kigen report 9

THE UNIVERSITY OF NAIROBI

DEPARTMENT OF ELECTRICAL AND INFORMATION

ENGINEERING

MSC (ELECTRICAL AND INFORMATION ENGINEERING)

UNIT: FEE 650 — RESEARCH METHODOLOGY

NAME: KIGEN CHRISTOPHER KIMOSOP

REG NO: F56/64415/2010

RESEARCH REPORT:

CONVERSION OF P-Q BUSES INTO P-V BUSES IN

ORDER TO MINIMISE POWER SYSTEM LOSSES

Abstract

Power utility companies are constantly seeking ways to increase efficient transmission of

power by reducing technical losses. This paper proposes a method that seeks to reduce

these transmission losses.

In recent times, reduction of such losses has been a subject of interest among many

researchers. Most have focussed on optimisation of power transmission networks taking

multiple objectives into consideration such as voltage constraints in addition to stability and

losses. Recent research has predominantly made use of artificial intelligence techniques

such as genetic algorithms and particle swarm optimisation. However, the method proposed

in this paper makes use of classical reactive power dispatch to solve the power transmission

optimisation problem.

In the method proposed, PQ buses are iteratively converted to PV buses. This is done to

establish the optimal location for reactive power support in the network. In this way, it is

possible to find an optimal network configuration that minimises losses. Implemented in

MATLAB, the proposed algorithm is tested on standard IEEE 14-bus, 30-bus and 57-bus test

networks. The simulations run using IEEE test networks are successful. In all three test

networks, transmission losses are reduced by using the proposed method.

The results obtained during simulation are promising. The proposed method can be scaled

up and implemented on the Kenyan national power transmission network. This can be done

without alterations to the algorithms developed here.

Contents

Abstract.................................................................................................................................................2

Contents................................................................................................................................................3

1. INTRODUCTION.............................................................................................................................4

1.1. Problem Statement................................................................................................................4

1.2. Objectives:.............................................................................................................................5

1.3. List of Symbols and Abbreviations.........................................................................................6

1.4. List of Figures.........................................................................................................................6

2. LITERATURE REVIEW......................................................................................................................7

2.1. Power System Buses..............................................................................................................7

2.2. Converting PQ Buses to PV....................................................................................................7

2.3. Load Flow Problem................................................................................................................8

2.4. Newton-Raphson Method.....................................................................................................9

2.5. Active transmission losses...................................................................................................11

2.6. Optimal Location of Reactive Power Support......................................................................11

2.6.1. Classical Method of Reactive Power Dispatch.............................................................12

2.6.2. Linear Programming Approach....................................................................................12

2.6.3. Newton approach........................................................................................................13

2.6.4. Artificial Intelligence Methods.....................................................................................13

2.6.4.1. Fuzzy Techniques.....................................................................................................13

2.6.4.2. Genetic and Evolutionary Algorithms.......................................................................14

2.6.4.3. Particle swarm optimization techniques..................................................................14

3. Methodology...............................................................................................................................15

3.1. Objectives............................................................................................................................15

3.2. Bus Conversion Algorithm....................................................................................................15

4. Simulation and Results................................................................................................................19

4.1. Test Network: IEEE 14-bus...................................................................................................19



4.4. Summary of Results.............................................................................................................26

5. Conclusion...................................................................................................................................29

5.1. Future Work.........................................................................................................................29

6. References...................................................................................................................................31

3

1. INTRODUCTION

1.1.Problem Statement

The problem of minimising real power losses in transmission networks is a major part of the

work of a power engineer. Transmission losses in a network can be reduced in a number of

ways such as the use of high efficiency cables and transformers, as well as optimal supply of

reactive power in the network. This reactive power support to the grid is traditionally

achieved by switched capacitors and phase-shifting transformers. These devices are passive

and controlled by system control personnel through SCADA. They are put into use when the

operators deem it necessary through past experience.

In recent times, advances in computing hardware and the affordability of computing power

have led to a higher degree of automation in the area of reactive power support. Flexible AC

Transmission Systems (FACTS) have been developed. These are active devices which are

power-electronics-based. They include thyristor-switched capacitor (TSC), static

compensators (STATCOM), static VAR controller (SVC) and Unified Power Flow Controller

(UPFC). [1]

These devices tend to be expensive to install and run. The power utility company must

therefore select the optimal locations within the grid in which to install such devices. The

procedure of identifying these optimal locations is the subject of much research.

The purpose of this paper is therefore to develop a method in which the minimisation of

power losses can be achieved. This is done through the optimal location of reactive power

support.

4

1.2.Objectives:

In this report, the main objective is to minimise real transmission power losses in power

transmission networks. This paper proposes a method that achieves this through the

optimal location for reactive power support. The method proposed is based on classical

reactive power dispatch. Instead of identifying the optimal location of a specific type of

FACTS device or capacitor, an optimal bus is selected. The reactive power support at the

identified bus can be of any type, whether passive or active. Thus the practical

implementation of the solution in a network is more flexible with regards to the device

used.

Based on the literature review in section below, the following research objectives can be

pursued:

Use MATLAB to perform the iterative conversion of PQ buses into PV buses in a given

power network.

Calculate total transmission losses in each different configuration of the power

network.

Analyse the data obtained to identify the configuration that has lowest transmission losses.

The scope of the work will be limited as follows:

The criterion for optimisation is real power transmission losses. Voltage limits,

network stability and cost of reactive power support will not be considered.

During each iteration, only one PQ bus will be converted into a PV bus. The

optimised network will have only one converted PQ bus.

5

1.3.List of Symbols and Abbreviations

Si Apparent power at bus ‘i’Pi Active power at bus ‘i’Qi Reactive power at bus ‘i’Vi Voltage at bus ‘i’i Power angle at bus ‘i’Ii Current injected into the network at bus ‘i’Yin Line admittance θin Phase angle of line of the line between bus ‘i’ and bus ‘n’Sij apparent power leaving bus i to bus j on line i—jPL Real power transmission lossesGij Conductance of line between bus ‘i’ and ‘j’Bij Susceptance of line between bus ‘i’ and ‘j’

1.4.List of Figures

Figure 1: PV to PQ Bus Conversion Algorithm.....................................................................................17Figure 2: IEEE 14-Bus Network............................................................................................................20Figure 3: IEEE 14-bus Network Transmission Losses with Converted PQ Buses..................................21Figure 4: IEEE 30 Bus Network.............................................................................................................22Figure 5: IEEE 30-bus Network Transmission Losses with Converted PQ Buses..................................23Figure 6: IEEE 57-bus Network.............................................................................................................24Figure 7: IEEE 57-bus Network Transmission Losses with Converted PQ Buses..................................25Figure 8: Real Power Losses in the Test Networks...............................................................................26Figure 9: Total Reactive Power Injected into Test Networks...............................................................27

6

2. LITERATURE REVIEW

2.1.Power System Buses

A given power network has various parameters, which are either specified or unknown.

These are real power, P, reactive power, Q, voltage, V, and power angle, . At any given bus,

two variables are specified while the other two are variable.

Voltage-controlled bus (PV bus) is a bus for which the voltage magnitude (V) and the

injected real power (P) are specified. The unknown variables are reactive power (Q) and

angle (). A PV bus must have a variable source of reactive power.

“In all realistic cases, the voltage magnitude is specified at generator buses to take

advantage of the generator’s reactive power capability. Specifying the voltage

magnitude at a generator bus requires a variable specified in the simple analysis

discussed earlier to become an unknown (in order to bring the number of unknowns

back into correspondence with the number of equations). Normally, the reactive

power injected by the generator becomes a variable, leaving the real power and

voltage magnitude as the specified quantities at the generator bus.

“Generally, the PV buses and the voltage-controlled buses are grouped together but

these buses have physical difference. The voltage controlled bus has also voltage

control capabilities, and uses a tap adjustable transformer and/or a static VAR

compensator instead of a generator.” [1]

2.2.Converting PQ Buses to PV

The proposed method involves converting PQ (load) buses into PV buses. This will allow the

converted buses to supply reactive power to the network. In the literature, a similar

methodology is used in modelling of SVCs. The SVC is modelled as a PV bus in [6] and [7].

7

When connected to a bus, it generates reactive power up to the limit of its rated size in VAR.

Beyond the rating limits, the bus remains as a PQ bus.

The mechanism by which the SVC is modelled is similar to the paradigm used in this

research. Therefore, the procedure used in this research will be similar to that used in

optimally locating SVCs in a network.

2.3.Load Flow Problem

As shown in [12], complex power injected into the “i”th bus of a power system is given by

Si=Pi+ jQi=V i I i¿ (1)

The net current injected into the network at bus i is given by

I i=∑n=1

N

Y ¿V n

(2)

Where Yin represents line admittance of the line between bus i and bus n.

The complex conjugate of power injected into the ith bus is given by

Si=Pi− jQ i=V i¿ I i (3)

Substituting (2) into (3), we get

Pi−¿V i¿∑n=1

N

Y ¿V n=∑n=1

N

|V i|∨V n∨¿V ¿∨¿cos (θ¿+❑n−❑i)¿

(4)

Equating the real and imaginary parts,

8

Pi=¿V i∨∑n=1

N

¿Y ¿∨¿V n∨¿cos (θ¿+❑n−❑i)¿

(5)

Qi=−¿V i∨∑n=1

N

¿Y ¿∨¿V n∨¿sin (θ¿+❑n−❑i)¿

(6)2.4.Newton-Raphson Method

The Newton Raphson method makes use of the fact that the power flow problem has two

sets of known variables and two sets of unknown variables for each equation. The load flow

equations are expressed in polar form as follows.

Pi=|V i|2Gii+ ∑

n=1 ,n≠i

N

|Y ¿||V n|cos (θ¿+❑n−❑i )

(7)

Qi=−¿V i∨¿2Bii ∑n=1 , n≠i

N

¿Y ¿∨¿V n∨¿ sin (θ¿+❑n−❑i)¿¿

(8)These equations can be readily differentiated with respect to voltage angles and magnitudes

and hence, mismatch equations can be written as follows:

For real power Pi the increment ΔPi is determined by:

9

∆ Pi=∂ Pi∂δ2

∆δ2+∂P i∂δ3

∆δ 3+…+∂Pi∂δn

∆δ n+∂ Pi

∂∨V 2∨¿ ∆|V 2|+∂ Pi∂|V 3|

∆|V 3|+…+∂Pi

∂∨V n∨¿∆∨V n∨¿¿¿

(9)The terms with voltages can be multiplied and divided by their respective voltage

magnitudes without altering their values, and so the following is obtained:

∆ Pi=∂ Pi∂δ2

∆δ2+∂P i∂δ3

∆δ 3+…+∂Pi∂δn

∆δ n+∂Pi

∂∨V 2∨¿∆|V 2|

¿V 2∨¿+∂Pi∂|V 3|

∆|V 3||V 3|

+…+∂Pi

∂∨V n∨¿ ∆∨V n∨¿

¿V n∨¿¿¿¿

¿

¿ (10)

Similarly, mismatch equation can be written for reactive power Qi with increment ΔQi given

by:

∆Qi=∂Qi∂δ 2

∆δ2+∂Qi∂δ3

∆δ 3+…+∂Qi∂δ n

∆δ n+∂Qi

∂∨V 2∨¿∆|V 2|

¿V 2∨¿+∂Qi∂|V 3|

∆|V 3||V 3|

+…+∂Qi

∂∨V n∨¿ ∆∨V n∨¿

¿V n∨¿¿¿¿

¿

¿

(11)

10

Each non-slack bus of the system has two equations like those for ΔPi and ΔQi. Collecting all

the mismatch equations into a vector-matrix yields

(12)In the above equations, all the elements in the sub matrices J2 and J4 are pre-multiplied by

the relevant V, then all ΔV elements in the right-hand vector are divided by the relevant V to

compensate. Therefore, the relationship may be rewritten as follows

[∆P∆Q ]=[ J1 J 2J 3 J 4]¿ (13)

This may be re-written as

[ ∆δ∆|V||V| ]=[J 1 J2

J 3 J 4]−1

[∆ P∆Q ] (14)If the inverse matrix J-1 exists. The solution of the above equation provides the correction

vector i.e. Δδ for all the PV and PQ buses and ΔV for all the PQ buses which in turn are used

to update the values of δ and V . This iterative process is continued until the elements of the

mismatch vector i.e. ΔP for all the PV and PQ type buses and ΔQ for all the PQ buses

become less than a tolerance value ∈.

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2.5.Active transmission losses

The transmission losses in a line between bus i and bus j are calculated at both the sending

and receiving ends of the line. The apparent power leaving bus i to bus j on line i—j is

Sij=V i δi(I ji+ j B ij2 V i δ i)¿

(15)

And the power received at bus j from bus i on line i—j is

S ji=V j δ j(I ji− j Bij2 V j δ j)¿

(16)

The transmission loss in each branch of the network is given by the sum of (15) and (16)

SLij=S ji+Sij (17)

Therefore the total transmission loss for the entire network is given by:

SL=12∑i=1

N

∑j=1

N

S ji+S ij(18)

From this the real transmission losses are given by the real part of the total actual power

losses. This is expressed as follows:

PL=ℜ(S¿¿ L)¿ (19)

2.6.Optimal Location of Reactive Power Support

In the research to be carried out, the location of P-V buses is to be studied. As stated above

the PV bus must have a variable source of reactive power. Therefore the location of PV

buses is the same as location of reactive power sources.

“The objectives of reactive power (VAR) optimization are to improve the voltage

profile, to minimize system active power losses, and to determine optimal VAR

compensation placement under various operating conditions. To achieve these

objectives, power system operators utilize control options such as adjusting

generator excitation, transformer tap changing, shunt capacitors, and SVC.”[13]

12

The selection of the optimal location for these sources of reactive power has been carried

out in a number of ways. All these methods involve converting the power system into a

mathematical model. This model is a function which is then minimised as stated above,

usually by linear programming. The techniques of minimisation including the following:

2.6.1. Classical Method of Reactive Power Dispatch

For the classic reactive power dispatch problem, the real power outputs of the generators

are already known. The constraint is reactive power balance equation, that is,

∑i=1

N

QGi=QD−QL(20)

Where QGi represents generated reactive power at bus ‘i’, and QD and QL represent reactive

power demand and losses respectively.

A Lagrangian factor, is calculated for all reactive power sources. Using this factor, various

sources are selected for variation. Increase or decrease of reactive power sources is carried

out. Transmission losses are then calculated. This procedure is repeated until the

configuration that gives rise to minimum transmission losses is established, as in [13].

2.6.2. Linear Programming Approach

In the classical reactive power dispatch, only transmission losses are taken into

consideration. When we include other constraints such as voltage stability and network

security the problem becomes more complex.

The linear programming technique provides a solution for the problem through the use of

sensitivity matrices. This is described in [14]. The technique uses the sensitivity relationships

of power systems to determine the linearized sensitivity relationships linking the dependent

and control variables. This is done by taking advantage of the decoupled nature of power

systems. Using this, the reactive power at various buses can be linked to voltage.

13

The reactive power allocation problem is then formulated as a linear programming problem

and voltage parameters are used as limits.

2.6.3. Newton approach

This is based on Newton approach and the primal-dual logarithmic barrier method [16]. A

Lagrangian function is associated with the modified problem. The first order necessary

conditions for optimality are fulfilled by Newton’s method and by updating the penalty and

barrier terms.

2.6.4. Artificial Intelligence Methods

These techniques take into consideration all the equality and inequality constraints [18, 19,

and 20]. The improvement in system performance is based on reduction in cost of power

generation and active power loss.

2.6.4.1. Fuzzy Techniques

In this technique [15], a strategy for placement of reactive power based on a fuzzy

performance index is used. The index is based on three objectives—increase in loading

margin, improvement in voltage profile, and reduction of the system reactive power loss.

The index can be used to find the most effective location of the shunt flexible AC

transmission systems device.

2.6.4.2. Genetic and Evolutionary Algorithms

The simple Genetic Algorithm first expresses the optimisation problem as a population of

binary numbers [18, 19, and 20]. In this case, the binary numbers are the degree to which

reactive power is added to a bus. The binary numbers are transformed by three genetic

operations. Selection or reproduction is the process by which a set of binary numbers are

selected to reproduce a set of new strings in a random manner. Crossover is then carried

14

out. This is a process of randomly interchanging digits within a binary number. Mutation is

the random changing of the value of digits in a binary number. These genetic operations are

performed iteratively on the system until the optimal results are obtained based on pre-

determined criteria.

2.6.4.3. Particle swarm optimization techniques

Particle swarm optimization (PSO) was introduced as an alternative to Genetic Algorithms.

The PSO technique consists of a population refining its knowledge of the given search space.

PSO is inspired by particles moving around in the search space. The individuals in a PSO thus

have their own positions and velocities. These individuals are denoted as particles.

Traditionally, PSO has no crossover between individuals and has no mutation, and particles

are never substituted by other individuals during the run. Instead, the PSO refines its search

by attracting the particles to positions with good solutions. This method is used in [18] and

[21].

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3. Methodology

3.1.Objectives

In this report, the objective is to minimise real transmission power losses. As detailed above,

a common solution to the problem is to identify the optimal location for reactive power

support. This paper proposes a method that is similar to this. However the method

proposed is more generalised. Instead of identifying the optimal location of a specific type

of FACTS device or capacitor, an optimal bus is selected. The reactive power support at the

identified bus can be of any type, whether passive or active. Thus the practical

implementation of the solution in a network is more flexible with regards to the device

used.

3.2.Bus Conversion Algorithm

The proposed method is the iterative conversion of PQ buses to PV buses. During an

iteration, one PQ bus is selected as a candidate for conversion to PV. This selected bus is

converted into a PV bus. This is achieved by changing its characteristics in the network

model during load flow analysis.

A PQ bus has no power sources, whether real or reactive. However, the bus that is selected

for conversion is assumed to have a reactive power source. In other words it is modelled as

a PV bus. This is only the case during the current iteration. In the next iteration, the selected

bus reverts back to the parameters it had in the original network model. A different PQ bus

is then selected for conversion to PV.

After all PQ buses have in turn been converted to PV, the configuration with the lowest

transmission losses is selected as the optimal configuration.

16

In order to find the optimal position for PQ bus to PV bus conversion, the following

methodology is used.

Step 1: A single PQ bus is selected to be converted to PV, as described in section 4 above.

Step 2: The load flow analysis is then carried out with this network configuration using the

Newton Raphson method.

Step 3: The transmission losses in the network are then calculated using equation (21).

Step 4: If the losses are lower than the original network losses, this bus location is noted as a

possible optimal location.

Step 5: The converted PV bus is then returned to its original PQ bus status. A different PQ

bus is selected and the procedure carried out once more from Step 1.

This sequence of steps is repeated for all PQ buses in the network. After all PQ buses have

each been converted, the network configuration with the lowest transmission losses is

noted.

The flow chart of this procedure is shown below.

17

Figure 1: PV to PQ Bus Conversion Algorithm

A number of papers use optimal load flow to identify the location of reactive power support.

In the method proposed in this paper, classical reactive power dispatch is used, as described

in section above. Because this is a generalised method, the use of optimal load flow is

beyond the scope of this report.

Various optimization techniques based on linear programming techniques and artificial

intelligence algorithms are used in the literature as described in section above. The method

used in this report does not require these optimization techniques. Classical reactive power

dispatch is sufficient for the purposes of the proposed algorithm.

The above algorithm is implemented in a MATLAB program. The program is based on [11].

To carry out load flow solution, the Newton Raphson method is used, as described in section

18

above. A tolerance ∈ of 10-8 is used in calculations. Power losses are then calculated using

the method described in section above.

19

4. Simulation and Results

Three networks are used to test the algorithm. These are the IEEE 14-bus [8], 30-bus [9] and

57-bus [10] networks.

The program iteratively converts each PQ bus in the network under test into a PV bus. A

load flow analysis is then carried out on the modified network. The real power losses for the

whole network are then calculated.

The real losses for each modified network are listed below. The indexes represent the

number of the bus that is converted to PV during the iteration in question. (A ‘0’ index

indicates the original network configuration.)

4.1.Test Network: IEEE 14-bus

The IEEE 14-bus network comprises five PV buses and nine PQ buses. There are two

generator buses and three buses with synchronous generators injecting reactive power.

The IEEE 14-bus network is shown below:

20

Figure 2: IEEE 14-Bus Network

The IEEE 14-bus network comprises five PV buses. There are two generator buses and three

buses injecting reactive power. The bulk of the load buses are concentrated in one region of

the network. Total load across the network is 259MW, with total injected reactive power of

105.29MVAr.

In its original form, the transmission losses for the IEEE 14-bus network are 13.5929MW. It

is these transmission losses that will be minimised.

After applying the proposed method, the minimum transmission loss is observed when Bus

5 is converted to PV. In this configuration, the network properties are as follows:

21

Table 1: IEEE 14-bus Network Optimal Properties

Transmission Losses 13.5233MW

Total Injected Reactive Power 104.98MVAr

Reactive Power Injected at Converted Bus 21.95MVAr

Figure 3: IEEE 14-bus Network Transmission Losses with Converted PQ Buses


The characteristics of the proposed approach are examined with the IEEE 30 - bus system.

The IEEE 30 - bus system has 2 generators, 4 synchronous condensers, 21 loads, and 41

branches.

Total load across the network is 283.4MW, with total injected reactive power of

150.408MVAr.

In its original form, the transmission losses for the IEEE 30-bus network are 17.9145MW. It

is these transmission losses that will be minimised.

22

The IEEE 30-bus network is illustrated below:

Figure 4: IEEE 30 Bus Network

After applying the proposed method, the following results are observed.

23


The minimum transmission loss is observed when Bus 21 is converted to PV. In this

configuration, the network properties are as follows:





The IEEE-30 network power losses reduce when the configuration is changed, as shown in

Table 2. It is further observed that 21 configurations have lower transmission losses than

the original configuration.


The system consists of seven synchronous machines including three synchronous

condensers. Synchronous condensers connected at bus 2, 6, and 9 inject reactive power.

24

Four generators are located at bus 1, 3, 8, and 12. There are 80 branches and 57 buses with

42 loads. Total load is 1250.8 MW and injected reactive power of 305.56MVAR in the

original configuration. Transmission losses in the base case are 25.031MW.

The IEEE 57-bus network is illustrated below:

Figure 6: IEEE 57-bus Network

25

Analysis shows that there are 6 configurations in which the IEEE-57 network has fewer

losses than the original network.


As seen in the figure above, the optimal bus after conversion to PQ is bus number 34. The

properties of the network with bus 34 converted to PV are shown below.





The optimal configuration has total transmission losses of 24.64MW, compared to the base

case losses of 25.031MW. It is also worth noting that total reactive power injected is lower

than the original configuration. It is 304.372MVAr compared to 305.56MVAr in the original.

26

4.4.Summary of Results

The results for the three simulations are as follows:

Table 4: Summary of Power Losses

IEEE Network: 14 30 57

Losses in Original Configuration: 13.59MW 17.91MW 25.03MW

Losses in Optimal Configuration: 13.52MW 17.79MW 24.64MW

Loss reduction 0.52% 0.67% 1.56%

Reactive Power Injected at Converted PQ Bus: 21.95MVAr 5.01MVAr 6.59MVArTotal Reactive Power Injected in Original Configuration: 105.29MVAr 150.41MVAr 305.56MVAr

Total Reactive Power Injected in Optimal Configuration: 104.98MVAr 149.95MVAr 304.37MVAr

14-BUS 30-BUS 57-BUS0

5

10

15

20

25

30

13.59

17.91

25.03

13.52

17.79

24.64

Losses in Original Configuration (MW)Losses in Optimal Configuration (MW)

Figure 8: Real Power Losses in the Test Networks

27

14-BUS 30-BUS 57-BUS0

50

100

150

200

250

300

350

105.29150.41

305.56

104.98149.95

304.37

Total Reactive Power Injected in Original Configuration (MVAr)Total Reactive Power Injected in Optimal Configuration (MVAr)

Figure 9: Total Reactive Power Injected into Test Networks

The above summary illustrates the following:

In all test simulations, the proposed method has achieved its main objective (reduce

total real power transmission losses).

In all test cases, the total injected power across the networks was reduced.

The objectives have therefore been achieved.

The full results for each network are shown below.

Table 5: Minimum Transmission Losses

IEEE Network:

14 30 57

Bus No. Losses (MW)

Bus No. Losses (MW)

Bus No.

Losses (MW)

1 5 13.5233 21 17.7897 34 24.63962 14 13.5896 23 17.7972 31 24.64673 9 13.5905 7 17.7978 14 24.71164 0 13.5929 24 17.8067 35 24.71755 10 13.6010 25 17.8120 26 24.7346 4 13.6216 18 17.8154 30 24.74237 13 13.6683 19 17.8265 33 24.76838 12 13.6895 3 17.8298 32 24.77069 11 13.6902 6 17.8350 25 24.8551

10 7 13.7209 26 17.8422 40 24.879811 10 17.8464 15 24.9195

28

12 17 17.8470 36 24.933113 20 17.8620 13 24.935114 30 17.8626 57 24.959315 15 17.8677 20 24.962416 22 17.8678 42 24.962817 28 17.8734 56 24.971418 16 17.8765 17 24.990019 29 17.8783 19 24.992820 27 17.8977 11 24.994821 14 17.9021 10 25.013622 0 17.9145 16 25.014223 9 18.0129 21 25.021124 12 18.0621 23 25.021325 4 18.3637 55 25.029326 0 25.031327 18 25.040128 53 25.041929 22 25.064630 50 25.108231 41 25.126732 39 25.134933 4 25.136134 5 25.143335 27 25.154836 43 25.160237 49 25.163538 38 25.190839 51 25.196940 37 25.217841 7 25.257442 44 25.275943 54 25.276744 24 25.307045 28 25.334746 52 25.341847 29 25.348548 45 25.518049 48 25.682750 47 25.862551 46 26.7837

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5. Conclusion

In the method proposed, PQ buses are iteratively converted to PV buses. This is done to

establish the optimal location for reactive power support in the network. In this way, it is

possible to find an optimal network configuration that minimises losses. The proposed

algorithm is implemented in MATLAB. It is tested on standard IEEE 14-bus, 30-bus and 57-

bus test networks. The simulations run using IEEE test networks are successful. In all three

test networks, transmission losses are reduced by using the proposed method. In addition

to this, total reactive power injected into the system is also reduced.

It must however that the loss reductions may not be significant in a practical

implementation. In order to have further power loss reduction, more work needs to be

carried out, as detailed in section 5.1 below.

5.1.Future Work

These simulation results are promising. The proposed method can be scaled up and

implemented on the Kenyan national power transmission network. This can be done

without alterations to the algorithm. Transmission losses can be reduced by applying

reactive power support to the converted buses in the optimal solution. The quantity of

reactive power injected at the converted buses is obtained during the simulation, as shown

in the results above.

In this report, the method used was to determine the optimal location of one bus that could

be converted to a PV bus. If more then one bus is converted to PV, it may be possible that

losses would be further reduced.

Also, further constraints could be added to the optimisation process. In particular, the size

of reactive support added at the converted buses is significant to a power utility company.

30

The larger the reactive support, the more expensive its installation may be. The algorithm

could be modified to include this constraint.

31

6. References

[1] Grigsby, Leonard “Electric Power Engineering Handbook” 2nd Edition

[2] Laifa Abdelaziz and Boudour Mohamed, “Optimal Location of SVC for Voltage Security

Enhancement using MOPSO”, Journal of electrical systems, Special Issue No. 01: Nov. 2009

[3] Gerbex, S., Cherkaoui, R., Germond, A.J. “Optimal location of multi-type FACTS devices in

a power system by means of genetic algorithms” IEEE Transactions on Power Systems, Aug

2001 Volume 16 Issue 3 pp. 537 – 544

[4] Pezzini P, Gomis-Bellmunt O, Gonzalez-de-Miguel C, Junyent-Ferre, A and Sudri`a-Andreu,

A “Genetic Algorithm approach in FACTS devices location for the improvement of energy

efficiency in distribution networks” International Conference on Renewable Energies and

Power Quality 2009

[5] Faur Z.T., “Effects of FACTS Devices on Static Voltage Collapse Phenomena,” M.S.

dissertation, Dept. Elect. Eng., Univ. of Waterloo, 1996

[6] Chakrabarti/ Halder Power System Analysis Operation And Control 2ed

[7] Thukaram D. and Lomi A., ‘Selection of static VAR compensator location and size for

system voltage stability improvement’, Electr. Power Syst. Res., 54(2) (2000), 139–150.

[8]http://www.ee.washington.edu/research/pstca/pf14/pg_tca14bus.htm retrieved on

28/11/11

[9] http://www.ee.washington.edu/research/pstca/pf30/pg_tca30bus.htm retrieved on

28/11/11

[10] http://www.ee.washington.edu/research/pstca/pf57/pg_tca57bus.htm retrieved on

28/11/11

[11] Newton-Raphson Load Flow MATLAB program

http://www.mathworks.com/matlabcentral/fileexchange/21059-newton-raphson-loadflow

by P. G. Praviraj retrieved on 03/10/11

32

http://www.mathworks.com/matlabcentral/fileexchange/21059-newton-raphson-loadflow

http://www.ee.washington.edu/research/pstca/pf57/pg_tca57bus.htm

http://www.ee.washington.edu/research/pstca/pf30/pg_tca30bus.htm

http://www.ee.washington.edu/research/pstca/pf14/pg_tca14bus.htm%20

[12]Stevenson, W and Grainger, J Power System Analysis 1994

[13] Jizhong Zhu, Ph.D Optimization of Power System Operation, 2009 Institute of Electrical

and Electronics Engineers

[14] Emad Ibrahim (2003): Optimal Allocations of SVCs for Improvement of Power System

Performance, Electric Power Components and Systems, 31:1, 27-46

[15]R. Phadke, Manoj Fozdar & K. R. Niazi (2009): A New Multi-objective Formulation for

Optimal Placement of Shunt Flexible AC Transmission Systems Controller, Electric Power

Components and Systems, 37:12, 1386-1402

[16] Vanusa A. De Sousa & Geraldo R. M. Da Costa (2007): Optimal Reactive Dispatch

Problem via Improved Newton Approach, Electric Power Components and Systems, 35:3,

319-336

[17] R. A. Jabr (2011): Optimization of Reactive Power Expansion Planning, Electric Power

Components and Systems, 39:12, 1285-1301

[18] Rambabu C.H., Dr. Y.P. Obulesh & Dr. CH. Saibabu (August 2011): Multi-Objective

Optimization using Evolutionary Computation Techniques, International Journal of Computer

Applications, Volume 27– No.11

[19] Kwang Y. Lee, Xiaomin Bai, Young -Moon Park (November 1995): Optimization Method

for Reactive Power Planning by Using a Modified Simple Genetic Algorithm, IEEE Transactions

on Power Systems, Vol. 10, No. 4

[20] Shoorangiz Shams Shamsabad Farahani, Mehdi Nikzad, Mohammad Bigdeli Tabar,

Mehdi Ghasemi Naraghi, Ali Javadian (2011): Reactive Power Planning Based on Genetic

Algorithms, Australian Journal of Basic and Applied Sciences, 5(7): pp 565-569

[21] Hernandez, J. C., Y. del Valle, G. K. Venayagamoorthy, and R. G. Harley (May 2006):

Optimal Allocation of a STATCOM in a 45 Bus Section of the Brazilian Power System Using

Particle Swarm Optimization, IEEE Swarm Intelligence Symposium, Indianapolis, Indiana, USA

33

kigen report 9

Documents

electric power

power utility

reactive power

minimum transmission

reactive power

load flow

particle swarm

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