formation of voltage control areas for...

__________________________________________________________

*Some parts of this chapter have been published in the following papers:

• Saran Satsangi, Ashish Saini and Amit Saraswat, “Clustering based Voltage Control Areas for Localized Reactive Power Management in Deregulated Power System”, Int. J. of Electrical and Computer Engineering (IJECE), Vol. 6, No.1, pp. 21-27, Winter 2010.

• Saran Satsangi, Ashish Saini and Amit Saraswat, “Voltage Control Areas for Reactive Power Management using Clustering Approach in Deregulated Power System”, Proc. of IET, Second Int. Conf. on Sustainable Energy and Intelligent System (IET SEISCON 2011), pp. 409-414, Chennai, India, 20th -22nd July 2011.

• Saran Satsangi, Ashish Saini and Amit Saraswat, “Identification of Clustering based Voltage Control Areas for Reactive Power Management in Deregulated Power System”, Proc. of First Int. Conf. on Adaptive Computing Technologies in Various Engineering Applications (ICACTEA-2011), Jaipur, India, 25th–26th February 2011.

Chapter 6

Formation of Voltage Control Areas for

Localized/Zonal Reactive Power Management using

K-means Clustering Approach*

6.1. Introduction

The reactive power is inherently of localized nature and therefore, it cannot travel over a

long distance in the power system. As high reactive power transmission losses are associated

with the reactive power transfer, therefore it is preferred to provide reactive power ancillary

services locally. This localized nature of reactive power results in limited number of

suppliers, generally available at any individual location (usually near a load center) to

provide the reactive power needed. In order to improve the voltage profile of the system, the

sufficient reactive power supports should be provided at different load centers in the power

system. However, from an economic point of view, the control of reactive power at every

load point of the grid is not viable. Since reactive power transmission over long distances is

also not economical, therefore the balance between reactive power generation and demand

must be maintained on a regional basis within the area of operation concerned. In this

situation, it is preferred that system operation should be optimized on a local basis so that the

balance of reactive power must be maintained.

A localized/zonal reactive power management may be an appropriate approach

because of the local nature of the reactive power and the common practices amongst most

Chapter 6: Formation of VCAs for Localized Reactive Power Management using K-means Clustering Approach 2013

Dept. of Electrical Engg., Faculty of Engineering, Dayalbagh Educational Institute, Agra-282110. 172

electric utilities to split the whole system into various reactive zones or Voltage Control

Areas (VCAs). In this approach, the whole power system is separated in to minimum

number of VCAs/Zones (appropriately selected) on the basis of electrical distances among

the different buses. The concept of VCAs/Zones based on electric distances ensures that the

reactive power injection at any bus in a particular VCA/Zone is able to control the voltage at

all the buses lying in the same VCA/Zone. The amount of reactive power injected or

absorbed at any bus is determined by using the sensitivity matrix (i.e. inverse Jacobian

matrix) of the system for a particular state of the power system. The reactive power and

voltage control based on the VCAs/Zones approach helps the ISO to achieve following goals

in a competitive electricity market:

• Improvement in the system security by improving the bus voltages.

• Reduction in real power losses in the transmission lines, efficiently.

• Improvement in transfer capability of transmission lines, and allows more

transactions to take place.

• Reduction in line flows in comparison to the line flows without reactive power

support. It reduces the cost of transacting real power, where transmission pricing

method is based on the line flows, i.e. MW-mile method. The cost of providing

reactive power comes out to be lesser than the saving in the cost of real power

transaction.

• Useful to create a localized/zonal reactive power market segregated from the real

power market. The investment in reactive power control centers is small and

hence it attracts more players to come in picture.

In order to incorporate the above advantages, an efficient and optimal reactive power

management scheme based on localized/zonal concept is advocated in the literature.

Although, the conventional hierarchical clustering based approaches [35], [180]-[181] are

adopted for the formation of VCAs/Zones. This approach requires the heuristics about the

power system topology [35]. In this chapter, an attempt is made to develop a more efficient

and robust approach based on K-means clustering to identify the desired VCAs/Zones for a

given power system. The proposed methodology may facilitate the ISO to automate the

VCAs/Zones identification processes and be used in a day-ahead reactive power

management model.

This chapter is further organized as follows: In Section 6.2, a brief description about

the significance of voltage control areas or reactive zones is given along with the concept of



electrical distance. Section 6.3 presents the formation of VCAs/Zones based on the

conventional hierarchical clustering based approach and the proposed K-means clustering

based approach. In Section 6.4, the simulation results for the VCAs/Zones formation are

discussed for three different power systems such as IEEE 24 bus reliability test system, IEEE

30 bus power system and IEEE 118 bus power system. The concluding remarks are provided

in Section 6.6.

6.2. Voltage Control Areas/Reactive Zones

The formation of Voltage Control Areas (VCAs/Zones) for any electric power system is a

process of identifying some non overlapping coherent bus groups. These groups are the sets

of buses forming voltage control areas if they are sufficiently uncoupled electrically, from

their neighbouring areas. Each VCA consists of those buses which have significant electrical

couplings (dependencies) among them. A bus voltage profile of each VCA may be

effectively controlled by the localized reactive power supports within it and the controls

within the area are less influenced by other areas [182]. In Ref. [183], a two-stage systematic

method is reported for identification of VCAs in the French power system. This method

involves determination of electrical distance between the buses in the system, and

subsequently hierarchical clustering algorithm is applied to classify the areas and decide the

borders of each VCA. In Ref. [184], a conventional method is used to analyze “local”

voltage stability problems and assess voltage security, while it has been used for examining

localized/zonal voltage-control services in Ref. [180]. The significance of VCAs/Zones may

be explained based on the two concepts: The localized nature of reactive power and the

electrical distance between the nodes (buses) in a power system.

6.2.1. Localized Nature

It is a well known fact that for the most system contingencies related to bus voltages are due

to reactive power demand at load buses, the influence (of these abnormal conditions) on the

system are of a local nature, which means that the major influence of a perturbation (i.e.

contingency) in limited to a certain neighborhood close to the original perturbation point.

This concept has been well exploited in static voltage security analysis also, from the

concentric relaxation method [185] to the complete bounding method [186]. Since the major

concern in static voltage security analysis is the violation of system operational limits [184],

like the upper and lower voltage magnitude limits at buses, it is not necessary to take into

account the control relations between load buses and generation buses. The system is just



divided into the inner subsystem near the contingency, the outer subsystem that is not

affected and the boundary subsystem, according to the contingency and system topology.

In the study of voltage stability problems, the local nature of contingency effects.

However, the local area (subsystem) studied must include the controlling buses (usually the

generation buses) as well as those load buses that they control, and sometimes the boundary

(interface) flow information. Thus, we may consider such a subsystem (i.e. local area) as a

self-contained voltage control area with its reactive power support services. The problem

then is how to properly define such a subsystem. Moreover, the reactive power and voltage-

control services are the eminently localized in nature and required to be provided locally.

Therefore, a competitive reactive power market must be considered more as a

localized/zonal market than a system-wide market. A localized/zonal reactive power market

settlement model based on these VCAs/Zones, where the prices of reactive power ancillary

services are determined on the basis of uniform price auction within each VCA/Zone, is thus

proposed in Chapter 7. Since all the buses in one voltage control area should have low

impedance paths to each other, the electrical distance developed in Ref. [183] may be a good

measure to decide the proper VCAs/zones.

6.2.2. Electrical Distance

The concept of electrical distance is used to measure the voltage interactions between

different buses of the electrical power system. Therefore, the electrical distance is physical

relationship between two buses in power system [187]. With the usual hypothesis of the real

and reactive decoupled system, the reactive model is written as:

[ ] [ ][ ]Q Q V V∆ = ∂ ∂ ∆ (6.1)

rewriting the eq.(6.1).

[ ] [ ] [ ] [ ][ ]1V Q V Q V Q Q

−∆ = ∂ ∂ ∆ = ∂ ∂ ∆ (6.2)

where [ ]Q V∂ ∂ is part of the power flow Jacobian matrix J and [ ]V Q∂ ∂ is its inverse and

is called as the sensitivity matrix.

Both matrices are real and non symmetrical. The elements of [ ]V Q∂ ∂ reflect the

propagation of voltage variation following reactive power injection at a bus. The degree of

voltage coupling [180] between two buses can be quantified by the maximum attenuation of



voltage variation between these two buses. These attenuations are easy to obtain from

[ ]V Q∂ ∂ the matrix, by just dividing the elements of each column by the diagonal term. A

matrix of attenuations between all the buses of the system, whose terms are written as ijα is

then available. The degree of voltage coupling between two buses can be defined by the

maximum attenuation of voltage variations between the two buses:

i ij jV Vα∆ = ∆ (6.3)

Where

jiij

j j

VV

Q Qα

∂∂= ∂ ∂ (6.4)

Thus, the term “ ijα ” represents the normalized voltage attenuation on ith bus with

respect to the perturbation at jth bus. In general, ij jiα α≠ . In order to have symmetric

property in the electrical distance, the formulation below is used to define the electrical

distance between two buses i and j [2] as follows:

( )ij ji ij jiD D Log α α= = − � (6.5)

where ijD is the electrical distance between ith bus and jth bus, and it has the properties of

positivity and symmetry. This electrical distance represents the degree of influence arising

from voltage changes on other buses. The step-by-step method to obtain the separate

voltage-control areas is given as follows.

1. Calculate the Jacobian matrixJ and hence obtain the sub-matrix4J , where

[ ]4J Q V= ∂ ∂ .

2. Invert 4J . Say, ( ) 14B V Q J −= ∂ ∂ = , and the elements of matrix B are written asijb ,

where ij i jb V Q= ∂ ∂ .

3. Obtain attenuation matrix, ijα , between all the buses as follows: ij ij jjb bα = .

4. Calculate electrical distances ( , )ij ij jiD Log α α= −

5. Normalize the electrical distances as follows: 1Max( ,....., )ij ji i iND D D D=

In practice, instead of[ ]Q V∂ ∂ , the susceptance matrix “B” can be used.



6.3. Formation of Voltage Control Areas / Reactive Zones

Once the electrical distances for any pair of buses in the system are completely determined,

it is possible to trace the boundary of VCAs/Zones [180]. It is intended to group (cluster) the

set of buses within close range to form VCAs/Zones. These ranges of electrical distances

may be decided based on the judgment and experience of ISO. There is no unique way to do

so. The general idea is to give autonomy and independence, from a reactive power

management standpoint, to each VCA/Zone. This may be accomplished in different ways

depending on the power system, which requires an efficient clustering algorithm to form the

desired VCAs/Zones. The concept of VCA clustering, which is the main focus of the present

chapter, may be exploited by use of a robust clustering algorithm which is suitable for the

given data set of electrical distances of a large power system.

Table 6.1: Comparison of hierarchical and partitional methods of data clustering [188]

S.No. Hierarchical Clustering Approach Partitional Clustering Approach

1 Proper speed Relatively slow convergence

2 Number of clusters is determined automatically Number of clusters must be predefined

3 Probability to lead to incorrect results Tend to produce better results

4 Related to the initial seed points for clusters Related to the initial seed points for clusters

It is a complicated task to form effective and most accurate VCAs for any large-scale

power system in the absence of well defined deterministic method. Fortunately, there are

some data management contrivances that help to have more accurate results [188]. Data

clustering is one of the main branches in the field of data mining where clustering is one of

the main tasks of knowledge discovery from databases. The clustering aims to discover

sensible organization of objects in a given dataset by identifying and quantifying similarities

(dissimilarities) between the objects. The fundamental clustering problem is to partition a

given data set into groups (clusters), such that the data points in a cluster are more similar to

each other than points in different clusters. In literature of data clustering [188], the

multitude clustering methods are available, which may be broadly classified into the

following types according to the nature of their search [189]: (a) Partitional clustering; (b)

Hierarchical clustering; (c) Density based clustering; and (d) Grid-based clustering.

Moreover, the common clustering methods are based on the first two categories. A

hierarchical clustering procedure achieves its clustering through a nested sequence of



partitions, which can be represented in a tree-like structure. On the other hand, partitional

clustering method performs clustering in one shot. Historically, the hierarchical clustering

techniques have been more popular in biological, social and behavioural sciences, whereas

partitional methods are more frequent in engineering applications. According to the Ref.

[188], a glance of advantages and disadvantages of the two categories of clustering methods

are listed in Table 6.1. The partitional methods usually lead to better results due to the nature

of iterative and revised-type grouping method and hence they are preferable if there is no

emphasis on speed. Unfortunately the fastness of the convergence could not have much

effect to overcome the deficiency of capturing in local minimums. The common method is to

run the algorithm several times and return the best (not necessary the optimal) clustering

found. The K-means clustering algorithm is well-known partitional clustering method. It is

popular because of its following advantages:

(a) The K-means clustering algorithm converges very fast in practice.

(b) The results of K-means clustering algorithm can be used as a pre estimation of final

clustering due to its fast convergence. This feature is suitable to be considered as the

initial values in advanced clustering algorithms like evolutionary based algorithms to

make a more efficient hybrid clustering algorithm.

(c) Although there is no guarantee of achieving a global minimum, though the

convergence of this algorithm is ensured [190].

A hierarchical classification algorithm based approach is reported in Ref. [35] to

identify the VCAs/Zones according to the electrical distances. In present chapter, an

alternative approach based on the K-means clustering algorithm is proposed to identify the

VCAs/Zones for the reactive power management and voltage control. These two approaches

are described in following subsections for VCAs/Zones formation.

6.3.1. Conventional Hierarchical Clustering based Approach

In this subsection, the procedure of a hierarchical classification algorithm to determine the

VCAs/Zones according to the electrical distances is described. A block diagram, as shown in

Fig.6.1, illustrates the procedural steps to identify the VCAs/Zones using a hierarchical

clustering based approach. The power flow analysis is performed on the given power system

data, the sensitivity matrix (i.e. V Qδ δ matrix) is computed and subsequently normalized

electrical distances are calculated (using all the five steps as explained in subsection 6.2.2).



Fig.6.1: Procedural steps for the formation of voltage control areas using hierarchical clustering

Thereafter, the normalized electrical distances ijD corresponding to each ith bus with

respect to other buses “j” ( , )j n j i∀ ∈ ≠ are classified into some ranges such as Range#1,

Range#2, Range#3,..........., which are in an ascending order. The relationships between

them may be expressed as follows:

1

1 2

2 3

1 2 3

0

......

..............

R

R R

R R

R R R

≤≤≤

Range#1 <

Range#2 <

Range#3 <

< < <

(6.6)

Then, we start from Range#1. For each bus “j” whose electrical distance to generator

“ i” is shorter than1R , i.e., ijD ∈ Range#1, the bus will be put in the same group as generator

“ i”. This grouping step is repeated to all the generator buses for Range#1. We can repeat the

grouping steps for Range#2, Range#3,......, until all the buses are at least in one of the

groups. The smaller the ranges, the better the grouping effects will be. There may be a few

overlaps between groups, in other words, there may be a few buses belong to more than one

groups. For this case, according to its electrical distance to other buses, a simple judgment

can be done to classify it to one of the groups. Here, the voltage-control areas and their

borders can be determined.

6.3.2. Proposed K-means Clustering based Approach

A two stage approach based on K-means clustering algorithm is proposed to identify the

desired VCAs/Zones. At first stage, the sample data for clustering is prepared based on the

normalized electrical distances, as computed by applying the power flow analysis by

following the five stage procedure as presented in Subsection 6.2.2. At second stage, the

standard K-means clustering is applied to form the desired VCAs/Zones. The proposed

approach is illustrated in Fig.6.2.

At second stage as shown in Fig.6.2, the K-means clustering algorithm begin with

specifying the number of clusters i.e. K. Any initial partition that classifies the data into K



clusters is put by assigning the training samples randomly or systematically as: the first ‘k’

training samples are taken as single-element clusters and subsequently, assign each of the

remaining training samples to the cluster with the nearest centroid. After each assignment,

the centroid of the gaining cluster is recomputed. Further, a systematic procedure is followed

by taking each sample in a sequence and its distance is computed from the centroid of each

of the clusters. Subsequently, the grouping based on minimum distance is achieved until no

data object is moving to another cluster anymore.

Fig.6.2: Formation of VCAs/Zones using K-means clustering based approach

Moreover, the standard K-means clustering algorithm is based on the Euclidean

distance. The Euclidean distance in a plan is the “ordinary” distance between two points that

one would measure with ruler. In N dimension space, the Euclidean distance between two

points P and Q is

( ) ( ) ( )2 2 2

1 1 2 2 ...... n nP Q p q p q p q− = − + − + + − (6.7)

where pi (or qi ) is the coordinate of p (or q) in dimension i .

The K-means clustering algorithm uses the concept of Euclidean distance to measure

the similarity (or dissimilarity) between each point in the database and the centre of the

clusters to determine to which cluster the point is better dependent. It tries to separate the

data points into an adequate number of clusters in a way that the sum of the Euclidean



distances of all points of database to the centroid of their own cluster become minimized (at

least locally minimized as mentioned before). This procedure consists of the following steps:

Step 1: Choose K initial cluster centres z1(1), z2(1), . . ., zk(1) arbitrarily.

Step 2: At the rth iterative step distributes the samples {X} among the K cluster domains,

using the relation,

( ) ( ) < ( ) 1,2,...., andj j ix S r if x z r x z r i K i j∈ − − ∀ = ≠ (6.8)

where ( )jS r denotes the set of samples whose cluster centre is( )iz r .

Step 3: From the results of Step 2, compute the new cluster centers ( 1), 1,2,......,jz r j K+ = ,

such that the sum of the squared distances from all points in ( )jS r to the new cluster

centre is minimized. Those cluster centres are considered simply the sample mean of

( )jS k .

( )

1( 1) 1,2,..........,

j

jX S k

z k X j KN ∈

+ = =∑ (6.9)

where Nj is the number of samples in( )jS r .

Step 4: if ( 1) ( )j jz r z r+ = , for 1,2,......,j K= , the algorithm has converged and the

procedure is terminated. Otherwise go to Step 2.

6.4. Simulation Results and Discussion

The simulations related to the formation of VCAs/Zones are carried out on three different

power systems such as: IEEE 24 bus reliability test system, IEEE 30 bus power system and

IEEE 118 bus power system. These simulations comprise the formation of VCAs/Zones

obtained from the proposed K-means clustering based approach and subsequently, its

comparison with the conventional hierarchical clustering based approach.

Earlier, Nobile and Bose have conducted load flow simulations before and after

adding new reactive power load at specific location to verify the formation of different

VCAs in their work presented in Ref. [180]. The similar kinds of simulations are conducted

in present research work. The proposed methodology is tested for various disturbances as

created by sudden increments in the real and reactive power demand simultaneously at any



load bus. Any such load disturbance may result in voltage fall at that particular bus below its

minimum acceptable limit and poor voltage profile at other buses lying in the same

VCA/Zone. In order to bring back the voltage profile within their permissible limits, the

required voltage control actions may be either by increasing the generator voltages or by

increasing the reactive power support from shunt capacitors installed in same VCA/Zone.

All the simulations are carried out using MATLAB 7.0 on a Pentium IV, 2.26 GHz, 2 GB

RAM computer system.

6.4.1. IEEE 24 bus Reliability Test System

The detailed description about the IEEE 24 bus reliability test system (i.e. IEEE 24 bus RTS)

including the Single Line Diagram (SLD) is given in Appendix A. Using the methodology as

described in previous section, the buses were grouped according to their electrical distances

for the system intact condition. The given IEEE 24 bus RTS is divided in to two

VCAs/Zones (namely VCA-I and VCA-II) by using the conventional hierarchical clustering

approach and the proposed K-means clustering approach as described in subsections 6.3.1

and 6.3.2 respectively.

(a) Conventional hierarchical clustering approach (b) K-means clustering approach

Fig.6.3: Formation of two VCAs/Zones for IEEE 24 bus RTS by using (a) Conventional hierarchical clustering

approach and (b) K-means clustering approach



Table 6.2: Comparison of the two VCAs/Zones obtained from Hierarchical and K-means clustering approach

for IEEE 24 bus RTS

S.No. Approach VCAs/Zones

1 Conventional hierarchical clustering based approach

VCA-I = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 24}

VCA-II = {11, 12, 13, 14a, 15, 16, 17, 18, 19, 20, 21, 22, 23}

2 K-means clustering based

approach

VCA-I = { 1, 2, 4, 5, 6, 7, 8, 9, 10}

VCA-II = {3, 11, 12, 13, 14a, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24} a Synchronous condenser (SC)

The results of the formation of two VCAs/Zones from the above mentioned two

approaches are given in Table 6.2. In this table, the generator buses are marked by bold

letters. The two VCAs/Zones formed by using conventional hierarchical clustering and K-

means clustering approaches are illustrated in Fig.6.3 and enclosed by dashed lines. It is

noticed that the VCA-I comprises of three generator buses (i.e. Bus 1, Bus 2 and Bus 7),

whereas the VCA-II comprises of seven generator buses (i.e. Bus 13, Bus 15, Bus 16, Bus

18, Bus 21, Bus 22 and Bus 23) and a synchronous condenser at Bus 14 as obtained by both

the clustering approaches (i.e. hierarchical and K-means). The only discrepancy is about the

Bus 3 i.e. whether it should be in VCA-I or in VCA-II (see Table 6.2 and Fig. 6.3).

The disturbances are created at Bus 3, Bus 5, Bus 10 and Bus 19 by sudden

increment in load (real power as well as reactive power demand) till voltage is reduced

below the specified minimum permissible limit (let say 0.94 p.u.). Consequently, there is

also a significant voltage fall at other buses lying within the same VCA/Zone too. Several

control actions are attempted by increasing all the generator bus voltages (one at a time) to

bring back these bus voltages within their specified minimum permissible limit. The

simulation result of these voltage control actions are analyzed with reference to VCAs/Zones

as formed by K-means clustering based approach as summarized in Table 6.3. For example,

if the load (real as well as reactive power demand) at Bus 3 is increased by (0.45+j0.0925)

p.u., there is a voltage fall at the same bus from base value of 0.94695 p.u. to 0.93342 p.u. It

is a violation of minimum permissible bus voltage limit. To maintain the voltage at Bus 3

within its minimum permissible limit, the effective voltage control actions are achieved by

increasing the voltages of the generator at Bus 13 and Bus 15. In case of the load disturbance

at Bus 3, the best voltage control scenario is illustrated in Fig.6.4 (a).



Table 6.3: Simulation results under different loading conditions for VCAs/Zones for IEEE 24 bus RTS using k-means clustering based approach

VCA-I = {1, 2, 4, 5, 6, 7, 8, 9, 10} VCA-II = {3, 11, 12, 13, 14a, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}

Other Effected Buses due to disturbance bus no.10

Voltage Control Area (VCA) VCA-II VCA-I VCA-I Bus No. Bus 3 Bus 19 Bus 5 Bus 10 Bus 6

Permissible voltage (p.u) Maximum 1.05000 1.05000 1.05000 1.05000 1.05000 Minimum 0.94000 0.94000 0.94000 0.94000 0.94000

Base Voltage (p.u.) (i.e. at normal condition) 0.94695 0.99152 0.98100 0.99018 -

Load Increment (p.u.) Real power (P) 0.45000 9.05000 1.77500 2.92500 - Reactive Power (Q) 0.09250 1.85000 0.35000 0.60000 -

Voltage after disturbance before voltage control (p.u.) 0.93342 0.93712 0.92826 0.93791 0.93022

Control with

VCA-I

For Gen. at Bus 1 Increment in Gen. Voltage (p.u.) 0.02300 0.05000 0.01800 0.05000 0.05000 Load bus voltage (p.u.) 0.94013 0.93712 0.94039 0.94942 0.93955



Control with

VCA-II

For Gen at Bus 13 Increment in Gen. Voltage (p.u.) 0.05000 0.05000 0.05000 0.03500 0.03500 Load bus voltage (p.u.) 0.94073 0.93714 0.93750 0.95106 0.94073

For Gen. at Bus14 Increment in Gen. Voltage (p.u.) 0.05000 0.05000 0.05000 0.05000 0.05000 Load bus voltage (p.u.) 0.93738 0.93713 0.93301 0.94754 0.93793







Remarks Controlled by both VCAs, but effective

control is achieved by VCA-II

Only Controlled by VCA-II

Only Controlled by VCA-I

Controlled by both VCAs, but effective control is achieved

by VCA-I

Voltage at Bus 6 is also effectively controlled by

VCA-I

a Synchronous condenser (SC)



(a) Control of the disturbance at Bus 3

(b) Control of the disturbance at Bus 19

(c) Control of the disturbance at Bus 5

(d) Control of the disturbance at Bus 10

Fig.6.4: Voltage profiles at normal condition, after disturbances and after voltage control actions in the VCAs simulations for IEEE 24 bus RTS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

Bus Number

Bus

Vol

tage

(in

p.u

.)

Base voltage at normal condition

Voltage after disturbance

Voltage after control action

Minimum permissible bus voltage limit

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

Bus Number

Bus

Vol

tage

(in

p.u

.)

Base voltage at normal condition




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240.92

0.94

0.96

0.98

1

1.02

Bus Number

Bus

Vol

tage

(in

p.u

.)

Base Voltage at nornal condition




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0.94

0.96

0.98

1

1.02

Bus Number

Bus

vol

tage

(in

p.u

.)

Base Voltage at normal condition






In a same manner, the voltage control actions are analyzed for subsequent

disturbances at Bus 19, Bus 5 and Bus 10 and are summarised in Table 6.3. The best voltage

control scenarios achieved for these load disturbances are also shown in Fig.6.4.

From this study, it is clear that Bus 3, Bus 13 and Bus 15 have strong electrical

coupling and therefore they must be in same VCA/Zone. This observation justifies that the

two VCAs/Zones as determined by the proposed K-means clustering based approach are

more appropriate in comparison to the conventional hierarchical clustering based approach

for the IEEE 24 bus RTS.

Table 6.4: Comparison of the three VCAs/Zones obtained from Hierarchical and K-means clustering approach for IEEE 24 bus RTS


1 Conventional hierarchical clustering

based approach

Zone#1 = {1, 2, 3, 4, 5, 6, 7, 8}

Zone#2 = {9, 10, 11, 12, 13, 14a, 20, 23}

Zone#3 = {15, 16, 17, 18, 19, 21, 22, 24}

2 K-means clustering based approach

Zone#1 = {1, 2, 3, 4, 5, 6, 7, 8}

Zone#2 = {9, 10, 11, 12, 13, 14a, 20, 23}

Zone#3 = {15, 16, 17, 18, 19, 21, 22, 24} a Synchronous condenser (SC)

Zone#2

Zone#1

Zone#3

SLD

IEEE-24 bus RTS

Fig.6.5: Formation of three VCAs/Zones for IEEE 24 bus RTS



Further, the given IEEE 24 RTS is divided into three VCAs/Zones (namely Zone#1,

Zone#2 and Zone#3) by using the proposed K-means clustering based approach as shown in

Fig.6.5. Interestingly, the same VCAs/Zones are obtained from the conventional hierarchical

clustering based approach as shown in Table 6.4. Zone#1 consists of three generators at bus

number 1, 2 and 7 along with five load buses (Bus 3, Bus 4, Bus 5, Bus 6 and Bus 8);

Zone#2 is having two generator buses (bus number 13 and 23), one synchronous condenser

at Bus 14 and five load buses (Bus 9, Bus 10, Bus 11, Bus 12 and Bus 20); and Zone#3

includes five generator buses (Bus 15, Bus 16, Bus 18, Bus 21 and Bus 22) and three load

buses (Bus 17, Bus 19 and Bus 24).

6.4.2. IEEE 30 bus Power System

The proposed methodology for the formation of VCAs/Zones is also tested on IEEE 30 bus

power system. The detailed description about the IEEE 30 bus power system including the

Single Line Diagram (SLD) is given in Appendix B. The given IEEE 30 bus power system is

divided in to three VCAs/Zones (namely VCA-I, VCA-II and VCA-III) by using the

conventional hierarchical clustering approach and the proposed K-means clustering approach

as shown in Fig.6.6. The results of the formation of three VCAs/Zones by using the above

mentioned two approaches are also compared in Table 6.5. In this table, the generator buses

are marked by bold letters.

Table 6.5: Comparison of the three VCAs/Zones obtained from Hierarchical and K-means clustering approach

for IEEE 30 bus power system


1 Conventional hierarchical clustering based approach

VCA-I = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 17, 21, 22, 24, 28}

VCA-II = {12, 13, 14, 15, 16, 18, 19, 20, 23, 25, 26}

VCA-III = {27, 29, 30}

2 K-means clustering based

approach

VCA-I = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 28}

VCA-II = {10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}

VCA-III = {25, 26, 27, 29, 30}

The same simulation scheme as adopted in previous subsection is followed to

evaluate and compare the performance of both the VCAs/Zones formation approaches. For

this purpose, various disturbances (one at a time) are created at Bus 7, Bus 17, Bus 21, Bus

24 and Bus 30 by sudden increment in load (real power and reactive power demand) till

voltage magnitude reduced below the specified minimum limit (0.94 p.u.). As a consequence



of any disturbance, there are also significant voltage violations in their corresponding VCAs.

Again, several control actions are attempted by increasing all generator bus voltages (one at

a time) to bring back these bus voltages within their specified minimum permissible limits.

The simulation results of these voltage control actions are analyzed with reference to three

VCAs/Zones obtained by K-means clustering based approach and summarized in Table 6.6.

From Table 6.6, it is clear that when the load (real as well as reactive power) demand

is increased by an amount of (0.3045+j0.2345) p.u. at Bus 24, this load disturbance affects

the bus voltage i.e. the voltage fall at the same bus from base value 1.0216 p.u. to 0.93701

p.u. It is the violation of minimum permissible bus voltage limit. Therefore, in order to bring

back this bus voltage within its permissible bus voltage limits, the control action is obtained

by increasing the voltage of the generator at Bus 13. The best voltage control action is

obtained in the case of disturbance at Bus 24 as illustrated in Fig.6.7 (c). In the same

manner, the various voltage control actions taken for the other load disturbances are also

summarised in Table 6.6 and corresponding voltage profiles are shown in Fig.6.7.

From this study, it is evident that Bus 24 and Bus 13 have strong electrical coupling

and hence they must be in same VCA/Zone. The proposed K-means clustering based

approach includes Bus 24 and Bus 13 in same VCA/Zone whereas the conventional

hierarchical clustering based approach fails to do so. Further, it is also clear (see Table 6.6)

that if any VCA/Zone is formed in such a manner that no generator lies in same VCA/Zone

and load is increased in this VCA, then bus voltage profile is maintained within permissible

limits by providing reactive power support from local capacitor banks within the same

VCA/Zone. Moreover, if the load (real and reactive power demand) increment at Bus 30 is

about (0.212+j0.038) p.u., it results in voltage fall at the same bus and its neighbouring Bus

29. The best voltage control action is obtained in the case of disturbance at Bus 30 as

illustrated in Fig.6.7 (d). The detailed analysis of capacitor value for controlling the same is

also given in Table 6.6. Hence, this analysis supports that three VCAs/Zones as obtained by

proposed K-means based methodology are more appropriate in comparison to conventional

hierarchical based approach.



SLD

IEEE 30 bus SystemVCA - 1

VCA - II

VCA - III

(a) Conventional hierarchical clustering approach (b) K-means clustering approach Fig.6.6: Formation of three VCAs/Zones for IEEE 30 bus power system by using (a) Conventional hierarchical clustering approach and (b) K-means clustering approach



Table 6.6: Simulation results under different loading conditions for VCAs/Zones for IEEE 30 bus power system using k-means clustering based approach

VCA-I = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 28} VCA-II = {10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23} VCA-III = {25, 26, 27, 29, 30}

Other effected buses due to disturbance

bus no.21

Other effected buses due to disturbance

bus no.30 Voltage Control Area (VCA) VCA-I VCA-II VCA-II VCA-III VCA-III

Bus No. Bus 7 Bus 17 Bus 24 Bus 21 Bus 22 Bus 30 Bus 29

Permissible voltage (p.u) Maximum 1.06000 1.06000 1.06000 1.06000 - 1.06000 - Minimum 0.94000 0.94000 0.94000 0.94000 - 0.94000 -

Pre disturbance Voltage(p.u.) 1.00240 1.03990 1.02160 1.03270 - 0.99191

Load Increment (p.u.) Real power (P) 1.25400 0.63000 0.30450 0.61250 - 0.21200 - Reactive Power (Q) 0.59950 0.40600 0.23450 0.39200 - 0.03800 -

Post disturbance Voltage(p.u.) 0.93532 0.93446 0.93701 0.93218 0.93983 0.87107 0.91819

Control with

VCA #1

For Gen. at bus 1 Increment in Gen. Voltage (p.u.) 0.04000 0.04000 0.04000 0.04000 0.04000 0.04000 0.04000 Load bus voltage (p.u.) 0.93723 0.93730 0.93910 0.93498 0.94260 0.87421 0.92115



For Gen at bus 8 Increment in Gen. Voltage (p.u.) 0.01510 0.02020 0.01010 0.02020 0.02020 0.09000 0.09000 Load bus voltage (p.u.) 0.94076 0.94185 0.94125 0.94070 0.94788 0.93468 0.97834

For Gen. at bus11 Increment in Gen. Voltage (p.u.) 0.01800 0.01800 0.01800 0.01800 0.01800 0.01800 0.01800 Load bus voltage (p.u.) 0.93594 0.93953 0.94116 0.93767 0.94519 0.87370 0.92068

Control with

VCA #2 For Gen. at bus 13

Increment in Gen. Voltage (p.u.) 0.02900 0.01710 0.00930 0.02780 0.02780 0.02900 0.02900

Load bus voltage (p.u.) 0.93630 0.94035 0.94002 0.94021 0.94786 0.87658 0.92339

Control with

VCA #3

At bus 25 Capacitor provided(MVAR) - - - - - 21 21 Load bus voltage (p.u.) - - - - - 0.93522 0.97886





Remarks Only

controlled by VCA-I

Controlled by both VCAs, but

effectively controlled by

VCA-II



VCA-II



VCA-II

Voltage at bus No. 22 also controlled

effectively by VCA-II

Only controlled by

VCA-III

Voltage at Bus No. 29 also effectively

controlled by VCA-III



(a) Control of the disturbance at Bus 7

(b) Control of the disturbance at Bus 17

(c) Control of the disturbance at Bus 24

(d) Control of the disturbance at Bus 30

Fig.6.7: Voltage profiles at normal condition, after disturbances and after voltage control actions in the VCAs simulations for IEEE 30 bus power system

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

Bus Number

Bus

Vol

tage

(in

p.u

.)

Base voltage



Maximum permissible bus voltage limit


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

Bus Number

Bus

Vol

tage

(in

p.u

.)

Base voltage





1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

Bus Number

Bus

vol

tage

(in

p.u

.)

Base Voltage





1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.86

0.9

0.94

1

1.05

1.11.1

Bus Number

Bus

Vol

tage

(in

p.u

.)

Base Voltage







6.4.3. IEEE 118 bus Power System

In order to further explore the effectiveness of the proposed methodology for the formation

of VCAs/Zone, it is also tested for a bigger power system i.e. IEEE 118 bus power system.

The complete description of the IEEE 118 bus power system along with its Single Line

Diagram (SLD) is given in Appendix D. Three VCAs/Zones (namely VCA#1, VCA#2 and

VCA#3) are determined for given IEEE 118 bus power system by using the conventional

hierarchical clustering approach and the proposed K-means clustering approach as shown in

Fig.6.7 and Fig.6.8 respectively. The results of the formation of three VCAs/Zones using the

above mentioned two approaches are given in Table 6.7. In this table, the generator buses are

marked by bold letters.

Table 6.7: Comparison of the two VCAs/Zones obtained from Hierarchical and K-means clustering approach

for IEEE 118 bus power system


1

Conventional hierarchical clustering

based approach

VCA#1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,

23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 113, 114, 115, 117}

VCA#2 = {38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,

59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 97, 116, 118}

VCA#3 = {80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99,

100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112}

2

K-means clustering

based approach

VCA#1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,

23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 113, 114, 115, 117}

VCA#2 = {42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,

62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 116, 118}

VCA#3 = {80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,

100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112}

From Table 6.7 along with Fig.6.8 and Fig.6.9, it is clear that the positions of the five

buses (i.e. Bus 38, Bus 41, Bus 43, Bus 80 and Bus 97) in different VCAs/Zones obtained by

the above two methodologies are debatable. For example, Bus 41 is placed in VCA#2 using

the proposed K-means clustering approach whereas the same bus is placed in VCA#1 by the



conventional hierarchical clustering approach. The similar simulation scheme (as adopted in

previous two studies) is followed to evaluate and compare the performance of both the

VCAs/Zones formation approaches. For this purpose, various disturbances (one at a time)

are created at Bus 41, Bus 43, Bus 83, Bus 97, Bus 98, Bus 44, Bus 78 and Bus 75 by sudden

increment in load (real and reactive power demand) till bus voltage reduced below the

specified minimum limit (0.94 p.u.). As the consequence of any load disturbance, there are

also be the significant voltage reduction within the respective VCA/Zone. Again, several

control actions are attempted by increasing the generator bus voltages (one at a time) to

bring back these bus voltages within their specified minimum permissible limit. The

simulation results of these voltage control actions are analyzed with reference to three

VCAs/Zones obtained from the proposed K-means clustering based approach and

summarized in Table 6.8.

Based on the simulation results as presented in Table 6.8 with reference to the three

VCAs/Zones obtained by the proposed methodology based on K-means clustering approach,

the following inferences may be drawn:

� Although the voltage at Bus 41 of VCA#1 is controlled by the generators at Bus 40,

Bus 34, Bus 36 (within VCA#1) and Bus 42 (of VCA#2), but it is effectively

controlled by the generator situated at Bus 40 as compared to the generator at Bus 42

(See Table 6.8). This observation supports that the Bus 40 and Bus 41 have stronger

coupling in comparison to the coupling between Bus 40 and Bus 42. Therefore, Bus

40 and Bus 41 must remain in the same group (or VCA/Zone) which is obtained by

using K-means clustering based approach in contrast to the conventional hierarchical

clustering based approach.

� Although, the voltage at Bus 43 of VCA#1 is controlled by the generators at Bus 40,

Bus 34 (within VCA#1) and Bus 46 (of VCA#2), bus it is effectively controlled by

the generator at Bus 34 in comparison to the generator at Bus 46 (See Table 6.8).

Therefore, two buses (i.e. Bus 43 and Bus 34) must be in the same group (i.e.

VCA#1) as obtained by the proposed K-means Clustering based approach.

� From Table 6.7, the voltage at Bus 97 of VCA#3 is controlled only by the generators

at Bus 80, Bus 85, Bus 92 and Bus 100 (all four generators are within the same VCA

i.e. VCA#3) as obtained by the proposed methodology based on K-means Clustering

in contrast to other approach.



Fig.6.8: Formation of three VCAs/Zones for IEEE 118 bus power system by using conventional hierarchical clustering based approach



Fig.6.9: Formation of three VCAs/Zones for IEEE 118 bus power system by using K-means clustering based approach



Table 6.8: Simulation results under different loading conditions for VCAs/Zones for IEEE 118 bus power system using k-means clustering based approach

VCA#1 = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43,113,114,115,117} Other Effected Buses due to disturbance at bus

no.75 of VCA#2 VCA#2 = {42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,81,116,118} VCA#3 = {80, 82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112}

Voltage Control Area (VCA) VCA#1 VCA#3 VCA#2 VCA#2 Bus No. 41 43 83 97 98 44 78 75 118

Permissible voltage (p.u) Maximum 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 Minimum 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94 0.94

Pre disturbance Voltage(p.u.) 0.96683 0.96967 0.97558 1.0091 1.0235 0.96653 1.0018 0.96733 0.94416

Load Increment (p.u.) Real power (P) 1.2025 0.45 0.98 1.47 2.21 0.288 7.81 2.256 - Reactive Power (Q) 0.325 0.17 0.49 0.882 0.52 0.144 2.86 0.528 -

Post disturbance Voltage(p.u.) 0.93882 0.93865 0.93897 0.93736 0.93429 0.93502 0.93686 0.93834 0.93397

Control With

VCA #1

For Gen. at bus 40 Increment in Gen. Voltage (p.u.) 0.00194 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 Load bus voltage (p.u.) 0.9403 0.9401 0.93897 0.93796 0.93436 0.93502 0.93686 0.93836 0.93397



Control with

VCA #2






Control with

VCA #3





For Gen. at bus 100

Increment in Gen. Voltage (p.u.) 0.043 0.043 0.023 0.022 0.0137 0.043 0.043 0.043 0.043 Load bus voltage (p.u.) 0.93382 0.93865 0.94088 0.94016 0.94019 0.93502 0.93686 0.93836 0.93397

Remarks Control by both VCA#1 & VCA#2 but effectively

by VCA#1 Control by VCA#3 only

Control by both VCA#1 & VCA#2 but effectively by

VCA#2

Control by both VCA#2 & VCA#3 but effectively by

VCA#2

Control by

VCA#2 only

Control by VCA#2 only



Therefore, the above simulations and the subsequent analysis suggest that the

proposed methodology based on K-means clustering approach is also an appropriate method

for splitting the IEEE 118 bus power system in to the better VCAs/Zones in comparison to

the conventional hierarchical clustering based approach. Further, these VCAs/Zones may be

used in any voltage control and reactive power management applications in the present

deregulated environment.

6.5. Concluding Remarks

This chapter presents a new K-means clustering based approach to identity the desired

Voltage Control Areas (VCAs) for a given power system. Similar to the conventional

hierarchical clustering based approach, the proposed methodology based on K-means

clustering algorithm also exploits the concept of electrical distance and localized nature of

reactive power. In proposed methodology, the choice of K-means clustering algorithm is

obvious because of its robustness and suitability for engineering applications. Moreover, the

proposed methodology is compatible for the establishment of a localized/zonal day-ahead

reactive power market necessary for effective reactive power management as dealt in the

next chapter. The effectiveness of the proposed K-means clustering based approach has been

demonstrated on three different power system such as IEEE 24 bus RTS, IEEE 30 bus power

system and IEEE 118 bus power system for the different load disturbances. The results and

subsequent discussions presented show that the K-mean clustering based methodology is a

well deserved approach for the effective identification of desired VCAs/Zones and compete

with the conventional hierarchical clustering based approach. The extensive simulations for

different critical load disturbances are applied to verify and compare the clustering

performances of both the approaches. It is found that the K-means clustering based approach

provides more appropriate VCAs/Zones as compared to other existing approach.

Furthermore, the developed methodology is useful for determining the allowable voltage

ranges for each cluster, which facilitates the effective and secure reactive power supply in

the power system operation. And it is also valuable for providing the signal for reactive

power management in each cluster and hence may be used for managing the price-related

risk in the competitive market operation.

***

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