Voltage Stability of Converter-Interfaced Energy Storage Systems⁎

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IFAC PapersOnLine 52-4 (2019) 222–227

Voltage Stability of Converter-Interfaced Voltage Voltage Stability Stability of of Converter-Interfaced Converter-Interfaced Storage Systems  Voltage Energy Stability of Converter-Interfaced Energy Storage Energy Storage Systems Systems  Energy Storage Systems∗ ∗ ´

Alvaro Ortega ´ Federico Milano Milano ∗ Alvaro Ortega ∗∗ Federico ´ Alvaro Ortega ∗ Federico Milano ∗∗ ´ Alvaro Ortega Federico Milano ∗ of Electrical & Electronic Engineering ∗ School ∗ School of Electrical & Electronic Engineering School of Electrical & Electronic Engineering University College Dublin, ∗ University College Dublin, Ireland Ireland School of Electrical & Electronic Engineering University College Dublin, Ireland (e-mails: [email protected]; [email protected].) (e-mails: [email protected]; University College Dublin,[email protected].) Ireland (e-mails: [email protected]; [email protected].) (e-mails: [email protected]; [email protected].) Abstract: Abstract: This This paper paper discusses discusses the the contribution contribution of of converter-interfaced converter-interfaced energy energy storage storage devices devices Abstract: Thisstability paper discusses the contribution ofTo converter-interfaced energy storage devices to the voltage in transmission systems. this aim, the paper presents static and to the voltage stability in transmission systems.ofTo this aim, the paper presents static and Abstract: This paper discusses the contribution converter-interfaced energy storage to the voltage stability in transmission systems. To this aim, the paper presents static and dynamic voltage voltage stability stability analyses analyses based based on on aa modified modified version version of of the the well-known well-known WSCC WSCCdevices 9-bus, dynamic 9-bus, to the voltage stability in transmission systems. To this aim, the paper presents static and dynamic voltage stability analyses based on a modified version of the well-known WSCC 9-bus, 3-machine test system. Results of the analyses, which have been compared with those of the 3-machine test system. Results of based the analyses, which version have been compared withWSCC those of the dynamic voltage stability analyses on a modified of the well-known 9-bus, 3-machine test system. Results of the analyses, which have been compared with those of the more common Static Synchronous Compensator (STATCOM) devices, indicate that convertermore common Static Synchronous Compensator (STATCOM) devices, indicate that converter3-machine test Static system. Results ofwill theplay analyses, which have been compared with those ofwith the more common Synchronous Compensator (STATCOM) devices, indicate that converterinterfaced energy storage systems a crucial role in the voltage stability of systems interfaced energy storage systems will play a crucial role in the devices, voltage stability systems with more common Static Synchronous Compensator (STATCOM) indicate of that converterinterfaced energy storage systems will play a crucial role in the voltage stability of systems with high penetration of renewable energy sources. high penetration renewable energy interfaced energy of storage systems will sources. play a crucial role in the voltage stability of systems with high penetration of renewable energy sources. high penetration of renewable energyof sources. © 2019, IFAC (International Federation Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Keywords: Voltage Voltage stability, stability, converter-interfaced converter-interfaced energy energy storage storage system system (CI-ESS), (CI-ESS), static static Keywords: Voltage stability, converter-interfaced energy storage static synchronous compensator (STATCOM), renewable energy sourcesystem (RES),(CI-ESS), Hopf bifurcation. bifurcation. synchronous compensator (STATCOM), renewable energy source (RES), Hopf Keywords: Voltage stability, converter-interfaced energy storage system (CI-ESS), static synchronous compensator (STATCOM), renewable energy source (RES), Hopf bifurcation. synchronous compensator (STATCOM), renewable energy source (RES), Hopf bifurcation. 1. INTRODUCTION areas areas of of the the system system that that may may provoke provoke undesired undesired tripping tripping 1. 1. INTRODUCTION INTRODUCTION areas of the system that may provoke tripping of some components [Kondragunta and WSCC of some components [Kondragunta and undesired WSCC Reliability Reliability 1. INTRODUCTION areas of the system that may provoke undesired tripping of some components [Kondragunta and WSCC Reliability Subcommittee (1994)]. 1.1 Motivation Subcommittee (1994)]. 1.1 Motivation of some components [Kondragunta and WSCC Reliability 1.1 Motivation Subcommittee (1994)]. Studies An effective and and widely widely implemented implemented solution solution to to overover- Subcommittee (1994)]. the 1.1 Motivation Studies that that discuss discuss the contribution contribution of of STATCOMs STATCOMs An effective An widelyis implemented solution over- Studies that discussand theshort-term contribution of STATCOMs to either long-term voltage stability comeeffective voltage and instability the installation installation of local localtosources sources to either long-term and short-term voltage stability of of come voltage instability is the of Studies that discuss the contribution of STATCOMs An effective and widely implemented solution to overcome voltagepower instability is the installation ofnetwork. local sources to either long-term and short-term voltage stability of power systems with high shares of RESs abound in of reactive distributed over the The power systems with high shares of RESs abound in of reactive power distributed over the network. The to either long-term short-term stability of come voltagepower instability is the installation local sources systems withand high shares ofvoltage RESs abound in of reactive distributed over the ofnetwork. The power the literature [Kolluri (2002); Kawabe and Yokoyama Voltage-Sourced Converter (VSC) included in Converterthe literature [Kolluri (2002); Kawabe and abound Yokoyama Voltage-Sourced Converter (VSC) included in Converterpower systems with high shares of RESs in of reactive power distributed over the network. The Voltage-Sourced Converter (VSC) included in Converterthe literature [Kolluri (2002); Kawabe and Yokoyama Ca˜ n et Arabi and (1996); Interfaced Energy Energy Storage Storage Systems Systems (CI-ESSs) (CI-ESSs) can can concon- (2013); (2013); Ca˜ nizares izares et al. al. (1999); (1999); and Kundur Kundur (1996); Interfaced literature [Kolluri (2002);Arabi Kawabe and Yokoyama Voltage-Sourced Converter included in ConverterInterfaced Energy Storage (VSC) Systems (CI-ESSs) can con- the (2013); Ca˜ nizares et al. (1999); Arabi and Kundur (1996); Ca˜ n izares (2000)]. tribute to the the enhancement of the voltage voltage stability margin Ca˜ n izares (2000)]. tribute to enhancement of the stability margin (2013); Ca˜ n izares et al. (1999); Arabi and Kundur (1996); Interfaced Energy Storage Systems (CI-ESSs) can contribute to the enhancement of the voltage stability margin Ca˜ nizares (2000)]. of the system in a similar way as Flexible AC Transmisof the system in a similar way as Flexible AC TransmisCa˜ n izares (2000)]. tribute to the enhancement of the voltage stability margin of theSystems system (FACTS) in a similar wayasasSTATCOMs. Flexible AC The Transmission such paper 1.3 1.3 Contributions Contributions sion (FACTS) such paper of theSystems system in astatement. similar wayas Flexible AC The Transmission Systems (FACTS) such asasSTATCOMs. STATCOMs. The paper 1.3 Contributions elaborates on this elaborates on this statement. To the best 1.3 Contributions sion Systems (FACTS) such as STATCOMs. The paper To the best of of the the authors’ authors’ knowledge, knowledge, aa study study that that gathers gathers elaborates on this statement. To the best of the authors’ knowledge, a the study that gathers and discusses all relevant aspects of corresponding elaborates on this statement. and discusses all relevant aspects of the corresponding 1.2 Literature Review To the best ofofthe authors’ study thatnot gathers and discusses relevant ofa the corresponding 1.2 contribution CI-ESSs in knowledge, single document document has been contribution of all CI-ESSs in aaaspects single has not been 1.2 Literature Literature Review Review and discusses all relevant aspects of the corresponding contribution of CI-ESSs in a single document has not been presented yet. This paper aims to fill this gap, and provides Voltage instability is mostly a consequence of the weakness 1.2 Literature Review yet. This paper aims to fill this gap, and provides Voltage instability is mostly a consequence of the weakness presented contribution ofThis CI-ESSs inaims a single document has not been presented yet. paper to fill this gap, and provides Voltage instability is mostly a shortage consequence of the weakness static and dynamic analyses of the voltage stability of of the network and/or the of reactive power static andyet. dynamic analyses of fill thethis voltage stability of of the network and/or the shortage of reactive power presented This paper aims to gap, and provides Voltage instability is mostly a consequence of the weakness static and dynamic analyses of the voltage stability of of the network and/or the shortage of reactive power transmission systems with inclusion of CI-ESSs and high sources, rather than a specific contingency. This allows transmission systems with inclusion of CI-ESSs and high sources, rather than a specific contingency. This allows static and dynamic analyses of the voltage stability of of the network and/or the shortage of reactive power transmission systems with inclusion of CI-ESSs and high sources, rather than a specific contingency. This allows RES penetration. penetration. using static-analysis static-analysis techniques, techniques, or or dynamic dynamic simulations simulations RES using transmission systems with inclusion of CI-ESSs and high sources, rather than a specific contingency. This allows using static-analysis techniques, dynamic that span span several minutes minutes and that thatorcan can simulatesimulations cascading RES penetration. that several and simulate cascading The also penetration. usingspan static-analysis techniques, dynamic simulations The paper paper also compares compares the the impact impact of of CI-ESSs CI-ESSs on on the the that several minutes and thator can simulate cascading events. These studies are referred to as long-term voltage RES The paper also stability compares thethat impact of CI-ESSsdevices. on the events. These studies are referred to as long-term voltage system voltage with of STATCOM that span several minutes and that can simulate cascading system voltage stability with that of STATCOM devices. events. These studies are referred to as long-term voltage stability [IEEE/CIGRE Joint Task Force on Stability The paper also compares the impact of CI-ESSs on the voltage stability with that of STATCOM stability [IEEE/CIGRE Joint Task on Studies show saturation of quantities of events. and These studies are referred to asForce long-term voltage system Studies show that that saturation of certain certain quantitiesdevices. of the the stability [IEEE/CIGRE Joint Task Force on Stability Stability Terms Definitions (2004)]. system voltage stability with that of STATCOM devices. Studies showlead thatto saturation ofof certain quantities ofsome the Terms Definitions can some kinds instabilities or, in stabilityand [IEEE/CIGRE Joint Task Force on Stability CI-ESS CI-ESS can lead to some kinds of instabilities or, in some Terms and Definitions (2004)]. (2004)]. Studies showcompromise thattosaturation ofofcertain quantities ofsome the CI-ESS can lead some kinds instabilities or, in other cases, the overall response of the system Less commonly, another type of voltage instability may Terms and Definitions (2004)]. other cases, compromise the overall response of or, theinsystem Less commonly, another type of voltage instability may CI-ESS can lead to some kinds of instabilities some other cases, compromise the overall response of the system Less commonly, another type of voltage instability may [Xin et al. (2016); Ortega and Milano (2015)]. also occur occur in in the few few seconds after after aa large large disturbance disturbance [Xin et al. (2016); Ortega and Milano (2015)]. also compromise overall response of the system Less occur commonly, another typeif of voltage instability may other [Xin etcases, al. (2016); Ortegathe and Milano (2015)]. also in the the few seconds seconds after a large disturbance such as a short short circuit. Even no voltage collapse occurs such as a circuit. Even if no voltage collapse occurs [Xin et al. (2016); Ortega and Milano (2015)]. also occur in the few seconds after a large disturbance such as a short circuit. Even if no voltage collapsevoltage occurs 1.4 Organization as aa consequence consequence of the the disturbance, poor dynamic Organization as of poor voltage such as a short circuit. Even if no voltage collapse occurs 1.4 1.4 Organization as a consequence of thetodisturbance, disturbance, poor dynamic dynamic voltage performance can lead voltage oscillations in the weaker performance can lead to voltage oscillations in the weaker The paper 1.4 as a consequence thetodisturbance, poor dynamic paper is is organised organised as as follows. follows. Section Section 22 briefly briefly dedeperformance can of lead voltage oscillations in the voltage weaker The Organization  The paper isdifferent organised as follows. Section 2 briefly deThis material materialcan is based based upon works oscillations funded by by European European Union’s  scribes the kinds of voltage stability analysis performance lead to voltage in the weaker This is upon works funded Union’s scribes the different kinds of voltage stability analysis  The paper is organised as follows. Section 2 briefly deHorizon 2020 research and innovation programme under grant agreeThis material is based upon works funded by European Union’s scribes the different kinds of voltage stability analysis of transmission transmission systems systems proposed proposed in in [IEEE/CIGRE [IEEE/CIGRE Joint Joint Horizon 2020 research and innovation programme under grant agree of This material isF.based works funded byScience European Union’s scribes the on different kinds of voltage stability analysis Horizon 2020 research andupon innovation programme under grant agreement No. 727481. Milano is also also funded by the the Foundation of transmission systems proposed in [IEEE/CIGRE Joint Task Force Stability Terms and Definitions (2004)]. ment No. 727481. F. Milano is funded by Science Foundation Task Force on systems Stabilityproposed Terms and Definitions (2004)]. Horizon research and innovation programme under grant agreeIreland, under grant No. ment No.2020 727481. F. Milano is also funded by the Science Foundation of transmission in [IEEE/CIGRE Joint Task Force on Stability Termsof and Definitions and (2004)]. Ireland, under grant No. SFI/15/IA/3074. SFI/15/IA/3074. Section 33 provides the models the STATCOM the mentopinions, No.under 727481. F. Milano is also funded by the Science Foundation Section provides the models of the STATCOM and the The findings, conclusions and recommendations expressed Ireland, grant No. SFI/15/IA/3074. Task Force on Stability Terms and Definitions (2004)]. The opinions, findings, conclusions and recommendations expressed Section 3 provides the models of the STATCOM and the CI-ESS, as well as their controllers, considered in this Ireland, under grant No. SFI/15/IA/3074. CI-ESS, as well as their controllers, considered in this in this work are those of the authors and do not necessarily reflect The opinions, findings, conclusions and recommendations expressed Section 3 provides the models of the STATCOM and the in this work are those of the authors and do not necessarily reflect CI-ESS, as well as their controllers, considered in this paper. A A case case study study based based on on the the well-known well-known WSCC WSCC 9-bus, 9-bus, The opinions, findings, conclusions and recommendations expressed the views of the European or Science Foundation Ireland. in work of theUnion authors do not necessarily reflect paper. CI-ESS, asbenchmark well as based their controllers, considered in9-bus, this thethis views of are thethose European Union orand Science Foundation Ireland. paper. A case study on the well-known WSCC 3-machine system is presented in Section 4. in this work are those of the authors and do not necessarily reflect The European Commission Science Foundation Ireland are the of the European and Union or Science Foundation 3-machine benchmark system presented WSCC in Section 4. The views European Commission and Science Foundation Ireland Ireland. are not not paper. ASection case study based on theis well-known 9-bus, 3-machine benchmark system is presented in Section 4. the views offorthe European Union ormade Science Foundation Ireland. Finally, 5 draws conclusions, and outlines future responsible any use that may be of the information that The European Commission and Science Foundation Ireland are not Finally, Section 5 draws conclusions, and outlines future responsible for any use that may be made of the information that 3-machine benchmark system is presented in Section 4. The European Foundation Ireland arethat not Finally, Section 5 draws conclusions, and outlines future this work contains. work directions. responsible for Commission any use thatand mayScience be made of the information this work contains. work directions. Finally, Section 5 draws conclusions, and outlines future responsible for any use that may be made of the information that this work contains. work directions. this work contains. work directions. 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Copyright © 2019 245 Copyright 2019 IFAC IFAC 245 Control. Peer review© under responsibility of International Federation of Automatic Copyright © 2019 IFAC 245 10.1016/j.ifacol.2019.08.187 Copyright © 2019 IFAC 245

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2. VOLTAGE STABILITY ANALYSIS OF TRANSMISSION SYSTEMS A common approach to study the long-term voltage stability of a system is by means of static analysis by observing the active power vs. voltage characteristics (often called pv curves, or informally, nose curves due to their characteristic shape) [Western Power Reserve Work Group (RRWG) (1998)]. pv curves are generated by plotting the power flow solutions of the network for different loading levels, which is used to parametrically increase all load powers with respect to the system base-case conditions. Another long-term, small-signal voltage stability approach implies the use of dynamic models of power system devices and controllers. This method, used for example in modal analysis, implies the study of the eigenvalues of the Jacobian matrix of the system, or a reduced version of such a matrix that considers only the equations of the bus active and reactive power injections [Gao et al. (1992); Chakravorty and Patra (2016)]. The fast response of STATCOMs and CI-ESSs has been proven to greatly improve the dynamic voltage performance and, consequently, the short-term voltage stability of the grid [Kolluri (2002); Kawabe and Yokoyama (2013)]. The capability of CI-ESSs to effectively flatten voltage oscillations due to disturbances such as wind perturbations, and reduce the voltage drops due to line outages and short circuits, is studied through time domain simulations.

connection of a STATCOM device and a CI-ESS to the main grid is the same, and is based on the VSC, whose scheme coupled to the VSC inner current-control loop is shown in Fig. 2 [Yazdani and Iravani (2010); Chaudhuri et al. (2014)]. Inner Current-Control Loop ref iac,d

+

−

KI (s)

The general configuration in the dq-reference frame of the two converter-interfaced devices discussed in this paper is presented in Fig. 1 [Ortega and Milano (2016)]. The

Converter vac,d

vac,d

+ +

md vt,d − 2 vdc

Lac

vdc 2

ωac

mq

+

−

vt,q

−

ωac Laciac,d ref iac,q

+

KI (s)

Lac

+ + +

−

iac,d

1 Rac +sLac

−

+ +

ωacLaciac,q

vac,q

iac,q

1 Rac +sLac

vac,q

Fig. 2. Block diagram of the VSC inner current-control and converter in the dq frame. ref The reference dq currents, iref ac,d and iac,q , are imposed by the decoupled outer voltage-control loop depicted in Fig. 3.

PI control LPF1 vdc

Kmdc

− + ref vdc

1 + sTmdc

Kmac 1 + sTmac

+

ref iac,q

xq +

Ki,q s

ref,min iac,q

Lead compensator

LPF2 vac

ref,max iac,q

Kp,q

vmdc

3. VOLTAGE CONTROL OF CONVERTERINTERFACED REACTIVE POWER SOURCES This section presents the scheme of the voltage control of CI-ESSs and STATCOM devices, as well as of the main device responsible of providing such a control, namely the Voltage Sourced Converter (VSC).

223

vmac − + vacref

xd

Kp,d Kd,d + sT2,d

ref,max iac,d ref iac,d

1 + sT1,d ref,min iac,d

Fig. 3. Outer DC- and AC-voltage controllers of the VSC. 4. CASE STUDY

PCC

vac

LPF2

Grid y

Figure 4 shows a modified version of the well-known WSCC 9-bus, 3-machine test system originally presented in [Sauer and Pai (1998)].

vmac − + ref vac

iac,abc

9

md +

VSC Control

VSC mq

− y ref

− +

vdc

vmdc LPF1 −

3 ref vdc +

S

8

W 6

idc Storage Control

u

Storage Device

G

G

2 uref

1

7

Fig. 1. Overall scheme of a converter-interfaced reactive power source connected to the AC grid. Light gray: STATCOM. Dark gray: CI-ESS. 246

5

4

Fig. 4. Modified WSCC 9-bus, 3-machine system.

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Since the original WSCC system is fairly symmetrical, some modifications to the base-case data are introduced with the aim of creating a weak area, i.e., the bus where the wind turbine is installed and neighbouring buses. The modifications are as follows. • The power base of the system has been reduced by 3 times, i.e., sn = 33.3 MVA. • The√voltage of all transmission lines has been reduced by 3 times. • The synchronous machine at bus 3 has been replaced by a wind power plant of the same capacity. The wind power plant is modelled as an aggregation of 18 fifthorder doubly-fed induction generators with optimal cubic MPPT approximation, first-order primary voltage regulation and static turbine governor. • In time domain simulations, the wind follows a stochastic, exponentially autocorrelated Weibull-distributed process modelled as a set of stochastic differential equations [Z´ arate Mi˜ nano and Milano (2016)]. • Consistently with time scales and conventional assumptions, loads are modelled as constant PQ for the continuation power flow analysis and as constant impedances for time domain simulations. • The voltage at the synchronous machine buses is reduced by 2% with respect to the base case. • The system includes a secondary frequency controller (AGC) with gain Ko = 2. • When considered, the CI-ESS and the STATCOM device are connected to bus 8 through a 133/21 kV transformer. • The CI-ESS is a Battery Energy Storage (BES) modelled using the well-known Sheperd’s model [Shepherd (1965); Ortega and Milano (2016)]. • The active power rating of the BES is 3.2 MW. • The CI-ESS active power control is designed to regulate the frequency at the point of common coupling (PCC) with the grid, i.e., the frequency at bus 8. The frequency is estimated by means of a phase-locked loop (PLL) device [Cole (2010)]. Two main scenarios are considered. First, Subsection 4.1 discusses the long-term voltage stability of the WSCC system using both static and dynamic models of the power system devices and controllers. Then, the shortterm voltage stability of the dynamic model of the WSCC system is studied through time domain simulations in Subsection 4.2. All simulations included in the paper are obtained using the Python-based software tool Dome [Milano (2013)]. The Dome version utilised is based on Ubuntu Linux 18.04, Python 3.6.7, cvxopt 1.2.2, klu 1.3.8, and magma 2.2.0.

247

1

0.8 0.6 0.4

No STATCOM With STATCOM

0.2 1 1.5 2 2.5 3 3.5 4 psys/pbc

vbus 6 [pu(kV)]

1

0.8 0.6 0.4

No STATCOM With STATCOM

0.2 1 1.5 2 2.5 3 3.5 4 psys/pbc

(a) Load at bus 5

(b) Load at bus 6

1 vbus 8 [pu(kV)]

The WSCC 9-bus system is often utilized for transient and frequency stability analysis. While focusing on voltage stability, this network is considered in this case study, as the main transient effect of the BES is its ability to exchange active power with the grid. As any other network, however, the WSCC 9-bus system shows a maximum loading condition and, consequently, can face voltage collapse. This network is thus as good as any other system to carry out voltage stability analysis.

vbus 5 [pu(kV)]

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0.8 0.6 0.4

No STATCOM With STATCOM

0.2 1 1.5 2 2.5 3 3.5 4 psys/pbc

(c) Load at bus 8 Fig. 5. pv curves at the load buses of the modified WSCC 9-bus system with and without a STATCOM. The xaxis represents the ratio between the loading level of the system, psys , and the base-case condition, pbc . 4.1 Long-Term Voltage Stability The pv curves of the three loads of the modified WSCC system of Fig. 4 with and without a 20 MVAr STATCOM at bus 8 are shown in Fig. 5. Reactive power limits of the generators are of ±42 and ±55 MVAr for the synchronous machines at buses 1 and 2, respectively, and of ±10 MVAr for the wind power plant at bus 3. In steady state, the active power output of a CI-ESS is null, as generation and demand are balanced. Therefore, the static models of a STATCOM device and a CI-ESS coincide. In particular, the STATCOM is modelled as a constant active power, with pac = 0, and constant voltage if the reactive power is within the limits, and as a constant active and reactive power with pac = 0 and qac = ±20 MVAr, otherwise.

Figure 5 shows that the STATCOM allows increasing the loading level of the system up to 3.7 times the base-case conditions, as opposed to maximum ratio of 3.47 of the case without STATCOM, i.e., a 6.56% relative increase. The STATCOM also maintains the voltage of the load at the PCC (i.e., bus 8) almost at a constant value up to near the point of collapse.

The impact of the STATCOM on the voltage stability is more relevant in the event of the outage of one of the transmission lines, as represented in Fig. 6, where the pv curves are computed considering that the line connecting buses 4 and 5 has been disconnected. After the line outage, the maximum ratio psys /pbc decreases to 2.64 and 2.86 without and with the STATCOM, respectively, i.e., a 8.24% relative increase. The outage of the line implies approximately a 24% reduction with respect to the fully connected system. Similar conclusions can be drawn considering voltage-dependent load models.

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0.6

0.2 1

No STATCOM With STATCOM

1.5

2

2.5

psys/pbc

0.6 0.4 0.2 1

3

1.5

2 2.5 psys/pbc

−5 −0.2

3

(b) Load at bus 6

−0.1 Re

0

(a) WSCC system with BES. psys /pbc = 1.673

0

−5 −0.2

−0.1 Re

0

(b) WSCC system with BES. psys /pbc = 2.5

5

0.8 0.6 0.4

No STATCOM With STATCOM

1.5

2 2.5 psys/pbc

3

Fig. 6. pv curves at the three load buses of the modified WSCC system with and without a STATCOM. The line between buses 4 and 5 is disconnected. 5

Im

5

0

−0.1 Re

0

−0.1 Re

0

(c) WSCC system with STATCOM. psys /pbc = 2.5 Fig. 8. Eigenvalue loci of the rightmost eigenvalues of the WSCC system with a BES and a STATCOM. Dashdot lines indicate 5% damping. a BES or a STATCOM device is connected to bus 8. In this case, the reactive power rate of both devices is set to 20 MVAr.

0

−5 −0.2

0

−5 −0.2

(c) Load at bus 8

Im

0

No STATCOM With STATCOM

1

0.2 1

−5 −0.2

5

0.8

(a) Load at bus 5

vbus 8 [pu(kV)]

5

Im

0.4

225

Im

0.8

1

Im

1

vbus 6 [pu(kV)]

vbus 5 [pu(kV)]

2019 IFAC CSGRES Jeju, Korea, June 10-12, 2019

−0.1 Re

0

(a) WSCC system without (b) WSCC system without BES. psys /pbc = 1.0 BES. psys /pbc = 1.673 Fig. 7. Eigenvalue loci of the rightmost eigenvalues of the WSCC system. Dash-dot lines indicate 5% damping. A second long-term, small-signal voltage stability analysis is presented below which considers dynamic models of the power system devices and controllers of the WSCC system. For this study, the increasing loading level of the system is compensated by the two synchronous machines of the system, as it is assumed that no more active and reactive power can be extracted from the wind power plant. Figure 7 shows the rightmost eigenvalues of the WSCC system for two loading levels: (i) the base-case condition, and (ii) 1.673 times pbc . It can be seen that, for psys /pbc ≥ 1.673, a complex pair of eigenvalues, which is related to the states er,q and ve of the synchronous machine at bus 1, crosses the imaginary axis, thus becoming unstable modes. The Hopf bifurcation Seydel (2010) occurring when psys /pbc = 1.673 prevents the operation of the system at higher loading levels which, from the static analysis above, could be up to 3.47. The installation of additional sources of reactive power such as STATCOM and BES devices allows increasing the loading level of the system beyond the critical value of 1.673 times the base-case condition, as these devices shift to the left the pair of eigenvalues that cause the Hopf bifurcation. This is shown in Fig. 8 for the scenarios where 248

In Fig. 8(a), the inclusion of a BES system shifts the eigenvalues that caused the Hopf bifurcation in the system to a value of −0.396 ± j0.924. The 6 rightmost eigenvalues are in this case within the 5% damping thresholds, being the eigenvalue #7, which is related to the rotor speeds of the two synchronous machines, the first one that shows poorly damped behaviour (−0.288 ± j10.59). This result holds even for larger loading levels, as shown in Fig. 8(b) for psys /pbc = 2.5. In this case, the aforementioned poorly damped eigenvalues are −0.249 ± j10.76. The real part of such eigenvalues is still about an order of magnitude larger than the dominant modes of the system. Finally, from the voltage stability point of view, no relevant differences can be observed between installing a BES or a STATCOM device, as observed from comparing Figs. 8(b) and 8(c). This is an expected result due to the similar configuration of the reactive power support of both devices. This result also indicates that the active power support of the BES does not compromise the voltage stability of the overall system for relatively large loading levels. 4.2 Short-Term Voltage Stability This section studies, through time domain simulations, the short-term dynamic response of the modified WSCC system with inclusion of CI-ESSs. Two scenarios are presented to analyse both small- and large-disturbance voltage stabilities. The reactive power rate of the CI-ESS and the STATCOM device used in the comparison is 3.2 MVAr. This value is chosen with the aim of analysing the impact

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Finally, despite the local nature of the voltage control from both devices, their effect can be observed also at the system level, as shown in Fig. 9(b), which includes the trajectories of the voltage at the load bus 6. Such a voltage shows a better profile when a CI-ESS or a STATCOM is included in bus 8. The last scenario presented in this paper studies largedisturbance voltage stability. With this aim, the outage of the line connecting buses 4 and 5 is simulated at t = 1 s, and simulation results are shown in Fig. 10. The wind turbine is assumed to include a low-voltage ridethrough protection that prevents its disconnections after the disturbance. Installing a BES allows reducing the voltage sag by about 30%. Moreover, after the voltage sag, large-amplitude voltage oscillations lasting about 10 s can be observed in the case without additional reactive power support. Such oscillations are remarkably flattened with both the BES and the STATCOM devices. The steady-state value of the voltage at the PCC is also kept at its reference value, as opposed to the base case which shows a slightly lower value in steady state. Similarly to the small-disturbance scenario, the effect of installing a local reactive power source are observed in the overall system, as shown in Fig. 10(b). Finally, Fig. 10(c) shows that the saturation of the current of the outervoltage control of the VSC, while limiting its regulation capability, does not deteriorate the voltage response of the overall system. 5. CONCLUSIONS This paper presents a detailed analysis of the impact of CI-ESSs on the voltage stability of transmission systems with large penetration of RESs. The performance of CIESSs is duly compared with that of more conventional STATCOM devices. Several relevant aspects of voltage stability analysis are studied and discussed, including longterm, steady-state analysis, as well as short-term dynamic 249

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The average value of the voltage varies substantially with respect to the operating condition during the simulation. The inclusion of a CI-ESS or a STATCOM in the system allows reducing to a great extent the voltage oscillations, and keeps the average voltage close to its reference value. While both the CI-ESS and the STATCOM device show similar performance, the ability of the CI-ESS to also provide active power control leads to a more efficient voltage regulation with respect to the STATCOM, as it requires less reactive power support and proved better voltage response (see Fig. 9(c)).

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Small disturbances are modelled as stochastic wind perturbations that follow a Weibull distribution with exponential autocorrelation. The response of the WSCC system following such perturbations is shown in Fig. 9. Figure 9(a) depicts the voltage at bus 8, i.e., the PCC with the CI-ESS or the STATCOM device. Wind perturbations create sustained voltage oscillations which, despite having relatively small magnitude, can deteriorate certain components of the load connected at the bus, and/or compromise their operation.

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(c) Reactive power output of the VSC Fig. 9. Response of the WSCC system following stochastic wind variations. simulations, based on a modified model of the well-known WSCC 9-bus system. Simulation results indicate that the inclusion of fastresponding reactive power support improve every aspect of the voltage stability studied as it: (i) increases the maximum loading level of the system; (ii) improves the small-signal stability for large loading conditions; (iii) reduces voltage oscillations due to perturbations such as those caused by the wind; (iv) maintains the voltage at the bus of connection at its reference value for a variety of disturbances, and (v) reduces the voltage sag resulting from large disturbances such as line outages and faults. Other less intuitive results have also been observed in this paper: (i) CI-ESSs provide more efficient voltage regulation than STATCOM devices thanks to their capability to provide simultaneously active and reactive power support; (ii) the dynamics of the energy storage device and its active power control do not deteriorate the small-signal voltage stability of the system even for large loading levels; (iii) current saturations of the power converter do not appear to compromise the short-term voltage stability of the overall system, at least in the considered scenarios; (iv) the impact of the local voltage support provided by CI-ESSs can be observed at a system level.

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(c) Reactive power output of the VSC Fig. 10. Response of the WSCC system following a line outage. Future work will focus on the study of the stability of CIESSs included in microgrids. Low X/R ratios of microgrids feeder lines imply strong couplings between voltage and frequency. The capability of CI-ESSs to simultaneously regulate the frequency and voltage at the PCC in a very short time frame makes these devices excellent candidates to cope with such couplings. REFERENCES Arabi, S. and Kundur, P. (1996). A versatile FACTS device model for powerflow and stability simulations. IEEE Transactions on Power Systems, 11(4), 1944–1950. Ca˜ nizares, C., Corsi, S., and Pozzi, M. (1999). Modeling and implementation of TCR and VSI based FACTS controllers. Internal report, ENEL and Politecnico di Milano. Ca˜ nizares, C.A. (2000). Power flow and transient stability models of FACTS controllers for voltage and angle stability studies. In 2000 IEEE Power Engineering Society Winter Meeting. Conference Proceedings, volume 2, 1447–1454 vol.2. Chakravorty, M. and Patra, S. (2016). Voltage stability analysis using conventional methods. In 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), 496–501. 250

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