AUPEC Final Paper ID 163 Shahariar Kabir

8/13/2019 AUPEC Final Paper ID 163 Shahariar Kabir

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Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, TAS, Australia, 29 September 3 October 2013 1

Impact of Large-Scale Photovoltaic System on Short

and Long Term Voltage Stability in Sub-

Transmission Network

Shahariar Kabir, Olav Krause, Simon Bartlett

School of Information Technology and Electrical Engineering

University of Queensland

Brisbane, Australia

[email protected]

AbstractIntegration of solar energy based large scale

Photovoltaic (PV) generation can offer significant benefits to the

power system. Since PV units can be installed close to load

centers, improvement in reliability of the network can occurtogether with a decrease in greenhouse gas emissions. Despite

these general benefits, the dynamic voltage characteristics of sub-

transmission networks under the influence of large scale PV

installations need to be carefully analyzed and existing standards

revisited for potential upgrade. This research paper offers

analyses of the impact of large scale PV on dynamic voltage

stability in sub-transmission network while considering the

presence of a number of power system devices typically found in

this kind of network. From preliminary results, obtained using

the IEEE 14 bus test network, it can be concluded that the

integration of large scale PV with proper controller settings can

positively influence the dynamic voltage stability with respect to

short and long term state variables. It can be also concluded that

static voltage stability analysis alone does not adequately capture

the implication of large-scale PV on sub-transmission system.

Keywordscontingency; photovoltaic (PV); static and dynamic

loads; short and long term state variables; static and dynamic

voltage stability

I. INTRODUCTIONIn the past, power systems have been designed based on

unidirectional power flow concept only. However due to theincreased concern about future availability of non-renewableenergy sources and about global warming, there is globalinterest in non-fossil fuel based power generation schemes.Among the existing renewable energy technologies, solar,

geothermal, wind and biofuel power generation schemes aregradually becoming popular as alternative forms of productionschemes [1]. Eco-friendliness and energy independence are thetwo most significant attributes of solar energy basedphotovoltaic (PV) technology. In Australia, it is expected thatthe renewable energy sources including PV will produce 25%of the total electricity demand by 2020 [1]. Thus, it is widelyanticipated that the operational characteristics and dynamics ofthe existing transmission and sub-transmission networks willbe significantly influenced in the near future by the integrationof large scale PV.

Voltage stability is designated as one of the mostsignificant factors for stable operation of the power system.Voltage instability is defined as the inability to maintain

satisfactory voltage levels throughout the network duringdifferent operating conditions [2]. Voltage collapse is theprocess by which the voltage falls to a low, unacceptable value[2]. The implications of large scale PV on all aspects of voltagestability are not yet fully known [1]. Therefore, their effects interms of voltage stability with respect to state variables need tobe methodically analyzed.

From previous research work, some of the key findingshave been highlighted below: Crow and Ayyagari [3] definedthe relationship between the dynamic models and steady statebehaviour of traditional power system. Afterwards, withrespect to the defined dynamic system models, impact of themaximum excitation limits of synchronous generators on

voltage stability was analysed and corrective actions wereproposed. Potamianakis and Vournas [4] analysed differentvoltage stability situations for short-term state variables withrespect to synchronous and induction machines. Cutsem [5]proposed an innovative algorithm to identify the buses intraditional power system where load restoration with respect todisturbances caused voltage collapse. The algorithm wascapable of identifying appropriate corrective actions. Lee andLee [6] studied the voltage stability issues by means ofsynchronous motor loads and examined the eigenvalues of thelinearized system matrix to address dynamic voltage stability.Cutsem and Vournas [7] reviewed the general method ofinvestigating voltage stability in midterm and transient timescale. Based on their findings, an algorithm was developed to

predict the stability of midterm dynamics of a power systemwith constant power loads. Tuglie et al. [8] formulated anonlinear programming method for assessing precautionaryactions with respect to voltage transients to improve thedynamic voltage security of power systems. Lof et al. [9]studied power system models to develop advancedmethodologies for analysis and simulation in the vicinity of thedynamic voltage stability limits. Vu and Liu [10] analysed thedynamic voltage collapse phenomena of a traditional powersystem with respect to on-load tap changing transformer,dynamic load and generator excitation limiter while confirming


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the presence of the state space region corresponding tomonotonic voltage collapse.

It can be concluded that a number of studies have beenperformed in the past in the field of voltage stability withrespect to short and long term state variables. However, inthese studies, the impact of large scale PV units has not beenadequately assessed. Thus, the main objective of this research

paper is to show the richness of the qualitative and quantitativecharacteristics of voltage for short and long term state variablesin sub-transmission network with the presence of large scalePV. The remaining paper is organized as follows: Section IIand III present details of IEEE 14 bus network and PV systemrespectively. Section IV describes the modelling of networkcomponents such as turbine governor (TG), synchronousgenerator, power system stabilizer (PSS), over excitationlimiter (OXL) and automatic voltage regulator (AVR) essentialfor the study of dynamics in the context of the presented work.Section V demonstrates and analyses the impact of large scalephotovoltaic with respect to short term voltage stability. Insection VI, considerations regarding long term voltage stabilityare offered. Subsequently, the difference between static and

dynamic voltage stability analysis processes are highlighted insection VII to illustrate the importance of performed time scaledecomposition based time domain analysis. The conclusionsection summarizes key findings.

II. NETWORK CONFIGURATIONIn this study, IEEE 14 bus sub-transmission network has

been utilized as depicted in Fig. 1 [11]. The network withvoltage levels of 13.8 KV, 18 KV and 69 KV has been selectedas this is widely used in voltage stability studies [12].

Figure 1. Structural diagram of implemented IEEE 14 bus system.

The considered 14 bus sub-transmission network consistsof five synchronous machines, twenty branches, fourtransformers and eleven constant power (PQ) loads. The initialloading level has been selected as 362.6 MW and 113.96MVAR. Synchronous machines at bus 3, 6 and 8 are used asreactive power compensators only. The remaining two locatedat bus 1 and 2 are used as synchronous generators producing

both active and reactive powers. Network data of theimplemented system is available in [11].

III. MODELLING OF GRID CONNECTED PHOTOVOLTAICTo analyze the interaction of large scale PV with the rest of

the power system, PV system has been modelled as a singlestage power source as depicted in Fig. 2.

Figure 2. Schematic diagram of implemented grid connected PV system.

The large scale PV module suitable for voltage stabilityanalysis has been modelled as a single-generator equivalent inthis paper. The modelled PV unit has a rating equivalent to thetotality of the single units as the main objective is to observe

the effects of various integration techniques on the externalgrid rather than within the module [13]. In the developed unit,nonlinear characteristics of the voltage source inverter, PVarray and inverter controller mechanisms contribute to thedynamic performance. Inverter transfer function is a first orderfunction with unity steady state gain [13]. Current set pointshave been accomplished with respect to the desired powers andmeasured terminal voltages as following:

idiq= Vd VqVq Vd1 PQ (1)

where the notations carry their standard meanings as in[13]. In this paper, based upon the aforementioned model, the

dynamics of large scale PV has been analysed under thefollowing operational modes: (1) constant P and constant Vcontrol (PV mode), (2) constant P and constant Q control (PQmode). It is presumed in this paper that PV units operate at100% of their capacity [13].

IV. MODELLING OF SYSTEM COMPONENTSA. Turbine Governor

In this paper, type II turbine speed governor has beenimplemented as per followings [11]:

t = ((1 ) ( ) t)/T (2)T!"#= t$ ( ) $ T!"% (3)

where the notations carry standard meanings as in [11].

B.Automatic Voltage RegulatorIn this paper, type II automatic voltage regulator has been

implemented as per (4-8) to maintain the terminal voltage ofthe generator at the pre-defined value [11]:

& = (V &)/T (4)& =('& & & *++&, &)/T (5)


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Figure 5. Voltage profile of IEEE 14 bus system without PV (exponentialrecovery loads).

Figure 6. Voltage profile of IEEE 14 bus system with PV (exponentialrecovery loads).

From the recovery characteristics depicted in Figures 3-6, itcan be concluded that the integration of appropriately tunedlarge scale PV has the potential to improve the voltage profileof the network while reducing initial voltage dips. It has beenalso observed that as load changes take place, the systemmoves along a trajectory on system manifold before settlinginto the new equilibrium point. If the attained point is stable,the system produces stable response as depicted in Figures 3-6while for unstable equilibrium point, the system producesoscillatory or unstable response that can lead to voltagecollapse. In depth analysis of the results have shown that themain contributing factor limiting stable operation of thenetwork is the generators reaching their reactive powergeneration limits. Another important factor is the fixedexcitation in emergency situations that also limits thesynchronous generators capability to support voltages. Afterlosing the reactive power reserve, the generator loses thecapability of voltage control. It has been noted that the powertransfer capability of the remote generators as well as thetransmission voltage of the network decrease correspondinglywith the increase in a deficiency in reactive power support.

Stability of equilibrium points can be obtained bylinearizing differential-algebraic equations around theequilibrium point [14]:

Cg = .2 .rl2 lr C (26)By assuming lras a nonsingular matrix, the following has

been obtained after the elimination of 1se:C = [.2.rlrl2]u C (27)

Thus, the state matrix A has been expressed as following[14]:

v = w2= x.2 .rlrl2y (28)

It has been observed that all the real parts of eigenvalues ofthe state matrix A with and without PV for both the consideredload cases are negative representing asymptotically stablesystem. The eigenvalues of the network are either decayingmodes (real) or sufficiently damped oscillatory modes(complex conjugates). The critical eigenvalue of the networkgoverning the dynamic behaviour (the eigenvalue positionedcloser to the imaginary axis) with and without PV is in

decaying mode for both PQ and exponential loads. Theeigenvalue is related to the transient gain time of the turbinegovernor at bus 2. The dynamic order of the network increasesby 3 after the integration of PV as stated in section 3.

In this paper, hopf bifurcation has been utilized to definethe dynamic loadability of the network [14]. Worst casescenario has been considered by increasing all the loads by thesame factor while maintaining constant power factor [14].After the integration of PV, the loading margin for PQ loadsincreases by 28.10%. With and without PV, the critical purelyimaginary eigenvalues are related to the q axis internal voltageand exciter control voltage of the synchronous generatorlocated at bus 1. For exponential loads, with PV, the loading

margin improves by 19.79% while the critical eigenvalues arerelated to the same components of generator 1. It has beenobserved that the dynamic voltage stability of the consideredsub-transmission network with the presence of large scale PVdepends on both the load parameters and loading level. Thecomputed dynamic loadability limits are less than the staticlimits corresponding to saddle node bifurcation. From theliterature review, it has been noted that the PSS devices arewidely used to resolve small oscillation issues in power system[14]. As the dynamic loading level of IEEE 14 bus systemincreases after the integration of large scale PV, it can beconcluded that the voltage regulator of integrated PVinfluences the system damping like PSS. It has been also notedthat the network damping performance can be significantlyimproved by appropriately fine-tuning voltage controllerparameters of the integrated PV.

Short term voltage instability can occur due to excessivetime delay in fault clearing as well. In this section, analyseshave been performed with respect to static constant power (PQloads) and then by dynamic induction motor loads (Type I) ascharacterized below [11]:

z = {|(T(}) ~\

~^ (2^ 2~) ) (29)where the notations carry their standard meanings as in

[11]. In this part, three phase unbolted fault has been applied atbus 14 at t = 5 sec for 0.5 sec to attain the following figures:

Figure 7. Voltage profile of IEEE 14 bus system for fault without PV (PQloads).

0 10 20 30

0.9

0.92

0.94

0.96

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1

1.02

1.04

Time (sec)

Voltage

(pu)

Bus 3

Bus 7

Bus 14

0 10 20 300.92

0.94

0.96

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1.02

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Time (sec)

Voltage(pu)

Bus 3

Bus 7

Bus 14

0 5 10 15 20 25 300.2

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1.2

Time (sec)

Voltage

(pu)

Bus 3

Bus 7

Bus 14


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Figure 8. Voltage profile of IEEE 14 bus system for fault with PV (PQloads).

Figure 9. Voltage profile of IEEE 14 bus system for fault without PV(Induction motor loads).

Figure 10. Voltage profile of IEEE 14 bus system for fault with PV(Induction motor loads).

With respect to the PQ loads, analysis based on energyfunction and time domain indicates that the critical faultclearing time without PV is 2.8 sec. However, it can be notedfrom Fig. 8 that the controller parameters of the integratedlarge scale PV negatively influences the system as there is nopost disturbance stable equilibrium point that shortly leads tovoltage collapse. On the contrary, for induction motor loads,without PV, post disturbance network is oscillatory unstable.The critical pair of complex conjugate eigenvalues withpositive real part is related to the q-axis internal voltage andexciter control voltage of the synchronous generator located atslack bus 1. But, with the presence of an adequately tuned 100MVA rated large scale PV at bus 5, additional damping

provided lets the oscillation die out as visible in Fig. 10. Thus,it can be concluded that the integration result of large scale PVin sub-transmission network during fault analysis depend onfactors such as network topologies, PV characteristics and faultfeatures. It has been noted that the dynamic characteristics ofinduction motor play a significant role to determine thesystems response during fault conditions. If there is excessivedelay in fault clearing, the slip of the motor goes beyond theunstable equilibrium point though the electrical and mechanicaltorque curves do intersect. Thus, for a delayed fault clearing,the induction motor decelerates past the region of stability andbecomes incapable of reaccelerating even after the fault

clearance leading to system instability. Thus, it can beconcluded from above analyses that with the presence of largescale PV in sub-transmission network, short term voltageinstability can occur due to the following three reasons: (1) lossof equilibrium of variables corresponding to fast dynamics, (2)lack of attraction of the fast dynamics towards the stableequilibrium after disturbance and (3) oscillatory instability ofequilibrium after disturbance.

VI. ANALYSIS OF LONG TERM VOLTAGE STABILITYFor a comprehensive analysis of voltage stability under the

influence of large scale PV, short term voltage stabilityanalysis has to be complemented by long term analysis. In thelong term stability study, it has been presumed that the networkhas survived the transient period after the initial disturbance.After performing feasibility analysis, loss of transmission line5-4 at t = 5 sec has been selected as the large disturbance in thissection to obtain the following figure while considering thedynamics of the generators, PSS, TG, OLTC and AVR at aloading level of 466.2 MW and 113.96 MVAR:

Figure 11. Voltage profile of IEEE 14 bus system for long term voltagestability analysis without and with PV.

It can be observed from Fig. 11 that after losing thetransmission line, networks reactive power loss considerablyincreases while negatively impacting the total transmissioncapacity and bus voltages. After the instigation of AVR, thefield currents of the generators are increased to maintain theterminal voltage constant. Thus, the system is transient stablewithout and with PV though the settling time for later is muchless. Switching time for OLTC has been selected as t = 40 sec.With PV, it can be observed from Fig. 11 that the transformerslower their tap ratios to restore the voltage into dead-bandwhile the generators supply the requisite reactive power.However, without PV, while the loads attempt to recuperatepre-disturbance powers through LTC, the system becomesoscillatory unstable. The most critical eigenvalues have beennoted as 0.11 j8.79 confirming that the network has crossedthe hopf bifurcation loading level. It has been also noted that

excessive time delay in corrective measures to restore longterm equilibrium can also cause voltage instability with thepresence of large scale PV in sub-transmission network.

VII. IMPORTANCE OF DYNAMIC VOLTAGE STABILITYANALYSIS

The static or steady state voltage stability analysistechniques depend on the steady state model of the powersystem such as power flow model or linearized dynamic modeldefined by the steady state operation. Such analyses have beenperformed by authors in [15] while considering the followingtechniques: (1) singular value decomposition (SVD) and (2)

0 5 10 15 20 25 30

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Time (sec)

Voltage(pu)

Bus 3

Bus 7

Bus 14

0 5 10 15 20 25 300.2

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Time (sec)

Voltage

(pu)

Bus 3

Bus 7

Bus 14

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Bus 7

Bus 14

0 50 100 150 2000.95

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1.01

Time (sec)

Voltage

(pu)

Bus 14 without PV

Bus 14 with PV


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AUPEC Final Paper ID 163 Shahariar Kabir

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