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Optimal Placement and Tuning Approach for Design of Power System Stabilizers and Wide Area Damping Controllers Considering Transport Delay
17th IFAC Workshop on Control Applications of Optimization 17th IFAC Workshop onOctober Control 15-19, Applications Optimization Yekaterinburg, Russia, 2018 of Available at www.sciencedirect.com 17th IFAC Workshop Workshop onOctober Control 15-19, Applications ofonline Optimization 17th IFAC on Control Applications Optimization Yekaterinburg, Russia, 2018 of 17th IFAC Workshop on Control 15-19, Applications of Optimization Yekaterinburg, Yekaterinburg, Russia, Russia, October October 15-19, 2018 2018 Yekaterinburg, Russia, October 15-19, 2018
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IFAC PapersOnLine 51-32 (2018) 534–539
Optimal Optimal Placement Placement and and Tuning Tuning Approach Approach for for Design Design of of Power Power System System Stabilizers Stabilizers Optimaland Placement andDamping Tuning Approach forConsidering Design of Power System Stabilizers Wide Area Controllers Transport Delay Optimaland Placement and Tuning Approach for Design of Power System Stabilizers Wide Area Damping Controllers Considering Transport Delay and Wide Area Damping Controllers Considering Transport Delay and Wide Damping Controllers Transport Delay Yoshiaki.Area Matsukawa*, Masayuki. Watanabe*,Considering Hibiki. Takahashi*, Yasunori. Mitani*
Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Takahashi*, Yasunori. Mitani* Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Takahashi*, Takahashi*, Yasunori. Yasunori. Mitani* Mitani* Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Takahashi*,1-1 Yasunori. Mitani* Institute *Department of Electrical and Electronic Engineering, Kyushu of Technology, Sensui-cho, Tobata-ku, Kitakyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu *Department of Electrical and Electronic Engineering, Kyushu 804-8550, Japan (Tel: +81-93-884-3227; e-mail: p349532y@ mail.kyutech.jp). *Department of Electrical and Electronic Engineering, Kyushu Institute Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu *Department and Engineering, Kyushu ofp349532y@ Technology, 1-1 804-8550, Japan (Tel: +81-93-884-3227; e-mail:of *Department of of Electrical Electrical and Electronic Electronic Engineering, Kyushu Institute Institute Technology,mail.kyutech.jp). 1-1 Sensui-cho, Sensui-cho, Tobata-ku, Tobata-ku, Kitakyushu Kitakyushu 804-8550, Japan (Tel: (Tel: +81-93-884-3227; e-mail:ofp349532y@ p349532y@ mail.kyutech.jp). 804-8550, Japan +81-93-884-3227; e-mail: mail.kyutech.jp). 804-8550, Japan (Tel: +81-93-884-3227; e-mail: p349532y@ mail.kyutech.jp). Abstract: In this paper, a novel optimal placement and parameter tuning approach for Power System Abstract: In this paper, a novel optimal placement and parameter tuning approach for Power System Stabilizer proposed to damp bothplacement local and and inter-area modes in mesh like power system. The Abstract: (PSS) In this thisispaper, paper, novel optimal placement and parameter tuning approach for Power Power System Abstract: In aaa novel optimal parameter tuning approach for System Stabilizer (PSS) is proposed to damp bothplacement local and inter-area modes inΔθ mesh like power system. The Abstract: In this paper, novel optimal and parameter tuning approach for Power System design target is two-level PSS consisting of ΔP type local PSS and type Wide Area Damping Stabilizer (PSS) proposed to damp both local inter-area modes mesh power system. The Stabilizer (PSS) is proposed to damp both local and inter-area modes in mesh like power system. The design target is is two-level PSS consisting of ΔPand type local PSS andin Δθ typelike Wide Area Damping Stabilizer (PSS) is proposed to damp both local and inter-area modes in mesh like power system. The Controller (WADC). For the PSS placement, modeshape with eigenvector sensitivity and coherency design target is two-level PSS consisting of ΔP type local PSS and Δθ type Wide Area Damping design target is two-level PSS consisting of ΔP type local PSS and Δθ type Wide Area Damping Controller (WADC). For the PSS placement, modeshape with eigenvector sensitivity and coherency design target is two-level PSS consisting of ΔP type local PSS and Δθ type Wide Area Damping analysis are(WADC). used to determine the appropriate placement ofwith botheigenvector local PSS sensitivity and WADC. Forcoherency the PSS Controller For the PSS placement, modeshape and Controller For placement, modeshape and coherency analysis are(WADC). used to determine the appropriate placement ofwith botheigenvector local PSS sensitivity and WADC. the PSS Controller (WADC). For the the PSS PSS placement, modeshape with eigenvector sensitivity andFor coherency parameter tuning, metaheuristics based approach via Mean Variance Mapping Optimization (MVMO) is analysis are used to determine the appropriate placement of both local PSS and WADC. For the PSS analysis are used to determine the appropriate both PSS WADC. For the PSS parameter tuning, metaheuristics based approachplacement via Mean of Variance Mapping Optimization (MVMO) is analysis are used to determine the appropriate placement of both local local PSS and and WADC.designs For the PSS employed in order to consider the time domain analysis. The proposed objective function at first parameter tuning, metaheuristics based approach via Mean Variance Mapping Optimization (MVMO) is parameter tuning, approach via Mean Variance Mapping Optimization (MVMO) is employed in ordermetaheuristics to consider thebased time domain analysis. The proposed objective function designs at first parameter tuning, approach via Mean Variance Optimization (MVMO) is the local PSS onlymetaheuristics to improve coefficient and damping ratio Mapping ofobjective eigenvalue. After designs that, it designs employed in order consider damping thebased time domain domain analysis. The proposed objective function designs at first first employed in order to consider the time analysis. The proposed function at the local PSS only to improve damping coefficient and damping ratio of eigenvalue. After that, it designs employed in order to consider the time domain analysis. The proposed objective function designs at first the WADC overlapping with already designed local PSS by time domain analysis, taking into account the local PSS only to improve damping coefficient of eigenvalue. After that, it designs the local only to damping coefficient and damping ratio of After that, it designs the WADC overlapping with already designed localand PSSdamping by time ratio domain analysis, taking into account the the local PSS PSS only to improve improve damping coefficient damping of eigenvalue. eigenvalue. After that, itproposed designs transport delay in the remote signal between Phasor Measurement Unit (PMU) and PSS.into The the WADC WADC overlapping with already already designed localand PSS by time time ratio domain analysis, taking into account the the overlapping with designed local PSS by domain analysis, taking account the transport delay in the remote signal between Phasor Measurement Unit (PMU) and PSS. The proposed the WADC overlapping with already designed local PSS by time domain analysis, taking into account the method isdelay applied in remote IEEE New England 39-Bus (NE 39-bus) system model.and Then, modeshape and transport in the signal between Phasor Measurement Unit (PMU) PSS. The proposed transport delay in the remote signal between Phasor Measurement Unit (PMU) and PSS. The proposed method isdelay applied in remote IEEE New England 39-Bus (NE 39-bus) system model.and Then, modeshape and transport in the signal between Phasor Measurement Unit (PMU) PSS. The proposed coherent grouping analysis give England us understandable system aspect, themodel. local Then, PSS and the WADC method applied in IEEE New 39-Bus (NE 39-bus) system modeshape and method is applied in IEEE 39-Bus (NE 39-bus) system modeshape and coherentis analysis give England us understandable system aspect, themodel. local Then, PSS and the WADC method isgrouping applied in IEEE New New England 39-Bus (NE 39-bus) system model. Then, modeshape and optimized by using MVMO considering the transport delay improve both local and inter-area modes coherent grouping analysis give us understandable system aspect, the local PSS and the WADC coherent grouping analysis give us understandable system aspect, the local PSS and the WADC optimized by using MVMO considering the transport delay improve both local and inter-area modes coherent grouping analysis give us understandable system aspect, the local PSS and the WADC whereas a method ignoring theconsidering transport delay make system poorly damped. optimized by using MVMO the transport delay improve both local and inter-area modes optimized by MVMO the delay improve both whereas a method ignoring theconsidering transport delay make system poorly damped. optimized by using using MVMO considering the transport transport delay improve both local local and and inter-area inter-area modes modes whereas a method ignoring the transport delay make system poorly damped. whereas a method ignoring the transport delay make system poorly damped. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Power ignoring System Stabilizers, Optimization, Transport Modes, whereas a method the transportParameter delay make system poorly damped. Delay, Small Signal Keywords: Power System Stabilizers, Parameter Optimization, Transport Delay, Small Signal Modes, Dynamic Inter-area Oscillations, Phasor Measurement Keywords:Stability, Power Stabilizers, Parameter Optimization, Transport Keywords: Power System System Stabilizers, Parameter Optimization,Unit Transport Delay, Delay, Small Small Signal Signal Modes, Modes, Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit Keywords: Power System Stabilizers, Parameter Optimization, Transport Delay, Small Signal Modes, Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit captured by actual voltage phasor data obtained by PMUs 1. INTRODUCTION captured by actual voltage phasor data obtained by PMUs (Matsukawa et al. (2016)), forphasor example. 1. INTRODUCTION captured by actual voltage data obtained by PMUs captured by actual voltage phasor data (Matsukawa al. (2016)), example. 1. INTRODUCTION captured by et actual voltagefor phasor data obtained obtained by by PMUs PMUs 1. INTRODUCTION (Matsukawa et al. (2016)), for example. For the stable operation of a large scale power system, a 1. INTRODUCTION et al. (2016)), for example. In recent studies, the Wide Area Damping Controller the stable operation of a large scale power system, a (Matsukawa (Matsukawa et al. (2016)), for example. For specific inter-area mode will be critical. Forpower example, a pooraa In recent studies, the Wide Area Damping Controller For the stable operation of aa large scale system, For the stable operation of scale system, (WADC) isstudies, applied the using the Area remoteDamping signal obtained by specific mode will be critical. Forpower example, aHz poor In recent Wide Controller For the inter-area stable operation of a alarge large scale power system, In recent studies, the Wide Area Controller damping inter-area mode with frequency of 0.3-0.5 ina (WADC) is applied using the oscillations. remoteDamping signal obtained by specific inter-area mode will be critical. For example, aa poor In recent studies, the Wide Area Damping Controller specific inter-area mode will be critical. For example, poor PMUs to damp out inter-area Because of the damping inter-area mode with frequency of 0.3-0.5 in (WADC) (WADC) is is applied applied using using the the remote remote signal signal obtained obtained by by specific inter-area mode will beaacan critical. example, aHz poor the Japanese power system be For identified, and the PMUs to is damp out inter-area Because of of the damping inter-area mode with frequency of 0.3-0.5 in (WADC) applied usingreflects the oscillations. remote signal obtained bya damping inter-area mode with aacan frequency of 0.3-0.5 Hz in remote signal dynamically the global information the Japanese power system be identified, andHz the PMUs to damp out inter-area oscillations. Because of the damping inter-area mode with frequency of 0.3-0.5 Hz in PMUs to damp out inter-area oscillations. Because of the instability of thepower inter-area modecan willbe probably be affected by remote signal dynamically reflects theimprove global information of a the Japanese system identified, and the PMUs to damp out inter-area oscillations. Because of the the Japanese power system can be identified, and the power system, it can significantly the inter-area instability of the inter-area mode will probably be affected by remote signal dynamically reflects the global information of aa the Japanese power system can be identified, and the remote signal dynamically reflects the global information of the fact that the inter-tie power flow has been getting heavier power system, it can significantly improve the inter-area instability of the inter-area mode will probably be affected by remote signal dynamically reflects the global information of instability of the inter-area mode will probably be affected by oscillation modeit and thesignificantly design of theimprove WADC has been donea the fact that the inter-tie power flow has been getting heavier power system, can the inter-area instability of the inter-area mode will probably be affected by power system, it can significantly improve the inter-area due to electric power exchange as a result of Japanese modeitand design ofa the WADCdelay has done the fact fact that that the the inter-tie inter-tie power power flow flow has has been been getting heavier heavier oscillation power system, canthe significantly improve the been inter-area the by many researchers. However, transport occurs in due to that electric power exchange a resultgetting of Japanese mode and the design of WADC has been done the the inter-tie power flowas heavier oscillation oscillation mode and the design of the WADC has been done electricity provision deregulation. by many researchers. However, a the transport delay occurs in due fact to electric electric power exchange ashasaa been resultgetting of Japanese Japanese oscillation mode and the design of the WADC has been done due to power exchange as result of the communication link among PMUs and Phasor Data electricity provision deregulation. by many researchers. However, a transport delay occurs in due to electric power exchange as a result of Japanese by many researchers. However, a transport delay occurs in the communication link among PMUs and Phasor Data electricity provision deregulation. by many researchers. However, a PMUs transport delay occurs in electricity provision deregulation. Concentrator (PDC), and PDC and PSSs and it significantly the communication link among and Phasor Data Power System Stabilizer (PSS) is generally applied to Concentrator electricity provision deregulation. the communication link among PMUs and Phasor Data (PDC), and PDC and PSSs and it significantly the communication link among PMUs and Phasor Data Power System Stabilizer (PSS) is generally applied to affects the damping performance. In fact, Naduvathuparambil Concentrator (PDC), (PDC), and and PDC PDC and PSSs PSSs and and it it significantly oscillation damping in power systems as the effective and Concentrator Power System Stabilizer (PSS) is generally applied to Power System Stabilizer (PSS) is applied to damping performance. In PSSs fact, Naduvathuparambil Concentrator (PDC), and PDC and and and it significantly significantly oscillation damping in power systems as the effective and et al. the (2002) investigated the transport delay in Power System Stabilizer (PSS) is generally generally appliedpoor to affects affects the damping performance. In fact, Naduvathuparambil economic method. The PSS is installed to improve affects the damping performance. In fact, Naduvathuparambil oscillation damping in power systems as the effective and oscillation damping in power systems as the effective and et al. the(2002) investigated the transport delay in affects damping performance. In fact, Naduvathuparambil economic method. The PSS is installed to improve poor communication link of WAMS by experimental research. oscillation damping in power systems as the effective and et al. al. (2002) (2002) investigated investigated the the transport transport delay delay in damping caused by The rapidPSS excitation of Automatic Voltage et in economic method. is installed to improve poor economic method. The PSS is installed to improve poor communication link of WAMS by experimental research. damping caused by rapid excitation of Automatic Voltage et al. (2002) investigated the transport delay in authors tested various communication links suchresearch. as fiber economic method. The PSS is installed to improve poor The communication link of WAMS by experimental Regulator (AVR). In such a case of uncertain and variable communication link of WAMS by experimental research. damping caused by rapid excitation of Automatic Voltage damping caused by rapid excitation of Automatic Voltage The authors tested various communication links such as fiber communication link of WAMS by experimental research. Regulator (AVR). In such a case of uncertain and variable optic cables,tested telephone links, and satellite links and soason. In damping caused byInPSS rapid of Automatic Voltage The authors various communication links such fiber power systems, the hasexcitation be of well-designed to mitigate The authors tested various communication links such fiber Regulator (AVR). such a to case uncertain and variable Regulator (AVR). such case uncertain and variable optic cables, telephone links, and satellite links soas In The authors tested various communication links and such ason. fiber power systems, theIn PSS hasaa to be of well-designed to mitigate particular, they noted that the severest transport delay is in Regulator (AVR). In such case of uncertain and variable optic cables, telephone links, and satellite links and so on. the inter-area oscillation effectively. optic cables, telephone links, satellite links so In power systems, the PSS has to be well-designed to mitigate particular, they noted that theand severest transport delay is In in power systems, the PSS has to be well-designed to mitigate optic cables, telephone links, and satellite links and and so on. on. In the inter-area oscillation effectively. satellite links at about 500 ms to 700 ms. power systems, the PSS has to be well-designed to mitigate particular, they noted that the severest transport delay is in particular, they noted that the severest transport delay is the inter-area oscillation effectively. satellite links at about 500 ms to 700 ms. the inter-area oscillation effectively. they noted 500 thatms thetoseverest transport delay is in in Recently, Phasor Measurement the inter-area oscillation effectively.Unit (PMU) has been particular, satellite links at about 700 ms. satellite links at about 500 ms to 700 ms. Recently, Phasor Measurement Unit (PMU) has been In some literatures, several approaches to WADC design satellite links at about 500 ms to 700 ms. developed as a sophisticated measurement device which is Recently, Phasor Phasor Measurement Measurement Unit Unit (PMU) (PMU) has has been been In some literatures, several approaches to WADC design Recently, developed as a bus sophisticated measurement device which is have beenliteratures, proposed.several Majumder et al. (2005) proposed a Recently, Phasor Measurement Unit (PMU) has been In some approaches to WADC design able to obtain voltage and line current phasor among In some literatures, several approaches to WADC design developed as aa sophisticated measurement device which is developed as sophisticated measurement device which is have been proposed. Majumder etthe al.transport (2005) proposed a In some literatures, several approaches to WADC design able to obtain bus voltage and line current phasor among unified Smith predictor approach to delay in the developed as a sophisticated measurement device which is have been proposed. Majumder et al. (2005) proposed a geographically distant places synchronized by Global have been proposed. Majumder al. (2005) proposed able to obtain bus voltage and line current phasor among able to bus voltage and line current phasor among unified Smith predictor approach toet theaa have been proposed. Majumder etthe al.transport (2005)indelay proposed geographically distant places synchronized by Global remote signals. However, a Smith predictor deadin time able to obtain obtainSystem bus voltage and The line current phasor among unified Smith predictor approach to the transport delay in the Positioning (GPS). concept of phasor unified Smith predictor approach to the transport delay in the geographically distant places synchronized by Global geographically distant (GPS). places synchronized signals. Smith predictor dead Positioning System The concept by of Global phasor remote unified Smith predictor approach to the delay the system cannot beHowever, applied ifaaathe delay istransport variantin and it in istime not geographically places synchronized Global remote signals. However, Smith predictor in dead time measurement wasdistant conceived by The Phadke (1993). by Since then, system remote signals. However, Smith predictor in dead time Positioning System (GPS). concept of phasor Positioning System (GPS). The concept of phasor cannot be applied if the delay is variant and it is not remote signals. However, a Smith predictor in dead time measurement was conceived by Phadke (1993). Since then, correctly identified. In power systems, the delay Positioning (GPS). The concept of phasor cannot be applied if the delay is variant and it isis not many researchSystem projects and practical tasks have utilized it for system system cannot be if is and is not measurement was conceived by Phadke (1993). Since then, measurement was conceived by Phadke Since then, identified. In power systems, the delay system cannot be applied applied if the the delay delay is variant variant andHit it∞is is not many research projects and practical tasks(1993). have utilized it for correctly constant. Hashmani and Erlich (2011) proposed -based measurement was conceived by Phadke (1993). Since then, correctly identified. In power systems, the delay is not the sake of stability monitoring, state estimation, control correctly identified. In power systems, the delay is many research research projects projects and and practical practical tasks tasks have have utilized utilized it it for for constant. Hashmani and Erlich (2011) proposed H -based many ∞is not correctly identified. In power systems, the compensation delay not the sake ofadaptive stability monitoring, state estimation, control robust PSS using remote signals with delay many research projects and practical tasks have utilized it for constant. Hashmani and Erlich (2011) proposed H -based application, protection and so on (Phadke and Thorp ∞ constant. Hashmani and Erlich (2011) proposed H the sake of stability monitoring, state estimation, control ∞-based the sake of stability monitoring, state estimation, control robust PSS using remote signals with delay compensation constant. Hashmani and Erlich (2011) proposed H -based application, adaptive protection and so on (Phadke and Thorp ∞ considering variable delay signals rangingwith between 100 ms to 700 the sake in ofadaptive stabilityof monitoring, estimation, control robust PSS using remote delay compensation (2008)), terms Wide and Areastate Measurement System robust PSS using remote signals with delay compensation application, protection so on (Phadke and Thorp application, adaptive protection so on (Phadke and Thorp considering delay ranging between ms toet700 robust PSS variable using remote signals with delay100 compensation (2008)), inThe terms of Wide and Area Measurement System ms according to the research by Naduvathuparambil al. application, adaptive protection and so on (Phadke and Thorp considering variable delay ranging between 100 ms to 700 (WAMS). above-mentioned inter-area mode can be also considering variable delay ranging between 100 ms to (2008)), in terms of Wide Area Measurement System ms (2008)), in of Wide Area Measurement accordingvariable to the delay research by Naduvathuparambil et700 al. ranging between 100 ms to 700 (WAMS). Theterms above-mentioned inter-area mode can System be also considering (2008)), in terms of Wide Area Measurement System ms according according to to the the research research by by Naduvathuparambil Naduvathuparambil et et al. al. (WAMS). The above-mentioned inter-area mode can be also ms (WAMS). (WAMS). The The above-mentioned above-mentioned inter-area inter-area mode mode can can be be also also ms according to the research by Naduvathuparambil et al.
2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 534 Peer review©under of International Federation of Automatic Copyright 2018 responsibility IFAC 534Control. 10.1016/j.ifacol.2018.11.477 Copyright © 2018 IFAC 534 Copyright © 2018 IFAC 534 Copyright © 2018 IFAC 534
IFAC CAO 2018 Yekaterinburg, Russia, October 15-19, 2018 Yoshiaki. Matsukawa et al. / IFAC PapersOnLine 51-32 (2018) 534–539
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(2002). Since Flexible AC Transmission System (FACTS) devices are also able to contribute to the inter-area oscillation problem, Hasanvand et al. (2016) proposed coordinated design of a PSS and Thyristor Controlled Series Compensator (TCSC) as one of the FACTS devices. However, the authors did not consider the remote signal transport delay.
x Ax Bu y Cx Du
(1)
Where Δx, Δu, and Δy are column vectors of the state variables, inputs and outputs of the system respectively. 2.2 Design Target
To design a well-tuned PSS and WADC which considers transport delay, this paper proposes a novel optimal placement and parameter tuning approach for those controllers. The authors propose an optimal tuning approach applied in IEEJ (The Institute of Electrical Engineers of Japan) WEST10-machine system model which is a longitudinal power system. Generally, the inter-area mode is the most dominant mode and the local modes do not really influence the oscillation in WEST10-machine system model. However, in some mesh-like power systems, local modes also have to be carefully considered. Therefore, this paper firstly proposes to identify the inter-area mode and the local modes by modeshape analysis (Vanfretti and Chow (2010)) and generator coherent groups by correlation coefficient matrix method (Aghamohammadi and Tabandeh (2016)) of the generator rotor speed considering several severe fault points, in order to select the local PSS placement. For those PSS and WADC parameter tuning, this paper employs metaheuristics based approach via Mean Variance Mapping Optimization (MVMO) proposed by Erlich et al. (2010). The reasons why the metaheuristics based approach is chosen are: this parameter tuning problem is a non-convex optimization problem and nonlinear simulations have to be included in the objective function to consider the transport delay with dead time. At the first phase, ΔP type local PSS is designed to mitigate the local mode oscillation by an eigenvalue based objective function. After that, the suitable remote signal and location of WADCs are selected by correlation coefficient matrix, WADCs are designed considering transport delay ranging between 500 ms to 700 ms by time domain analysis based objective function.
An overall target of designed PSS and WADC is shown in Fig. 1. The PSS and WADC are attached backward of the AVR, and supply supplemental signal to enhance damping effect because the AVR itself is able to suppress the first swing of oscillation when a large disturbance occurs, though the damping performance is deteriorated. The design method in this paper refers to the two-level PSS whereby only the local PSS is designed having certain damping level and after that, WADC is designed overlapping with already designed local PSS by Dotta et al. (2008). Therefore, the power system will be stable if the remote signal is lost by any PMU failures. In Fig. 1, K is PSS gain, TR, Tw, T1, T2, T3, T4, are time constants of the signal detector, the washout filter, lead/lag compensators, respectively. In these parameters, TR and Tw are fixed and others will be tuned by optimization, the rest of them are tuning parameters. 3. PROPOSED METHOD 3.1 Controller Placement Method Before designing the PSS and WADC, it is necessary to identify the locations to install them. Especially, in a meshlike structure power system which has multi unstable dominant modes, wrong input signal selection and misplacement can possibly cause system instability. Hence, this paper employs the network modeshape with sensitivity analysis and the correlation coefficients matrix of each pair of generator rotor speed.
As a result of numerical simulation in IEEE New England 39-bus system model (NE 39-bus), the local PSS and the WADC locations are clearly shown by the angle modeshape and the coherent area grouping. Also, optimized local PSSs and WADCs using the local generator active power output deviation and the bus voltage phase difference between generator buses oscillating each other, respectively, perform better damping effect for inter-area oscillation compared to the local PSS alone, even if the remote signal transport delay occurs by varying between 500ms to 700 ms with Gaussian distribution noise. For the comparison, the WADCs with local PSS are designed ignoring the transport delay, it makes the system stability worse when the variable transport delay occurs.
Here, the eigenvalue analysis is performed for the state matrix A in (1), the following equation is obtained:
AW(A) W(A)
(2)
Where, λ is eigenvalue and W(A) is eigenvector. The interest mode is found by eigenvalue λ. For sensitivity analysis, the following equation is represented by C in (1):
2. PROBLEM STATEMENT 2.1 Linearized Model of Power System In the PSS design, the power system is linearized to carry out eigenvalue analysis. Consider the following linearized model of a power system at the given operation point:
Fig. 1. Two-level PSS control system structure 535
IFAC CAO 2018 536 Yoshiaki. Matsukawa et al. / IFAC PapersOnLine 51-32 (2018) 534–539 Yekaterinburg, Russia, October 15-19, 2018
V θ C V
δ C θ ω
(4)
k
(11)
(5)
(12) lcl
Where, σ is a set of the real part of the eigenvalue, ζ is a set of the damping ratio of the local dominant mode, respectively. ne is the number of the eigenvalues, Kminlcl, Kmaxlcl, Tminlcl, and Tmaxlcl are the upper and the lower limit of gain, and time constants, respectively. σmax and ζmin are coefficients forming D-region boundary condition explained later. Damping ratio ζ is calculated by the following equation:
Additionally, generator grouping to coherent area by correlation coefficient matrix (Aghamohammadi and Tabandeh (2016)) is employed to determine local PSS and WADC placement. Here, Rijk is a correlation coefficient of a pair of rotor speeds of generator i and j in a case of fault point k as follows:
Rij
min n ( n 1,..., ne) lcl
Where, Sθ, is angle modeshape. This index helps to visualize the oscillation modes. By calculating modeshape, it is possible to know how much the signal influences the interarea oscillation mode in each component.
1 n (il i )( jl j ) n l 1 1 n 1 n (il i ) 2 ( jl j ) 2 n l 1 n l 1
(10)
n max ( n 1,..., ne)
Where, CV and Cθ are voltage amplitude and angle sensitivity matrix, respectively. When the above sensitivity matrices are corresponded to eigenvector, network modeshape is obtained as follows:
S θ Cθ W(A)
lcl lcl Tmin Tmlcl Tmax ( m 1,..., 4)
(3)
(13)
2 2
Where, ω is oscillation frequency and the imaginary part of the eigenvalue. The region formed by σmax and ζmin is called D-region in complex plane, some PSS parameter tuning studies have employed this D-region (Fig. 2). By moving dominant eigenvalues into the D-region by tuning of the controller, it is able to enhance small signal stability (Wang (2013)). If a pair of eigenvalues is outside of this region, a huge penalty value is added to the objective function (8). After the local PSS design, the WADC is designed by following time domain based objective function and updated constraints.
Where, n is the number of samples, ωil and ωjl are the rotor speed values at l th sample, i and j are the mean values of rotor speed. The closer value Rijk gets to 1, the more the pair of generators i and j are positively relevant and oscillating in phase. The closer value Rijk gets to -1, the more the pair of generators i and j are negatively relevant and oscillating antiphase. Because the rotor oscillation differs depending on the fault point, the matrix should be fair. Here, R0ij is defined as follows:
Minimize Ft max SMAE
(14)
K
(15)
s.t. K
W ADC min
W ADC
K
W ADC max
W ADC W ADC Tmin TmW ADC Tmax ( m 1,..., 4)
R0ij Rijh
(6)
h arg min | Rijk |
(7)
1k nf
Where, nf is the number of tested faults. R0ij refers to the value of Rijk when its absolute value is the most minimum in all considered fault cases. It means R0ij is the most irrelevant value for all considered faults, this value is used for coherent grouping in this paper.
(16)
n ( n 1,..., ne)
(17)
update n max ( n 1,..., ne)
(18)
update min
Where, SMAE is a set of Sum of Mean Absolute Error (SMAE) of the rotor speed of all generators for some critical fault points, KminWADC, KmaxWADC, TminWADC, and TmaxWADC are the upper and the lower limit of gain, and time constants, respectively. In the WADC design phase, the D-region eigenvalue constraint boundary condition is changed
3.2 Parameter Tuning Method For parameter tuning of the local PSS and the WADC, a metaheuristic approach using MVMO is employed in order to enhance damping performance. As already mentioned, design of the local PSS and the WADC is done separately. In this paper, different objective functions are proposed to solve those problems effectively. For the local PSS design, following eigenvalue based objective function and constraints are applied:
Minimize FL max lcl min lcl
(8)
lcl lcl s.t. K min K lcl K max
(9)
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Fig. 2. A conceptual diagram of D-region in complex plane
IFAC CAO 2018 Yekaterinburg, Russia, October 15-19, 2018 Yoshiaki. Matsukawa et al. / IFAC PapersOnLine 51-32 (2018) 534–539
following the former design phase, by substituting the worst values σ and ζ for σmaxupdate, ζminupdate like shown in Fig. 2. Therefore, it is expected that the small-signal stability is partially assured in terms of eigenvalue evaluation. However, in this proposed method, design of the WADC includes dead time system which is nonlinear characteristic to consider the transport delay. Hence, (14) minimizes the deviation of rotor speed by examining the actual swing response of all generator with consideration for the transport delay.
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closest node to the generator node. It is obvious that G1 and others are oscillating each other. Also, some generators are oscillating in phase, these can be grouped as {G1}, {G2, G3}, {G4, G5}, {G6, G7}, {G8, G10}, and {G9}. Thus, ΔP type local PSSs are placed at G2, G4, G7, G9, and G10 to mitigate the local oscillation. Table 1 shows the constraint values. In the local PSS and the WADC, TR=0.02 s, Tw=5.0 s, the limiter confines PSS output between -0.2 and 0.2 p.u.. The updated D-region boundary condition is set following the result of local PSS design. According to the design procedure, firstly the local PSS is only designed via MVMO by the eigenvalue based objective function (8). The number of iterations and individuals in MVMO is set to 1000 and 30, respectively. Fig. 6 shows the eigenvalues in each case. If there is no controller installed, the system is unstable. By designing 5 local PSSs, local modes are improved, however there is a possibility that the inter-area mode is improved. Table 2 shows the PSS and the WADC parameters designed by using MVMO.
In this design phase, the eigenvalue analysis is carried out for the cases with transport delay for 500 ms and 700 ms, considering the delay range of satellite wireless communication link between PMUs and PDC, PDC and PSS (Naduvathuparambil et al. (2002)). Then, all eigenvalues in all delay cases have to be within the D-region formed by σmaxupdate, ζminupdate, otherwise a huge penalty value is added to the objective function (14). If the eigenvalues in all delay cases are within the D-region constraints by (17) and (18), SMAE is calculated for a delay case which has the most unstable eigenvalues by time domain simulation with some critical fault points. Then the maximum value of SMAE in all fault points will be the evaluation value. The WADC design is carried out by overlapping with already designed local PSS in the former phase following to two-level PSS concept. Since this design procedure evaluates the actual swing of generator, it is able to consider the nonlinear factors including transport delay and PSS limiter.
After designing the local PSS, the power system state is changed. Hence, the correlation coefficient R0ij is calculated
To solve the abovementioned optimization problems, it is necessary to apply a better metaheuristic method as much as possible. In this paper, MVMO is chosen. The main features of MVMO are normalized decision variables and global search using special mapping function based on mean and variance of stored good solutions in the archive. MVMO includes crossover and mutation. Things that differ from Genetic Algorithm are that the crossover type is different from either good or bad solution, and mutation is carried out in accordance with the mapping function which reflects the search history. The detail of MVMO is mentioned in the paper by Erlich et al. (2010) Fig. 3. The single line connection diagram of NE 39-bus 4. NUMERICAL EXPERIMENT In this paper, NE 39-bus is employed to verify the significance of the proposed method. The single line connection diagram is shown in Fig. 3. In the test system, each synchronous generator is modelled as the sixth order which assumes the presence of a field circuit and an additional circuit along the d-axis and two additional circuits along the q-axis. In NE 39-bus, G1 is an aggregated generator of another area. Thus, AVR, governor, and PSS are not applied to G1 while others are. Figs. 4 and 5 show the angle modeshape and the correlation coefficient matrix without controller of NE 39-bus, respectively. From Fig. 4, the inter-area mode (mode1) is the rotor oscillation between G1 and other generators and other modes are the local oscillation. In Fig. 5, the correlation coefficient of each pair of generators is projected on the colour map. To calculate R0ij in (6), three-phase ground fault is selected at node 16 which is most critical one, and the each
mode1
Fig. 4. Angle modeshape with no controller (a slid line: mode1, dashed lines: other modes) 537
IFAC CAO 2018 538 Yoshiaki. Matsukawa et al. / IFAC PapersOnLine 51-32 (2018) 534–539 Yekaterinburg, Russia, October 15-19, 2018
ζminupdate σmaxupdate
700ms 500ms
Fig. 5. Correlation coefficient matrix R0ij with no controller Table 1. Constraints
Fig. 6. The eigenvalue placement in complex plane
Parameters
Values -0.100 σmax 3.00(%) ζmin update -0.427 σmax update 12.4(%) ζmin lcl glb Kmin = Kmin 0.100 Kmaxlcl 10.0 Kmaxglb 2.00 Tminlcl= Tminglb 0.0100 Tmaxlcl= Tmaxglb 5.00 in case of installing the local PSSs again and the projected colour map is shown in Fig. 7. It seems that coherent group {G4, G5, G6, G7} is more relatively relevant to {G1} than others. Therefore, the WADC is installed at G4, G5, G6, and G7. As the remote input signal of the WADC, the voltage angle difference between node 39 (G1 node) and each generator node which the WADC is installed. For comparison, not only the delay considered method, but also delay ignored design method is applied using MVMO by time domain based objective function (14) considering two critical fault points at nodes 16 and 4. In Fig. 6, the eigenvalues are plotted with transport delay between 500 ms and 700 ms by 10 ms intervals. By the delay considered method, all eigenvalues are within the updated D-region.
Fig. 7 Correlation coefficient matrix R0ij with the local PSS
On the other hand, the inter-area mode eigenvalue moves to the outer limit of the D-region, and much lower frequency mode moves to unstable direction by the delay ignored method. To evaluate the actual swing with transport delay, time-variable transport delay is applied by Gaussian distribution wherein the mean is 0.6 (=600 ms) and the standard deviation is 0.0577. Figs. 8, 9, and 10 show the generator rotor speed response examined by applying threephase ground fault at node 16. There still is the inter-area mode oscillation with a cycle about 1.5 s in the case of the local PSS alone. The inter-area oscillation is improved by the WADC designed according to the proposed method, with the above-mentioned variable transport delay, especially in G1 and G4 where it is dominant. However, if the time delay is
Fig. 8. Generator Rotor speed of G1 ignored in the optimal WADC design, it cannot mitigate the oscillation and, instead, makes the oscillation worse, the swing deviation is especially large in G10. It happened because the WADC by the delay ignored method is designed assuming there is no transport delay and the WADC worked at unwanted timing. 538
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simulation at two critical fault points. As a result, the proposed design method is more effective than the local PSS alone in mitigating the inter-area oscillation, even when variable transport delay occurs. ACKNOWLEDGEMENT This research was supported by research grant from Japan Power Academy. REFERENCES Aghamohammadi, M. R. and Tabandeh, S. M. (2016). A new approach for online coherency identification in power systems based on correlation characteristics of generators rotor oscillations. International Journal of Electrical Power & Energy Systems, 83(1), pp. 470-484. Dotta, D., Silva, A.S., and Decker, I.C. (2008). Wide-area measurements based two-level control design considering signal transmission delay. IEEE Transactions on Power Systems, 24(1), pp. 208-216. Erlich, I., Venayagamoorthy, G.K., and Worawat, N. (2010) A mean-variance optimization algorithm. WCCI 2010 IEEE World congress on Computational Intelligence, pp. 344-349. Hasanvand, H., Arvan, M.R., Mozafari, B., and Amraee, T. (2016). Coodinated design of PSS and TCSC to mitigate interarea oscillations. Electrical Power and Energy Systems, 78(1), pp.194-206. Hashmani, A., and Erlich, I. (2011). Delayed-input power system stabilizer using supplementary remote signals. Control Engineering Practice, 19(8), pp. 893-899. Manjuber, R., Chaudhuri, B., Pal, B.C., and Zhong, Q. (2005). A unified smith predictor approach for power system damping control design using remote signals. IEEE Transactions on Control Systems Technology, 13(6), pp. 1063-1068. Matsukawa, Y., Terashi, J., Watanabe, M., and Mitani, Y. (2017). Power systems inertia evaluation associated with PV installation by frequency analysis of inter-area oscillation based on phasor measurements. Journal of Internatinoal Council on Electrical Engineering, 7(1), pp. 153-158. Naduvathuparambil, B., Valenti, M.C., and Feliachi, A. (2002). Communication delays in wide area measurement systems. 34th Southeastern Symposium on System Theory, pp. 118-122. Phadke, A.G. (1993). Synchoronized phasor measurements in power systems. IEEE Computer Applications in Power, 6(2), pp. 10-15. Phadke, A. G., and Thorp, J., S. (2008). Synchronized Phasor Measurements and Their Applications, Chapter 7, 8, 9. Springer. Vanfretti, L. and Chow, J.H. (2010). Analysis of power system oscillations for developing synchrophasor applications. 2010 IREP Symp. – Bulk Power Syst. Dyn. Control – Ⅷ. Wang, S.K. (2013). A novel objective function and algorithm for optimal PSS parameter design in a multi-machine power system. IEEE Transactions on Power Systems, 28(1), pp. 522-531.
Fig. 9. Generator Rotor speed of G4
Fig. 10. Generator Rotor speed of G10 Table 2. The local PSS and the WADC parameters Location Local PSS
WADC proposed WADC delay ignored
G2 G4 G7 G9 G10 G4 G5 G6 G7 G4 G5 G6 G7
K 4.371 2.694 3.467 0.968 5.302 0.106 0.102 0.247 0.174 0.111 0.137 0.105 0.202
T1 2.077 4.639 2.419 3.078 3.646 0.791 0.216 0.046 0.077 4.977 0.833 0.351 0.444
T2 2.865 2.621 2.937 3.233 2.238 5.000 4.427 4.631 4.563 3.488 4.292 4.768 4.874
T3 1.554 2.637 2.831 4.032 1.874 4.044 0.477 0.050 0.613 4.401 1.529 0.407 0.202
T4 3.114 1.881 2.820 2.489 3.325 0.010 1.500 2.691 4.934 1.164 4.819 4.552 4.227
6. CONCLUSIONS This paper proposed the optimal placement and parameter tuning approach for the local PSS and WADC. For the placement of the controllers, modeshape and coherent grouping analysis are employed to identify the dominant mode and coherent area. MVMO is applied to the parameter tuning of both controller. In WADC design, transport delay is considered in the objective function by time domain 539
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Optimal Optimal Placement Placement and and Tuning Tuning Approach Approach for for Design Design of of Power Power System System Stabilizers Stabilizers Optimaland Placement andDamping Tuning Approach forConsidering Design of Power System Stabilizers Wide Area Controllers Transport Delay Optimaland Placement and Tuning Approach for Design of Power System Stabilizers Wide Area Damping Controllers Considering Transport Delay and Wide Area Damping Controllers Considering Transport Delay and Wide Damping Controllers Transport Delay Yoshiaki.Area Matsukawa*, Masayuki. Watanabe*,Considering Hibiki. Takahashi*, Yasunori. Mitani*
Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Takahashi*, Yasunori. Mitani* Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Takahashi*, Takahashi*, Yasunori. Yasunori. Mitani* Mitani* Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Yoshiaki. Matsukawa*, Masayuki. Watanabe*, Hibiki. Takahashi*,1-1 Yasunori. Mitani* Institute *Department of Electrical and Electronic Engineering, Kyushu of Technology, Sensui-cho, Tobata-ku, Kitakyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu *Department of Electrical and Electronic Engineering, Kyushu 804-8550, Japan (Tel: +81-93-884-3227; e-mail: p349532y@ mail.kyutech.jp). *Department of Electrical and Electronic Engineering, Kyushu Institute Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu *Department and Engineering, Kyushu ofp349532y@ Technology, 1-1 804-8550, Japan (Tel: +81-93-884-3227; e-mail:of *Department of of Electrical Electrical and Electronic Electronic Engineering, Kyushu Institute Institute Technology,mail.kyutech.jp). 1-1 Sensui-cho, Sensui-cho, Tobata-ku, Tobata-ku, Kitakyushu Kitakyushu 804-8550, Japan (Tel: (Tel: +81-93-884-3227; e-mail:ofp349532y@ p349532y@ mail.kyutech.jp). 804-8550, Japan +81-93-884-3227; e-mail: mail.kyutech.jp). 804-8550, Japan (Tel: +81-93-884-3227; e-mail: p349532y@ mail.kyutech.jp). Abstract: In this paper, a novel optimal placement and parameter tuning approach for Power System Abstract: In this paper, a novel optimal placement and parameter tuning approach for Power System Stabilizer proposed to damp bothplacement local and and inter-area modes in mesh like power system. The Abstract: (PSS) In this thisispaper, paper, novel optimal placement and parameter tuning approach for Power Power System Abstract: In aaa novel optimal parameter tuning approach for System Stabilizer (PSS) is proposed to damp bothplacement local and inter-area modes inΔθ mesh like power system. The Abstract: In this paper, novel optimal and parameter tuning approach for Power System design target is two-level PSS consisting of ΔP type local PSS and type Wide Area Damping Stabilizer (PSS) proposed to damp both local inter-area modes mesh power system. The Stabilizer (PSS) is proposed to damp both local and inter-area modes in mesh like power system. The design target is is two-level PSS consisting of ΔPand type local PSS andin Δθ typelike Wide Area Damping Stabilizer (PSS) is proposed to damp both local and inter-area modes in mesh like power system. The Controller (WADC). For the PSS placement, modeshape with eigenvector sensitivity and coherency design target is two-level PSS consisting of ΔP type local PSS and Δθ type Wide Area Damping design target is two-level PSS consisting of ΔP type local PSS and Δθ type Wide Area Damping Controller (WADC). For the PSS placement, modeshape with eigenvector sensitivity and coherency design target is two-level PSS consisting of ΔP type local PSS and Δθ type Wide Area Damping analysis are(WADC). used to determine the appropriate placement ofwith botheigenvector local PSS sensitivity and WADC. Forcoherency the PSS Controller For the PSS placement, modeshape and Controller For placement, modeshape and coherency analysis are(WADC). used to determine the appropriate placement ofwith botheigenvector local PSS sensitivity and WADC. the PSS Controller (WADC). For the the PSS PSS placement, modeshape with eigenvector sensitivity andFor coherency parameter tuning, metaheuristics based approach via Mean Variance Mapping Optimization (MVMO) is analysis are used to determine the appropriate placement of both local PSS and WADC. For the PSS analysis are used to determine the appropriate both PSS WADC. For the PSS parameter tuning, metaheuristics based approachplacement via Mean of Variance Mapping Optimization (MVMO) is analysis are used to determine the appropriate placement of both local local PSS and and WADC.designs For the PSS employed in order to consider the time domain analysis. The proposed objective function at first parameter tuning, metaheuristics based approach via Mean Variance Mapping Optimization (MVMO) is parameter tuning, approach via Mean Variance Mapping Optimization (MVMO) is employed in ordermetaheuristics to consider thebased time domain analysis. The proposed objective function designs at first parameter tuning, approach via Mean Variance Optimization (MVMO) is the local PSS onlymetaheuristics to improve coefficient and damping ratio Mapping ofobjective eigenvalue. After designs that, it designs employed in order consider damping thebased time domain domain analysis. The proposed objective function designs at first first employed in order to consider the time analysis. The proposed function at the local PSS only to improve damping coefficient and damping ratio of eigenvalue. After that, it designs employed in order to consider the time domain analysis. The proposed objective function designs at first the WADC overlapping with already designed local PSS by time domain analysis, taking into account the local PSS only to improve damping coefficient of eigenvalue. After that, it designs the local only to damping coefficient and damping ratio of After that, it designs the WADC overlapping with already designed localand PSSdamping by time ratio domain analysis, taking into account the the local PSS PSS only to improve improve damping coefficient damping of eigenvalue. eigenvalue. After that, itproposed designs transport delay in the remote signal between Phasor Measurement Unit (PMU) and PSS.into The the WADC WADC overlapping with already already designed localand PSS by time time ratio domain analysis, taking into account the the overlapping with designed local PSS by domain analysis, taking account the transport delay in the remote signal between Phasor Measurement Unit (PMU) and PSS. The proposed the WADC overlapping with already designed local PSS by time domain analysis, taking into account the method isdelay applied in remote IEEE New England 39-Bus (NE 39-bus) system model.and Then, modeshape and transport in the signal between Phasor Measurement Unit (PMU) PSS. The proposed transport delay in the remote signal between Phasor Measurement Unit (PMU) and PSS. The proposed method isdelay applied in remote IEEE New England 39-Bus (NE 39-bus) system model.and Then, modeshape and transport in the signal between Phasor Measurement Unit (PMU) PSS. The proposed coherent grouping analysis give England us understandable system aspect, themodel. local Then, PSS and the WADC method applied in IEEE New 39-Bus (NE 39-bus) system modeshape and method is applied in IEEE 39-Bus (NE 39-bus) system modeshape and coherentis analysis give England us understandable system aspect, themodel. local Then, PSS and the WADC method isgrouping applied in IEEE New New England 39-Bus (NE 39-bus) system model. Then, modeshape and optimized by using MVMO considering the transport delay improve both local and inter-area modes coherent grouping analysis give us understandable system aspect, the local PSS and the WADC coherent grouping analysis give us understandable system aspect, the local PSS and the WADC optimized by using MVMO considering the transport delay improve both local and inter-area modes coherent grouping analysis give us understandable system aspect, the local PSS and the WADC whereas a method ignoring theconsidering transport delay make system poorly damped. optimized by using MVMO the transport delay improve both local and inter-area modes optimized by MVMO the delay improve both whereas a method ignoring theconsidering transport delay make system poorly damped. optimized by using using MVMO considering the transport transport delay improve both local local and and inter-area inter-area modes modes whereas a method ignoring the transport delay make system poorly damped. whereas a method ignoring the transport delay make system poorly damped. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Power ignoring System Stabilizers, Optimization, Transport Modes, whereas a method the transportParameter delay make system poorly damped. Delay, Small Signal Keywords: Power System Stabilizers, Parameter Optimization, Transport Delay, Small Signal Modes, Dynamic Inter-area Oscillations, Phasor Measurement Keywords:Stability, Power Stabilizers, Parameter Optimization, Transport Keywords: Power System System Stabilizers, Parameter Optimization,Unit Transport Delay, Delay, Small Small Signal Signal Modes, Modes, Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit Keywords: Power System Stabilizers, Parameter Optimization, Transport Delay, Small Signal Modes, Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit Dynamic Stability, Inter-area Oscillations, Phasor Measurement Unit captured by actual voltage phasor data obtained by PMUs 1. INTRODUCTION captured by actual voltage phasor data obtained by PMUs (Matsukawa et al. (2016)), forphasor example. 1. INTRODUCTION captured by actual voltage data obtained by PMUs captured by actual voltage phasor data (Matsukawa al. (2016)), example. 1. INTRODUCTION captured by et actual voltagefor phasor data obtained obtained by by PMUs PMUs 1. INTRODUCTION (Matsukawa et al. (2016)), for example. For the stable operation of a large scale power system, a 1. INTRODUCTION et al. (2016)), for example. In recent studies, the Wide Area Damping Controller the stable operation of a large scale power system, a (Matsukawa (Matsukawa et al. (2016)), for example. For specific inter-area mode will be critical. Forpower example, a pooraa In recent studies, the Wide Area Damping Controller For the stable operation of aa large scale system, For the stable operation of scale system, (WADC) isstudies, applied the using the Area remoteDamping signal obtained by specific mode will be critical. Forpower example, aHz poor In recent Wide Controller For the inter-area stable operation of a alarge large scale power system, In recent studies, the Wide Area Controller damping inter-area mode with frequency of 0.3-0.5 ina (WADC) is applied using the oscillations. remoteDamping signal obtained by specific inter-area mode will be critical. For example, aa poor In recent studies, the Wide Area Damping Controller specific inter-area mode will be critical. For example, poor PMUs to damp out inter-area Because of the damping inter-area mode with frequency of 0.3-0.5 in (WADC) (WADC) is is applied applied using using the the remote remote signal signal obtained obtained by by specific inter-area mode will beaacan critical. example, aHz poor the Japanese power system be For identified, and the PMUs to is damp out inter-area Because of of the damping inter-area mode with frequency of 0.3-0.5 in (WADC) applied usingreflects the oscillations. remote signal obtained bya damping inter-area mode with aacan frequency of 0.3-0.5 Hz in remote signal dynamically the global information the Japanese power system be identified, andHz the PMUs to damp out inter-area oscillations. Because of the damping inter-area mode with frequency of 0.3-0.5 Hz in PMUs to damp out inter-area oscillations. Because of the instability of thepower inter-area modecan willbe probably be affected by remote signal dynamically reflects theimprove global information of a the Japanese system identified, and the PMUs to damp out inter-area oscillations. Because of the the Japanese power system can be identified, and the power system, it can significantly the inter-area instability of the inter-area mode will probably be affected by remote signal dynamically reflects the global information of aa the Japanese power system can be identified, and the remote signal dynamically reflects the global information of the fact that the inter-tie power flow has been getting heavier power system, it can significantly improve the inter-area instability of the inter-area mode will probably be affected by remote signal dynamically reflects the global information of instability of the inter-area mode will probably be affected by oscillation modeit and thesignificantly design of theimprove WADC has been donea the fact that the inter-tie power flow has been getting heavier power system, can the inter-area instability of the inter-area mode will probably be affected by power system, it can significantly improve the inter-area due to electric power exchange as a result of Japanese modeitand design ofa the WADCdelay has done the fact fact that that the the inter-tie inter-tie power power flow flow has has been been getting heavier heavier oscillation power system, canthe significantly improve the been inter-area the by many researchers. However, transport occurs in due to that electric power exchange a resultgetting of Japanese mode and the design of WADC has been done the the inter-tie power flowas heavier oscillation oscillation mode and the design of the WADC has been done electricity provision deregulation. by many researchers. However, a the transport delay occurs in due fact to electric electric power exchange ashasaa been resultgetting of Japanese Japanese oscillation mode and the design of the WADC has been done due to power exchange as result of the communication link among PMUs and Phasor Data electricity provision deregulation. by many researchers. However, a transport delay occurs in due to electric power exchange as a result of Japanese by many researchers. However, a transport delay occurs in the communication link among PMUs and Phasor Data electricity provision deregulation. by many researchers. However, a PMUs transport delay occurs in electricity provision deregulation. Concentrator (PDC), and PDC and PSSs and it significantly the communication link among and Phasor Data Power System Stabilizer (PSS) is generally applied to Concentrator electricity provision deregulation. the communication link among PMUs and Phasor Data (PDC), and PDC and PSSs and it significantly the communication link among PMUs and Phasor Data Power System Stabilizer (PSS) is generally applied to affects the damping performance. In fact, Naduvathuparambil Concentrator (PDC), (PDC), and and PDC PDC and PSSs PSSs and and it it significantly oscillation damping in power systems as the effective and Concentrator Power System Stabilizer (PSS) is generally applied to Power System Stabilizer (PSS) is applied to damping performance. In PSSs fact, Naduvathuparambil Concentrator (PDC), and PDC and and and it significantly significantly oscillation damping in power systems as the effective and et al. the (2002) investigated the transport delay in Power System Stabilizer (PSS) is generally generally appliedpoor to affects affects the damping performance. In fact, Naduvathuparambil economic method. The PSS is installed to improve affects the damping performance. In fact, Naduvathuparambil oscillation damping in power systems as the effective and oscillation damping in power systems as the effective and et al. the(2002) investigated the transport delay in affects damping performance. In fact, Naduvathuparambil economic method. The PSS is installed to improve poor communication link of WAMS by experimental research. oscillation damping in power systems as the effective and et al. al. (2002) (2002) investigated investigated the the transport transport delay delay in damping caused by The rapidPSS excitation of Automatic Voltage et in economic method. is installed to improve poor economic method. The PSS is installed to improve poor communication link of WAMS by experimental research. damping caused by rapid excitation of Automatic Voltage et al. (2002) investigated the transport delay in authors tested various communication links suchresearch. as fiber economic method. The PSS is installed to improve poor The communication link of WAMS by experimental Regulator (AVR). In such a case of uncertain and variable communication link of WAMS by experimental research. damping caused by rapid excitation of Automatic Voltage damping caused by rapid excitation of Automatic Voltage The authors tested various communication links such as fiber communication link of WAMS by experimental research. Regulator (AVR). In such a case of uncertain and variable optic cables,tested telephone links, and satellite links and soason. In damping caused byInPSS rapid of Automatic Voltage The authors various communication links such fiber power systems, the hasexcitation be of well-designed to mitigate The authors tested various communication links such fiber Regulator (AVR). such a to case uncertain and variable Regulator (AVR). such case uncertain and variable optic cables, telephone links, and satellite links soas In The authors tested various communication links and such ason. fiber power systems, theIn PSS hasaa to be of well-designed to mitigate particular, they noted that the severest transport delay is in Regulator (AVR). In such case of uncertain and variable optic cables, telephone links, and satellite links and so on. the inter-area oscillation effectively. optic cables, telephone links, satellite links so In power systems, the PSS has to be well-designed to mitigate particular, they noted that theand severest transport delay is In in power systems, the PSS has to be well-designed to mitigate optic cables, telephone links, and satellite links and and so on. on. In the inter-area oscillation effectively. satellite links at about 500 ms to 700 ms. power systems, the PSS has to be well-designed to mitigate particular, they noted that the severest transport delay is in particular, they noted that the severest transport delay is the inter-area oscillation effectively. satellite links at about 500 ms to 700 ms. the inter-area oscillation effectively. they noted 500 thatms thetoseverest transport delay is in in Recently, Phasor Measurement the inter-area oscillation effectively.Unit (PMU) has been particular, satellite links at about 700 ms. satellite links at about 500 ms to 700 ms. Recently, Phasor Measurement Unit (PMU) has been In some literatures, several approaches to WADC design satellite links at about 500 ms to 700 ms. developed as a sophisticated measurement device which is Recently, Phasor Phasor Measurement Measurement Unit Unit (PMU) (PMU) has has been been In some literatures, several approaches to WADC design Recently, developed as a bus sophisticated measurement device which is have beenliteratures, proposed.several Majumder et al. (2005) proposed a Recently, Phasor Measurement Unit (PMU) has been In some approaches to WADC design able to obtain voltage and line current phasor among In some literatures, several approaches to WADC design developed as aa sophisticated measurement device which is developed as sophisticated measurement device which is have been proposed. Majumder etthe al.transport (2005) proposed a In some literatures, several approaches to WADC design able to obtain bus voltage and line current phasor among unified Smith predictor approach to delay in the developed as a sophisticated measurement device which is have been proposed. Majumder et al. (2005) proposed a geographically distant places synchronized by Global have been proposed. Majumder al. (2005) proposed able to obtain bus voltage and line current phasor among able to bus voltage and line current phasor among unified Smith predictor approach toet theaa have been proposed. Majumder etthe al.transport (2005)indelay proposed geographically distant places synchronized by Global remote signals. However, a Smith predictor deadin time able to obtain obtainSystem bus voltage and The line current phasor among unified Smith predictor approach to the transport delay in the Positioning (GPS). concept of phasor unified Smith predictor approach to the transport delay in the geographically distant places synchronized by Global geographically distant (GPS). places synchronized signals. Smith predictor dead Positioning System The concept by of Global phasor remote unified Smith predictor approach to the delay the system cannot beHowever, applied ifaaathe delay istransport variantin and it in istime not geographically places synchronized Global remote signals. However, Smith predictor in dead time measurement wasdistant conceived by The Phadke (1993). by Since then, system remote signals. However, Smith predictor in dead time Positioning System (GPS). concept of phasor Positioning System (GPS). The concept of phasor cannot be applied if the delay is variant and it is not remote signals. However, a Smith predictor in dead time measurement was conceived by Phadke (1993). Since then, correctly identified. In power systems, the delay Positioning (GPS). The concept of phasor cannot be applied if the delay is variant and it isis not many researchSystem projects and practical tasks have utilized it for system system cannot be if is and is not measurement was conceived by Phadke (1993). Since then, measurement was conceived by Phadke Since then, identified. In power systems, the delay system cannot be applied applied if the the delay delay is variant variant andHit it∞is is not many research projects and practical tasks(1993). have utilized it for correctly constant. Hashmani and Erlich (2011) proposed -based measurement was conceived by Phadke (1993). Since then, correctly identified. In power systems, the delay is not the sake of stability monitoring, state estimation, control correctly identified. In power systems, the delay is many research research projects projects and and practical practical tasks tasks have have utilized utilized it it for for constant. Hashmani and Erlich (2011) proposed H -based many ∞is not correctly identified. In power systems, the compensation delay not the sake ofadaptive stability monitoring, state estimation, control robust PSS using remote signals with delay many research projects and practical tasks have utilized it for constant. Hashmani and Erlich (2011) proposed H -based application, protection and so on (Phadke and Thorp ∞ constant. Hashmani and Erlich (2011) proposed H the sake of stability monitoring, state estimation, control ∞-based the sake of stability monitoring, state estimation, control robust PSS using remote signals with delay compensation constant. Hashmani and Erlich (2011) proposed H -based application, adaptive protection and so on (Phadke and Thorp ∞ considering variable delay signals rangingwith between 100 ms to 700 the sake in ofadaptive stabilityof monitoring, estimation, control robust PSS using remote delay compensation (2008)), terms Wide and Areastate Measurement System robust PSS using remote signals with delay compensation application, protection so on (Phadke and Thorp application, adaptive protection so on (Phadke and Thorp considering delay ranging between ms toet700 robust PSS variable using remote signals with delay100 compensation (2008)), inThe terms of Wide and Area Measurement System ms according to the research by Naduvathuparambil al. application, adaptive protection and so on (Phadke and Thorp considering variable delay ranging between 100 ms to 700 (WAMS). above-mentioned inter-area mode can be also considering variable delay ranging between 100 ms to (2008)), in terms of Wide Area Measurement System ms (2008)), in of Wide Area Measurement accordingvariable to the delay research by Naduvathuparambil et700 al. ranging between 100 ms to 700 (WAMS). Theterms above-mentioned inter-area mode can System be also considering (2008)), in terms of Wide Area Measurement System ms according according to to the the research research by by Naduvathuparambil Naduvathuparambil et et al. al. (WAMS). The above-mentioned inter-area mode can be also ms (WAMS). (WAMS). The The above-mentioned above-mentioned inter-area inter-area mode mode can can be be also also ms according to the research by Naduvathuparambil et al.
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(2002). Since Flexible AC Transmission System (FACTS) devices are also able to contribute to the inter-area oscillation problem, Hasanvand et al. (2016) proposed coordinated design of a PSS and Thyristor Controlled Series Compensator (TCSC) as one of the FACTS devices. However, the authors did not consider the remote signal transport delay.
x Ax Bu y Cx Du
(1)
Where Δx, Δu, and Δy are column vectors of the state variables, inputs and outputs of the system respectively. 2.2 Design Target
To design a well-tuned PSS and WADC which considers transport delay, this paper proposes a novel optimal placement and parameter tuning approach for those controllers. The authors propose an optimal tuning approach applied in IEEJ (The Institute of Electrical Engineers of Japan) WEST10-machine system model which is a longitudinal power system. Generally, the inter-area mode is the most dominant mode and the local modes do not really influence the oscillation in WEST10-machine system model. However, in some mesh-like power systems, local modes also have to be carefully considered. Therefore, this paper firstly proposes to identify the inter-area mode and the local modes by modeshape analysis (Vanfretti and Chow (2010)) and generator coherent groups by correlation coefficient matrix method (Aghamohammadi and Tabandeh (2016)) of the generator rotor speed considering several severe fault points, in order to select the local PSS placement. For those PSS and WADC parameter tuning, this paper employs metaheuristics based approach via Mean Variance Mapping Optimization (MVMO) proposed by Erlich et al. (2010). The reasons why the metaheuristics based approach is chosen are: this parameter tuning problem is a non-convex optimization problem and nonlinear simulations have to be included in the objective function to consider the transport delay with dead time. At the first phase, ΔP type local PSS is designed to mitigate the local mode oscillation by an eigenvalue based objective function. After that, the suitable remote signal and location of WADCs are selected by correlation coefficient matrix, WADCs are designed considering transport delay ranging between 500 ms to 700 ms by time domain analysis based objective function.
An overall target of designed PSS and WADC is shown in Fig. 1. The PSS and WADC are attached backward of the AVR, and supply supplemental signal to enhance damping effect because the AVR itself is able to suppress the first swing of oscillation when a large disturbance occurs, though the damping performance is deteriorated. The design method in this paper refers to the two-level PSS whereby only the local PSS is designed having certain damping level and after that, WADC is designed overlapping with already designed local PSS by Dotta et al. (2008). Therefore, the power system will be stable if the remote signal is lost by any PMU failures. In Fig. 1, K is PSS gain, TR, Tw, T1, T2, T3, T4, are time constants of the signal detector, the washout filter, lead/lag compensators, respectively. In these parameters, TR and Tw are fixed and others will be tuned by optimization, the rest of them are tuning parameters. 3. PROPOSED METHOD 3.1 Controller Placement Method Before designing the PSS and WADC, it is necessary to identify the locations to install them. Especially, in a meshlike structure power system which has multi unstable dominant modes, wrong input signal selection and misplacement can possibly cause system instability. Hence, this paper employs the network modeshape with sensitivity analysis and the correlation coefficients matrix of each pair of generator rotor speed.
As a result of numerical simulation in IEEE New England 39-bus system model (NE 39-bus), the local PSS and the WADC locations are clearly shown by the angle modeshape and the coherent area grouping. Also, optimized local PSSs and WADCs using the local generator active power output deviation and the bus voltage phase difference between generator buses oscillating each other, respectively, perform better damping effect for inter-area oscillation compared to the local PSS alone, even if the remote signal transport delay occurs by varying between 500ms to 700 ms with Gaussian distribution noise. For the comparison, the WADCs with local PSS are designed ignoring the transport delay, it makes the system stability worse when the variable transport delay occurs.
Here, the eigenvalue analysis is performed for the state matrix A in (1), the following equation is obtained:
AW(A) W(A)
(2)
Where, λ is eigenvalue and W(A) is eigenvector. The interest mode is found by eigenvalue λ. For sensitivity analysis, the following equation is represented by C in (1):
2. PROBLEM STATEMENT 2.1 Linearized Model of Power System In the PSS design, the power system is linearized to carry out eigenvalue analysis. Consider the following linearized model of a power system at the given operation point:
Fig. 1. Two-level PSS control system structure 535
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V θ C V
δ C θ ω
(4)
k
(11)
(5)
(12) lcl
Where, σ is a set of the real part of the eigenvalue, ζ is a set of the damping ratio of the local dominant mode, respectively. ne is the number of the eigenvalues, Kminlcl, Kmaxlcl, Tminlcl, and Tmaxlcl are the upper and the lower limit of gain, and time constants, respectively. σmax and ζmin are coefficients forming D-region boundary condition explained later. Damping ratio ζ is calculated by the following equation:
Additionally, generator grouping to coherent area by correlation coefficient matrix (Aghamohammadi and Tabandeh (2016)) is employed to determine local PSS and WADC placement. Here, Rijk is a correlation coefficient of a pair of rotor speeds of generator i and j in a case of fault point k as follows:
Rij
min n ( n 1,..., ne) lcl
Where, Sθ, is angle modeshape. This index helps to visualize the oscillation modes. By calculating modeshape, it is possible to know how much the signal influences the interarea oscillation mode in each component.
1 n (il i )( jl j ) n l 1 1 n 1 n (il i ) 2 ( jl j ) 2 n l 1 n l 1
(10)
n max ( n 1,..., ne)
Where, CV and Cθ are voltage amplitude and angle sensitivity matrix, respectively. When the above sensitivity matrices are corresponded to eigenvector, network modeshape is obtained as follows:
S θ Cθ W(A)
lcl lcl Tmin Tmlcl Tmax ( m 1,..., 4)
(3)
(13)
2 2
Where, ω is oscillation frequency and the imaginary part of the eigenvalue. The region formed by σmax and ζmin is called D-region in complex plane, some PSS parameter tuning studies have employed this D-region (Fig. 2). By moving dominant eigenvalues into the D-region by tuning of the controller, it is able to enhance small signal stability (Wang (2013)). If a pair of eigenvalues is outside of this region, a huge penalty value is added to the objective function (8). After the local PSS design, the WADC is designed by following time domain based objective function and updated constraints.
Where, n is the number of samples, ωil and ωjl are the rotor speed values at l th sample, i and j are the mean values of rotor speed. The closer value Rijk gets to 1, the more the pair of generators i and j are positively relevant and oscillating in phase. The closer value Rijk gets to -1, the more the pair of generators i and j are negatively relevant and oscillating antiphase. Because the rotor oscillation differs depending on the fault point, the matrix should be fair. Here, R0ij is defined as follows:
Minimize Ft max SMAE
(14)
K
(15)
s.t. K
W ADC min
W ADC
K
W ADC max
W ADC W ADC Tmin TmW ADC Tmax ( m 1,..., 4)
R0ij Rijh
(6)
h arg min | Rijk |
(7)
1k nf
Where, nf is the number of tested faults. R0ij refers to the value of Rijk when its absolute value is the most minimum in all considered fault cases. It means R0ij is the most irrelevant value for all considered faults, this value is used for coherent grouping in this paper.
(16)
n ( n 1,..., ne)
(17)
update n max ( n 1,..., ne)
(18)
update min
Where, SMAE is a set of Sum of Mean Absolute Error (SMAE) of the rotor speed of all generators for some critical fault points, KminWADC, KmaxWADC, TminWADC, and TmaxWADC are the upper and the lower limit of gain, and time constants, respectively. In the WADC design phase, the D-region eigenvalue constraint boundary condition is changed
3.2 Parameter Tuning Method For parameter tuning of the local PSS and the WADC, a metaheuristic approach using MVMO is employed in order to enhance damping performance. As already mentioned, design of the local PSS and the WADC is done separately. In this paper, different objective functions are proposed to solve those problems effectively. For the local PSS design, following eigenvalue based objective function and constraints are applied:
Minimize FL max lcl min lcl
(8)
lcl lcl s.t. K min K lcl K max
(9)
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Fig. 2. A conceptual diagram of D-region in complex plane
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following the former design phase, by substituting the worst values σ and ζ for σmaxupdate, ζminupdate like shown in Fig. 2. Therefore, it is expected that the small-signal stability is partially assured in terms of eigenvalue evaluation. However, in this proposed method, design of the WADC includes dead time system which is nonlinear characteristic to consider the transport delay. Hence, (14) minimizes the deviation of rotor speed by examining the actual swing response of all generator with consideration for the transport delay.
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closest node to the generator node. It is obvious that G1 and others are oscillating each other. Also, some generators are oscillating in phase, these can be grouped as {G1}, {G2, G3}, {G4, G5}, {G6, G7}, {G8, G10}, and {G9}. Thus, ΔP type local PSSs are placed at G2, G4, G7, G9, and G10 to mitigate the local oscillation. Table 1 shows the constraint values. In the local PSS and the WADC, TR=0.02 s, Tw=5.0 s, the limiter confines PSS output between -0.2 and 0.2 p.u.. The updated D-region boundary condition is set following the result of local PSS design. According to the design procedure, firstly the local PSS is only designed via MVMO by the eigenvalue based objective function (8). The number of iterations and individuals in MVMO is set to 1000 and 30, respectively. Fig. 6 shows the eigenvalues in each case. If there is no controller installed, the system is unstable. By designing 5 local PSSs, local modes are improved, however there is a possibility that the inter-area mode is improved. Table 2 shows the PSS and the WADC parameters designed by using MVMO.
In this design phase, the eigenvalue analysis is carried out for the cases with transport delay for 500 ms and 700 ms, considering the delay range of satellite wireless communication link between PMUs and PDC, PDC and PSS (Naduvathuparambil et al. (2002)). Then, all eigenvalues in all delay cases have to be within the D-region formed by σmaxupdate, ζminupdate, otherwise a huge penalty value is added to the objective function (14). If the eigenvalues in all delay cases are within the D-region constraints by (17) and (18), SMAE is calculated for a delay case which has the most unstable eigenvalues by time domain simulation with some critical fault points. Then the maximum value of SMAE in all fault points will be the evaluation value. The WADC design is carried out by overlapping with already designed local PSS in the former phase following to two-level PSS concept. Since this design procedure evaluates the actual swing of generator, it is able to consider the nonlinear factors including transport delay and PSS limiter.
After designing the local PSS, the power system state is changed. Hence, the correlation coefficient R0ij is calculated
To solve the abovementioned optimization problems, it is necessary to apply a better metaheuristic method as much as possible. In this paper, MVMO is chosen. The main features of MVMO are normalized decision variables and global search using special mapping function based on mean and variance of stored good solutions in the archive. MVMO includes crossover and mutation. Things that differ from Genetic Algorithm are that the crossover type is different from either good or bad solution, and mutation is carried out in accordance with the mapping function which reflects the search history. The detail of MVMO is mentioned in the paper by Erlich et al. (2010) Fig. 3. The single line connection diagram of NE 39-bus 4. NUMERICAL EXPERIMENT In this paper, NE 39-bus is employed to verify the significance of the proposed method. The single line connection diagram is shown in Fig. 3. In the test system, each synchronous generator is modelled as the sixth order which assumes the presence of a field circuit and an additional circuit along the d-axis and two additional circuits along the q-axis. In NE 39-bus, G1 is an aggregated generator of another area. Thus, AVR, governor, and PSS are not applied to G1 while others are. Figs. 4 and 5 show the angle modeshape and the correlation coefficient matrix without controller of NE 39-bus, respectively. From Fig. 4, the inter-area mode (mode1) is the rotor oscillation between G1 and other generators and other modes are the local oscillation. In Fig. 5, the correlation coefficient of each pair of generators is projected on the colour map. To calculate R0ij in (6), three-phase ground fault is selected at node 16 which is most critical one, and the each
mode1
Fig. 4. Angle modeshape with no controller (a slid line: mode1, dashed lines: other modes) 537
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ζminupdate σmaxupdate
700ms 500ms
Fig. 5. Correlation coefficient matrix R0ij with no controller Table 1. Constraints
Fig. 6. The eigenvalue placement in complex plane
Parameters
Values -0.100 σmax 3.00(%) ζmin update -0.427 σmax update 12.4(%) ζmin lcl glb Kmin = Kmin 0.100 Kmaxlcl 10.0 Kmaxglb 2.00 Tminlcl= Tminglb 0.0100 Tmaxlcl= Tmaxglb 5.00 in case of installing the local PSSs again and the projected colour map is shown in Fig. 7. It seems that coherent group {G4, G5, G6, G7} is more relatively relevant to {G1} than others. Therefore, the WADC is installed at G4, G5, G6, and G7. As the remote input signal of the WADC, the voltage angle difference between node 39 (G1 node) and each generator node which the WADC is installed. For comparison, not only the delay considered method, but also delay ignored design method is applied using MVMO by time domain based objective function (14) considering two critical fault points at nodes 16 and 4. In Fig. 6, the eigenvalues are plotted with transport delay between 500 ms and 700 ms by 10 ms intervals. By the delay considered method, all eigenvalues are within the updated D-region.
Fig. 7 Correlation coefficient matrix R0ij with the local PSS
On the other hand, the inter-area mode eigenvalue moves to the outer limit of the D-region, and much lower frequency mode moves to unstable direction by the delay ignored method. To evaluate the actual swing with transport delay, time-variable transport delay is applied by Gaussian distribution wherein the mean is 0.6 (=600 ms) and the standard deviation is 0.0577. Figs. 8, 9, and 10 show the generator rotor speed response examined by applying threephase ground fault at node 16. There still is the inter-area mode oscillation with a cycle about 1.5 s in the case of the local PSS alone. The inter-area oscillation is improved by the WADC designed according to the proposed method, with the above-mentioned variable transport delay, especially in G1 and G4 where it is dominant. However, if the time delay is
Fig. 8. Generator Rotor speed of G1 ignored in the optimal WADC design, it cannot mitigate the oscillation and, instead, makes the oscillation worse, the swing deviation is especially large in G10. It happened because the WADC by the delay ignored method is designed assuming there is no transport delay and the WADC worked at unwanted timing. 538
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simulation at two critical fault points. As a result, the proposed design method is more effective than the local PSS alone in mitigating the inter-area oscillation, even when variable transport delay occurs. ACKNOWLEDGEMENT This research was supported by research grant from Japan Power Academy. REFERENCES Aghamohammadi, M. R. and Tabandeh, S. M. (2016). A new approach for online coherency identification in power systems based on correlation characteristics of generators rotor oscillations. International Journal of Electrical Power & Energy Systems, 83(1), pp. 470-484. Dotta, D., Silva, A.S., and Decker, I.C. (2008). Wide-area measurements based two-level control design considering signal transmission delay. IEEE Transactions on Power Systems, 24(1), pp. 208-216. Erlich, I., Venayagamoorthy, G.K., and Worawat, N. (2010) A mean-variance optimization algorithm. WCCI 2010 IEEE World congress on Computational Intelligence, pp. 344-349. Hasanvand, H., Arvan, M.R., Mozafari, B., and Amraee, T. (2016). Coodinated design of PSS and TCSC to mitigate interarea oscillations. Electrical Power and Energy Systems, 78(1), pp.194-206. Hashmani, A., and Erlich, I. (2011). Delayed-input power system stabilizer using supplementary remote signals. Control Engineering Practice, 19(8), pp. 893-899. Manjuber, R., Chaudhuri, B., Pal, B.C., and Zhong, Q. (2005). A unified smith predictor approach for power system damping control design using remote signals. IEEE Transactions on Control Systems Technology, 13(6), pp. 1063-1068. Matsukawa, Y., Terashi, J., Watanabe, M., and Mitani, Y. (2017). Power systems inertia evaluation associated with PV installation by frequency analysis of inter-area oscillation based on phasor measurements. Journal of Internatinoal Council on Electrical Engineering, 7(1), pp. 153-158. Naduvathuparambil, B., Valenti, M.C., and Feliachi, A. (2002). Communication delays in wide area measurement systems. 34th Southeastern Symposium on System Theory, pp. 118-122. Phadke, A.G. (1993). Synchoronized phasor measurements in power systems. IEEE Computer Applications in Power, 6(2), pp. 10-15. Phadke, A. G., and Thorp, J., S. (2008). Synchronized Phasor Measurements and Their Applications, Chapter 7, 8, 9. Springer. Vanfretti, L. and Chow, J.H. (2010). Analysis of power system oscillations for developing synchrophasor applications. 2010 IREP Symp. – Bulk Power Syst. Dyn. Control – Ⅷ. Wang, S.K. (2013). A novel objective function and algorithm for optimal PSS parameter design in a multi-machine power system. IEEE Transactions on Power Systems, 28(1), pp. 522-531.
Fig. 9. Generator Rotor speed of G4
Fig. 10. Generator Rotor speed of G10 Table 2. The local PSS and the WADC parameters Location Local PSS
WADC proposed WADC delay ignored
G2 G4 G7 G9 G10 G4 G5 G6 G7 G4 G5 G6 G7
K 4.371 2.694 3.467 0.968 5.302 0.106 0.102 0.247 0.174 0.111 0.137 0.105 0.202
T1 2.077 4.639 2.419 3.078 3.646 0.791 0.216 0.046 0.077 4.977 0.833 0.351 0.444
T2 2.865 2.621 2.937 3.233 2.238 5.000 4.427 4.631 4.563 3.488 4.292 4.768 4.874
T3 1.554 2.637 2.831 4.032 1.874 4.044 0.477 0.050 0.613 4.401 1.529 0.407 0.202
T4 3.114 1.881 2.820 2.489 3.325 0.010 1.500 2.691 4.934 1.164 4.819 4.552 4.227
6. CONCLUSIONS This paper proposed the optimal placement and parameter tuning approach for the local PSS and WADC. For the placement of the controllers, modeshape and coherent grouping analysis are employed to identify the dominant mode and coherent area. MVMO is applied to the parameter tuning of both controller. In WADC design, transport delay is considered in the objective function by time domain 539