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Adequacy Assessment of Composite Power Systemswith FACTS Devices Using a DC Load Flow MethodROY BILLINTON a & YU CUI aa Power System Research Group, University of Saskatchewan, Saskatchewan, CanadaPublished online: 24 Jun 2010.

To cite this article: ROY BILLINTON & YU CUI (2004) Adequacy Assessment of Composite Power Systems with FACTS DevicesUsing a DC Load Flow Method, Electric Power Components and Systems, 32:11, 1137-1149, DOI: 10.1080/15325000490441354

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Electric Power Components and Systems, 32:1137–1149, 2004Copyright c© Taylor & Francis Inc.ISSN: 1532-5008 print/1532-5016 onlineDOI: 10.1080/15325000490441354

Adequacy Assessment of Composite PowerSystems with FACTS Devices Using a

DC Load Flow Method

ROY BILLINTONYU CUIPower System Research GroupUniversity of SaskatchewanSaskatchewan, Canada

The rapid development of flexible AC transmission technology and its immensepotential for future use dictate the need to seriously consider the associatedreliability benefits that can be obtained. There is, however, relatively littleliterature that includes FACTS in reliability studies, particularly in compositesystem evaluation. The utilization of FACTS devices within bulk transmissionsystems to change the basic load flow patterns is increasing in the new marketenvironment as existing systems became increasingly loaded and congested.A methodology for incorporating FACTS devices in composite system reliabilityevaluation is presented in this article.

Keywords composite electric power system, flexible AC transmission systems,reliability evaluation

1. Introduction

Power system performance can be enhanced by the ability to control power flowwithout involving generation rescheduling or topological changes. Load flow pat-terns in a transmission system can be changed using controllable devices to optimizethe system operation and increase the system stability margin without violating theeconomic generation dispatch. Flexible AC transmission system (FACTS) technolo-gies were developed to fulfill this requirement.

FACTS is the designation given to the concept of using solid-state power elec-tronic converters for power flow control at the transmission level. The transmissioncomponents become active elements by self-adjusting their related parameters, andplay important roles in meeting power transfer requirements and increasing the se-curity margins. This technology has attracted significant attention in recent yearsdue to the ever-increasing electric power demand, the deregulation of bulk powersystems, and environmental concerns associated with building new transmissionlines.

Manuscript received in final form on 24 September 2003.Address correspondence to Dr. Roy Billinton, University of Saskatchewan, Depart-

ment of Electrical Engineering, 57 Campus Drive, Saskatoon, SK S7N 5A9, Canada.E-mail: roy billinton@engr.usask.ca

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The utilization of FACTS technologies can have significant positive impactson power system reliability performance, and the actual benefits obtained can bequantitatively assessed using suitable models and techniques. This is an attractiveongoing research area and some studies have been conducted in this field. Refer-ences [1, 2] present methods to incorporate high voltage direct current (HVDC)in a composite system reliability evaluation using analytical and Monte Carlosimulation methods, respectively. These studies combined the generation and theHVDC outage levels to create a single multi-state generation model, and were con-ducted using conventional composite system evaluation techniques. Reference [3]incorporated FACTS devices in the interconnecting links between major systemsand conducted the analysis at the HL-I level. Reference [4] presents a method toincorporate FACTS devices in a composite power system using a network flowmethod.

The techniques illustrated in this article have been used to conduct a series ofstudies on two widely used reliability test systems; the Roy Billinton test system(RBTS) [5] and the IEEE reliability test system (IEEE-RTS) [6]. The models,techniques, and the results described in this article should prove useful to largeelectric power utilities planning and operating transmission facilities using FACTStechnologies.

2. Methodology

The adequacy assessment of a composite power system involves four key steps:reliability modeling of the generation and transmission units; the enumeration ofall possible system contingencies; the determination of load curtailment under eachcontingency; and the calculation of the reliability indices at each load point [7]. Thefirst and the third steps have been extended in order to incorporate FACTS in theoverall evaluation.

2.1. Reliability Modeling of FACTS Devices

The main benefits associated with the utilization of FACTS are as follows:

1. Improved steady-state system performance due to increased transmissioncapacity and controlled transmission flows.

2. Improved system transient and dynamic stability due to expanded dynamicvoltage control and dampened system oscillations.

3. Reduced financial costs and environmental impacts associated with buildingnew transmission lines.

4. FACTS devices are highly reliable and require minimal maintenance.

There are many different FACTS devices, each of which has specific workingprinciples, and thus different reliability models. In this article, a simplified trans-mission line with a unified power flow controller (UPFC) model is utilized in thestudies described, and only steady state impacts are considered.

The UPFC device shown in Figure 1 has two voltage source inverters sharinga common DC storage capacitor, and is connected to the system through couplingtransformers. The inverter connected to a series transformer (Inverter 2) can injecta voltage of controllable magnitude and phase angle in series with the line to controlactive and reactive power flows on the transmission line, while Inverter 1 can provide

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Adequacy Assessment with FACTS Devices 1139

Figure 1. Simplified transmission and UPFC model.

Figure 2. Three-state model of the transmission element with a UPFC.

or absorb the real power demand of Inverter 2 through the common DC link. TheUPFC itself can be represented by a two-state model. In the up state, the UPFCis capable of providing load flow control and maximum transmission capacity. Inthe down state, the UPFC is bypassed by a fully reliable circuit breaker and thetransmission element operates as a normal transmission line [3]. Figure 2 showsa state space model describing the three states associated with the transmissionelement containing the transmission line and the UPFC.

The probability and frequency values associated with each state can be obtainedusing the following equations:

P (up) = A/D F (up) = P (up) ∗ (λl + λu)

P (derated) = B/D F (derated) = P (derated) ∗ µu

P (down) = C/D F (down) = P (down) ∗ µl

where

A = µuµl C = λlµu

B = λuµl D = A+B + C

λl, µl, λu, and µu are the failure and repair rates of the transmission line andUPFC, respectively.

2.2. Determination of Load Curtailment

The calculation of load curtailment resulting from network contingencies is a keyfactor in composite system reliability evaluation. The network solution techniques

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used for contingency evaluation are the power system steady state analysis tools ofnetwork flow and AC/DC load flow methods. The AC load flow approach providescomplete information on system performance including voltage violations and as-sociated reactive power adjustments. The AC load flow method, however, requireslarge computation times. The network flow method requires the smallest compu-tation times but provides the least accurate evaluation of the system performance.The DC load flow approach provides satisfactorily accurate adequacy indices withacceptable computation times, and is widely used in composite system adequacyevaluation when the effect of voltage violations is not included in the analysis.A modified DC load flow method is used in this article in order to incorporate theimpact of FACTS devices.

2.2.1. Mathematical Description. The DC load flow technique is actually a sub-set of the fast decoupled AC load flow technique. The DC load flow techniqueestablishes the relationship between the real power injection and bus voltage an-gles, while neglecting the effect of the reactive power flows and bus voltage magni-tudes.

The DC load flow technique is based on the following four assumptions [8]:

1. Branch resistances are much smaller than branch reactances. Branch sus-ceptances can be approximated by

Bij ≈ − 1xij

2. Susceptances between buses and ground are neglected.3. All bus voltages are assumed to be 1.0.4. Voltage angle difference between two buses of a line is small, and therefore

sin δij ≈ δi − δj

cos δij ≈ 1.0Based on the above assumptions, the real power flow in a branch between two busescan be calculated by

Pij =δi − δj

xij

and therefore the bus real power injections are

Pi =∑

j∈Ri

Pij = B′iiδi +

∑

j∈Ri

B′ijδij

where

B′ij = − 1

xij, B′

ii = −∑

j∈Ri

B′ij

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The above equation can be expressed in a matrix form:

[P ] = [B′][δ]

If bus n is selected as the swing bus and letting δn = 0, [B′] is a (n−1)-dimensionalsquare matrix.

2.2.2. Modified Algorithm. A UPFC device can simultaneously control all threeparameters of line power flow (line impedance, bus voltage, and phase angle). In aDC load flow calculation, the effect of the reactive power flows and bus voltagemagnitudes are neglected. All the bus voltages are assumed to be constant at1.0 pu. Composite power system adequacy assessment is mainly concerned withthe ability of the system to satisfy the load demand given a system disturbance(such as a component failure). During a disturbance, a UPFC device will generallyoperate in response to the perceived disturbance. Its controlled parameter will beadjusted to alleviate the system severity. Based on these considerations, the UPFCmodel utilized in the DC load flow calculation is a normal transmission line withan adjustable reactance. As noted earlier, in the up state, the UPFC providesmaximum transfer capability for the combined transmission element. When theUPFC is in the failed state, the transmission element capacity is simply that of thetransmission line. The complete algorithm of the modified DC load flow method isshown in Figure 3.

Figure 3. Basic steps in the modified DC load flow method.

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2.3. Reliability Indices

The following indices are described in detail in [7].

2.3.1. Load Point Indices.

Probability of failure

=∑

j

PjPkj

Frequency of failure

=∑

j

FjPkj

Expected load curtailed

=∑

j

LkjFj (MW)

Expected energy not supplied (EENS)

=∑

j

LkjPj ∗ 8760 (MWh)

where:

j is an outage condition in the network;Pj is the state probability of the outage event j;Fj is frequency of occurrence of the outage event j;Pkj is the probability of load curtailment at bus k during outage event j;Lkj is the load curtailment at bus k during outage event j; andDkj is the duration in hours of load curtailment at bus k during outage event j.

2.3.2. System Indices.

Bulk power supply disturbances

=∑

k

∑

j

Fj

Bulk power interruption index

=∑

k

∑

j

LkjFj/Ls (MW/MW-Year)

Bulk power energy curtailment index (severity index)

=∑

k

∑

j

60 ∗ LkjDkjFj/Ls (system minutes)

where Ls is the total system load.

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3. Reliability Assessment Study Results

Reliability studies were conducted using the RBTS [5], which has 6 buses, 9 trans-mission lines and 11 generating units, and the IEEE-RTS [6], which has 24 buses,38 lines/transformers and 32 generating units. The bus, line and generator data aregiven in [5, 6]. The single line diagrams for the RBTS and IEEE-RTS are shown inFigures 4 and 5, respectively.

A seven-step load model based on the IEEE-RTS load duration curve was usedin these studies to calculate the annual reliability indices of both the RBTS andthe IEEE-RTS. The model is shown in Table 1.

A number of studies have been conducted to evaluate the impact of UPFCdevices on the composite system reliability. In these studies, the UPFC devicewas assumed to provide the ability to double the related transmission line loadcarrying capability. The failure rate and repair time of the UPFC were assumed tobe 0.02 f/yr and 60 hours, respectively [3].

In the first series of studies, the transmission lines 1 and 6 in the RBTS andthe transmission lines 25 and 26 in the IEEE-RTS were replaced by two UPFCtransmission links. Tables 2–5 show the load point and system indices for theoriginal and modified systems

Tables 2 and 3 show that the system reliability is only slightly improved afteradding the UPFC to the RBTS. In the case of the IEEE-RTS (Tables 4 and 5), thereplacement of a particular double circuit AC transmission line by FACTS systemshas virtually no effect on the system reliability indices. This is basically due tothe fact that both the RBTS and the IEEE-RTS have strong transmission systemscompared with generating capacity and load demand. Further improvement in thetransmission system does not provide much benefit in terms of the overall systemreliability indices.

Another RBTS study was conducted involving system load growth. The gen-erating capacity and the system peak load in the RBTS were modified by a simplemultiplication factor ranging from 1.0 to 1.5. These modified values were usedto calculate the corresponding reliability indices for the RBTS and the modified

Figure 4. Single line diagram of the RBTS.

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Figure 5. Single line diagram of the IEEE-RTS.

RBTS, in which transmission lines 1 and 6 were replaced by UPFC transmissionunits. The corresponding reliability indices were determined as a function of thegenerating capacity and the system peak load.

Figure 6 shows the variation in the system expected energy not supplied indexwith generation capacity and load demand. The system expected energy not sup-plied (EENS) index increases, as the generating capacity and load demand increase,and the transmission system becomes more heavily utilized. The probabilities ofhaving difficulties in transferring the required energy from the generating stationsto the load points increase as the demand increases. It can be seen from Figure 6that the addition of the FACTS devices considerably improves the system relia-bility at the higher load levels. The study conducted show that this improvementbecomes increasingly significant as the transmission loading conditions increase.This is due to the fact that the major objective in applying FACTS devices is tostrengthen the transmission network. If the transmission system is quite adequate,then FACTS devices should not be installed, since the outcome will be very limited.

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Table 1Seven-step load model data for the IEEE-RTS

Load (p.u.) Probability Duration (hr)

1.0 0.01316392 115.00.9 0.11103478 970.00.8 0.16540752 1445.00.7 0.23202837 2027.00.6 0.22630489 1883.00.5 0.22630489 1977.00.4 0.03651559 379.0

Table 2System indices for the RBTS

System indices Original UPFC

Bulk power supply disturbances 1.083 1.064Bulk power interruption index 0.0839 0.0826Severity index (system minutes) 42.837 42.449

Table 3Load point indices for the RBTS

Expected energyProbability of failure not supplied

Busno. Original UPFC Original UPFC

2 0.000387 0.000388 3.5056 3.51003 0.000459 0.000445 23.1740 22.63274 0.000449 0.000438 10.2521 9.64875 0.000448 0.000445 4.8567 4.88886 0.001151 0.001147 90.2931 90.2047

Table 4System indices for the IEEE-RTS

System indices Original UPFC

Bulk power supply disturbances 1.5310 1.5310Bulk power interruption index 0.0689 0.0689Severity index (system minutes) 56.439 56.439

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Table 5Load point indices for the IEEE-RTS

Expected energyProbability of failure not supplied (MW)

Busno. Original UPFC Original UPFC

1 0.00233362 0.00233362 101.578 101.5782 0.00233362 0.00233362 91.232 91.2323 0.00233363 0.00233363 169.296 169.2964 0.00233371 0.00233371 69.628 69.6285 0.00233370 0.00233369 66.800 66.8006 0.00233391 0.00233390 128.122 128.1227 0.00233260 0.00233260 117.533 117.5338 0.00233365 0.00233365 160.832 160.8329 0.00233364 0.00233364 164.593 164.59310 0.00233364 0.00233364 183.404 183.40413 0.00233362 0.00233362 249.241 249.24114 0.00233373 0.00233373 182.560 182.56015 0.00233363 0.00233362 298.149 298.14916 0.00233362 0.00233362 94.053 94.05318 0.00233362 0.00233362 313.197 313.19719 0.00233364 0.00233364 170.237 170.23720 0.00233364 0.00233364 120.388 120.388

Figure 6. System EENS as a function of generating capacity and load demand—RBTS.

As an alternative to building new transmission lines, FACTS devices can be used tomeet system growth. This may be a good approach to reduce environment impactsand financial costs while increasing system reliability. It should be noted, however,that the reliability benefits obtained by using FACTS devices are accompanied byadditional system costs such as equipment, installation, maintenance and operatingcosts. The actual benefit, therefore, should be analyzed in terms of both adequacyand costs. Related economic analyses were not considered in this article.

The third study examines the impact of the location of the UPFC devices inthe RBTS. The installation locations of FACTS devices are important parameters

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Adequacy Assessment with FACTS Devices 1147

Figure 7. System EENS as a function of the FACTS installation location—RBTS.

that influence the impacts of FACTS devices on composite system reliability. Thesystem reliability may be significantly improved by installing FACTS devices atcertain locations while other installations may have minimum effect. In order toillustrate this condition, a UPFC device was individually installed at every possiblelocation in the RBTS. It was assumed in this study that the system generatingcapacity and peak load are increased to 150% of their base values.

Figure 7 compares the system expected energy not supplied index for UPFCinstalled at the different locations in the RBTS. It can be seen that only those in-stalled on transmission lines 1, 6, 2, or 7 significantly improve the system reliability,while other installations have minimal effects.

It can been seen from Figure 4 that transmission lines 1, 6, 2, and 7 are themajor links between the generation stations (Bus No. 1 and 2) and the load centers(Bus No. 3, 4, 5, and 6). The application of FACTS devices in these locations ismuch more effective than applying them in the other lines.

The fourth study illustrates the impact of FACTS device capacity on systemreliability indices. As noted in the previous studies, the presence of FACTS devicescan enhance the reliability of a composite power system. The capacity of the FACTSdevices is an important parameter and dictates the ability of the FACTS device toenhance the load carrying capability of the corresponding transmission unit.

Two UPFC were applied to transmission lines 1 and 6 in the modified RBTS(generation capacity and load demand at 150% of their base values). The UPFCcapacity was varied from 100 MW to 180 MW. The results are shown in Figure 8.

Figure 8 shows the system expected energy not supplied index as a function ofthe FACTS capacity. The relationship between the FACTS capacity and the systemexpected energy not supplied index is not linear. The system risk decreases withincrease in the capacity additions. It can be seen, however, from Figure 8 that theincremental benefit in the system expected energy not supplied index with FACTSdevice investment becomes relatively small after a certain point. This is due tothe load carrying capability limitations of other transmission links in the system.It is therefore impractical to try to improve the reliability of a composite powersystem only by increasing the FACTS capacity of a few transmission units withoutconsidering the whole network. Studies such as this can be used to help optimizeFACTS investment in a system.

It should be noted that it is almost impossible to determine the optimumFACTS capability for composite power systems in general, since there are too many

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Figure 8. System EENS as a function of the FACTS capacity—RBTS.

Figure 9. System EENS as a function of FACTS device failure rate.

factors involved in the evaluation of reliability benefits due to the FACTS devicesinstallations. These factors include the installed generating capacity, the systempeak load and load factor, the generating capacity and load demand distributionand the network connection topology. It is, therefore, impossible to predeterminean optimum FACTS device capacity level.

The last study illustrates the impacts of FACTS forced unavailability rateon the RBTS adequacy. The failure rate of each UPFC device was varied from0.01 to 10 occurrences/year. Transmission lines 1 and 6 were replaced by UPFCtransmission units (system generation capacity and peak load at 150% of their basevalues).

It can be seen from Figure 9 that the system reliability decreases with increasein the forced unavailability of FACTS devices. FACTS devices are normally morereliable than conventional generation and transmission units. The results found inthis research show that the system reliability is relatively constant over a widerange of variation in the failure rate of FACTS devices. At the present time, thereis relatively little actual data available on the long term performance of FACTSdevices. They are expected to be highly reliable, but this will have to be supportedby operating data and experience.

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Adequacy Assessment with FACTS Devices 1149

4. Conclusions

The utilization of FACTS devices to enhance transmission system capability is in-creasing due to their technical and economic advantages [9]. This article illustratesa method to incorporate FACTS devices in composite electric power system reliabil-ity evaluation. The proposed method has been used to conduct a series of studies ontwo widely used reliability test systems; the Roy Billinton test system (RBTS) andthe IEEE reliability test system (IEEE-RTS). The study results show that undersome circumstances, the installation of FACTS devices has considerable positiveimpact on overall system reliability. This ability is dependant on the transmissionsystem loading conditions and the locations where the FACTS devices are installed.The models, techniques, and the results presented in this article should prove use-ful to electric power utilities planning and operating transmission facilities usingFACTS technologies.

References

[1] D. Ahluwalia, “Adequacy assessment of composite power systems with HVDC links,”Master’s thesis, University of Saskatchewan, November 1990.

[2] R. Billinton and A. Sankarakrishnan, “Adequency assessment of composite powersystems with HVDC links using Monte Carlo simulation,” IEEE Trans. on PWRS,vol. 9, no. 3, pp. 1626–1633, 1994.

[3] R. Billinton, M. Fotuhi-Firuzabad, S. O. Faried, and S. Aboreshaid, “Impact of unifiedpower flow controllers on power system reliability,” IEEE Trans. on PWRS, vol. 15,no. 15, pp. 410–415, 2000.

[4] R. Billinton and Y. Cui, “Reliability evaluation of composite electric power systemsincorporating FACTS,” IEEE CCECE02 Proceedings, vol. 1, pp. 1–6, 2002.

[5] R. Billinton, S. Kumar, N. Chowdhury, K. Chu, K. Debnath, L. Goel, E. Khan,P. Kos, G. Nourbakhsh, and J. Oteng-Adjei, “A reliability test system for educationpurposes—Basic data,” IEEE Trans. on PWRS, vol. 4, no. 3, pp. 1238–1244, 1989.

[6] IEEE Probability Methods Subcommittee, “IEEE reliability test system,” IEEE Trans.,vol. PAS-98, no. 6, pp. 2047–2054, 1979.

[7] R. Billinton and R. N. Allan, Reliability Evaluation of Electric Power System, 2nd edi-tion, New York: Plenum Press, 1996.

[8] R. Billinton and W. Li, Reliability Assessment of Electrical Power Systems Using MonteCarlo Methods, New York: Plenum Publishing, 1994.

[9] N. G. Hingorani and L. Gyugyi, Understanding FACTS, New York: IEEE Press, 1999.

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