The Dynamic of Synchronous Generator Under

The Dynamic of Synchronous Generator Under Unbalanced Steady State Operation: A Case of Virtual Generator Laboratory Sugiarto Kadiman, Arif Basuki, Mytha Arena Departement of Electrical Engineering, Sekolah Tinggi Teknologi Nasional, Yogyakarta

ABSTRACT The purpose of this study is to design and develop a synchronous generator virtual laboratory for undergraduate student courses, which can be treated as an accessorial tool for enhancing instruction. The study firstly reviews the general concept and algorithm of synchronous generator model. Secondly, the simulation method of this system is discussed. Finally, the paper introduces its example and analysis. One of the major objectives of this project is the dynamics of synchronous generators connected to the 500 kV EHV Jamali (Jawa-Madura-Bali) System under unbalanced steady state condition could be modeled as a balanced synchronous generator’s model based on qd0 reference frame with unbalanced voltage inputs. With utilizing the loadflow analysis, phase and sequence currents, and average bus voltages of the 500 kV EHV Jamali grid considering unbalanced portion variations, several studied cases is derived. To find the dynamic of synchronous generator, the balanced synchronous generator model based on the rotor’s qd0 reference frame is chosen to substitute generator’s model embeded in loadflow analysis which are active and reactive power injections. The verification of the proposed generator’s model was checked by comparing it with a PSS Tecquiment NE9070 simulator. The developed tool with given example demonstrates the usefulness of its for studying synchronous generator at undegraduate courses.

Keyword: 500 KV EHV Jamali System Unbalanced steady state qd0 reference frame Tecquiment NE9070 simulator

Corresponding Author: Sugiarto Kadiman, Departement of Electrical Engineering, Sekolah Tinggi Teknologi Nasional, Jl. Babarsari, Catur Tunggal, Depok, Sleman, Yogyakarta 55281, Indonesia. Email: [email protected]

1.

INTRODUCTION In electrical engineering education, written exercises are necessary for undergraduate students to master conception while experimentations emphasize the understanding of the subject. Real experiments are essential for developing skills to deal with instrumentation and physical processes and no doubt that nothing will replace synchronous learning through face to face interaction [1]. Virtual Laboratory can be treated as an accessorial tool of real laboratory to enhance instruction for conventional on-campus students, which can enable students to improve the skills before going to the actual laboratory, to learn breaking the limitation of real laboratory dealing with advanced topics, such as unbalanced operation in synchronous generators. So, Virtual Laboratory can effectively help to overcome the barriers imposed by the traditional education by using an innovative combination of a new approach to education and the application of new technologies. Many studies considering unbalanced steady state operating conditions of synchronous generators as a source electrical energy have done using the analytical approaches. The nature of the unbalance comprises unequal voltage magnitudes at the fundamental system frequency and fundamental phase angle deviation. One of causal factors is the appearance of unbalanced loads of the generator. In crucial unbalanced systems, negative sequence current may cause overheating of the machineries; zero sequence current may cause improper action of the protective relaying [2].

Unbalanced short-circuits calculating of synchronous generator under steady state operation has been perfectly understood [3]. Analysis based on mathematical theory which includes single line-to-neutral fault and the line-to-line fault, is been utilized. But the other problem of the unbalance when the system is connected the grids has not been thoroughly solved [4]. Salim et al [5] analyzes the small signal dynamic performance of synchronous generator connected to the load under any unbalanced operation conditions. But they only focus on the SEIG case [6] and Single Machine Infinite Bus or SMIB. Acha [7] suggested that load-flow program can be used to analyze unbalanced steady-state problems of synchronous generator as long as more realistic synchronous generator model is implemented. So the goal of this paper is to obtain a complete mathematical model of balanced synchronous generator operated under unbalanced steady state condition. This needs a synchronous generator model which has a completely enough framework for analyzing the small-signal dynamic performance of power systems under unbalanced conditions and also can accommodate the load-flow analysis to determine values of generator’s terminal inputs when the changing loads happened in the grid connected to it. Until now there is no theoretic mathematics models of synchronous generators used to analyze this kind of problems mentioned above. The presented study considers several typical synchronous generators which are connected to 500 kV EHV Jamali System, Indonesia. The study is carried out through the “hybrid” method by combination between unbalanced loadflow under EDSA 2000 [8] to analyze the grid and determine the inputs of the test generator and the rotor’s qd0 reference frame of synchronous generator model to substitute the load-flow generator’s model. The verification of the proposed model was checked by comparing it with a Tecquiment NE9070 simulator. The developed tool is a synchronous generator virtual laboratory. This work is organized as follows. A brief explanation about the concepts and algorithms involving the unbalanced condition of balanced synchronous generator is defined on Section 1. Section 2 presents the simulation method of synchronous generator dynamic. The example and analysis are presented on Section 3. Section 4 presents the final conclusion obtained with the present study.

2.

REVIEW CONCEPTS AND ALGORITHMS A brief discussion considering the operation of power system with synchronous generators under steady state unbalanced conditions is presented in the present section. A. Steady State Unbalanced Operation Many large synchronous generators connected to the power grid are usually found in recent power system, which is common in several countries around the world, including Indonesia. The 500 kV EHV Jamali Systems is one of an example. Synchronous generators often operate on unbalanced three-phase loading. That is the stator currents have different amplitudes, and their phase displacement differs from 120 O [9]. These phase currents can be decomposed in positive, negative and zero sequence currents according to Fortesque’s transform. At rotor speed, the positive sequence components produce a forward-traveling magneto motive force and are only appeared in balanced operation of the synchronous generator. The negative sequence components produce magneto-motive force that travels opposite rotor speed. Meanwhile, the zero sequence components produce a zero traveling field in an air-gap and do not interact with the rotor in term of the fundamental component. Both, Positive and negative sequence components under unbalanced steady state condition produce a net magneto-motive force with a sinusoidal variation of its maximum amplitude and will also appear a sinusoidal variation with a frequency two times higher than the fundamental frequency. Consequently, the speed of the generator will not be constant in steady state condition. B. Synchronous Generator Dynamic Mathematical Model For all of usual generator application, there is more than one generator operating in parallel to supply demanded by the loads. To analyze the dynamic of generators under unbalanced steady state operation, which is power angle or load angle characteristic, a “hybrid” method by combination between unbalanced three phase load flow analysis and rotor’s qd0 reference frame of generator model which substitutes the model of generator in load flow analysis can be used. The dynamic mathematical model of a balanced synchronous generator with one q-axis damping winding is composed by the set differential equation as presented in [10] and also below. The differential equations of electrical dynamic that describe the stator and rotor windings and are written in qd0 reference frame are, shown in (1).

𝜔𝑟 𝑟 𝑝 𝑟 𝜓𝑑𝑠 + 𝜓 𝜔𝑏 𝜔𝑏 𝑞𝑠 𝑝 𝑟 𝑟 𝑟 𝑣0𝑠 = −𝑟𝑠 𝑖0𝑠 + 𝜓 𝜔𝑏 0𝑠 𝑝 𝑟 𝑟 𝑣𝑘𝑑 = −𝑟𝑘𝑑 𝑖𝑘𝑑 + 𝜓𝑟 𝜔𝑏 𝑘𝑑

𝜔𝑟 𝑟 𝑃 𝑟 𝜓𝑞𝑠 + 𝜓 𝜔𝑏 𝜔𝑏 𝑑𝑠 𝑝 𝑟 𝑟 𝑟 𝑣𝑘𝑞 = −𝑟𝑘𝑞 𝑖𝑘𝑞 + 𝜓 𝜔𝑏 𝑘𝑞 𝑝 𝑟 𝑟 𝑣𝑓𝑑 = −𝑟𝑓𝑑 𝑖𝑓𝑑 + 𝜓𝑟 𝜔𝑏 𝑓𝑑 𝑟 𝑟 𝑣𝑑𝑠 = −𝑟𝑠 𝑖𝑑𝑠 +

𝑟 𝑟 𝑣𝑞𝑠 = −𝑟𝑠 𝑖𝑞𝑠 +

(1)

The first three equations describe the stator winding (subscript s) and the following three equations describe the rotor winding (superscript r). The subscript k is used for the damping windings (kq for q-axis damping winding and kd for direct axis) while the subscript f is used for the field winding. In these v represents the voltage of windings, I describes the electrical current flowing in the winding, 𝜓 represents the magnetic flux connecting the winding, p represents differential operator (d/dt), 𝜔𝑟 and 𝜔𝑏 are angular speed of the rotor refered to a two pole generator and reference angular speed corresponded to the rated frequency, respectively. The magnetic flux 𝜓 for each winding is represented in (2). Since the damping 𝑟 𝑟 windings are short-circuited so the value of 𝑣𝑘𝑞 and 𝑣𝑘𝑑 are null. 𝑟 𝑟 𝑟 𝑟 𝜓𝑞𝑠 = −𝑥𝑙𝑠 𝑖𝑞𝑠 + 𝑥𝑚𝑞 (−𝑖𝑞𝑠 + 𝑖𝑘𝑞 )

𝑟 𝑟 𝑟 𝑟 𝑟 𝜓𝑑𝑠 = −𝑥𝑙𝑠 𝑖𝑑𝑠 + 𝑥𝑚𝑑 (−𝑖𝑑𝑠 + 𝑖𝑓𝑑 + 𝑖𝑘𝑑 )

𝑟 𝜓0𝑠 = −𝑥𝑙𝑠 𝑖0𝑠

𝑟 𝑟 𝑟 𝑟 𝜓𝑘𝑠 = 𝑥𝑙𝑘𝑞 𝑖𝑘𝑞 + 𝑥𝑚𝑞 (−𝑖𝑞𝑠 + 𝑖𝑘𝑞 )

𝑟 𝑟 𝑟 𝑟 𝑟 𝜓𝑘𝑑 = 𝑥𝑙𝑘𝑑 𝑖𝑘𝑑 + 𝑥𝑚𝑑 (−𝑖𝑑𝑠 + 𝑖𝑓𝑑 + 𝑖𝑘𝑑 )

(2)

𝑟 𝑟 𝑟 𝑟 𝑟 𝜓𝑓𝑑 = 𝑥𝑙𝑓𝑑 𝑖𝑓𝑑 + 𝑥𝑚𝑑 (−𝑖𝑑𝑠 + 𝑖𝑓𝑑 + 𝑖𝑘𝑑 )

Where 𝑟𝑠 , 𝑟𝑘𝑞 , 𝑟𝑘𝑑 , 𝑟𝑓𝑑 , 𝑥𝑙𝑠 , 𝑥𝑙𝑘𝑞 , 𝑥𝑙𝑘𝑑 , 𝑥𝑙𝑓𝑑 , 𝑥𝑚𝑞 and 𝑥𝑚𝑑 are the electrical fundamental parameters of synchronous generator. The direct-axis reactance 𝑥𝑑 and the quadrature-axis reactance 𝑥𝑞 are given by (3). 𝑥𝑑 = 𝑥𝑙𝑠 + 𝑥𝑚𝑑

𝑥𝑞 = 𝑥𝑙𝑠 + 𝑥𝑚𝑞

(3)

The mechanical part of the generator is described by two differential equations as described in (4). 2𝐻

𝑝𝛿 = 𝜔𝑟 − 𝜔𝑠

𝜔𝑠

𝑝𝜔𝑟 = 𝑇𝑚 − (𝜓𝑑 𝑖𝑞𝑠 − 𝜓𝑑 𝑖𝑞𝑠 ) − 𝑇𝑑𝑎𝑚𝑝

(4)

In equation (4), H is an inertia constant of the turbine-generator set, 𝑇𝑚 is the mechanical torque of the turbine and 𝑇𝑑𝑎𝑚𝑝 is a damping torque. The damping torque represents the rotational losses of the rotating parts which consist of the magnetic losses and the mechanical losses.

𝐜𝐨𝐬 𝜽 𝐬𝐢𝐧 𝜽 (𝟐𝒗𝒂 − 𝒗𝒃 − 𝒗𝒄 ) ∕ 𝟑

𝒗𝒒 𝒄𝒐𝒔 𝜽 − 𝒗𝒅 𝒔𝒊𝒏 𝜽

(𝒗𝒄 − 𝒗𝒃 ) ∕ 𝟑 𝒗𝒒 𝒔𝒊𝒏 𝜽 + 𝒗𝒅 𝒄𝒐𝒔 𝜽 (𝒗𝒂 + 𝒗𝒃 + 𝒗𝒄 ) ∕ 𝟑

𝒗𝟎

abc to dq0 Converter 𝑽𝒂𝒈

𝑽𝒎𝟏 𝐜𝐨𝐬(𝝎𝒕 − 𝜸𝟏 )

𝒐𝒖𝒕_ 𝑽𝒕 𝒐𝒖𝒕_ 𝑰𝒕

𝑽𝒒𝒊𝒆 𝑽𝒅𝒊𝒆

𝒐𝒖𝒕_𝑷𝒈𝒆𝒏 𝑽𝒃𝒈

𝑽𝒎𝟐 𝐜𝐨𝐬 𝝎𝒕 +

𝟐𝝅 − 𝜸𝟐 𝟑

𝑽𝒎𝟑 𝐜𝐨𝐬 𝝎𝒕 +

𝟒𝝅 − 𝜸𝟑 𝟑

𝑽𝒄𝒈

𝒐𝒖𝒕_𝑸𝒈𝒆𝒏

𝑬′𝒇

𝒐𝒖𝒕_𝜹 𝒐𝒖𝒕_ 𝝎𝒓 𝝎𝒃

𝑻𝒎

𝒐𝒖𝒕_𝑻𝒆

Generator Block

Fig. 1. Balanced generator with unbalanced inputs, 𝛾1 ≠ 𝛾2 ≠ 𝛾3

𝑽𝒕

𝒗𝒒𝒕

𝒙𝒅 − 𝒙𝒅′

(𝒗𝟐𝒒 + 𝒗𝟐𝒅 )

Gain 1

𝑬′𝒇

𝒊𝒒 – + –

𝑰𝒕 (𝒊𝟐𝒒 + 𝒊𝟐𝒅 )

𝟏 𝒔

𝟏/𝑻′𝒅𝟎

𝑬′𝒒

𝑷𝒈𝒆𝒏

𝒗𝒅𝒕

𝒗𝒒 𝒊𝒒 + 𝒗𝒅 𝒊𝒅

ADD

𝑽𝒒𝒊𝒆 X

𝒗𝒒 𝒊𝒅 − 𝒗𝒅 𝒊𝒒

VIPQ

MUX

Stator Winding

qde to qdr Converter

𝟏 𝒔

– +

𝒊𝒅

𝑽𝒅𝒊𝒓

𝒗𝒒𝒆 ∗ 𝐬𝐢𝐧 𝜹 + 𝒗𝒅𝒆 ∗ 𝐜𝐨𝐬 𝜹

𝑽𝒅𝒊𝒆

𝑸𝒈𝒆𝒏

𝑽𝒒𝒊𝒓

𝒗𝒒𝒆 ∗ 𝐜𝐨𝐬 𝜹 − 𝒗𝒅𝒆 ∗ 𝐬𝐢𝐧 𝜹

𝑬′𝒅

𝟏 𝒔

𝟏/𝑻′𝒒𝟎

𝐬𝐥𝐢𝐩 𝑬′𝒒

+ + –

ADD

𝝎𝒆 𝝎𝒃

𝟏/(𝟐 ∗ 𝑯)

𝜹

𝟏 𝒔

𝝎𝒃

+ +

𝐬𝐥𝐢𝐩(𝐩𝐮) 𝟐

X 𝒙𝒒 − 𝒙′𝒅

𝑻𝒎𝒆𝒄𝒉

𝝎𝒓 /𝝎𝒃

𝑻𝒆𝒎 Gain 2

− 𝑬′𝒒 ∗ 𝒊𝒒 + 𝑬′𝒅 ∗ 𝒊𝒅 + 𝒊𝒒 ∗ 𝒊𝒅 (𝒙𝒒 − 𝒙′𝒅 )

MUX

Rotor

Fig. 2. Inner block of transient operation of three-phase synchronous generator [11]

3. SIMULATION METHOD OF SYNCHRONOUS GENERATOR DYNAMIC To study the dynamic of synchronous generator from the small-signal point of view, several simulations were performed under EDSA 2000 and Matlab/Simulink. The process of numerical simulation method can be presented by the block diagram of Fig. 3, in which the role and content of the box simply illustrated a follows: START

Input the raw data and information before the flow calculation and calculate the dynamics of synchronous generator

Model the 500 KV EHV Jamali System

Model the balanced synchronous generator using qd0 3-Φ reference frame

Analyze the system using unbalanced Three-phase Newton-Raphson loadflow (EDSA 2000), Loads are unbalance Verify the model using PSS Tecquipment NE9070; Have a similar trend?

Calculate the contribution of each generator to loads and flows using “common” and “link” method

Yes

Simulate the dynamics of unbalanced steady state condition of balanced synchronous generator connected to 500 KV EHV (Tanjung Jati B and Grati )

Present the results

STOP

Fig. 3. Simulation flowchart

No

The unbalanced Three-phase Newton-Raphson Loadflow, EDSA 2000, is used to analyze unbalanced steady state condition of the 500 kV EHV Jamali Systems. The substitution of the loadflow generator’s model consisted of active and reactive power injections by the rotor’s qd0 reference frame of synchronous generator model is intended to find the phenomenon influenced by unbalanced three-phase. To determine the verified model, the proposed generator model of balanced synchronous generator is compared with PSS Techquipment NE 9070 through similarity of their trends. The results of loadflow analysis are then used as the inputs of balanced synchronous generator’s model which uses qd0 reference frame. 4.

RESULTS AND ANALYSIS

A. The 500 kV EHV Jamali System The studied system is the 500 kV EHV Jamali System that comprises 4-regions, such as Region I: Banten-Jakarta, Region II: West Java, Region III: Central Java-Yogyakarta and Region IV: East Java-Bali. It also has 71 line nodes, 27 lines of inter buses and 9 generator nodes ,such as Suralaya 2450 MW, Cirata 1400 MW, Muara Tawar 500 MW, Saguling 450 MW, Grati 750 MW, and Gresik 298 MW, shown in Fig. 3. In this system, Paiton’s bus is the swing node and others are the PV nodes. System capacity is 100,000 MVA. The Test generators are Tanjung Jati B as a remote site. B. Load-flow Calculation The scheme definition is unbalanced condition. According to this plan, using EDSA 2000 software program based on Newton-Raphson method we can get the flow calculation results in Fig. 4. Table (I) presents a three-phase volatge values of generator terminal before and after loading conditions. It is shown that voltage variatons of the generator terminal influenced by unbalanced load and the phenomenons are happent at their angle phases which are swung from their origin values .

G_TJ.T-B

G

G

G G6_TJ.T-

G6_GRESK

G4_SGL

GN G1_SRLYA

G

Remot e site

G2_SRLYA BEKASI

G

GRESK

SBYBART

G2_SRLY G1_SRLYA 5V A

G

SAGULING

1902 A 288660 SURALAY V A

BDGSLTAN

IBT_BKS 1

IBT_SBT1 IBT_SBT 2

IBT_GRS K

IBT_BKS 2 CAWANG

G8_GRATI G5_CRATA

202 A 280424 CAWAN V

IBT_BKS 1 IBT_BKS 2

1505

G

CILEGON

283070 V

_

IBT_SLY IBT_SLY 2 1

UNGARN

GRATI

BDGSLTAN

992 A

2A

IBT_GRS K

G8_GRATI

IBT_BDG IBT_BDG 2 1

1027

IBT_CWG 2

263246 V

CIRATA

IBT_CLG 2

IBT_UGN2

IBT_CRT1IBT_CRT2

G

1170

IBT_CLG1 IBT_GRTI

281141 V GANDU

IBT_UGN1

L

CIBNONG

IBT_CLG2

670 A 296 A

280511 VCIBNONG

1954

PAITON

MDRNCANG

G_PAITN

N

IBT_CBG1 IBT_CBG

IBT_MDRC CIBATU

G

TASIK

IBT_PTN1

DEPOK

PEDAN

IBT_PTN2

277169 V

IBT_GDL 1

IBT_GDL 2

KEMBN GA

279972 IBT_CBG1 V IBT_CBG

IBT_DPOK

516 A IBT_CBT IBT_CBT3 1 IBT_CBT2

IBT_KBG1 IBT_KBG2

IBT_TSIK IBT_PDN 1

IBT_PD N2

G3_MTWA R

G

MDRNCANG

2605 A 404 A

IBT_GRTI

288657 VPAITO N

265921 V

TASIK

305 A

M.TAWAR

299 A

(a)

896 A

IBT_MDRC

1280 A 288676292 A V

IBT_DPOK

IBT_KDR I

284001 VCIBAT U

2

DEPOK

KEDIRI

M.TAWAR

IBT_KBG1 IBT_KBG2

266289 V

812 A

795 A G3_MTWAR

G

IBT_UGN2 IBT_UGN1

602 A

841 A IBT_GDL IBT_GDL 2 1 KEMBNGA

608 A

IBT_CRT1IBT_CRT2

I

1302

459 A IBT_CLG1

587 A 288666 GRAT V

UNGAR N

G7_PAITN

GANDUL

G

1194

288675 V

IBT_CWG1

IBT_SBT 2

IBT_SBT1

485A

G5_CRAT A

1183 A

287662 VCILEGON

2292

SBYBAR T

76 A

G

IBT_BDG IBT_BDG 2 1 CIRATA

IBT_CWG 1 IBT_CWG

K

288673 992 A 288676 VTJATI B 932 AV GRESK

277616 884 A V

G

G IBT_SLY IBT_SLY 2 1

G G7_GRES

B

G4_SG LN

288676 1178 A SAGULING V

280345 V BEKASI

G

2165 A SURALAYA

G

288675 TJATI_B

IBT_CBT1 IBT_CBT3 IBT_CBT2

IBT_TSIK

IBT_PTN1

253881 V

PEDAN

257373 V

IBT_PTN2

KEDIRI

579 A IBT_PDN1 IBT_PD N2

IBT_KDR I

(b)

Fig. 4. The 500 kV EHV Jamali System: (a) Single-line diagram (b) Distribution of flow calculation

Table 1. Values of Generator Terminal Voltages Condition Stand-alone Connected grid and all of IBTs are balanced Connected grid and all of IBTs are 5% of unbalanced Connected grid and all of IBTs are 7.5% of unbalanced

Phase

Tanjung Jati.B

a b c a b c a b c a b c

1∠0O 1∠120 O 1∠240 O 1∠ − 12 O 1∠120 O 1∠240 O 1∠ − 13.5 O 1∠120 O 1∠240 O 1∠ − 13.8 O 1∠120 O 1∠240 O

C. Synchronous Generator Model Verification A software package which embedded in generator virtual laboratory and applied Matlab’s GUI facilities has been created for analysis synchronous generator under unbalanced steady-state conditions (Fig. 6). Matlab’s GUI is a graphical display that contains devices, or components, that enable a user to perform interactive tasks [12]. As an example of using Matlab’s GUI capabilities, menu and plotting commands are implemented in a script file to provide interactive windows. The main menu, which is displayed after running the file, are shown in Fig. 7 and Fig. 8. The verification of the generator model is judged through comparing between generator’s respon by PSS Tecquipment NE9070 (Fig. 9) and by the proposed simulator under no load, balanced and unbalanced conditions, respectively.

User Request

GUI

Simulation Command

Matlab

Result Plot

Simulink

Result Data

Fig. 6 Designed Simulator with GUI

Fig. 7 The main window of the developed tool

Under no load, the output respons of PSS Techquipment NE9070 are non-sinusoidal with varied excitations shown in Fig. 9, eventhough the P.F value is more than 0.8. The generator’s outputs are always non-sinusoidal under standalone operation. The waveform of it will change into sinusoidal form when the generator is connected to the grids.

Inserting for generator parameters Inserting for generator inputs

Fig. 8 The window of inserting the inputs for balanced generator and unbalanced inputs

Fig. 9 PSS Tecquipment NE9070

The results of proposed generator’s model simulation considering P.F variations are described in Fig. 12. It is shown that output respons are in non-sinusoidal forms although the value of P.F excitation is reached up to 0.9. Comparing the result between Fig. 10 and Fig. 12 concludes that the output respons of proposed generator model have similar trend to the output PSS Techquipment NE9070. Figure 11 presents the respons of PSS Techquipmen NE9070. When synchronous generator is under unbalanced load condition, its steady state respon will oscillates less than under balanced load condition. The oscillation magnitude of unbalanced load during transient condion is bigger than balanced loads counterpart. This condition is also occured during simulation of the proposed synchronous model shown in Fig. 13. The oscillation of stator voltage of synchronous generator during interconnecting with 7.5% unbalanced grid is bigger than it is connected to balanced grid. Concludely, the proposed model is valid as a synchronous generator test model.

Staor Cur entMagnitude 3 Grid

Grid

connected Stator Cur ent Magnitude connected 3 Standalone transient steadystate

Grid connected Standalone transient

Grid connected steadystate

2. 5 2. 5

2 2

(0.72 PF exct.) (0.81 PF exct.) Fig. 10 The output of PSS Tecquipment NE 9070

(unbalanced loads) (balanced loads) Fig. 11 Outputs of the PSS Tecquipment NE 9070

1. 5 Stator Current Magnitude

1. 5

8.8

[pu]

Stator Current Magnitude 9.25

9.2

8.7 9.15

It

[pu]

8.75

It

8.65

It [pu]

It [pu]

It [p.u]

8.55

8.5

8.45

9

It [p.u]

8.6 9.1

9.05

1

1

8.4 8.95

8.35 8.9 0.5

1

1.5

2

2.5

3

8.3

0.5

Time [second]

0

5 10 15 20 25 Waktu [mdet]

1

0

1.5

5

2

2.5

0. 5

3

Time [ms]

10 15 20 25 Waktu [mdet]

(0.8 PF exct.) (0.89 PF exct.) Fig. 12 The output of proposed standalone gen.

0.5 0 25 50 75 100 125 150 200 Waktu [mdet]

0 25 50 75 100 125 150 200 Waktu [mdet]

(unbalanced loads) (balanced loads) Fig. 0 13 The outputs of the proposed connected gen. 0

D. Dynamic Simulation of Unbalaced Steadystate Condition -0.5

The simulation represents that a three-phase unbalanced in the angle of phase-a of 0 0.5 1 load 1.5 2 causes 2.5 3 a3.5 shift 4 Waktu [ mdet] generator terminal at steady state condition. The percentage of unbalanced load is proportional to the value of -0.5 0 by 0.5 15%1.5 will 2 2.5increase 3 3.5 4 in phase angle shift. An increase in the percentage of unbalanced load on the entire grid Time [second] O the phase-shift angle of 1.5 ; a further percentage increase by 2.5% would only increase the shift of the phase angle of 0.3O. In contrast, the increase in the percentage of unbalance in the significant loads do not alter the phase angle but will only lead the power flow analysis to faster convergence, i.e. is at 3.5% unbalance (at the entire load of grid, the unbalance of more than 7.5% will result in power flow analysis be convergent).

Magnituda Arus Stator

Magnituda Tegangan Stator 1.001

1.0008

1.6

Generator standalonedata1 Tersambung grid yang seluruh bebannya seimbang Tersambung grid yang seluruh bebannya takseimbang 7.5% It (p.u)

1.0006

1.0004

1.4

1.0002 Vt (p.u)

1.2 1

1

0.9998

0.9996

0.8

Generator standalone Tersambung grid yang seluruh bebannya seimbang Tersambung grid yang seluruh bebannya takseimbang 7.5%

0.9994

0.9992

0.999

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

1

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Waktu (detik)

Waktu (detik)

(Stator voltage magnitude)

(Stator current magnitude)

Daya Aktif Dibangkitkan

Daya Reaktif Dibangkitkan

1.6

1.6

1.4

1.4

1.2

Qgen (p.u)

Pgen (p.u)

1.2

1

0.8

1

0.8

0.6 0.6

0.4

Generator standalone Tersambung grid yang seluruh bebannya seimbang Tersambung grid yang seluruh bebannya takseimbang 7%

0.2

0

0.2

0

0.5

1

1.5

2

2.5

3

3.5

Waktu (detik)

(Generated active power)

4

4.5

Generator standalone Tersambung grid yang seluruh bebannya seimbang Tersambung grid yang seluruh bebannya takseimbang 7.5%

0.4

5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Waktu (detik)

(Generated reactive power)

Fig. 13 The steady state of dynamic generator (voltage, current, and power)

0.8

0.9

1

Arus Fasa - a

Kecepatan Putar Rotor 1.01

2.5

1.008

Generator standalone Tersambung grid yang seluruh bebannya seimbang Tersambung grid yang seluruh bebannya takseimbang 7.5%

2

1.006

1.5 1.004

1

Ia (p.u)

wr/wb (p.u)

1.002

1

0.5

0

0.998

-0.5

0.996

0.992

0.99

-1

Generator standalone Tersambung grid yang seluruh bebannya seimbang Tersambung grid yang seluruh bebannya takseimbang 7.5%

0.994

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

-1.5

-2

5

Waktu (detik)

0

0.5

(Rotor speed) Arus Fasa - b

Arus Fasa - c 2.5

Generator standalone Tersambung grid yang bebannya seimbang Tersambung grid yang bebannya takseimbang 7.5%

2

Generator standalone Tersambung grid yang seluruh bebannya seimbang Tersambung grid yang seluruh bebannya takseimbang 7.5%

2

1.5

1.5

1

1

0.5

0.5

Ic (p.u)

Ib (p.u)

1.5

(Phase-a current)

2.5

0

-0.5

0

-0.5

-1

-1

-1.5

-1.5

-2

1

Waktu (detik)

0

0.5

1

Waktu (detik)

(Phase-b current)

1.5

-2

0

0.5

1

1.5

Waktu (detik)

(Phase-c current)

Fig. 14 The steady state of dynamic generator (rotor speed and phase currents)

The unbalanced load does not affect the two variables of generator, namely stator voltage magnitude and the rotational speed of the rotor. However, a significant influence occurs in other variables that are power angle, generator stator current, generated active power and reactive power and electrical torque. Generated active power has the greatest influence on the effects of 7.5% unbalance that is up to 0.52 p.u. In the phase-a, the grid experienced a moment of loading, both in balance and unbalance; the zero-axis increases from point 0 p.u to the point 0.6 p.u. In contrast, both the phase-b and phase-c are actually declining, from the point 0 p.u to -0.6 p.u.

5.

CONCLUSION The combination between unbalanced three-phase Newton-Raphson load-flow and the rotor’s qd0 reference frame of synchronous generator model can be used to describe the dynamic of synchronous generator under unbalanced steady state operation. In term of computation, unbalanced three-phase load cause a shift in the angle of phase-a of generator terminal at steady state condition. The increasing in the percentage of unbalanced load on the entire grid by 5% will increase in the phase-shift angle of 1.5O; a further percentage increase by 2.5% would only increase the shift of the phase angle of 0.3O. The significant influence of unbalanced load occurs in generated active and reactive powers, stator current magnitude, and phase currents. Other variables of generator, namely stator voltage magnitude and the rotor speed are remain constan.

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Gustavsson I. Laboratory Experiments in Distance Learning. International Conference on Engineering Education. 2001; 8B:1-14. Birt KA, Graffy JJ, McDonald JD. Three-Phase load Flow Program. IEEE Transaction on Power Apparatus System. 1976; 95(1) : 59-66. Saha TN, Basu TK. Analysis of Asymetrical Faults in Synchronous Generators by dq0 Frame of Reference,.Proceeding IEE. 1972; 119(5) : 587-595. Peng L. Overloading Algorithm of Synchronous Generators Under Unbalanced Steady State Operation. International Conference on Electrical Machine and system (ICEMS). 2011; :1-6

[5]

Salim RH, Ramos RA, Bretas NG. Analysis of the Small Sygnal Dynamic Performance of Sysnchronous generators under Unbalanced Operation Conditions. Power and Energy Society General Meeting, IEEE. 2010; :1-8. [6] Trinadha A, Kumar A, Sandhu KS. Study of Wind Turbine based SEIG under Balanced/Unbalanced Loads and Excitation. International Journal of Electrical and Computer Engineering (IJECE). 2012; 2(3) : 353-370. [7] Acha E, Fuerte-Esquivel C, Ambriz-Pérez H, Angeles-Camacho. FACTS, Modelling and Simulation in Power Networks, John Willey & Sons, LTD., Chicester, England. 2005. [8] EDSA Technical. 2000. Available : http://www.edsa.com [9] Boldea I. Synchronous Generator. Boca Raton, FL: Taylor & Francis Group, LLC. 2006. [10] Krause PC, Wasynczuk O, Sudhoff SD. Analysis of Electric Machinery and Drive Systems. Willey-InterScience, A John Willey & Sons, Inc. Publishing, New York. 2002. [11] Sugiarto, Hadi SP, Tumiran, Wijaya FD. Teaching the Large Synchronous Generator Dynamic Model under Unbalanced Steady-State Operation. The 5th International Conference on Information technology and Electrical Engineering (ICITEE). 2013; :425-429. [12] Suryasen K, Devadas, KV, Harish A. GUI based Testing Tool for Transformer. International Journal of Electrical and Computer Engineering (IJECE). 2014; 4(3) : 356-365.