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Electric Power Systems Research 119 (2015) 377–384

Contents lists available at ScienceDirect

Electric Power Systems Research

j o ur na l ho mepage: www.elsev ier .com/ locate /epsr

econdary voltage control system based on fuzzy logic

.V. Santos, A.C. Zambroni de Souza ∗, B.I.L. Lopes, D. Marujonstitute of Electrical and Energy Systems, Federal University of Itajuba, BPS Av., 1303. P.B. 50, ZIP 37500-903 Itajuba, MG, Brazil

r t i c l e i n f o

rticle history:eceived 1 August 2014eceived in revised form 21 October 2014

a b s t r a c t

This paper discusses the problem of secondary voltage control in power systems. This problem is ofdeep interest for researchers and engineers, since it imposes serious restrictions to system’s operators.In general, this problem is resolved by selecting pilot buses representative of a region. Instead, in this

ccepted 23 October 2014

eywords:econdary voltage controluzzy logicodal analysis

angent vector

paper, modal analysis is used to identify a coherent group of buses to be monitored. The set of informationcollected by modal analysis is considered by a fuzzy logic-based algorithm, so a voltage control policyis implemented. The academic IEEE 118-bus system is employed with all its limits considered, so theresults may be reproduced.

© 2014 Elsevier B.V. All rights reserved.

. Introduction

Large interconnected power systems pose a complex reactiveower control problem for operators in general. Unlike the fre-uency control, the problem of voltage control must be locallyddressed, since reactive power cannot travel far. Hence, an effec-ive voltage control depends on the availability of generators andynchronous condensers and tap changers.

The Secondary Voltage Control (SVC) has the purpose to con-rol the transmission-side voltage by adjusting generator AVRAutomatic Voltage Regulator) setpoints, synchronous compen-ator, transformers taps, etc. [1]. The studies for application of theVC on power systems were firstly addressed in the late 1980s [2].rom then on, many papers have discussed and proposed differentpproaches on SVC. References [3] and [4] present the results ofhe SVC applied to the Spanish and Italian power systems, respec-ively. In [5], the authors present the benefits that can be achievedy using a coordinated secondary voltage control applied to a trans-ission and subtransmission system of an electric power utility in

outh of Brazil. A decentralized SVC methodology is employed in6] by using an effective adjustment at the joint line drop com-ensator to control the voltage level in a point far from the power

lant.

In order to realize a better coordination scheme of the con-rol elements, many papers have employed Artificial Intelligence

∗ Corresponding author. Tel.: +55 35 3629 1242; fax: +55 35 3629 1365.E-mail addresses: marcossantos.ee@gmail.com (M.V. Santos),

ambroni@unifei.edu.br (A.C. Zambroni de Souza), isaias@unifei.edu.brB.I.L. Lopes), diogomarujo@gmail.com (D. Marujo).

ttp://dx.doi.org/10.1016/j.epsr.2014.10.022378-7796/© 2014 Elsevier B.V. All rights reserved.

(AI). The authors in [7] propose a coordinated voltage controlby using several FACTS spread over the New England system incontingencies scenarios. A fuzzy logic approach is used to enhance asuccessful coordination. Similarly, in [8], a fully decentralized SVC isproposed by using an Artificial Neural Network (ANN) trained fromoptimal power flow results. In references [9–11] AI tools to supportthe decisions of the Brazilian system operators are presented. Thefirst uses an ANN approach while a Fuzzy Inference System (FIS) isapplied in the others.

References above drive one to conclude that an effective reac-tive power control is obtained by adopting correct control actions.Large power systems require extensive analysis and communica-tion systems for this sake. This may be overcome by subdividingthe power system into areas and subareas. In [12], two techniquesfor system reduction are proposed in order to reduce the compu-tational burden to trace bifurcation diagrams. First, tangent vectorinformation is used to eliminate system variables that suffer littlechanges along the bifurcation path. The second technique createsan area formed by the buses around the critical bus. Modal anal-ysis is used in [13] to identify coherent buses and form controlareas.

This paper proposes a new methodology for developing a sec-ondary voltage control system that meets the voltage operatingcriteria while not compromising the voltage stability margin. How-ever, unlike the classic concept of SVC, which uses only the pilot businformation, the methodology assembles the information about allthe load buses within a specific region of interest. For this sake,

the mode-shape analysis is used to identify subareas of controland to provide coherent control actions information. Then, a fuzzyinference system is established for each of the subareas based onmode-shape information. This decentralizes the voltage control

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78 M.V. Santos et al. / Electric Power

nd enables one to visualize the most effective control actions.ctually, the methodology proposed here follows the structureresented in [14], which considers capacitor/reactor switching,ap changers and adjustment of Automatic Voltage Regulatorsetpoints. This paper proposes a novel approach for the lat-er topic and the SVC proposed is applied to the IEEE 118 busystem.

. Modal analysis for voltage control areas identification

The voltage stability is essentially a dynamic process. Thismplies in extended transient simulations which are time consum-ng and do not promptly provide access to sensitivity informationr voltage stability indexes. Meanwhile, due to its slow dynamicesponse, static methods are suitable to approach voltage stabilitynformation [15–17].

The modal analysis affords sufficient information for the evalua-ion of the voltage stability. Furthermore, by an appropriate choicef the Jacobian matrix formulation, the modal analysis can providehe reactive power sensitivity for all the system buses, includ-ng that with generating units. Herewith, it permits the properdentification of coherent load buses and, accordingly, the estab-ishment of voltage control areas, which are helpful in the definitionf the control hierarchy required for the design of a fuzzy controlystem.

.1. Extended power flow Jacobian

The traditional power flow formulation describes the power sys-em by a set of equations which can be written in the matrix form,s in (1).

�P

�Q

]=

[H N

M L

].

[��

�V

](1)

where �P and �Q represent the mismatch vectors for the activend reactive power equations, respectively. �� and �V are columnectors of the angular and magnitudes variations of the buses vol-ages. Finally, the H, N, M and L are submatrices that form the powerow Jacobian matrix or Jca.

The traditional Jca includes solely the reactive power equationsf the load buses in the formulation. Therefore, for further analysis,n extended formulation of the power flow Jacobian also providinghe voltage–reactive power relationship of the generators buses isequired [13,18].

Adding the equations referred to the control devices to the tra-itional power flow formulation in (1), it can be rewritten as:

�v�y

]=

[Jca Jvx

Jyu Jyx

].

[�u

�x

](2)

where �v represents the column vector on the left-side of Eq.1). �y is a column vector which represents the mismatches ofhe additional equations. Jca matrix is the traditional power flowacobian. Jvx is a non-quadratic matrix which represents the partialerivatives of the active power equations with respect to the newtate variables. The Jyu and Jyx matrices are the partial derivatives ofhe additional equations with respect to the original state variablesnd the new ones, respectively.

The extended Jacobian allows the representation of several con-rol devices at the traditional power flow formulation [13,18,19].

he reactive power equations of the PV buses and the Swing busre inserted into the problem and, for each bus, a control equations included (represented by �y in (2)), so the Jacobian matrix isept square.

s Research 119 (2015) 377–384

2.2. Modal analysis of the extended Jacobian

Assuming the insertion of the reactive power equations of allPV buses and the Swing bus and neglecting the control equationsin (2), the linear system can be written as:[�P

�Q

]=

[JP� JPV

JQ� JQV

].

[��

�V

](3)

where the submatrix JP� represents the partial derivatives of theactive power equations with respect to the state variable � of the PVand PQ buses. The submatrix JPV represents the partial derivativesof the active power equations with respect to the state variable V forall system buses. The submatrix JQ� denotes the partial derivativesof the reactive power equations with respect to the state variable� of the PV and PQ buses. Finally, the submatrix JQV represents thepartial derivatives of the reactive power equations with respect tothe state variable V for all system buses, including the swing bus.

Assuming �P = 0, Eq. (3) is reduced to:

�Q = (JQV + JQ� · −J−1P�

· JPV ) · �V (4)

Then, it is possible to set a QV sensitivity matrix as follows:

JSQV = JQV + JQ� · −J−1P�

· JPV (5)

The inverse matrix of JSQV gives the voltage-reactive power sen-sitivity information. Also, given the similarity transformation, J−1

SQVcan be written by means of the right and left eigenvectors and thesystem eigenvalues, leading to:

�V = ˚.�−1.�.�Q (6)

where and � are the right and left eigenvectors matrices, respec-tively, and � is the eigenvalues matrix of the system.

If the eigenvalues of JSQV are sorted in an increasing order bytheir magnitudes values and assuming the first eigenvalue �1 tobe meaningfully lower than the others, the voltage-reactive powersensitivity of the system could be assessed by its right and lefteigenvectors. Accordingly, it could be written as in (7):

�V ≈ (�1 · 1)�1

· �Q (7)

where �1 is a column vector (nx1) in which its kth-element isrelated to bus k and 1 is a row vector (1xn) in which its mth-element is related to bus m.

Eq. (7) could be expanded in a matrix form as:

�V

�Q≈

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

�11 · 11

�1�11 · 12

�1· · · �11 · 1n

�1

�21 · 11

�1�21 · 12

�1· · · �21 · 1n

�1

......

. . ....

�n1 · 11

�1�n1 · 12

�1· · · �n1 · 1n

�1

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)

where the first index of � is related to the system buses numbersand the second one is related to the eigenvalue �1 of the system.Similarly, the first index of is related to �1 and the second indexis related to the system buses numbers.

The examination of the matrix rows in (8) shows the voltagesensitivity of a bus k with respect to the reactive power injection inall system buses. On the other hand, the columns represent the volt-age sensitivity of all the buses with respect to the reactive powerinjection at bus m.

A further and careful inspection of the formerly matrix pre-sented in (8) indicates that the rows are composed by identicalelements multiplied by their corresponding right eigenvector ele-ment. Just like the extended power flow Jacobian, the sensitivity

M.V. Santos et al. / Electric Power Systems Research 119 (2015) 377–384 379

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Table 1Voltage area control for the IEEE 118 system.

Area Load buses Generation buses

1 71, 73, 78, 79, 82, 83, 84, 86, 88,93, 94, 95, 96, 97, 98, 101, 102,106, 108, 109, 118

76, 77, 80, 85, 87, 89, 90, 91, 92,99, 100, 103, 104, 105, 107,110, 111, 112

2 2, 3, 5, 7, 9, 11, 13, 14, 16, 17,20, 21, 22, 23, 28, 29, 30, 33,114, 115, 117

1, 4, 6, 8, 10, 12, 15, 18, 19, 25,26, 27, 31, 32, 113

Fig. 1. Mode-shape of the �2 for the IEEE 14 test system.

atrix JSQV is a symmetric and real matrix, which results in botheal eigenvalues and eigenvectors. Hence, the rows of the JSQV areollinear and the analysis of the right eigenvectors elements areufficient to infer about the voltage-reactive power sensitivity ofhe system and, also, identify the voltage control areas [13].

.3. Voltage area identification

The analysis of the right eigenvectors elements of the extendedacobian can afford information about the voltage sensitivity of theystem due to a reactive power variation. The graphic plot usingnformation of the right eigenvectors is usually called Mode-shapend provides a quick and efficient approach of the system charac-eristics.

The voltage area identification proposed in [13] uses theeal characteristics of the eigenvectors elements of the extendedacobian to identify coherent areas. Such particularity creates a

ode-shape plot with data along the real axis only.Due to the insertion of reactive power equations of the Swing

nd PV buses, the system of equations become ill conditioned. Thateflects at the mode-shape for the least eigenvalue, which indicates

coupling between all the system buses [13]. Then, the voltage areadentification must be held from the second smallest eigenvalue, �2.

Fig. 1 shows the mode-shape related to �2 for the IEEE 14est system. The elements of the eigenvectors were sorted in

decreasing order by their magnitudes values into the Y-axishereas the X-axis identifies the system buses.

In Fig. 1, it is observed that Buses 12 and 3 have the largestagnitudes at the mode-shape but opposite directions. Hence, for

he same reactive power variation applied to the system, Buses 3nd 12 will be exposed to similar, but contrary, voltage variations.

The voltage area identification is made by aggregation of theoherent buses, i.e., by analyzing the elements with similar mag-itudes and directions at the mode-shape. Hence, one can identifyn area formed by Buses 12, 13, 14, 11 and 6. A second area can beeached by aggregating Buses 3, 1, 2, 4 and 5. Similarly, this processan be done successively for each of the least eigenvalues of theystem until all buses or a percentage of the buses are addressed to

specific area of the system.The process to identify the voltage area through mode-shape

nalysis can be easily applied for larger system, as the IEEE 118 busest system. Performing such analysis for the smallest eigenvaluesf the system yields three voltage areas, as shown in Table 1.

In most cases, the areas identified by mode-shape analysis coin-ide with a geographic division. However, the mode-shape analysisdentifies coherent areas by its reactive power/voltage relationship.hen, such areas are formed by electric proximity.

One can observe that regardless of the areas identified, the largeize of the system ends up with a large number of buses in the sub-

reas. Thus, large power systems require special attention, oncehe areas identified by modal analysis comprises a considerableumber of buses, which hinders the correct coordination of the con-rol elements. Therefore, in such systems, subareas identification is

3 41, 43, 44, 45, 47, 48, 50, 51, 52,53, 57, 58, 60, 63, 64, 67

42, 46, 49, 54, 55, 56, 59, 61, 62,65, 66

necessary in order to perform a local control and ease the coordi-nation. This issue will be addressed in the next sections.

3. Methodology

An adequate voltage control philosophy requires a complexanalysis and seldom more than a unique or trivial solution. Actually,there are several concerns behind a single control action, like busesvoltages levels, availability of reactive power resources and tapposition of transformers. Large power systems add more complex-ity to the voltage control issue, since the hierarchy of the controldevices must be carefully defined, not to mention the huge com-munication system required for such coordination.

The voltage area identification reduces the system size consid-ered and minimizes analysis by decoupling the control actions.However, for large power systems, some areas may be composedby several generation and load buses, leading to difficulties on thevoltage control coordination. A simple and efficient solution can beachieved by the identification of subareas of voltage control, whichact as a more dedicated and local control.

The fuzzy set theory has the ability to represent the humanknowledge combined with measurement information and, then,provide control actions with satisfactory results over a specificsystem control. The modal analysis used for area and subarea iden-tification provides valuable information about coherent buses andvoltage/reactive power relationship. Such knowledge can form thefirst approach to the establishment of the fuzzy rules.

In this context, a methodology is proposed for the develop-ment of fuzzy systems applied to secondary voltage control. Suchmethodology affords an easy approach to aggregate the fuzzy setstheory and voltage control by using modal analysis.

The methodology proposed here can be divided in two steps, asfollows:

Step 1: Voltage subareas identification;Step 2: Development of the fuzzy inference systems.The first step attempts to reduce the overall efforts to correctly

coordinate the voltage control elements in large power systems.After, the modal information is properly adapt into several fuzzyinference systems, for each subareas of control, which groupedforms the secondary voltage control system based on fuzzy logic.

4. Voltage control subareas identification

The smallest eigenvalues of the Jsqv matrix in (5) determine thedominant modes related to the voltage variation sensitivity withrespect to the reactive power injection. The analysis of the respec-tive eigenvectors allows the voltage control area identification [13].

Likewise, an extension of the mode-shape analysis can be pro-posed. For a defined voltage control area, one can define a subareacomposed by the buses with similar magnitudes of the mode-

shape.

Thereby, assuming the Area 3 (Table 1), which is defined by theeigenvector related to the eigenvalue �3, Fig. 2 depicts the first ele-ments of its mode-shape. The darker bars plotted represent the load

380 M.V. Santos et al. / Electric Power Systems Research 119 (2015) 377–384

Fig. 2. First elements of the mode-shape for Area 3.

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Table 2Summary of the areas and subareas for the IEEE118 system.

Area Subarea Load buses Generation buses

1

A 106, 108, 109 104, 105, 107, 110, 111,112

B 84, 86, 88, 93, 94,101, 102

85, 87, 89, 90, 91, 92,100, 103

C 78, 79 77, 80D 71, 75, 118 70, 73, 74, 76

2A 2, 3, 5, 7, 9, 11, 13,

1171, 4, 6, 8, 10, 12

B 17, 20, 21, 22, 28,29, 30, 114, 115

15, 18, 19, 25, 26, 27,31, 32, 113

3A 51, 52, 53, 58 54, 55, 56B 44, 45, 47, 48, 50, 46, 49, 59, 61, 62, 66

Briefly, the secondary voltage control based on fuzzy logicdescribed in this paper operates directly in regions with voltagecontrol problems, trying to mitigate them locally.

Fig. 3. Mode-shape of the eigenvector most related to the critical bus.

uses and the lighter ones represent the buses with reactive powerontrol devices such as generators or synchronous compensators.t is seen that the first eight buses of the mode-shape have simi-ar magnitudes, which suggests a greater coupling between theseuses compared to other ones of the same control area. Hence, for aiven reactive power variation in this area, the first group of busess more prone to suffer similar variations, since they are the mostffected buses of the area. The other buses should present varia-ions in the same direction, but with lower magnitudes. Therefore,he first eight buses should be grouped in a subarea of control.

As Buses 53, 52, 58 and 51 are load buses, they are more likelyo voltage drops due to loading increases in this area. On the otherand, the generation Buses 55, 56 and 54 are candidates for theoltage control of this subarea. In addition, their similar magnitudesre a sign that they are sensitive to a control action performed byne of them, which will prove to be a valuable information for theurther development of the fuzzy rules.

The subsequent buses, in Fig. 2, also have similar magnitudesmong themselves and can be grouped into a second subarea con-rol.

As the amplitudes reduce at the mode-shape, the remaininguses start to have a more uniform influence on the eigenvaluender analysis, regardless of the buses location. This makes diffi-ult to visualize and identify new subareas of control. Therefore, aareful analysis must be held in order to group the buses correctly.

Tangent vector [20,21] identifies the critical bus of the system.or the IEEE118 system considered, the tangent vector pointed theus 41, grouped in the Area 3, as the critical bus. The voltage insta-ility is a local problem due to lack of reactive power support. Thus,

subarea of control comprised by the buses nearby the critical busay be formed in order to manage the local voltage issues.Fig. 3 depicts the mode-shape for the eigenvector that is the

ost related to the critical bus of the system.

From Fig. 3, the load buses 41, 39, 43, 35 and 37 have a strong

elationship, as well as the generation buses 40, 36, 34 and 42. Then,ne can form a subarea of control with these buses around the

60, 63, 64, 67C 35, 37, 39, 41, 43 34, 36, 40, 42

critical bus. Also, it is seen a small relationship between the genera-tion buses (55, 56 and 54) from the first identified subarea, althoughwith opposite direction. Hence, a loss of reactive power support ofany of these machines directly impacts the loading margin of thesystem, since they present a relationship at the eigenvector underanalysis.

The further analysis of the mode-shapes related to Area 3 allowspartitioning this area in three different subareas of control. Suchsubareas are named as “3A”, “3B” and “3C”.

The methodology of subareas identification presented previ-ously can be easily extended for other areas of the system underanalysis. Accordingly, Table 2 summarizes the subareas identi-fied for the complete system. The single line diagram is shown inAppendix Fig. A.1

5. Fuzzy inference system

The fuzzy system in this paper seeks primarily to correct volt-age violations of the system. However, concomitantly, the controlactions taken should manage the reactive power reserves. Thus, agiven control action is not supposed to cause a reduction in thesystem loading margin. Thereby, the voltage information at theload buses and the reactive power information from the generatorsshould be entered as input variables of the control problem.

For this sake, each control subarea of the system is covered bytwo control stages. The first stage comprises the secondary volt-age control in its pure approach. The voltage level at the load busesis used as input at this stage. The second stage is responsible fordefining the rules and operative guidelines of the elements of con-trol within a subarea. The output of the first stage is used as aninput for the second stage, as well as the reactive power reserveinformation of the participating machines. The control diagram isdepicted in Fig. 4.

Fig. 4. Loop control of the fuzzy inference system.

M.V. Santos et al. / Electric Power Systems Research 119 (2015) 377–384 381

5

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t(fv

tvcFsd

tbr

psc

•

•

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•

5

tb

Fig. 6. Reactive power reserve input MFs for the second stage.

Fig. 5. MFs for the first stage: (a) Input and (b) Output.

.1. First stage of control

This stage is responsible for verifying the voltage levels of theoad buses, VLi , in a given subarea of control. Then, it returns a sin-le variable VCA which indicates the control action needed for suchubarea. This output is used as input at the following stage.

The input variables, crisp information, are mapped into linguis-ic variables, or fuzzy sets, through three membership functionsMF) in a universe of discourse comprised by the voltage levelsrom 0.7 to 1.1 [p.u.], as shown by Fig. 5a. Such MFs indicate theoltage level of the buses as: low, adequate or high, respectively.

For the output variable, VCA, five MFs were design to cover allhe universe of discourse. Each MF is associated with a linguisticariable which describes the action needed to be performed by theontrol elements of the subarea. The MFs forms are depicted inig. 5b, and each one represents the action required as: large ormall increase in voltage, maintain the voltage and small or largeecrease in voltage, respectively.

The fuzzy sets and the respective actions considered representhe results of the inference fuzzy step that uses the fuzzy rulease designed heuristically for each subarea. The aggregation of theesults from all the fuzzy rules determines the first stage output.

As mentioned in previous sections, the mode-shape analysisrovides sensitivity information that may be useful to determineuited fuzzy rules for each subarea. Hence, the fuzzy rules definedan be summarized as:

Load buses with the largest magnitudes at the mode-shapeimpact most of the control elements within the subarea;Load buses with voltage control problems and small magnitudesat the mode-shape: the output must inflict in a small voltagevariation;Buses with great participation at the tangent vector must com-prise specific rules, in order to preserve the loading margin;No-load buses are not monitored.

.2. Second stage of control

The first stage output, VCA, suggests the best control actionso correct the voltage levels at load buses. These actions muste performed by the generators/compensators of the subarea.

Fig. 7. MFs for the (a) synchronous compensator and (b) generators.

However, in extreme scenarios, such as heavy or light load, thecontrol elements may not have sufficient reactive power reserve tokeep adequate voltage levels at load buses.

As depicted in Fig. 4, besides the output of the first stage, theremaining inputs of the second stage are comprised by a percentagevalue of the reactive power available by the machines within thesubarea. This value can be calculated as:

RQGk = QGk − Qkmin

Qkmax − Qkmin

(9)

where RQGk is the percentage value of the reactive power available,QGk is the actual reactive power generation, Qkmax and Qkmin

are thelimits of reactive power generation.

For each input related to the reactive power generation, threeMFs are designed to indicate the reactive power reserve marginand named as: low, medium or high reserve margin. The MFs canbe seen in Fig. 6.

Fig. 4 shows k-outputs for the second stage of control, where kis the number of control elements participating of the local control.The correlations and coordination of the outputs are held throughthe fuzzy rules which could define a joint action of the elements.

The reactive power generation capacity of the generators andcompensators are different and the MFs associated with them mustcomprise such information. Thus, two set of membership functions

were designed, as presented in Fig. 7.

The meanings of the linguistics variables associated with theMFs are: large or small voltage decrease, maintain voltage and smallor large voltage increase. The outputs of this stage reflect a system

382 M.V. Santos et al. / Electric Power Systems Research 119 (2015) 377–384

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Table 3Status after the control.

Bus number V [p.u.] QG [Mvar] QGmin[Mvar] QGmax [Mvar]

01 0.955 1.1 −5.0 15.004 1.050 247.3 −300.0 300.006 1.000 −13.0 −13.0 50.008 1.027 27.1 −300.0 300.012 0.990 56.1 −35.0 120.0

Now the loading of the IEEE 118 system was increased by 100%at Buses 35, 36, 39 and 41, by 120% at Bus 43 and by 150% at Bus

Table 4Status after the fuzzy control.

Bus number V [p.u.] QG [Mvar] QGmin[Mvar] QGmax [Mvar]

01 0.955 2.1 −5 1504 1.038 188.4 −300 300

Fig. 8. Voltage profile for the 2A subarea.

equirement face to voltage problems in an area or subarea ofontrol. However, the generators/compensators actions must beeld without compromising the reactive power generation limits.herefore, the fuzzy rules base is built according to the premisesescribed below:

Generation buses with the largest magnitudes at the mode-shapeare assigned to make the greatest contribution to the subareacontrol;In case of lack of sufficient reactive power reserve for such gen-erators, the remaining control elements should not operate;Synchronous compensators must be coordinated with the gen-erators having similar magnitudes at the mode-shape;If a subarea presents an adequate voltage level, the fuzzy rulesmust attempt to retrieve at least a portion of the reactive powerreserve.

. Results

In order to evaluate the methodology proposed for the sec-ndary voltage control based on fuzzy logic, this section presentshe results obtained with the IEEE118 system. Since the purpose iso assess the control effects face to voltage problems, the systemoading was slightly changed in specific points to impose largeroltage drops.

Firstly, it is presented a simple voltage violation eliminated by non-coordinated control. Then, the secondary voltage controlroposed is considered for comparison. The results on control effi-iency and reactive power reserve management are analyzed. Theroblem is also studied under a voltage stability perspective.

.1. Non-coordinated control

A base case system was considered by increasing the loading atuses 2, 3 and 117 by 120% and at bus 11 by 100%. Fig. 8 depictshe voltage profile for the subarea 2A buses before and after theon-coordinated control takes place.

Due to the loading increase, Bus 117 presents an abnormal volt-ge profile, as well as the synchronous compensator at Bus 1, whichas lost its ability of reactive power support. After taking the con-rol actions, the subarea voltage profile presents adequate levels.owever, the generator at Bus 4 can no longer support the subareaue to the system operating limits. As well as the generator at Bus, which reactive support is restricted by the voltage levels at Buses

and 10. In fact, only the generator at Bus 12 is able to control theubarea in case of a new loading increase.

Despite the voltage violation elimination at Bus 117, the con-rol action adopted decreases the loading margin from 0.7409.u. to 0.6932 p.u. This is due to the lack of coordination within

he control elements of the subarea. Such statement may be con-rmed by Table 3. After the control actions, Bus 6 is not allowedo provide further reactive power due to its limits. Also, the gen-rator unit at Bus 4, which has a large influence over the subarea,

Fig. 9. Voltage profile for the subarea 2A.

operates near its maximum reactive power limit. As a result, theload margin decreases.

6.2. Fuzzy control system

The results obtained from the non-coordinated control makesclear that such control may not properly consider some voltagestability issues, and so far can depreciate the stability margin byexhausting reactive power support in a certain subarea. At the pre-vious scenario, Fig. 9 depicts the voltage profile for the subarea 2Abefore and after the fuzzy control proposed takes place.

The fuzzy control corrects the voltage violations presented byBuses 1 and 117. In fact, a wide effect can be seen over the subareadue to the coordinated control. Unlike the non-coordinated controlcase, the voltage at Bus 4, with the largest generator, ended in alower level. Such results suggest a reallocation in the reactive powerflow due to the control. Table 4 confirms these facts.

From Table 4, the control elements present a larger reactivepower reserve than the non-coordinated case. It allows a moreflexible operation in case of a new loading variation.

The voltage control coordination did not improve the voltagestability margin of the system. However, the fuzzy control appliedlocally to the subarea preserve the loading margin around 0.7409p.u. Regarding the active power losses in the circuits of the subarea2A, the non-coordinated control resulted in active losses around23.0 MW. Meanwhile, despite not being the main objective of thefuzzy control, it presents a 3.3% reduction in the active power flow-ing through the subarea circuits.

6.3. Multiple subareas violation

06 1.002 4.9 −13 5008 1.018 3.2 −300 30010 1.050 −56.2 −147 20012 0.994 94.6 −35 120

M.V. Santos et al. / Electric Power System

Fig. 10. Voltage profile for the 3A and 3C subareas.

Table 5Status after the fuzzy control.

Subarea Bus V [p.u.] QG [p.u.] QGmin[p.u.] QGmax [p.u.]

3C

34 0.980 6.4 −8 2436 0.970 14.5 −8 2440 1.028 129.9 −300 30042 1.044 99.2 −300 300

3v

tfcet

3A54 0.963 14.0 −300 30055 0.959 −0.2 −8 2356 0.962 14.4 −8 15

4. The buses correspond to the subareas 3A and 3C. Such increaseiolates the voltage level at Buses 43 and 53.

Fig. 10 depicts the curves for the voltage profile of the buses ofhe subareas 3A and 3C before and after the fuzzy control is per-

ormed. The results confirm that the coordination through the fuzzyontrol was efficient to remove the voltage violation in both subar-as. Due to the large loading increase applied to the subarea 3C andhe electric distance between load and generation, the elements of

s Research 119 (2015) 377–384 383

control of this subarea needed to perform a large reactive powervariation to meet the operational requirements.

The status of the control elements of the subareas after the fuzzycontrol is summarized in Table 5. The values of reactive power gen-eration point a proper reactive management in such subareas. Thefuzzy control was also able to maintain the loading margin of thesystem, which varied from 0.6955 p.u. to 0.6992 p.u.

7. Conclusion

This work dealt with the problem of secondary voltage controlby the means of a combination of modal analysis and fuzzy logic.The importance of the problem is highlighted by the limitations ofthe reactive power to travel far. In this sense, local reactive powerinjections are necessary.

The approach proposed here assembles similar buses, formingsome areas of coherence by modal analysis. It is shown that, undercertain conditions, subareas may be further formed, improving thecontrol strategy. After identifying the areas and subareas of inter-est, fuzzy systems are employed to explore the reactive powerresources with the aim to enhance the system voltage security.

The results obtained with the help of the academic IEEE 118 bussystem render the proposed technique as effective for a secondaryvoltage control strategy.

Acknowledgments

M. V. Santos and D. Marujo would like to thank CNPq for thefinancial support. A. C. Zambroni de Souza thanks CNPq (grant301313/2011-3), a Brazilian Board of Education and INERGE, aresearch Institute formed by several Federal Universities in Brazil.

384 M.V. Santos et al. / Electric Power Systems Research 119 (2015) 377–384

Appendix A. Appendix

ed for

R [

[

[

[

[

[[

[[

[

[20] A.C.Z. de Souza, C.A. Canizares, V.H. Quintana, New techniques to speed up

Fig. A.1. Subareas identifi

eferences

[1] G.H. Taranto, N. Martins, D.M. Falcão, A.C.B. Martins, M.G. dos Santos, Bene-fits of applying secondary voltage control schemes to the brazilian system, in:Proceedings of IEEE PES Summer Meeting, Seattle, WA, 2000, July, pp. 937–942.

[2] J.P. Paul, J.Y. Leost, J.M. Tesseron, Survey of the secondary voltage control infrance: present realization and investigations, IEEE Trans. Power Syst. 2 (May(2)) (1987) 505–511.

[3] J.L. Sancha, J.L. Fernández, A. Cortés, J.T. Abarca, Secondary voltage control:analysis, solutions and simulation results for the spanish transmission system,IEEE Trans. Power Syst. 11 (May (2)) (1996) 630–638.

[4] S. Corsi, The secondary voltage regulation in Italy, in: Proceedings of the IEEEPES Summer Meeting, Seattle, WA, 2000, July, pp. 296–304.

[5] F.A.B. Lemos, L.C. Werberich, J.S. Freitas, M.A. Rosa, A new approach of coordi-nated secondary voltage control applied in transmission an sub-transmissionlevel, in: Proceedings of the IEEE PES International Conference on Power Indus-try Computer Applications, Sydney, NSW, 2001, May, pp. 223–228.

[6] R.J.G.C. da Silva, A.C.Z. de Souza, R.C. Leme, D. Sonoda, Decentralized secondaryvoltage control using voltage drop compensator among power plants, Int. J.Electric. Power Energy Syst. 47 (May) (2013) 61–68.

[7] H.F. Wang, H. Li, H. Chen, Coordinated secondary voltage control to eliminatevoltage violations in power system contingencies, IEEE Trans. Power Syst. 18(May (2)) (2003) 588–595.

[8] F. Gubina, A. Gubina, Decentralized secondary voltage control based on neu-ral network and its effect on generator interaction, in: Proceedings of the 8th

Mediterranean Electrotechnical Conference, vol. 2, 1996, May, pp. 913–916.

[9] R.T. Lima, M. Vellasco, Artificial neural networks in the voltage control of elec-trical power systems, in: Proceedings of the11th International Conference onOptimization of Electrical and Electronic Equipment, Brasov, 2008, May, pp.143–148.

[

the IEEE118 bus system.

10] G.N. Taranto, A.B. Marques e, D.M. Falcão, Coordinated voltage control usingfuzzy logic, in: Proceedings of the IEEE Power Engineering Society SummerMeeting, vol. 3, Chicago, IL, 2002, July, pp. 1314–1317.

11] A.B. Marques, G.N. Taranto, D.M. Falcão, A knowledge-based system for super-vision and control of regional voltage profile and security, IEEE Trans. PowerSyst. 20 (February (4)) (2005) 400–407.

12] C.A. Canizares, A.C.Z. de Souza, V.H. Quintana, Improving continuation methodsfor tracing bifurcation diagrams in power systems, in: Proceedings of the BulkPower System Voltage Phenomena – III Seminar, Davos, Switzerland, 1994,August, pp. 349–458.

13] R.M. Henriques, G.N. Taranto, J.A. Passos Filho, Using eigenvalues and eigen-vectors in power flow studies for identification of voltage control areas, in:Proceedings of XI SEPOPE, Belém, PA, 2009, March.

14] A.C. Zambroni de Souza, B.I. Lima Lopes, Quasi-dynamic model and strategy forcontrol actions, Electric Power Compon. Syst. 33 (2005) 1057–1070.

15] P. Kundur, Power System Stability and Control, Mcgraw Hill, Palo Alto, 1994.16] B. Gao, G.K. Morison, P. Kundur, Voltage stability evaluation using modal anal-

ysis, IEEE Trans. Power Syst. 7 (4) (1992) 1529–1542.17] C.W. Taylor, Power System Voltage Stability, McGraw-Hill, New York, 1994.18] J.A. Passos Filho, N. Martins, D.M. Falcão, Identifying power flow control infeasi-

bilities in large scale power system models, IEEE Trans. Power Syst. 24 (February(1)) (2009) 86–95.

19] A. Monticelli, Fluxo de Carga em Redes de Energia Elétrica, Edgard Blücher, SãoPaulo, 1983.

voltage collapse computations using tangent vectors, IEEE Trans. Power Syst.12 (3) (1997) 1380–1387.

21] A.Z. de Souza, Tangent vector applied to voltage collapse and loss sensitivitystudies, Electric Power Syst. Res. 47 (1998) 65–70.