive Power in KVAR
1 1 2 .0922 .047 100 90
2 2 3 .493 .2511 90 50
3 3 4 .366 .1864 120 80
4 4 5 .3811 .1941 60 40
5 5 6 .819 .707 60 40
6 6 7 .1872 .6188 200 120
7 7 8 1.7114 1.2351 200 120
8 8 9 1.03 .74 160 120
9 9 10 1.044 .74 60 40
10 10 11 .1966 .065 45 30
11 11 12 .3744 .1238 60 35
12 12 13 1.468 1.155 60 35
13 13 14 .5416 .7129 120 80
14 14 15 . 591 .526 60 40
15 15 16 .7463 .545 70 40
16 16 17 1.289 1.721 60 40
17 17 18 .732 .574 90 50
18 2 19 .164 .1565 90 50
19 19 20 1.5042 1.3554 90 60
20 20 21 .4095 .4784 90 50
21 21 22 .7089 .9373 90 60
22 3 23 .4512 .3083 90 50
23 23 24 .898 .7091 320 180
24 24 25 .896 .7011 320 200
25 6 26 .203 .1034 60 250
26 26 27 .2842 .1447 60 100
27 27 28 1.059 .9337 60 50
28 28 29 .8042 .7006 120 70
29 29 30 .5075 .2585 100 60
30 30 31 .9744 .963 150 200
31 31 32 .3105 .3619 210 170
32 32 33 .341 .5302 100 70
MODIFIED INPUT DATA OF A 33 BUS SYSTEM HAVING A BASE VOLTAGE OF 11KV AND BASE MVA OF 10.00
Branch No. Sending Node Receiving Node Resistance in Ohms Reactance in Ohm Active Power in KW Reactive Power in KVAR
1 1 2 .0922 .047 100 36.39
2 2 3 .493 .2511 90 1.751
3 3 4 .366 .1864 120 15.668
4 4 5 .3811 .1941 60 7.834
5 5 6 .819 .707 60 7.834
6 6 7 .1872 .6188 200 12.78
7 7 8 1.7114 1.2351 200 12.78
8 8 9 1.03 .74 160 34.224
9 9 10 1.044 .74 60 7.834
10 10 11 .1966 .065 45 5.8755
11 11 12 .3744 .1238 60 2.84
12 12 13 1.468 1.155 60 2.834
13 13 14 .5416 .7129 120 2.834
14 14 15 . 591 .526 60 15.668
15 15 16 .7463 .545 70 7.834
16 16 17 1.289 1.721 60 2.473
17 17 18 .732 .574 90 7.834
18 2 19 .164 .1565 90 1.751
19 19 20 1.5042 1.3554 90 1.751
20 20 21 .4095 .4784 90 11.751
21 21 22 .7089 .9373 90 1.751
22 3 23 .4512 .3083 90 11.751
23 23 24 .898 .7091 320 8.448
24 24 25 .896 .7011 320 28.448
25 6 26 .203 .1034 60 217.834
26 26 27 .2842 .1447 60 67.834
27 27 28 1.059 .9337 60 17.834
28 28 29 .8042 .7006 120 5.668
29 29 30 .5075 .2585 100 6.39
30 30 31 .9744 .963 150 119.58
31 31 32 .3105 .3619 210 62.419
32 32 33 .341 .5302 100 16.39
INPUT DATA OF A 12 BUS SYSTEM HAVING A BASE VOLTAGE OF
11 KV AND BASE MVA OF 10.00
Branch No. Sending Node Receiving Node Resistance in Ohms Reactance in Ohm Active Power in KW Reactive Power in KVAR
1 1 2 0.203 0.1034 120 80
2 2 3 0.341 0.5302 60 40
3 3 4 0.7463 0.545 120 80
4 4 5 1.059 0.9337 90 60
5 5 6 1.251 1.721 80 50
6 6 7 0.591 0.526 200 120
7 7 8 1.7114 1.2351 200 120
8 3 9 0.5075 0.2585 180 100
9 9 10 0.492 0.2513 60 40
10 10 11 0.769 0.582 45 30
11 11 12 0.203 0.1034 90 50
MODIFIED INPUT DATA OF A 12 BUS SYSTEM HAVING A BASE VOLTAGE OF 11 KV AND BASE MVA OF 10.00
Branch No. Sending Node Receiving Node Resistance in Ohms Reactance in Ohm Active Power in KW Reactive Power in KVAR
1 1 2 0.203 0.1034 120 15.68
2 2 3 0.341 0.5302 60 7.84
3 3 4 0.7463 0.545 120 15.68
4 4 5 1.059 0.9337 90 11.76
5 5 6 1.251 1.721 80 7.12
6 6 7 0.591 0.526 200 12.8
7 7 8 1.7114 1.2351 200 12.8
8 3 9 0.5075 0.2585 180 96.48
9 9 10 0.492 0.2513 60 7.84
10 10 11 0.769 0.582 45 5.88
11 11 12 0.203 0.1034 90 1.76
RESULTS AND CONCLUSIONS
5.1 RESULTS OF CASE STUDY “ 1
BEFORE COMPENSATION
B.No. Sending Node Receiving Node SENDING Receiving end Voltage Real Power Losses
(Kw) Reactive Losses (KVAR) Power Factor
Injecting Real Power P (Pu) Injecting Reactive Power Q (Pu)
1 1 2 P[1]=0.45458 Q[1]=0.43743 1.00000 2.9958 1.5271 0.7206
2 2 3 P[2]=0.45400 Q[2]=0.43713 0.99484 12.4262 6.3290 0.7204
3 3 4 P[3]=0.40479 Q[3]=0.39496 0.97006 19.2551 2.5611 0.7157
4 4 5 P[4]=0.30956 Q[4]=0.31159 0.95547 40.4721 9.1239 0.7048
5 5 6 P[5]=0.27830 Q[5]=0.30746 0.94115 9.0420 7.8055 0.6711
6 6 7 P[6]=0.23183 Q[6]=0.29755 0.90603 0.8717 2.8815 0.6146
7 7 8 P[7]=0.12894 Q[7]=0.19929 0.89259 7.2121 5.2049 0.5432
8 8 9 P[8]=0.10807 Q[8]=0.19514 0.85335 3.9541 2.8408 0.4845
9 9 10 P[9]=0.08086 Q[9]=0.18865 0.83187 3.6644 2.5974 0.3939
10 10 11 P[10]=0.06090 Q[10]=0.18239 0.81227 0.6720 0.2222 0.3167
11 11 12 P[11]=0.05124 Q[11]=0.17901 0.81007 1.2558 0.4153 0.2752
12 12 13 P[12]=0.04607 Q[12]=0.17820 0.80608 4.8358 3.8047 0.2503
13 13 14 P[13]=0.03881 Q[13]=0.17750 0.77953 1.7573 2.3132 0.2136
14 14 15 P[14]=0.02798 Q[14]=0.17341 0.76486 1.8524 1.6487 0.1593
15 15 16 P[15]=0.01422 Q[15]=0.16953 0.75438 2.3082 1.6856 0.0836
16 16 17 P[16]=0.00637 Q[16]=0.16710 0.74400 3.9737 5.3055 0.0381
17 17 18 P[17]=0.00294 Q[17]=0.16517 0.71326 0.0358 0.0342 0.0178
18 2 19 P[2]=0.01292 Q[2]=0.15908 0.70392 0.0363 0.0347 0.0809
19 19 20 P[19]=0.03621 Q[19]=0.03701 0.99387 0.2607 0.2349 0.6993
20 20 21 P[20]=0.02717 Q[20]=0.03680 0.98632 0.0542 0.0633 0.5940
21 21 22 P[21]=0.01791 Q[21]=0.03539 0.98429 0.0786 0.1040 0.4516
22 3 23 P[3]=0.00886 Q[3]=0.03515 0.98100 0.4235 0.2893 0.2444
23 23 24 P[23]=0.07381 Q[23]=0.07687 0.96520 0.7479 0.5906 0.6926
24 24 25 P[24]=0.06438 Q[24]=0.07640 0.95561 0.5043 0.3946 0.6444
25 6 26 P[6]=0.03164 Q[6]=0.07497 0.94863 0.2644 0.1347 0.3888
26 26 27 P[26]=0.08785 Q[26]=0.08967 0.90356 0.2653 0.1351 0.6998
27 27 28 P[27]=0.08158 Q[27]=0.06775 0.90054 0.8286 0.7305 0.7693
28 28 29 P[28]=0.07532 Q[28]=0.06083 0.88801 0.5558 0.4842 0.7780
29 29 30 P[29]=0.06849 Q[29]=0.05832 0.87908 0.2824 0.1438 0.7614
30 30 31 P[30]=0.05593 Q[30]=0.05727 0.87502 0.4496 0.4443 0.6987
31 31 32 P[31]=0.04565 Q[31]=0.05648 0.86568 0.0789 0.0920 0.6286
32 32 33 P[32]=0.03020 Q[32]=0.04408 0.86326 0.0460 0.0715 0.5652
AFTER COMPENSATION
B.No. Sending Node Receiving Node SENDING Receiving end Voltage Real Power Losses (Kw) Reactive Losses (KVAR) Power Factor
Injecting Real Power P (Pu) Injecting Reactive Power Q (Pu)
1 1 2 P[1]=0.43214 Q[1]=0.38253 1.00000 2.5093 1.2792 0.7488
2 2 3 P[2]=0.43164 Q[2]=0.38228 0.99523 10.1106 5.1496 0.7486
3 3 4 P[3]=0.38292 Q[3]=0.33555 0.97257 14.7593 1.9631 0.7521
4 4 5 P[4]=0.28990 Q[4]=0.25065 0.95959 30.4874 6.8730 0.7565
5 5 6 P[5]=0.26314 Q[5]=0.24068 0.94694 6.6732 5.7607 0.7379
6 6 7 P[6]=0.22666 Q[6]=0.22981 0.91656 0.5151 1.7028 0.7022
7 7 8 P[7]=0.12539 Q[7]=0.13257 0.90706 3.6168 2.6102 0.6872
8 8 9 P[8]=0.10487 Q[8]=0.11887 0.87735 1.6001 1.1496 0.6616
9 9 10 P[9]=0.08126 Q[9]=0.10426 0.86221 1.1801 0.8365 0.6147
10 10 11 P[10]=0.06366 Q[10]=0.09111 0.84939 0.1961 0.0648 0.5728
11 11 12 P[11]=0.05648 Q[11]=0.08627 0.84777 0.3383 0.1119 0.5477
12 12 13 P[12]=0.05178 Q[12]=0.08321 0.84488 1.1667 0.9180 0.5284
13 13 14 P[13]=0.04544 Q[13]=0.07959 0.82938 0.3759 0.4947 0.4958
14 14 15 P[14]=0.03828 Q[14]=0.07518 0.82198 0.2992 0.2663 0.4537
15 15 16 P[15]=0.02590 Q[15]=0.06668 0.81692 0.3192 0.2331 0.3621
16 16 17 P[16]=0.01960 Q[16]=0.06241 0.81200 0.4600 0.6141 0.2996
17 17 18 P[17]=0.01228 Q[17]=0.05818 0.80022 0.0357 0.0340 0.2065
18 2 19 P[2]=0.00582 Q[2]=0.05357 0.79661 0.0358 0.0341 0.1080
19 19 20 P[19]=0.03621 Q[19]=0.03645 0.99426 0.2149 0.1937 0.7048
20 20 21 P[20]=0.02718 Q[20]=0.03142 0.98732 0.0330 0.0385 0.6542
21 21 22 P[21]=0.01796 Q[21]=0.02522 0.98570 0.0291 0.0385 0.5801
22 3 23 P[3]=0.00893 Q[3]=0.02018 0.98358 0.4120 0.2815 0.4046
23 23 24 P[23]=0.07391 Q[23]=0.07475 0.96778 0.6731 0.5315 0.7031
24 24 25 P[24]=0.06449 Q[24]=0.06947 0.95863 0.2745 0.2148 0.6804
25 6 26 P[6]=0.03182 Q[6]=0.05094 0.95309 0.2601 0.1325 0.5298
26 26 27 P[26]=0.08859 Q[26]=0.08748 0.91412 0.2516 0.1281 0.7116
27 27 28 P[27]=0.08233 Q[27]=0.06235 0.91119 0.7527 0.6636 0.7972
28 28 29 P[28]=0.07608 Q[28]=0.05222 0.89946 0.4784 0.4168 0.8245
29 29 30 P[29]=0.06933 Q[29]=0.04656 0.89134 0.2094 0.1066 0.8302
30 30 31 P[30]=0.05685 Q[30]=0.03914 0.88773 0.2775 0.2743 0.8237
31 31 32 P[31]=0.04664 Q[31]=0.03303 0.88054 0.0315 0.0367 0.8161
32 32 33 P[32]=0.03137 Q[32]=0.01276 0.87919 0.0039 0.0061 0.9263
req=0.23637p.u xeq=0.09974p.u
5.2 RESULTS OF CASE STUDY “ 2
BEFORE COMPENSATION
B.No. Sending Node Receiving Node SENDING Receiving end Voltage Real Power Losses (Kw) Reactive Losses (KVAR) Power Factor
Injecting Real Power P (Pu) Injecting Reactive Power Q (Pu)
1 1 2 P[1]=0.12752 Q[1]=0.12979 1.00000 0.3602 1.1926 0.7288
2 2 3 P[2]=0.12728 Q[2]=0.12953 0.99584 0.7441 1.1570 0.7289
3 3 4 P[3]=0.11492 Q[3]=0.11677 0.98846 0.6723 0.4909 0.7014
4 4 5 P[4]=0.07059 Q[4]=0.07692 0.98055 0.7965 0.7022 0.6761
5 5 6 P[5]=0.05792 Q[5]=0.07486 0.96950 0.8258 1.1289 0.6119
6 6 7 P[6]=0.04812 Q[6]=0.07298 0.95363 0.3460 0.3080 0.5504
7 7 8 P[7]=0.03929 Q[7]=0.07114 0.94837 0.0591 0.0301 0.4835
8 3 9 P[3]=0.01895 Q[3]=0.06956 0.93810 0.1195 0.0609 0.2628
9 9 10 P[9]=0.03759 Q[9]=0.03791 0.98605 0.0729 0.0373 0.7041
10 10 11 P[10]=0.01947 Q[10]=0.03750 0.98446 0.0977 0.0739 0.4608
11 11 12 P[11]=0.01340 Q[11]=0.03668 0.98180 0.0234 0.0119 0.3431
AFTER COMPENSATION
B.No. Sending Node Receiving Node SENDING Receiving end Voltage Real Power Losses (Kw) Reactive Losses (KVAR) Power Factor
Injecting Real Power P (Pu) Injecting Reactive Power Q (Pu)
1 1 2 P[1]=0.12765 Q[1]=0.12478 1.00000 0.3658 1.2111 0.7351
2 2 3 P[2]=0.12740 Q[2]=0.12451 0.99680 0.7354 1.1434 0.7352
3 3 4 P[3]=0.11503 Q[3]=0.11530 0.98848 0.6312 0.4609 0.7063
4 4 5 P[4]=0.07065 Q[4]=0.07240 0.98077 0.6625 0.5841 0.6984
5 5 6 P[5]=0.05801 Q[5]=0.06394 0.97057 0.6069 0.8296 0.6719
6 6 7 P[6]=0.04835 Q[6]=0.05736 0.95698 0.2204 0.1961 0.6445
7 7 8 P[7]=0.03974 Q[7]=0.05153 0.95261 0.1190 0.0606 0.6107
8 3 9 P[3]=0.01952 Q[3]=0.03933 0.94550 0.1192 0.0607 0.4446
9 9 10 P[9]=0.03765 Q[9]=0.03775 0.98607 0.0469 0.0240 0.7061
10 10 11 P[10]=0.01953 Q[10]=0.02769 0.98468 0.0475 0.0360 0.5764
11 11 12 P[11]=0.01348 Q[11]=0.02367 0.98265 0.0086 0.0044 0.4950
req=0.11229p.u xeq=0.14530p.u
5.3 COMPARISON OF TEST SYSTEMS
Voltage comparison of a 12 Bus system :
Voltage
before compensation Voltage
after compensation
1 1
0.99584 0.9968
0.98846 0.98848
0.98055 0.98077
0.9695 0.97057
0.95363 0.95698
0.94837 0.95261
0.9381 0.9455
0.98605 0.98607
0.98446 0.98468
0.9818 0.98625
Power factor comparison of a 12 Bus system :-
Power factor
before compensation Power factor
after compensation
0.7288 0.7351
0.7289 0.7352
0.7014 0.7063
0.6761 0.6984
0.6119 0.6719
0.5504 0.6445
0.4835 0.6107
0.2628 0.4446
0.7041 0.7061
0.4608 0.5764
0.3431 0.495
Voltage comparison of a 33 Bus system :-
Voltage
before compensation Voltage
after compensation
1 1
0.99484 0.99523
0.97006 0.97257
0.95547 0.95959
0.94115 0.94694
0.90603 0.91656
0.89259 0.90706
0.85335 0.87735
0.83187 0.86221
0.81227 0.84939
0.81007 0.84777
0.80608 0.84488
0.77953 0.82938
0.76486 0.82198
0.75438 0.81692
0.744 0.812
0.71326 0.80022
0.70392 0.79661
0.99387 0.99426
0.98632 0.98732
0.98429 0.9857
0.981 0.98358
0.9652 0.96778
0.95561 0.95863
0.94863 0.95309
0.90356 0.91412
0.90054 0.91119
0.88801 0.89946
0.87908 0.89134
0.87502 0.88773
0.86568 0.88054
0.86326 0.87919
Power factor compensation of a 33 Bus system
Power factor
before compensation Power factor
after compensation
0.7206 0.7488
0.7204 0.7486
0.7157 0.7521
0.7048 0.7565
0.6711 0.7379
0.6146 0.7022
0.5432 0.6872
0.4845 0.6616
0.3939 0.6147
0.3167 0.5728
0.2752 0.5477
0.2503 0.5284
0.2136 0.4958
0.1593 0.4537
0.0836 0.3621
0.0381 0.2996
0.0178 0.2065
0.0809 0.108
0.6993 0.7048
0.594 0.6542
0.4516 0.5801
0.2444 0.4046
0.6926 0.7031
0.6444 0.6804
0.3888 0.5298
0.6998 0.7116
0.7693 0.7972
0.778 0.8245
0.7614 0.8302
0.6987 0.8237
0.6286 0.8161
0.5652 0.9263
CONCLUSION
Load flow is carried for the radial distribution system using dist flow method with and without capacitors.
The voltage profile throughout the system is improved and total power loss in the system has been reduced after the placement of capacitors at different of load points in the radial distribution systems.
The power factor of the system is also improved and reactive power compensation is done after the placement of capacitors at different load points in radial distribution systems using dist flow method.
APPENDIX (Software)
#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<graphics.h>
#define KVb 11.00
#define MVAb 10.00
#define h 1000
#define tn 33
int i,j,a,b,s,se[100],re[100],K,l,zz,z1,o,m;
int lt[15],rt[15];
int rts[15][15],rtr[15][15];
float E=0.0001;
double ppt,qqt,TR,TX,R[100],X[100],req,xeq,op[100],oop,ll,V[100],LR,LX,ttp,ttq;
double oq[100],ooq,ip,iq,K1,K2,K3,K4,K5,K6[100],K7,K8[100],K9,pt,qt,po,qo,L,poo,qoo;
double r[100],x[100],p[100],q[100],tp[100],tq[100],temp[50],temq[50],PR[50],QX[50];
double RL[100],XL[100],SI[100],TS,f,np[100],nq[100],pf,N2,N3,N4;
char ch;
FILE *f1,*fp1,*f2;
void main()
{
int w,pp;
char input[32],output[32];
static int z;
clrscr();
printf("enter the input file name: ");
scanf("%s",&input);
f1=fopen(input,"r");
do
{
printf("enter the output file name:");scanf("%s",&output);
fp1=fopen(output,"w");
for(i=1;i<tn;i++)
{
fscanf(f1,"%d%d%d%lf%lf",&i,&se[i],&re[i],&r[i],&x[i]);
printf(" %d\t%d\t%d\t%7.5lf\t%7.5lf\t",i,se[i],re[i],r[i],x[i]);
w=re[i];
r[i]=r[i]*MVAb/(KVb*KVb);
x[i]=x[i]*MVAb/(KVb*KVb);
fscanf(f1,"%lf%lf",&p[w],&q[w]);printf("%7.5lf\t%7.5lf\n",p[w],q[w]);
p[w]=np[w]=p[w]/(MVAb*1000);
q[w]=nq[w]=q[w]/(MVAb*1000);
}
/* for(i=1;i<tn;i++)
{
printf("\n%2d\t%2d\t%2d\t%7.5lf\t%7.5lf\t",i,se[i],re[i],r[i],x[i]);
w=re[i];
printf("%7.5lf\t%7.5lf",p[w],q[w]);
getch();
} */
printf("\n Enter the f value\n");
scanf("%lf",&f);
for(w=2;w<=tn;w++)
{
p[w]=f*np[w];
q[w]=f*nq[w];//printf("\n %7.5lf\t%7.5lf",p[w],q[w]);
}
for(s=0,i=1;i<(tn-1);i++)
{
pp=1;
rts[s+1][pp]=se[i];
rtr[s+1][pp]=re[i];
for(j=i+1;j<tn;j++)
if(se[i]==se[j])
{
pp++;
rts[s+1][pp]=se[j];
rtr[s+1][pp]=re[j];
}
if(pp>=2)
{
s++;
rt[s]=se[i];
lt[s]=pp;
if(s>=2)
for(a=1;a<s;a++)
if(rt[a]==rt[s])
{
rt[s]=0;
lt[s]=0;
s--;
}
}
}
printf(" repeated nodes are %d\n",s);
ttp=0;
ttq=0;
for(i=s;i>=1;i--)
{
temp[i]=0;
temq[i]=0;
LR=0;
LX=0;
for(j=1;j<=lt[i];j++)
{
K=1;
ppt=0;
qqt=0;
z=rtr[i][j];
a=z;
ppt=ppt+p[z];
qqt=qqt+q[z];
if(z>rt[s])
while(z<=tn)
{
if(se[z+1]==re[z])
{
z1=re[z];
ppt=ppt+p[z1];
qqt=qqt+q[z1];
z++;
b=z;
}
else
{
b=z;
ppt=ppt+p[z+1];
qqt=qqt+q[z+1];
ip=ppt;
iq=qqt;
tp[a]=ppt;
tq[a]=qqt;
while(z<100)
{
TR=0.0;
TX=0.0;
R[a-1]=(r[a-1])*((tp[a]*tp[a])+(tq[a]*tq[a]));
X[a-1]=(x[a-1])*((tp[a]*tp[a])+(tq[a]*tq[a]));
for(l=a;l<=b+1;l++)
{
tp[l+1]=tp[l]-R[l-1]-p[l];
tq[l+1]=tq[l]-X[l-1]-q[l];
R[l]=R[l-1]*(r[l]/r[l-1])*(((tp[l+1]*tp[l+1])+(tq[l+1]*tq[l+1]))/(((tp[l+1]+p[l])*(tp[l+1]+p[l]))+((tq[l+1]+q[l])*(tq[l+1]+q[l]))));
X[l]=X[l-1]*(x[l]/x[l-1])*(((tp[l+1]*tp[l+1])+(tq[l+1]*tq[l+1]))/(((tp[l+1]+p[l])*(tp[l+1]+p[l]))+((tq[l+1]+q[l])*(tq[l+1]+q[l]))));
TR=TR+R[l-1];
TX=TX+X[l-1];
}
req=TR/((tp[a]*tp[a])+tq[a]*tq[a]);
xeq=TX/((tp[a]*tp[a])+tq[a]*tq[a]);
K1=(2*xeq*xeq*ppt)-(2*req*xeq*qqt)+req;
K2=(2*((req*req)+(xeq*xeq)));
K3=((xeq*xeq*ppt*ppt)+(req*req*qqt*qqt)-(2*req*xeq*ppt*qqt)+(req*ppt));
K4=((xeq*xeq*ppt*ppt)+(req*req*qqt*qqt)-(2*req*xeq*ppt*qqt)+(xeq*ppt));
K5=((2*req*req*qqt)-(2*req*xeq*ppt)+xeq);
K6[K]=((K1*K1)-(2*K2*K3));
K7=(sqrt(fabs(K6[K])));
K8[K]=((K5*K5)-(2*K2*K4));
K9=(sqrt(fabs(K8[K])));
op[K]=K1/K2-K7/K2;
oq[K]=K5/K2-K9/K2;
ll=op[K]-tp[a-1];
if(fabs(op[K]-tp[a])>E)
{
tp[a]=op[K];
tq[a]=oq[K];
z++;
K++;
}
else
{
zz=rt[i];
temp[i]+=op[K];
op[a]=op[K];
temq[i]+=oq[K];
oq[a]=oq[K];
R[a]=(r[a-1])*((op[a]*op[a])+(oq[a]*oq[a]));
X[a]=(x[a-1])*((op[a]*op[a])+(oq[a]*oq[a]));
LR+=R[a];
LX+=X[a];
for(o=a;o<=b;o++)
{
op[o+1]=op[o]-R[o]-p[o];
oq[o+1]=oq[o]-X[o]-q[o];
R[o+1]=R[o]*(((r[o]/r[o-1])*((op[o+1]*(op[o+1])+(oq[o+1]*oq[o+1]))/((op[o+1]+p[o])*(op[o+1]+p[o])+(oq[o+1]+q[o])*(oq[o+1]+q[o])))));
X[o+1]=X[o]*(((x[o]/x[o-1])*((op[o+1]*(op[o+1])+(oq[o+1]*oq[o+1]))/((op[o+1]+p[o])*(op[o+1]+p[o])+(oq[o+1]+q[o])*(oq[o+1]+q[o])))));
TR+=R[o-1];
TX+=X[o-1];
}
break;
}
}
break;
}
}
}
zz=rt[i];
PR[a-1]=LR;
QX[a-1]=LX;
po=temp[i]+p[zz]+ttp;
qo=temq[i]+q[zz]+ttq;
R[zz]=(po*po+qo*qo)*r[zz-1];
X[zz]=(po*po+qo*qo)*x[zz-1];
TR=0;
poo=temp[i]+ttp;
qoo=temq[i]+ttq;
for(o=rt[i];o>rt[i-1];o--)
{
op[o]=poo+R[o]+p[o];
oq[o]=qoo+X[o]+q[o];
R[o-1]=R[o]*(((r[o-1]/r[o])*((op[o]+p[o])*(op[o]+p[o])+(oq[o]+q[o])*(oq[o]+q[o])))/((op[o]*op[o])+(oq[o]*oq[o])));
X[o-1]=X[o]*(((x[o-1]/x[o])*((op[o]+p[o])*(op[o]+p[o])+(oq[o]+q[o])*(oq[o]+q[o])))/((op[o]*op[o])+(oq[o]*oq[o])));
poo=op[o];
qoo=oq[o];
TR=R[o-1];
TX=X[o-1];
ttp=op[o];
ttq=oq[o];
}
}
V[1]=1;
TR=0;
TX=0;
ppt=0;
qqt=0;
for(i=1;i<tn;i++)
{
K1=2*(r[i]*op[i+1]+x[i]*oq[i+1]);
K2=(r[i]*r[i]+x[i]*x[i]);
K3=(op[i+1]*op[i+1]+oq[i+1]*oq[i+1])/(V[se[i]]*V[se[i]]);
V[i+1]=sqrt((V[se[i]]*V[se[i]])-K1+(K2*K3));
RL[i]=R[i+1]*h;
XL[i]=X[i+1]*h;
N2=((op[i]*op[i])+(oq[i]*oq[i]));
N3=sqrt(fabs(N2));N4=op[i];
pf=fabs(N4/N3);
printf("\n%d %d %d P[%d]=%7.5lf Q[%d]=%7.5lf %7.5lf",i,se[i],re[i],se[i],op[i],se[i],oq[i],V[i]);
printf(" %8.4lf %8.4lf %8.4lf",RL[i],XL[i],pf);
fprintf(fp1,"\n%d %d %d P[%d]=%7.5lf Q[%d]=%7.5lf %7.5lf",i,se[i],re[i],se[i],op[i],se[i],oq[i],V[i]);
fprintf(fp1," %8.4lf %8.4lf %8.4lf",RL[i],XL[i],pf);
TR+=R[i+1];
TX+=X[i+1];
ppt+=p[i+1];
qqt+=q[i+i];
getch();
}
req=TR/(op[2]*op[2]+oq[2]*oq[2]);
xeq=TX/(op[2]*op[2]+oq[2]*oq[2]);
printf("\nreq=%7.5lf\txeq=%7.5lf",req,xeq);
fprintf(fp1,"\nreq=%7.5lfp.u\txea=%7.5lfp.u",req,xeq);
printf("\nDo you want another input file with modified loads (Y/N);");
fflush(stdin);
ch=getchar();
}
while(ch=='y'||ch=='Y');
}
BIBLIOGRAPHY
1. Technical Reference Book - A.P.S.E.B.
2. A.S. PABLA, Electrical Power Distribution fifth edition TATA Mc. Graw-Hill Publication Company Limited, New Delhi “ 20
3. TURAN GONEN, Electrical Power Distribution System Engineering, TATA Mc GRAW-HILL, book Company, New York.
4. Suresh Kumar Application of Capacitors.
5. B.R. GUPTA Power System Analysis & Design 3rd Edition, wheeler publishing.
6. Balaguruswamy Programming in ANSI C Second Edition, TATA Mc GRAW-HILL Publishing Company Limited, New Delhi.
