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Electrical Power and Energy Systems

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Bus voltage control and optimization strategies for power flow analysesusing Petri net approach

Insu Kima,⁎, Shuo Xub

a Electrical Engineering, Inha University, Incheon 22212, Republic of Koreab Electrical Engineering, Alabama A&M University, AL 35811, USA

A R T I C L E I N F O

Keywords:Bus voltage control strategyDistributed generationPower flowP-Q busand P-V bus

A B S T R A C T

Distributed generation (DG) systems—particularly photovoltaic (PV) systems—that can control reactive powercan change the behavior of a power system network in spite of their relatively small individual capacities be-cause of bidirectional power flow and reactive power control. Therefore, power flow algorithms should be ableto accurately model the response of a power system network that includes DG systems. Various power flowalgorithms have modeled DG systems as either a P-Q or P-V bus. However, small DG systems connected to thegrid by a short line, but not a long transmission line, or predefined mutually between utilities and DG systemowners can participate in the control of reactive power. They can adaptively adjust the reactive power outputaccording to their bus voltage. Thus, the objective of this study is to present a strategy that participates in thecontrol of bus voltage within its limits and reactive power by either injecting or absorbing reactive power. Forthis purpose, this study presents a Petri net approach that a bus to which a DG system is connected is modeled asa P-Q or P-V bus with equality and inequality constraints. The proposed bus voltage control strategy is verifiedusing the well-known IEEE test feeders.

1. Introduction

An excellent example of a distributed generation (DG) system is aphotovoltaic (PV) system, which can be effectively dispersed as a largenumber of relatively small systems or clustered PV farms with highcapacity. It may be installed on the rooftop of residential or commercialbuildings, integrated within the building itself, or installed in any lo-cation in which electricity is required. As DG systems with the cap-ability of controlling reactive power have been connected to powersystem networks, they can change the behavior of the network becauseof bidirectional power flow and reactive power control [1]. Therefore,accurate system analysis algorithms capable of calculating the powerflow of microgrids and distribution networks that host DG systems arerequired. For example, various backward and forward sweep methodsfor radial distribution networks have been presented in [2], which arealso referred to as the ladder power-flow calculation algorithm. Fastand efficient algorithms for the radial distribution system were alsodeveloped in [3]. In these algorithms, the power flow equations of aradial network were directly solved through the application ofKirchhoff’s current law and Kirchhoff’s voltage law. However, thesebackward and forward sweep algorithms were not capable of re-presenting a DG system as a P-V bus. Thus, a P-V “sensitivity” modeling

method that represents a bus to which the DG system is connected aseither a P-Q or P-V bus was presented in [3,4]. In [5], a P-V bus was alsorepresented by power mismatch equations with an angle deviation,using the Newton–Raphson current injection method. To incorporatethe reactive power limits in the P-V bus, a reactive power–voltage curveof the P-V bus was approximated by the tanh (βx) function [6].

The previous studies, however, have not applied the modeling ofeither a P-Q or P-V bus to specific DG systems (e.g., PV systems, windfarms, or combined heat and power [CHP] systems). Thus, a power flowcalculation method that models randomly distributed PV generators asa constant P-Q bus like a negative load was presented in [7–12]. The10-kW grid-connected PV systems were modeled as either a constant P-Q or P-V bus and the effect of daily solar irradiance in 5-min re-solution—used as input to the system—on voltage, voltage unbalance,loading, and power losses was examined in [13]. A PV system was alsorepresented by a simplified composite load model that analyzes itsimpact on the grid connection application [14]. Decentralized electricalmicrogrids consisting of PV, diesel, CHP, wind turbines, and batterysystems were represented by (agent-based) P-Q and P-V buses [15]. DGsystems were also modeled as either a P-Q or P-V bus in the load-fol-lowing or maximum power point tracking modes [16].

Reactive power transferred between two buses proportionally

https://doi.org/10.1016/j.ijepes.2019.05.009Received 29 August 2018; Received in revised form 1 April 2019; Accepted 5 May 2019

⁎ Corresponding author.E-mail address: insu@inha.ac.kr (I. Kim).

Electrical Power and Energy Systems 112 (2019) 353–361

Available online 15 May 20190142-0615/ © 2019 Elsevier Ltd. All rights reserved.

T

depends on the ratio of their voltage magnitudes and their angle dif-ference. Typically, the angle difference in a transmission line is lessthan 30°. If large-capacity PV systems, wind farms, or other inverter-based distributed generators (IBDGs) are connected to the grid bymeans of long transmission lines and several step-up transformers, thevoltage magnitudes of the two buses will be close to 1 p.u. Thus, thereactive power support of DG systems to the grid may not be feasible.However, small DG systems such as small wind turbines or residentialand commercial PV systems can participate in reactive power support[17] because they are located within a relatively short distance fromthe grid. There are also situations where DG systems should changetheir operation mode from P-Q to P-V or vice versa in real time if theyactively participate in the control of reactive power upon voltage reg-ulation. For example, a DG system should be often curtailed to avoidfeeder congestion [18] or to satisfy the feeder capacity rating [19].Furthermore, utilities may request the capability of changing the re-active power support of DG systems in real time. In this situation, therules and procedures of the change in their operation mode should becorrectly planned between the DG system owners and the utilities [20].

A “PQV” bus is modeled as a bus type whose voltage is controlled bya remote bus that generates active and reactive power using theNewton–Raphson power flow method [21]. The three supplementarytransition rules that switch a P-V to P-Q bus (e.g., if the number ofswitching operations from P-V to P-Q is larger than three) were pre-sented in [22,23].

Grid codes may require small DG systems—connected to the gridwithin a short distance—to have the capability to change their opera-tion mode from P-Q to P-V or vice versa in real time [17] whilemaintaining the bus voltage within a specified range. Thus, the objec-tive of this study is to propose a bus voltage control strategy that makes

appropriate decisions for P-Q and P-V changes using the Petri net ap-proach [24,25]. For example, under normal conditions (e.g., the voltageis close to 1.0 p.u.), a bus is normally connected to the grid as a P-Q bus.However, if the bus voltage violates the lower and upper limits, it canparticipate in the control of reactive power upon voltage regulation inreal time.

Various DG systems capable of controlling reactive power whilemaintaining the bus voltage within a specified range under abnormalvoltage conditions or producing only active power under normal vol-tage conditions can be modeled as the proposed bus voltage controlstrategy. Thus, the proposed strategy can be used in power flow cal-culations of various distribution automation systems and supervisorycontrol and data acquisition (SCADA) systems consisting of DG systemsthat can control reactive power. The power flow calculation results canalso be helpful for designing, operating, or upgrading electric powersystems (EPSs) by providing various impact studies on power quality,protection coordination, or voltage regulation.

This paper is organized as follows. Section 2 introduces the problemstatement. Section 3 defines the bus control strategy that makes ap-propriate decisions for P-Q and P-V mode changes. Section 4 verifies theproposed bus voltage control strategy with IEEE test feeders. Finally,Section 5 summarizes the major conclusions.

2. Problem statement

The present voltage regulation codes require a DG system tomaintain its terminal voltage (e.g., the voltage of a bus to which the DGsystem is connected) within a range, particularly from 0.95 p.u. to 1.05p.u., or ± 5% of the rated voltage presented in ANSI C84.1-2011Range A [20]. Thus, a power flow analysis algorithm that models DG

Nomenclature

CHP combined heat and powerC cost functionCQ cost function for reactive power to be producedCV cost function for voltage variation to unity valueCVR conversation of voltage reductionDG distributed generationEPS electric power systemH total hours of the entire simulationIBDG inverter-based distributed generatorIVVC integrated Volt/Var controlN number of total busesOPF optimal power flowPk active power of bus kp.u. per unitPV photovoltaicQi or Qk reactive power of bus i or kQDi reactive power consumed by bus i

QGi reactive power supplied to bus iQk

max and Qkmin maximum and minimum reactive powers of bus k

Qset setting value of reactive power (e.g., Qmin and Qmax)S rated power of the PV inverterSCADA supervisory control and data acquisition

= −θ θ θik i k voltage angle difference between buses i and k∼ = ∠ °V V δ| |k

i( )voltage of bus k at iteration i

Vgrid grid voltageVi voltage of bus iVinv output voltage of an inverterVk

max and Vkmin maximum and minimum voltages of bus k

Vmpp voltage at maximum power pointVset setting value of voltage (e.g., Vmin and Vmax)Vtarget target voltage in p.u.

= +Y G jBik ik ik line admittance between buses i and kWV and WQ weighting factors for voltage and reactive powerX line reactance from the inverter to the grid

Fig. 1. Petri net diagram of the proposed bus voltage control strategy.

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systems should model a bus to which the DG system is connected aseither the following P-Q or P-V bus.

1) P-Q bus. A DG system injects fixed active and reactive power, andhence, it can be treated as a negative constant load.

2) P-V bus. A DG system injects fixed active power but acceptable re-active power, not known initially, so that its terminal voltagemagnitude can be maintained at a target value.

Thus, many previous studies have presented a method that models abus to which a DG system is connected as either a P-Q or P-V bus[3,4,26]. However, IBDGs may participate in the control of reactivepower under only abnormal voltage conditions. For example, undersuch a normal voltage condition, a DG system may produce constantactive and reactive power at a power factor of unity or close to it. Bycontrast, under abnormal situations (e.g., the bus voltage can increaseor decrease because of sudden energy overages or shortages), the DGsystems may support the voltage by either appropriately producing orconsuming reactive power. Thus, this study proposes a bus voltagecontrol strategy with lower and upper limits of the voltage magnitudeand reactive power, which switches from a P-Q to P-V bus and viceversa based on the bus voltage.

3. Bus voltage control strategy

3.1. Petri net

The Petri net in Fig. 1 presents the possible states of the proposedbus voltage control strategy in power flow computations. A power flowcalculation determines the transitions and places of a bus to which DGsystems capable of controlling reactive power is connected. The businitially behaves as a generic P-Q bus injecting fixed active power (P)and reactive power (Q) under normal conditions (i.e., the bus voltage iswithin the limits, or ⩽ ⩽V V Vk k k

min max). That is, the initial state is SPQ inFig. 1. However, after calculating power flow, if the bus voltage isoutside the minimum and maximum limits and the bus also has thecapability of adjusting Q to maintain the voltage of a bus to which theDG system is connected, the state changes to SPV. The detailed statetransitions can be summarized by following states:

1) A P-Q bus. For example, the kth bus to which a DG system able toparticipate in the control of Q under abnormal voltage conditions isconnected is set to the P-Q bus. If the voltage of the kth bus is insidethe lower and upper limits, or Vk

min≤ Vk≤ Vkmax, the bus is still

maintained as a P-Q bus, or the SPQ state. However, as a result ofabrupt energy overages or shortages of various generation units orvarious abnormal conditions (e.g., abrupt load changes, load shut-downs, or outages), if the bus voltage changes beyond the lower orupper limits and it could participate in the control of Q, based on thepredefined procedures, the bus is converted to a P-V bus, or the stateSPV.

2) A P-V bus. After comparing Qk with the upper and lower limits, if Qk

is inside the lower and upper limits, it produces acceptable Qk sothat it can maintain the bus voltage magnitude to a set value, orVk

min≤ Vk≤ Vkmax. That is, the state is still SPV.

3) Transitions of a P-V to P-Q bus. If Qk < Qkmin, Qk is set to Qk

min andthe bus is converted to a P-Q bus (i.e., SPQmin), and |V | and δ arecalculated. Similarly, if Qk > Qk

max, Qk is set to Qkmax, the bus is

converted to a P-Q bus, and |V | and δ are determined. Thus, if thevoltage is inside the limits, or Vk

min≤ Vk≤ Vkmax, the bus is main-

tained as a P-Q bus (i.e., SPQmax). Although the voltage of the P-Qbus violates the lower or upper limits (Vk≤ Vk

min or Vkmax≤ Vk),

the bus is continuously maintained as the SPQmax or SPQmin statebecause the allowable maximum or minimum Q can maintain thebus voltage close to the limit.

Fig. 2. DG system modeled as a P-Q bus, equipped with other reactive powercontrol systems.

Fig. 3. Q-V curve of inverter Volt/Var control [27].

Fig. 4. DG system modeled as a P-V bus.

Fig. 5. Capability curve of a PV inverter connected to the grid [28].

Fig. 6. DG system participated in the proposed bus voltage control strategy.

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3.2. Reactive power and voltage curve of bus types

A DG system that produces constant active and reactive poweroutputs regardless of the bus voltage (but it may be affected by the cut-off or minimum voltage) can be modeled as a P-Q bus such as a capa-citor bank, shunt reactors, static Var compensators, or other reactivepower control systems. If the DG system is equipped with other reactivepower control systems, the reactive power output can be adjusted in astepwise fashion according to the voltage level, as shown in Fig. 2.Further, a DG system is also modeled as a negative load if it operates ata fixed power factor. For example, in Fig. 2, if capacitor banks areswitched on or off, the reactive power output is positively stepped up ordown. If static Var compensators absorb reactive power, the reactivepower output is negative.

A DG system with power-electronics-based inverters (e.g., PV sys-tems and wind farms) can participate in the control of reactive powerbased on the bus voltage in Fig. 3, which is usually referred to as Volt/Var control. For example, if the bus voltage is close to 1.0 p.u., theinverter operates at a unity power factor. Thus, it produces only activepower. However, if the bus voltage decreases below the preset voltage(e.g., V1 in Fig. 3), it adjusts the power factor so that it can inject re-active power. In other words, it can regulate the bus voltage to the

target value (e.g., 1.0 p.u.). However, if the bus voltage increases overthe preset voltage (e.g., V2 in Fig. 3), it absorbs reactive power so that itcan decrease the bus voltage.

The reactive power output in Fig. 3 is determined by the followingproportional equation:

=

⎧

⎨

⎪⎪

⎩

⎪⎪

⩽

⩽ ⩽

⩽ ⩽

⩽ ⩽

⩽

−−

−−

Q V

Q V V

Q V V V

V V V

Q V V V

Q V V

( ) 0bus

max bus minV VV V max min bus

busV VV V min bus max

min max bus

( )1

1 2( )

2

busmin

busmax

11

22

(1)

The reactive power output determined by equation is proportionalto the distance of the present bus voltage (e.g., Vbus) to either V1 or V2.Thus, the output is not optimal because the gradient of the Q-V curve ispredefined. In other words, equation ignores the conditions changed ineach power flow calculation (e.g., the feeder impedances, loads, DGsystems, and switches).

In a P-V bus, the reactive power output is, however, optimal tomaintain the voltage of a bus to which the DG system is connected at aspecified setpoint. For example, in Fig. 4, if the bus voltage is Vbus, anoptimal amount of Q*

out is required for the bus voltage to be Vset, which

Fig. 7. Flowchart of the proposed bus voltage control strategy.

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is determined by

∑= − = −=

Q Q Q V V G θ B θ| || |( sin cos )i Gi Dik

n

i k ik ik ik ik1 (2)

If a PV inverter (whose output voltage is Vinv) is connected to thegrid (whose voltage is Vgrid) through a line reactance of X, active powerand reactive power that the grid-connected PV inverter can produce are

=PV V

Xδ3 singrid inv

(3)

= −QV

XV δ V3 ( cos )grid

inv grid (4)

The active and reactive powers are limited by their voltage andcurrent of the PV inverter. The limitation of active and reactive poweramounts can be expressed by

= +S P Q2 2 2 (5)

+ + =P QVX

V VX

(3

) (3 ) [28]grid grid inv22

2 2(6)

Fig. 5 shows the capability curve of a PV system connected to thegrid. The PV output current is mainly determined by the solar irra-diance, panel characteristics, and temperature. The PV output currentlimitation is determined by and on the outer circle of Fig. 5 (i.e., the redcolored circle). The voltage is also limited by the curve with an origin of− V X3 /grid

2 in the Q axis and a radius of V VX

3 grid inv (i.e., the black dashedcircle). The active power is also limited by Pmax, which depends on solarirradiance, temperature, and Vmpp.

This study focuses on the maximum effect of PV inverters partici-pating in the control of reactive power on voltage regulation. Thus, thisstudy assumes that the reactive power could be higher than activepower according to solar irradiance and temperature available to a PVinverter, i.e., the shaded area in Fig. 5, if the power factor limit is notset.

3.3. Reactive power control strategies

The bus with the proposed bus voltage control strategy initiallyoperates at a unity power factor under normal conditions. For example,if the present bus voltage is within a specified range (e.g., from V1 to V2

in Fig. 6), the proposed bus behaves like a P-Q bus. However, the DGsystem can also participate in the control of reactive power if the fol-lowing conditions are satisfied:

1) Sufficient Q. The total available reactive power of DG systems con-nected to the bus should be sufficiently large to maintain the busvoltage at the set voltage. The P-Q capability curve varies widelydepending on the design characteristics, rated capacity, type, andcontrol techniques of the inverter (e.g., Fig. 5).

2) Mutual agreement to participate and cease to energize the area EPS.Most grid codes may require the DG system to have the capability of

Fig. 8. Test system with two slack buses, three P-Q buses, and a DG system.

Table 1Voltage profile of the six-bus system in p.u.

Bus Type Newton-Raphsonimplemented by thisstudy

Newton-Raphson ofDIgSILENT

Newton-Raphson ofMATPOWER

1 Slack 1.00000∠0.000° 1.00000∠0.000° 1.00000∠0.000°2 P-Q 0.99153∠−1.458° 0.99153∠−1.458° 0.99153∠−1.458°3 P-Q 0.96608∠−3.130° 0.96608∠−3.130° 0.96608∠−3.130°4 P-Q 0.99941∠−0.693° 0.99941∠−0.692° 0.99941∠−0.693°5 Slack 1.00000∠0.000° 1.00000∠0.000° 1.00000∠0.000°6 P-V 1.02000∠2.682° 1.02000∠2.682° 1.02000∠2.682°

Table 2Three cases of the bus to which a DG system is connected.

Case Constant power loadin p.u.

Vmin and Vmax range inp.u.

Q limit in p.u.

1 0.2+ j0.05 0.95≤ V≤ 1.05 No limit2 0.99≤ V≤ 1.02 No limit3 0.99≤ V≤ 1.02 −0.005≤Q≤ 0.005

Table 3Voltage profile of the three cases in p.u.

Bus Case 1 Case 2 Case 3

1 V 1.0000∠0.000° 1.0000∠0.000° 1.0000∠0.000°2 V 0.9875∠−1.522° 0.9883∠−1.509° 0.9881∠−1.513°3 V 0.9562∠−3.154° 0.9582∠−3.149° 0.9576∠−3.151°4 V 0.9843∠−0.591° 0.9874∠−0.611° 0.9864∠−0.604°5 V 1.0000∠0.000° 1.0000∠0.000° 1.0000∠0.000°6 V 0.9824∠2.967° 0.9900∠2.908° 0.9875∠2.927°

Q 0 (P-Q bus) 0.007421 p.u.(injected) 0.005 p.u.(injected)

Fig. 9. Typical load profile in p.u.

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actively controlling active and reactive powers while maintainingnot only the power factor at least above a threshold at the inter-connection point but also the voltage and frequency of the area EPSwithin ANSI C84.1-2011 Range A (e.g., ± 5% of the rated value)[17,20,29]. The participation in the control of reactive powershould be under a mutual agreement among the DG owners, EPSoperators, and utilities in terms of the conditions, times, and pro-cedures for the control of reactive power. The clearing trip times andvoltage set points should also be complied with [20].

3) Protection coordination. The active participation in the control ofreactive power may cause voltage or frequency fluctuation at orclose to the interconnection point of DG systems. Thus, a DG systemconnected to the bus should be well coordinated with the protectivedevices installed at the area EPS. Further, such a fluctuation involtage and frequency should not cause abnormal tripping of theprotective relays. Therefore, the nearby protection devices shouldalso detect the voltage and frequency fluctuations, bidirectionalpower flow, back feeding, and the fault ride-through capability ofDG systems.

Fig. 6 shows a Q-V curve of the proposed bus voltage controlstrategy. If the bus voltage is inside a specified range (e.g., from V1 toV2), the bus is represented as a P-Q bus and the reactive power output,Q, is 0. If the bus voltage exceeds the specified range, the DG systemconnected to the bus actively participates in the control of reactive

power, which is the main difference of the proposed bus voltage controlstrategy in Fig. 6 to the Volt/Var control method in Fig. 3 and the P-Vbus in Fig. 4. Another difference is that the following control strategiesare also used:

1) Warning control level. A warning message to the bus that participatesin the proposed bus voltage control strategy and violates the con-straints (e.g., Vmin, Vmax, Pmin, Pmax, Qmin, and Qmax) is presented.

2) Cut-off. The DG systems connected to the bus that violates theconstraints are cut off to limit their output. For example, after amutual agreement among system operators, DG system owners, andutilities, DG systems that participate in reducing or disconnectingfrom the grid under abnormal voltage conditions can be modeled bythe cut-off strategy of the proposed bus control strategy.

3) Active participation. Fig. 7 presents a flowchart of the active parti-cipation mode that controls reactive power. After calculating thepower flow of the entire system, the buses that participate in theproposed bus voltage control strategy and violate the constraints(e.g., the upper and lower limits of the voltage and reactive power)are individually changed because a bus type change modifies theconvergence condition of the active and reactive power balanceequations.

3.4. Optimal power flow problem

In the active participation mode of DG systems in controlling

Fig. 10. Voltage profile of the bus that participates in the proposed bus voltagecontrol strategy.

Fig. 11. Reactive power profile injected by the bus that participates in theproposed bus voltage control strategy.

Fig. 12. IEEE 30-bus system.

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reactive power, this study attempts to change each bus that violates theconstraints after preferentially selecting one of the buses that is theremotest, closest, or first founded. Either the remotest or closest bus tothe slack bus indicates a bus with the highest or lowest total line im-pedance seen by the slack bus to the corresponding bus. Since changinga bus type (from a P-Q to P-V or vice versa) may modify the con-vergence condition of the power balance equations of the system, se-lecting one of the buses can be seen as an optimal power flow (OPF)problem. To solve the OPF problem, this study individually changes allbuses to which DG systems (able to control Q but violating the con-straints) are connected. After changing a bus from a P-Q to P-V bus, ifpower flow results do not meet the constraints, the bus is back con-verted to the P-Q bus (i.e., SPQmax or SPQmin states in Fig. 1) because theQ limit can maintain the bus voltage close to the limits. Finding the bestcombination of buses as an OPF problem is beyond the scope of thisstudy that presents the bus voltage control strategy.

To quantify the effect of the active participation on voltage reg-ulation during a total time period of H, the following cost function thatevaluates the voltage variation of all N buses to unity value (defined bycost function CV) and the reactive power to be produced (defined bycost function CQ) is defined as

∑ ∑= −= =

C W V V| |V Vh

H

i

N

i h target1 1

,(7)

∑ ∑== =

C W Q ,andQ Qh

H

i

N

i h1 1

,(8)

= +C C C( )V Q (9)

The cost functions, to, can be used in the objective function of anOPF problem of selecting the best combination of buses that participatein the proposed bus voltage control strategy. The Newton–Raphson,Gauss–Seidel, fast decoupled methods, backward and forward sweep, orcurrent injection matrix methods can be also used to calculate thepower flow of the system with the proposed bus voltage controlstrategy.

4. Case studies

4.1. 6-bus example

This study applies the proposed bus voltage control strategy to the

Newton–Raphson power flow algorithm in MATLAB [30–32]. To verifythe strategy, this study presents a test power system with two slackbuses, three P-Q buses, and a DG system at a base of 100 MVA in Fig. 8.The system also includes three grounded wye-delta transformers. TheDG system with a capacity of 10 MVA is connected to Bus 6 in Fig. 8 andadded to the system through the grounded wye-delta transformer.

As the first validation step, the DG system is modeled as a con-ventional P-V bus with a set voltage of 1.02 p.u. Subsequently, thepower flow of the system is calculated using the Newton-Raphsonmethod implemented by this study and the Newton-Raphson method ofDIgSILENT and the same method of MATPOWER. Table 1 shows thevoltage results demonstrating consistency between them.

The DG system without the upper and lower limits of V and Q wasmodeled as a conventional P-V bus that maintains the voltage of Bus 6at a target voltage of 1.02 p.u. As the subsequent validation step, the DGsystem participates in the proposed bus voltage control strategy. Undernormal conditions (e.g., Vmin≤ Vbus≤ Vmax), the DG system operateswith a fixed power factor (like a P-Q bus). However, if the voltage of abus to which the DG system is connected exceeds the normal condi-tions, it starts to participate in controlling Q. Table 2 presents threecases that validate the proposed bus voltage control strategy. Table 3shows the power flow results of each case. In the first case, Vmin andVmax have a relatively broad range, from 0.95 p.u. to 1.05 p.u. Thevoltage magnitude of the bus to which the DG system is connected is0.982424 p.u., which is within the normal range. Thus, the DG systemdoes not participate in the control of Q. In the second case, Vmin andVmax range from 0.99 p.u. to 1.02 p.u. and the Q limit is still not set. Thevoltage magnitude of the bus to which the DG system is connected is0.982424 p.u., which is outside the Vmin and Vmax range. Thus, the DGsystem participates in the control of Q by producing 0.0074 p.u. so thatit can maintain the bus voltage within the Vmin and Vmax range. In thethird case, the Q limit is set to± 0.005 p.u. As the voltage is outside theVmin and Vmax range, the DG system participates in the control of Q withthe limit of 0.005 p.u. Thus, the voltage of Bus 6 is 0.9875∠−57.07°p.u. because of the insufficient Q.

In the previous case, the load was fixed (e.g., 0.2+ j0.05 p.u. at abase of 100 MVA). However, the load always varies randomly withtime. To apply the proposed bus voltage control strategy to such a casewhere the load varies, this study assumes the load connected to Bus 3 tohave a maximum capacity of 30 MVA at a lagging power factor of 0.9.The load also changes according to the typical load profile presented inFig. 9. The load profile shows a late peak at 4p.m. and a load factor of0.67 [33]. The Q limit of the DG system is set to± 0.03 p.u.

If the DG system actively participates in the control of V, it could bemodeled as a P-V bus with Vset of 1.0 p.u. As a reference, the thick graystraight lines in Figs. 10 and 11 show the profile of the voltage andreactive power of Bus 6 to which the DG system is connected. In thegray straight line in Fig. 10, before 10 a.m., the DG system successfullyregulates the voltage to Vset (e.g., 1.0 p.u.). However, because of theconstraint of the reactive power (e.g., Qmin=−0.03 p.u. andQmax=0.03 p.u.), after 10 a.m., it sets the reactive power to its al-lowable maximum (e.g., 0.03 p.u.) in the gray straight line in Fig. 11.

If the DG system participates in the control of V only when the busvoltage is outside the limits, the proposed bus voltage control strategy

Table 4Voltage profile of the IEEE 30-bus system in p.u.

Bus Type Newton-Raphsonmethod implementedby this study

Newton-Raphsonmethod ofDIgSILENT

Newton-Raphsonmethod ofMATPOWER

1 Slack 1.060000∠0.0000° 1.06000∠0.000° 1.060000∠0.000°2 P-V 1.043134∠−5.3519° 1.04313∠−5.352° 1.043134∠−5.352°5 P-V 1.010000∠−14.1659° 1.01000∠−14.166° 1.010000∠−14.166°8 P-V 1.010000∠−11.8134° 1.01000∠−11.813° 1.010000∠−11.813°11 P-V 1.082000∠−14.1090° 1.08200∠−14.109° 1.082000∠−14.109°13 P-V 1.071000∠−14.9434° 1.07100∠−14.943° 1.071000∠−14.943°

Table 5Voltage and reactive power of the five P-V buses in p.u.

Bus Vmin and Vmax range in p.u. Q limit in p.u. The closest bus is preferentially controlled. The remotest bus is preferentially controlled.

V Q Cost V Q Cost

2 1.03≤ V≤ 1.05 −0.4≤Q≤ 0.5 1.0346∠−5.26° 0.500 0.964 1.0300∠−5.17° 0.321 1.0735 0.98≤ V≤ 1.02 −0.4≤Q≤ 0.4 0.9972∠−14.27° 0.400 0.9800∠−14.04° 0.2058 0.98≤ V≤ 1.02 −0.1≤Q≤ 0.4 0.9800∠−11.56° 0.166 0.9983∠−11.84° 0.40011 1.05≤ V≤ 1.10 −0.06≤Q≤ 0.24 1.0500∠−14.09° 0.131 1.0500∠−14.11° 0.08213 1.05≤ V≤ 1.10 −0.06≤Q≤ 0.24 1.0500∠−15.04° 0.113 1.0918∠−15.17° 0.240

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can be used. Further, if the voltage magnitude of Bus 6 is within thelimits (e.g., 0.98≤ V≤ 1.02 p.u.), the DG system does not participatein the control of V and it produces only P. However, if the bus voltage isoutside the limits, it actively participates in the control of V. Fig. 10 andFig. 11 present the voltage profile of the bus (in the red dashed line inFig. 10) and the Q profile produced by the bus (in the red dashed line inFig. 11), respectively. Before 7 a.m., as the bus voltage is higher than0.98 p.u., the bus does not produce Q. However, after 7 a.m., as the busvoltage decreases below Vmin (e.g., 0.98 p.u.), it starts producing Q. Forexample, it produces a reactive power of 0.023 p.u. at the peak hour(e.g., at 4p.m.) so that it can maintain the bus voltage above Vmin (e.g.,0.98 p.u.).

If the DG system participates in the conversation of voltage reduc-tion (CVR) or integrated Volt/Var control (IVVC) in order to reduce theoverall system voltages up to an allowable voltage level (e.g., 0.98 p.u.like this case study), the proposed bus voltage control strategy can beintegrated into the power flow analysis studies. For example, in thissimulation, if the DG system participates in the proposed bus voltage

control strategy (e.g., Vmin and Vmax range=0.98≤ V≤ 1.02 p.u.) or ismodeled as a P-V bus (with a Vset of 1.0 p.u.), the cost function definedin (with WV=0.5, WQ=0.5, and Vtarget=0.98 p.u.) are 2.4850 p.u.and 2.6456 p.u. Thus, the proposed bus voltage control strategy candecrease the cost function by as much as 2.4850 p.u. from 2.6456 p.u.

4.2. The IEEE 30-bus test system

The previous case study verified the behavior of a single bus par-ticipating in the proposed bus voltage control strategy on a relativelysimple test feeder. To verify the proposed control strategy on a rela-tively complex test feeder, the IEEE 30-bus transmission system ismodeled. The system consists of 30 buses at either 132 or 33 kV, five P-V buses, 21 loads, two shut capacitors, and four transformers in Fig. 12[34,35]. As the first validation, the five P-V buses are modeled as aconventional P-V bus. Table 4 presents the power flow results (e.g., avoltage profile in p.u.) of the five P-V buses calculated using theNewton-Raphson method implemented by this study in MATLAB[30–32] and the same method of DIgSILENT and MATPOWER. Theyshow consistency with each other.

As the second validation step, the five P-V buses participate incontrolling Q. Table 5 shows the power flow results of the five buses.The number of the buses is five, and hence, the two selection rules arecompared. In both cases, the limits of V and Q are maintained withinVset and Qset, respectively. However, the cost function (e.g., 0.964) inthe case of preferentially selecting one of the closest buses to the slackbus or the incoming substation that violate the limits is lower than thatof selecting the remotest bus (e.g., 1.073 p.u.). Thus, the strategy ofcontrolling the Q of DG systems close to the slack bus or the incomingsubstation is more effective than that of controlling DG systems far fromthe slack bus from the point of view of voltage regulation. This findingis comparable to the fact that the optimal locations of DG systems thatcan control Q show a pattern close to the main transformer or incomingsubstation [27,36].

4.3. The IEEE 14-bus test system

The previous case study verified the behavior of buses that inject Qwhen participating in the proposed bus voltage control strategy. Toverify a case that absorbs Q, the IEEE 14-bus system is modeled [34,37].The system consists of 14 buses, 4P-V buses with DG systems able tocontrol Q, 11 loads, 1 shut capacitor, and 3 transformers. Table 6presents the power flow results of the four P-V buses, calculated usingthe Gauss-Seidel method implemented in MATLAB [30–32]. The vol-tages in the third column indicate a case where the four buses aremodeled as a conventional P-V bus, which is the same solutions asavailable in [37]. Subsequently, the four buses participate in the pro-posed bus voltage control strategy. The Q limit of the bus with DGsystems is set to the original value. One of the closest buses to the slackbus is individually and preferentially selected. The sixth column ofTable 6 provides the voltage. For example, the DG system connected toBus 2 absorbs Q of 0.016 p.u. to maintain the bus voltage magnitudewithin the Vmin and Vmax range.

To apply the proposed bus voltage control strategy to a case where aload varies with time, this study changes the loads of the test systemaccording to the same load profile data as presented in Fig. 9. Figs. 13

Table 6Voltage and reactive power of the four buses that participate in the proposed bus voltage control strategy.

Bus Type V Vmin and Vmax range Q limit V Q Cost

2 P-V 1.0450∠−4.98° 1.02≤ V≤ 1.03 −0.4≤Q≤ 0.5 1.0200∠−4.68° −0.016 0.55153 P-V 1.0100∠−12.73° 1.02≤ V≤ 1.03 0≤Q≤ 0.4 0.9956∠−12.99° 0.4006 P-V 1.0700∠−14.22° 1.02≤ V≤ 1.03 −0.06≤Q≤ 0.24 1.0200∠−14.48° 0.0488 P-V 1.0900∠−13.36° 1.02≤ V≤ 1.03 −0.06≤Q≤ 0.24 1.0200∠−13.52° 0.054

Fig. 13. Voltage profile of the bus that participates in the proposed voltagecontrol strategy (i.e., Bus 2).

Fig. 14. Reactive power profile absorbed by the bus that participates in theproposed voltage control strategy (i.e., Bus 2).

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and 14 show the profile of V and Q of Bus 2 to which the DG system isconnected. In the gray straight line in Fig. 13 and Fig. 14, before 10a.m., the DG system modeled as a P-V bus successfully regulates thevoltage to Vset (e.g., 1.045 p.u.). However, because of shortage in thereactive power (e.g., Qmin=−0.4 p.u. and Qmax=0.5 p.u.), after 10a.m., it cannot maintain the bus voltage magnitude to Vset (e.g., 1.045p.u.). By contrast, in the red dashed line in Fig. 13 and Fig. 14, before 7a.m., because the bus voltage increases above Vmax (e.g., 1.03 p.u.), itabsorbs Q (e.g., 0.4 p.u. because of the Q limit). After 10 a.m., it alsoabsorbs reactive power to maintain the bus voltage above Vmin (e.g.,1.02 p.u.).

5. Conclusion

If DG systems such as residential or commercial PV systems andwind farms are connected to the grid by a short line, but not a longtransmission line, they can participate in the control of reactive power.Additionally, as a result of the advancement in power electronics, a DGsystem can actively participate in the control of voltage by eitherconsuming or producing reactive power. However, either a conven-tional P-Q or P-V bus is not appropriate to model a DG system thatswitches its operation mode based on the bus voltage in real time. Thus,the DG system can operate at a power factor of unity or close to it undernormal voltage conditions or adjust the reactive power output tomaintain the voltage of a bus to which the DG system is connectedwithin the set voltage range under abnormal voltage conditions (e.g., anincrease in over- or under-voltage conditions). Thus, this paper definesa bus voltage control strategy that makes appropriate decisions from P-Q to P-V or vice versa, using the Petri net approach. The proposed busdetermines the reactive power output to maintain the bus voltagemagnitude within the set range. For example, if the voltage of the bus towhich a DG system able to control reactive power is connected violatesthe lower and upper limits, it attempts to support the reactive power tomaintain the bus voltage within the lower and upper limits.

Various DG systems capable of controlling reactive power andmaintaining the bus voltage within the specified upper and lower limitscan be modeled as the proposed bus voltage control strategy.Furthermore, if the DG system participates in CVR or IVVC, the pro-posed bus voltage control strategy can be integrated into the powerflow analysis studies. The case study results (e.g., the strategy of con-trolling reactive power of DG systems close to the slack bus) can also beused for planning, maintaining, or upgrading distribution networks orSCADA systems that host DG systems with the capability of reactivepower control.

This work was supported by Inha University, South Korea ResearchGrant #60140-01.

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