CONTROL OF A UNIFIED POWER FLOW CONTROLLER (UPFC) –A SIMULATION STUDY USING MATLAB/SIMULINK A THESIS
SUBMITTED IN PARTIAL FULFILMENT OF THE
REQUIREMENTS FOR THE AWARD OF THE DEGREE OF
MASTER OF TECHNOLOGY IN
ELECTRICAL ENGINEERING (POWER ELECTRONICS) OF
THE UNIVERSITY OF CALICUT
BY
CH.SUDHAKARA BABU
DEPARTMENT OF ELECTRICAL ENGINEERING REGIONAL ENGINEERING COLLEGE CALICUT - 673 601, KERALA 2002
CERTIFICATE
This is to certify that the thesis entitled “CONTROL OF A UNIFIED POWER FLOW CONTROLER (UPFC) –A SIMULATION STUDY USING MATLAB/SIMULINK ” is a bonafide record of the work done by Mr. CHAKKIRALA.SUDHAKARA BABU, under my supervision and guidance. The
thesis is submitted to the University of Calicut in partial fulfillment of the requirements for the award of the degree of MASTER OF TECHNOLOGY in Electrical
Engineering (Power Electronics).
Dr.P.C.Baby, Professor and Head, Dept. of Electrical Engg., R.E.C., CALICUT
Date: Place:
Sri Suresh Kumar K.S, Asst. Professor, Dept. of Electrical Engg., R.E.C., CALICUT
ACKNOWLEDGMENT
I express my profound sense of gratitude to Mr K. S. Suresh Kumar, Assistant Professor, Department of Electrical Engineering, R.E.C, Calicut, for his systematic guidance, valuable advice and constant encouragement throughout this project work.
I wish to thank Dr. T. L . Jose, Professor and Former Head of the Department, and Dr. P. C. Baby, Professor and Head of the Department, for their
generous support during the course of this work.
I would also like to thank all staff members in the Department, Computer Centre and Library who extended all kind of co-operation for the completion of this
work.
Finally, it gives me a great pleasure to express my sincere thanks to all my
friends who have helped me during the course of this work.
CH.SUDHAKARA BABU
r’se
Series transformer resistance including line resistance
rsh
Shunt transformer resistance
xsh Shunt transformer reactance Synchronously revolving frequency in rad/sec
ωb
Base frequency in rad/sec
VS Generator bus voltage VR Receiving bus voltage
V1 Port 1 voltage
bcap Susaptence
ωo
V2 Port 2 voltage
d,q Direct and Quadrature axis components.
i
x’se Series transformer reactance including line reactance.
LIST OF SYMBOLS
Flexible AC Transmission System
GTO
Gate Turn Off Thyristor
PWM
Pulse Width Modulation
STATCOM Static Synchronous Compensator Static Var Compensator
TCSC
Thyristor Controlled Series Capacitor
UPFC
Unified Power Flow Controller
SVC
ii
FACTS
LIST OF ABBREVATIONS
LIST OF FIGURES
Fig No
Page No
Fig 1.1 Test system
3 6
Fig 2.2 Basic control functions
8
Fig 2.3 Simple two machine system
Fig 2.1 Basic circuit arrangement of Unified Power Flow Controller
Fig 2.4 Two machine system with Unified Power Flow Controller Fig 2.5 Attainable sending-end reactive power vs. transmitted power
10 12 14
and receiving-end reactive power vs. transmitted power values
with the UPFC at δ=0o, δ=30o,δ=60o,δ=90o.
19
Fig 3.2 Definition of orthogonal coordinates
20
Fig 3.3 Transformation in rotating reference frame
21
Fig 3.4 Simple balanced system
23
Fig 3.5 Simplified system of UPFC
26
Fig 3.6 Series injected voltage controller
29
Fig 3.7 Vector representation of real and reactive currents.
30
Fig 3.8 Shunt current controller
31
Fig 3.1 Vector representation of instantaneous three phase variables
Fig 3.9 Converter voltage calculator
32
iii
35
Fig 4.6 Transmission line 1 model
Fig 4.8 Inverter DC side control model Fig 4.9 Load modeling
Fig 4.11 Power calculator block
Fig 5.1 Test system
Fig 4.10 Series inverter control model
Fig 4.7 Transmission line 2 model
36
Fig 4.3 Organization of UPFC modeling blocks
Fig 4.5 Shunt converter control block
35
Fig 4.2 Transformation block in synchronous revolving reference frame
Fig 4.4 Unified Power flow Controller block
Fig 4.1 Transformation block in stationary reference frame
37
38 40 41 42 43 44 45 47 49
Fig 5.3-5.6 Simulation resu1ts for case (i) continued
50
Fig 5.7 Simulation results for case (ii)
55
Fig 5.2 Simulation results for case(i)
56
Fig 5.12 Simulation results for case (iii)
60
Fig 5.13-5.15 Simulation results for case (iii) continued
61
Fig 5.16 Simulation results for case (iv)
64
Fig 5.17-5.18 Simulation results for case (iv) continued
65
Fig 5.19 simulation results for case (v)
67
Fig 5.8-5.11 Simulation results for case (ii) continued
iv
Fig 5.20-5.22 Simulation results for case (v) continued
68
72
Fig 5.24-5.26 Simulation results for case (vi) continued
Fig 5.27 Simulation results for case (vii)
Fig 5.28-30 Simulation results for case (vii) continued.
Fig 5.23 Simulation results for case (vi)
v
73
77
78
CONTENTS
Page No.
ABSTRACT
i
LIST OF ABBREVATIONS LIST OF FIGURES
CHAPTER 1 INTROUCTION
1.1 Aim of the Project
LIST OF SYMBOLS
1.2 Organization of the Repot
ii iii
1 2 4
2.1 Introduction
CHAPTER 2 UNIFIED POWER FLOW CONTROLLER (UPFC) 5 5
2.3 Operation of UPFC
6
2.4 Basic Control Functions
7
2.5 Basic Functions of P and Q Control
9
2.2 Circuit Arrangement
2.6 Independent Real and Reactive Power Flow Control
13
2.7 Summary
CHAPTER 3 CONTROL STRATEGY FOR UPFC 3.1 Vector Representation of Instantaneous Three Phase Quantities
18
3.2 Three Phase to D-Q Transformation
19
3.3 Transformation of Impedance Matrix
23
3.4 Controller Design For UPFC
25
3.5 Series Injected Voltage Controller
3.5.1 Power Flow Control
26
29
3.6 Shunt Current Control
3.5.2 Port 2 Voltage Control
30
CHAPTER 4 SIMULINK MODELLING OF UPFC
4.1 Introduction to MATLAB/SIMULINK
33
4.2 Modeling 3ph to D-Q Transformation
34
4.3 Modeling of UPFC
35 36
4.3.2 Transmission Line 1 Model
39
4.3.1 Shunt converter Control Model
41
4.3.4 Inverter DC-side Control Model
41
4.3.3 Transmission Line 2 Model
43
4.3.6 Series Inverter Control Modeling
43
4.3.5 Load Modeling
CHAPTER 5 SIMULATION RESULTS AND DISCUSSIONS 46
5.2 Test System for Simulation
47
5.3 Simulation Results and Discussions
48
5.1 Challenges in Computer Simulation
CHAPTER 6 CONCLUSIONS REFERENCES
81 83
INTODUCTION
Chapter 1
What is most interesting for transmission planners is that FACTS
technology opens up new opportunities for controlling power and enhancing the usable capacity of the present transmission system[13]. The opportunities arise through the ability of FACTS controllers to control the interrelated parameters that govern the
operation of transmission systems including series impedance, shunt impedance, current, phase angle, and damping of oscillations at various frequencies below the rated
frequency. These constraints cannot be overcome otherwise, while maintaining the required system stability, by mechanical means without lowering the useable transmission capacity. By proving added flexibility, FACTS controllers can enable a line
to carry power closer to its thermal rating. Mechanical switching needs to be supplemented by rapid- response power electronics. Static VAR compensators control only one of the three important parameters (voltage, impedance, phase angle) determing the power flow in the AC power
systems viz. the amplitude of voltage at selected terminals of the transmission line. It has long been realized that an all solid-state or advanced, static VAR compensator, which is true equivalent of ideal synchronous condenser, is technically feasible with the use of gate turn-off (GTO) thyristors. The UPFC is a recently introduced FACTS controller which has the capability to control all the four transmission parameters. The UPFC not
only performs the functions of the STATCON, TCSC, and the phase angle regulator but
1
also provides additional flexibility by combining some of the functions of these
controllers.
1.1 Aim of the Project
The Unified Power Flow Controller (UPFC) consists of two voltage sourced converters using power switches, which operate from a common DC circuit of a DC-storage capacitor. This arrangement functions as an ideal ac to ac power converter in
which the real power can freely flow in either direction between the ac terminals of the two converters and each converter can independently generate (or absorb) reactive power at its own ac output terminal. .
The aim of the project is to develop a control strategy for UPFC, modeling UPFC using MATLAB/SIMULINK and to analyze the control strategy to use the series
voltage injection and shunt current injection for UPFC control. A UPFC control strategy, in general, should preferably have the following attributes: 1.Steady state objectives (i.e. real and reactive power flows) should be readily achievable by setting the references of the controllers.
2.Dynamic and transient stability improvement by appropriate modulation of controller references.
To simplify the design procedure we carry out the design for the series and shunt branches separately. In each case, a simple equivalent circuit represents the external system. The design has to be validated when the various subsystems are integrated.
The design tasks are
1. Series injected voltage control
2
(b) UPFC port 2 voltage control by using series voltage injection.
2. Shunt converter voltage control
(a) Power flow control by using series voltage injection.
(a) Closed loop current (real and reactive) control by shunt current injection. (b) UPFC port 1 voltage control using reactive current injection.
(c) DC side capacitor voltage regulation using active current injection.
Vs
VSI
PL+jQL
load
Psh+jQsh
Local
UPFC o/p bus(port2)
Rse
P1+ jQ1 Substation bus(port1) Xs
The test system is shown below:
P2+jQ Rse
Xs VR
VSI
Fig. 1.1. UPFC test system
of
the
system
Specifications
taken
for
testing
the
control
strategy
are:
Xse=0.075, Rse=0.0075,Xsh=0.15, Rsh=0.01, gcap= 0.02, bcap= 2.Vr=1∠0, Load 3p.u with p.f.0.8 (lag). All the above quantities are on the UPFC MVA base (33.33 MVA), which is assumed to be 1/3rd of the transmission line MVA base.
The proposed control strategy was tested for the following cases:
Case(i) :Vs=1∠0, initially shunt control is OFF ,shunt control on at T=0.04s, Pref=0,load
switch on at t=0.08sec, at t=0.25s load throughout and subsequently shunt control OFF. 3
Case(iii): repeating case(i) for Pref= 3 p.u Case(iv): repeat the case(I) for Vs =1.1∠20, Pref =3 p.u
Case(ii) : repeating the case(i) for load 3p.u with lead p.f 0.8
Similarly the control strategy was tested for 7 cases. In all the cases
performance of the system was analyzed through appropriate waveforms and control system gains were tuned for satisfactory performance.
1.2 Organization of the Report
The report of the work done is organised as follows: After this introductory Chapter, Chapter 2 gives a brief overview of
Unified Power Flow Controller. In this Chapter the circuit arrangement, operation, basic control functions and characteristics of the UPFC are discussed.
The Chapter 3 discusses the proposed control strategy. In this Chapter three-phase to D-Q transformation and mathematical modeling of the control strategy for independent control of shunt and series branches of the UPFC are discussed. The Chapter 4 presents an introduction to SIMULINK and modeling of
UPFC using MATLAB/SIMULINK.
The Chapter 5 discusses the challenges in computer simulation of Power
Electronic Systems and presents the simulation results on the test system for different cases.
The last Chapter presents important conclusions. Adequate references are
provided at the end of the chapter.
4
Chapter2
UNIFIED POWER FLOW CONTROLLER (UPFC) 2.1 Introduction
Gyugyi proposed the Unified Power Flow Controller (UPFC)
concept in 1991[13]. The UPFC was devised for the real time control and dynamic compensation of ac transmission systems, providing multifunctional flexibility required to solve many of the problems facing the delivery industry[1-3] . Within the framework
of traditional power transmission concepts, the UPFC is able to control, simultaneously or selectively, all the parameters affecting power flow in the transmission line (i.e.,
voltage, impedance and phase angle), and this unique capability is signified by the adjective “unified” in its name. Alternatively, it can independently control both the real and reactive power flows in the line.
2.2 Circuit Arrangement:
In the presently used practical implementation, the UPFC consists
of two switching converters, which in the implementations considered are voltage source inverters using gate turn-off (GTO) thyristor valves, as illustrated in the Fig 2.1.These back to back converters labeled “ Inverter 1” and “ Inverter 2” in the figure, are operated
from a common dc link provided by a dc storage capacitor. This arrangement functions as an ac to ac power converter in which the real power can freely flow in either direction 5
generate (or absorb) reactive power at its own ac output terminal.
between the ac terminals of the two inverters and each inverter can independently
Fig 2.1. Basic circuit arrangement of unified power flow controller
2.3 Operation of UPFC
Inverter 2 provides the main function of the UPFC by injecting an ac
voltage Vpq with controllable magnitude Vpq (0≤ Vpq ≤ Vpqmax) and phase angle ρ(0 ≤ ρ ≤ 360), at the power frequency, in series with the line via an insertion transformer. The injected voltage is considered essentially as a synchronous voltage source. The transmission line current flows through this voltage source resulting in real and reactive power exchange between it and the ac system. The real power exchanged at the ac
terminal (i.e.,at the terminal of insertion transformer) is converted by the inverter into dc
6
power that appears at the dc link as positive or negative real power demanded. The reactive power exchanged at the ac terminal is generated internally by the inverter.
The basic function of Inverter 1 is to supply or absorb the real power demanded by Inverter 2 at the common dc link. This dc link power is converted back to ac and coupled to the transmission line via a shunt-connected transformer. Inverter 1 can also generate or absorb controllable reactive power, if it is desired, and
there by it can provide independent shunt reactive compensation for the line. It is important to note that where as there is a closed “direct” path for the real power
negotiated by the action of series voltage injection through Inverters 1 and 2 back to the line, the corresponding reactive power exchanged is supplied or absorbed locally by inverter 2 and therefore it does not flow through the line. Thus, inverter 1 can be operated
at a unity power factor or be controlled to have a reactive power exchange with the line independently of the reactive power exchanged by the by the Inverter 2. This means there is no continuous reactive power flow through UPFC.
2.4 Basic Control Functions
Operation of the UPFC from the standpoint of conventional power
transmission based on reactive shunt compensation, series compensation, and phase shifting, the UPFC can fulfill these functions and thereby meet multiple control
objectives by adding the injected voltage Vpq, with appropriate amplitude
7
Vo
Vc
Vc
∆Vo
Vσ
σ
(b) series compensation
(a) voltage regulation
Vo+Vc
Vo
Vo
Vc
Vo+∆Vo
Vo
Vpq
Vo+Vσ
Vo+∆V0+Vc+Vσ (d) Multi-function Power flow control
(c) Phase angle Regulation
Fig. 2.2 - Basic UPFC control functions: (a) Voltage regulation, (b) Series compensation, (c) Angle regulation, and (d) Multifunction power
8
and phase angle, to the terminal voltage Vo. Using phasor representation, the basic UPFC power flow control functions are illustrated in Fig 2.2.
Terminal Voltage Regulation, similar to that obtainable with a transformer tap- changer having infinitely small steps, as shown at (a) where Vpq =∆V (boldface letters represent phasors) is injected in-phase (or anti-phase) with Vo.
Series Capacitor Compensation is shown at (b) where Vpq =Vc is in quadrature with the line current I.
Transmission Angle Regulation (phase shifting) is shown at (c) where Vpq=Vo is injected with angular relationship with respect to Vo that achieves the desired s phase shift
(advance or retard) with out any change in magnitude.
Multifunctional Power Flow Control, executed by simultaneous terminal voltage regulation, series capacitive compensation, and phase shifting, is shown at (d) where Vpq =∆V +Vc+Vo
2.5 Basic Principles of P and Q Control [1,3] Consider Fig 2.3. At (a) a simple two machine (or two bus ac
inter-tie) system with sending end voltage Vs, receiving-end voltage Vr, and line (or tie) impedance X (assumed, for simplicity, inductive) is shown. At (b) the voltages of the
system in the form of a phasor diagram are shown with transmission angle δ and |Vs|=|Vr|=V. At (c) the transmitted power P (P=V2/X sinδ) and the reactive power 9
Q=Qs=Qr (Q= V2/X (1-cosδ)) supplied at the ends of the line are shown plotted against
angle δ. At (d) the reactive power Q=Qs=Qr is shown plotted against the transmitted
P
Qs
Qs,Qr
Q
2
X
P
V
Vx
(b)
|Vs|=|Vr|
δ
(c)
δ=90
1
Vr δ
90
0
(a
Vs
2
P
Vs
power P corresponding to “stable values of δ (i.e., 0≤δ≤90°).
Qs Qr
P=V2/X sinδ
2
0
P
1
(d)
Fig 2.3. -Simple two machine system (a), related voltage phasors (b), real and reactive power verses transmission angle (c), and sending-end/ receiving- end reactive power verses transmitted real power(d).
10
Qs Qr
The basic power system of Fig 2.3 with the well known transmission characteristics is introduced for the purpose of providing a vehicle to
establish the capability of the UPFC to control the transmitted real power P and the reactive power demands, Qs and Qr, at the sending end, respectively, the receiving end of the line.
Consider Fig 2.4.The simple power system of Fig 2.3 is
expanded to include the UPFC. The UPFC is represented by a controllable voltage source in series with the line which, as explained in the previous section, can generate or absorb reactive power that it negotiates with the line, but the real power it exchanges must be
supplied to it, or absorbed from it, bye the sending end generator. The UPFC in series with the line is represented by the phasor Vpq having magnitude Vpq (0≤ Vpq ≤ Vpqmax) and
angle ρ(0 ≤ ρ ≤ 360) measured from the given phase position of phasor Vs, as illustrated in the figure. The line current represented by the phasor I, flows through the series voltage source, Vpq, and generally results in both reactive and real power exchanges. In order to represent UPFC properly, the series voltage source
is stipulated to generate only the reactive power Qpq it exchanges with the line. Thus the real power P pq it negotiates with the line is assumed to be transferred to the sending-end generators if a perfect coupling for real power flow between it and the sending-end generator excited. This is in arrangement with the UPFC circuit structure in which the dc
link between the two constituent inverters establishes a bi-directional coupling for real power flow between the injected series voltage source and the sending end bus. 11
As Fig 2.4 implies, in the present discussion it is further assumed
for clarity that the shunt reactive compensation capability of the UPFC not utilized. This
is the UPFC shunt inverter is assumed to be operated at unity power factor, its sole function being to transfer the real power demand of the series inverter to the sending-end
generator. With these assumptions, the series voltage source, together with the real power coupling to the sending end generator as shown in fig 2.4, is an accurate representation of
Vpq
P
Qr
ρ
Vpq
Ppq
Vs
Vx
Qs
the basic UPFC.
Vx
Vs
Vr
Vr δ
Fig 2.4.Two machine system with the unified power flow controller
It can be readily observed in Fig 2.4 shows that the
transmission line “sees” Vs+Vpq as the effective sending end voltage. Thus it is clear that
the UPFC effects the voltage (both its magnitude and angle) across the transmission line 12
and therefore it is reasonable to expect that it is able to control, by varying the magnitude and angle of Vpq, the transmittable real power as well as the reactive power demand of
the line at any given transmission angle between the sending-end and receiving-end voltages.
2.6 Independent Real And Reactive Power Flow Control
In Fig 2.5(a) through 2.5(d) the reactive power Qs supplied by the sending end generator, and Qr supplied by the receiving-end generator, are shown plotted separately against the transmitted power P as a function of the magnitude Vpq and
angle ρ of the injected voltage phasor Vpq at four transmission lines: δ=0, 30°, 60°, and 90°. At Vpq=0, each of these plots becomes a discrete point on the basic Q-P curve as
shown in Fig 2.3 (d), which is included in each of the above figures for reference. The curves showing the relationships between Qs and P, and Qr and P, for the transmission angle range of 0≤δ≤90°, when the UPFC is operated to provide the maximum transmittable power with no reactive power control (Vpq=Vpqmax and ρ=ρP=Pmax), are also
shown by a broken-line with the label “P(δ)=MAX” at the “sending end” and,
respectively , “receiving-end” plots of the figures.
13
Fig 2.5(a)&2.5(b). Attainable sending-end reactive power vs.transmitted power (left hand side plots)and receiving-end reactive power Vs transmitted power(right hand side plots) values with the UPFC at δ=0° and δ=30°.
14
Fig 2.5(c)&2.5(d). Attainable sending-end reactive power vs.transmitted power
(left-hand
reactive
power
side
plots)
side Vs
values
δ=90°. 15
plots)
transmitted with
the
and power UPFC
receiving-end (right at
hand
δ=60°and
Consider the first Fig. 5(a), which illustrates the case when the
transmission angle is zero (δ=0). With Vpq=0, P, Qs, and Qr are all zero, i.e., the system is
standstill at the origins of the Qs, P, and Qr, P coordinates. The circles around the origin of the {Qs, P} and {Qr, P} planes show the variation of Qs and P, and Qr and P, respectively. As the voltage phasor Vpq, with its maximum magnitude Vpqmax is rotated a full revolution (0≤ρ≤360°). The area with in these circles define all P and Q values
obtainable by controlling the magnitude Vpq and ρ of the phasor Vpq.
In other words, the circle in the {Qs, P} and {Qr, p} planes define
all P and Qs and, respectively, P and Qr values attainable with the UPFC of a given rating. It can be observed, for example, that the UPFC with the stipulated voltage rating of 0.5 p.u. is able to establish 0.5 p.u power flow, in either direction, without imposing
any reactive power demand on either the sending-end or the receiving-end generator. Of course, the UPFC, as seen, can force the generator at one end to supply reactive power for the generator at the other end. (In case of intertie, one system can be forced to supply
reactive power of the line.)
In general at any given transmission angle δ, the transmitted real
power P, and the reactive power demands at the transmission line ends, Qs and Qr, can be controlled freely by the UPFC within the boundaries obtained in the {Qs, P} and {Qr, P}
planes by rotating the injected voltage phasor Vpq with its maximum magnitude a full
revolution. The boundary in each plane is centered around the point defined by the
16
transmission angle on the Q verses P curve that characterizes the basic power transmission at Vpq=0.
Consider the next case of δ=30°(Fig. 5(b)), it is seen that the receiving-end control region boundary in the {Qs, P} plane become an ellipse. As the transmission angle δ is further increased, for example, to 60° (Fig.5(c)), the ellipse defining the control region for P and Qs in the {Qs, P} plane becomes narrower and
finally 90° (Fig.5 (d)) it degenerates into a straight line. By contrast, the control region boundary for p and Qr in the {Qr, P) plane remains a circle at all transmission angles.
2.7 Summary
In summary, the UPFC, with its unique capability to control
independently the real and reactive power flow at any transmission angle provides a
powerful new tool for transmission system control.
17
CONTROL STRATEGY FOR UPFC
Chapter 3
3.1 Vector Representation of Instantaneous Three Phase Quantities:
The notion of the real and reactive power is well known in the phasor sense. However, to study and control the dynamics of the UPFC within subcycle frame
and subject to line distortions, disturbances and unbalance, we need broader definition of reactive power which is valid on an instantaneous basis [4].
The instantaneous real power at a point on the line is given by P=VaIa+VbIb+VcIc. We can define instantaneous reactive voltages conceptually as a part of the three-phase voltage set that could be eliminated at any instant without altering p.
The definition of instantaneous reactive voltage is obtained by vector interpretation of the instantaneous values of the circuit variables. A set of three instantaneous phase variables that sum to zero can be
uniquely represented by a single point in a plane, as illustrated in Fig.3.1. By definition, the vector drawn from the origin to this point has a vertical projection onto each of the three symmetrically disposed phase axis, which corresponds to the instantaneous value of the associated phase variable. This transformation of phase variables to instantaneous vectors can be applied to voltages as well as currents. As the
values of phase variables change, the associated vector moves around the plane describing various trajectories. The vector contains all the information on the three-
18
phase set, including steady-state unbalance, harmonic waveform distortions, and
transient components.
Ib(-)
+C-phase axis I
Ic(+)
+A-phase axis
Va(+)
+B-phase axis
Fig.3.1 Vector representation of instantaneous three-phase variables
3.2Three Phase to D-Q Transformation
In Fig 3.2, the vector representation is extended by introducing an
orthogonal co-ordinate system in which each vector is described by means of its dsand qs- components. The transformation of phase variables to ds and qs co-ordinates is
as follows.
19
If Va, Vb, Vc are balnced set of voltages Va= √2 Vrms sinωt, Vb= √2 Vrms sin(ωt-120), Vc= √2 Vrms sin(ωt-240) +ds-axis
(C-axis)
MMF direction
+qs-axis
(A-axis)
2 − 1 = C 1 3 2
0
1
3 2
−
−
1
2 1 2
[ ]
Fig.3.2 Definition of orthogonal co-ordinates
1 2
3 2 1 − 2 1 2
then by using the above trasformation matrix, the ds and
(3.1)
qs axis coordinates are
given by
Vds = Vrms cosωt
Vqs = -Vrms sinωt
(3.2)
The per unit values represent rms qunatities.
The constants are derived based on power invarience principle
20
[C1]=
0 3 2 − 2 3 2
1 − −
1
2 1 2
1 2 1 2 1 2
The inverse trasformation matrix is given by Vold = C1 Vnew
Va Ia+ Vb Ib+ Vc Ic =Vds Ids +Vqs Iqs
(3.3)
Single phase per-unit system is used and the per-unit values represent rms quantities. Fig.3.3 shows how further manipulation of vector coordinate frame leads to a useful separation of variables for power control purposes. The d-axis voltage
component Vd, accounts for real component and q-axis voltage Vq, is the instantaneous reactive component. The d and q axes are not stationary in the plane. They follow the
trajectory of the voltage vector, and the d and q co-ordinates within this synchronously ds-axis
d-axis
qs-axis
θ
q-axis
Fig 3.3 Transformation in rotating reference frame
reference frame are given by the following time-varying transformation:
21
2
sin θ cosθ
(3.4)
θ [C ] = −cos sin θ
The transformation matrix in synchronously revolving reference frame is given by
For balanced set of phase voltages Va= √2 Vrms sin(ωt-θ) Vb= √2 Vrms sin(ωt-120-θ) Vc= √2 Vrms sin(ωt-240-θ) and θ=ωt. the d and q axis components are given by
Vd = Vrms cosθ
Vq = -Vrms sinθ
Under balanced steady-state conditions, the co-
ordinates of the voltage and current vectors in synchronous reference frame are
1
=[C]t
constant quantities. The inverse transformation in synchronous reference frame is [C]-
The d-q axis real power component is P= Vd Id + Vq Iq and the reactive power is given by Q= -Vq Id + Vd Iq. These represent power in single phase quantities. This can be
summarized this way, defining complex vectors in d-q plane is V∧ = Vd + j Vq, I∧ = Id +j Iq
P + jQ = V I* = ( Vd I d + Vq Iq )+ j (Vq I d –Vd I q )
22
3.3 Transformation of Impedance Matrix [5]
The transformation is explained by considering a simple three-phase
Ra
Ia
system as shown in Fig 3.4
La
V1a
V2a
Lb
Rb
V2b
V1b Lc
Rc
V2c
V1c
Fig 3.4 Simple balanced system
The balanced three-phase system can be transformed into a synchronously rotating
orthogonal system.
V 1a − V 2 a R + PL 0 0 R + PL 0 V 1b − V 2b = 0 V − V 0 0 R + PL 2c 1c
i a ib i c
(3.5)
Znew = C1t Z old C
in the ds- qs plane the impedance matrix transformed into
Z
new
=
R + PL 0 0 R + PL
(3.6)
Now in the synchronously revolving reference frame ( d-q transformation) the impedance matrix is transformed into
Z
'
new
=
R + PL − ωL R + PL ωL
(3.7) 23
Where P= d/dt , the voltage equations after d-q transformation is given by the above equation can be written as V d 1 − V d 2 R + PL − ωL i d = − ωL R + PL i d V q1 V q1
d iq dt
R V d1 −V d 2 ω + + iq L id L
=−
R V q1 − V q 2 − + ω id L iq L
dt
=−
(3.9)
(3.10)
d id
(3.8)
per-unit system is adopted according to the following definitions:
'
=
x
x
v =v v ω L x= z '
;
x
B
'
x
B
'
;
x
x
B
B
B
e
;
x
=
ex
'
R=
;
v
B
R
z
B
x = a, b, c
'
i i v z= i
i
by using the per unit system the above equations rewritten as d id dt
b
=−ω
b
R'
x'
R'
i
+ ω iq + ω b d
d iq
=−ω
dt
x'
iq − ω id +
(V d 1 − V d 2)
ω (V b
x'
q1
− V q 2)
x'
(3.11)
(3.12)
Where ωb = base frequency
ω = synchronously rotating system frequency
The significance of the transformation summarized as follows:
1. The physical significance of the phase transformation C1 is therefore to replace the
actual three phase system by an equivalent two phase system.
24
2. The original circuit produced in Fig 3.4 gave rise to an impedance matrix Z with
nine non-zero terms. The transformed impedance matrix Z’ has only four terms.
3.4 Controller Design [6-10]
A control strategy, in general, should preferably have the following attributes: 1.
Steady state objectives (i.e. real and reactive power flows) should be readily
2.
achievable by setting the references of the controllers.
Dynamic and transient stability improvement by appropriate modulation of
controller references.
To simplify the design procedure we carry out the design of the series and shunt branches separately. In each case, the external system is represented
are integrated.
by a simple equivalent. The design has to be validated when the various sub systems
The design tasks are listed below:
Series injected voltage control:
1. a.
Power flow control by series voltage injection.
b.
UPFC port 2-voltage control by series voltage injection.
Shunt converter voltage control a. Closed loop current (real and reactive) control
2.
b. UPFC port 1 voltage control using reactive current injection
25
c. Capacitor voltage regulation using real current injection.
The basic design considerations are illustrated using simplified
system models. The performance of all the controllers is subsequently evaluated using
detailed simulations for a case study.
3.5 Series Injected Voltage Controller
3.5.1 Power Flow Control
In this section we consider the control of real power using series voltage injection. We carry out analysis on the simplified system shown below in Fig.3.5. The
differential equations for the current at port 2 in the D-Q (synchronously rotating at system frequency ω0 ) frame of reference are given by:
dt r
= − r seω b
d iQse
x
i
Dse
se
= − r seω b
x
i
+ω
Qse
se
ese
+
VS
i
−ω
dt
+ ω b (v2 D − v RD )
d i Dse
Qse
i
x
Dse
(3.13)
se
+ ω b (v2Q − v RQ )
x
se
Rse
Xse
Port 2
VR
Fig.3.5 Simplified system UPFC
26
(3.14)
v v
= v1D + eDse
2Q
= v1Q + eQse
2D
where,
The subscripts ‘D’ and ‘Q’ denote the variables in D-Q reference frame.
SD
, v SQ = D − Q components of voltages at the sending end bus
RD
, v RQ = D − Q components of voltages at the receiving end bus
1D
, v1Q = D − Q components of voltages at the UPFC port 1
2D
, v2Q = D − Q components of voltages at the UPFC port 2
v v v v
Power at the receiving end bus PR is approximately equal to that at port 2 ( Pu2 ) of the UPFC in the study state ; therefore we control the power at port 2
P =v i 2
2D
Dse
since the feed back signal is readily available. + v2Q iQse
(3.15)
Power delivered by the series converter is
p
=
se
se
e i D
se D
+
se
se
Q
Q
e i
( 3 . 16 )
From the above equations we will get the actual D-Q currents flowing in the line. References for D-Q currents is set by the required real power flow and the port 2 voltage.
*
iDse =
1 P2 Re f 3 V1
*
iQse =
1 Q2 Re f 3 V1
(3.17)
27
Advanced Control Scheme [8]:- The reference voltage vector for the series device
e*se is generalized as follows: * K − K * − i D i Dse q e*dse = r * eqse K p K r iQ − iQse
(3.18)
From the above differential equations we can calculate the Kr, Kp , Kq values. The values are given by Kp= Kq = -Xse and Kr acts as the damping resistor
Note that the control scheme comprehends both phase angle and cross coupling
control schemes, so that it can be considered a generalized control scheme for UPFC. This scheme has two additional terms with identical gain Kr. A voltage vector
produced by the two terms is in phase with a current phasor vector of i*-i , paying attention to the polarity of the ese.
The above mentioned control strategy assumes that all quantities are referred to the synchronously revolving reference frame at bus 1. Hence the actual d-q currents '
X =i D
X
' Q
Dse
cos δ + iQse sin δ
= − i Dse sin δ + i qse cos δ
V V
δ = tan −1 (
1Q
)
(3.19)
1D
(referred to receiving end bus) are transformed based on V1 reference as above before they are used in the above control equation.Similarly the control references are transformed back into the synchronously revolving reference frame at receiving end
bus.. The transformed currents are given by
28
The assumption here for transient analysis is : the series device is
assumed to be an ideal and instantaneously controllable voltage source. Therefore, the output voltage vector ese is equal to its reference e*se .
3.5.2 Port 2 Voltage Control
The voltage at port 2 of the UPFC is algebraically related to that at port 1 and the series voltage injected for power flow control. (For simplicity the series
V
2
=
(V ) + (V ) = (V + e ) + (V 2
2
2D
2Q
2
1D
+ eQse 1Q
Dse
)
2
transformer reactance is clubbed with the line impedance). Since all the quantities are
(3.20)
locally available, we can easily calculate the series voltage to be injected to obtain desired magnitude of V2 .
Vu2REF
The series injected controller diagram in d-q axis referred to bus 1 is given by:
Q*
PI
Vu2
PREF
+
PU2
I*Q
÷
eDse
XQ
Vu1 I*D
÷
PI
Vu1
XD
Fig.3.6 Series injected voltage controller 29
Series Voltage Calcula tor eQse
3.6 Shunt Current Control
The shunt current is controlled by varying the magnitude and angle of the
d
i
Dsh
dt d
i
Qsh
r ω i x r ω i x sh
b
Dsh
sh
= −
sh
b
Qsh
sh
+ω
i
−ω
i
ω x + ω x +
Qsh
Dsh
b sh b sh
( e Dsh −
v
1D
( e Qsh −
v
1Q
)
( 3 . 21 )
)
( 3 . 22 )
dt
= −
shunt converter voltage. The dynamic equations in the D-Q frame are given by,
Where,
rsh, xsh = shunt transformer resistance and leakage reactance respectively eDsh,eQsh= converter output voltage components
V1D,V1Q= voltage components at the bus into which current injected (port 1 of
Id
UPFC)
Ir
Ip
V1
θ Iq
Fig 3.7 Vector representation of real and reactive currents
The reactive and real currents are defined as
i i
Rsh
= i Dsh cos (θ ) − iQsh sin (θ )
Psh
= i Dsh sin(θ ) + iQsh cos (θ )
(3.23) 30
= tan −1 ( v 1 D )
θ
v
v1
1Q
= ( v1 D ) 2 + ( v1Q ) 2
( 3 .24 )
The real and reactive voltages of the shunt converter is given by
s
Rsh
= eDsh cos(θ ) − eQsh sin(θ )
psh
= eDsh sin(θ ) + eQsh cos(θ )
+
V1REF
(3.25)
e e
where,
IRref
PI
ePshord
Shunt
V1 +
PI
VDCREF
current
eRshord
controls
IPref
VDC
Figure3.8. Shunt current controller
In shunt current control block we are calculating the shunt converter output voltages through the drop calculator block by using Idref and Iqref. The differential equations used in drop calculator are
e
psh
=
e
Rsh
= −
R i sh
dshref
−R i sh
qshref
x ω − x ω
−
d
sh
b
dshref
dt
b sh
i
d
i
qshref
dt
+
X i
−
X i
sh
31
sh
qshref
dshref
+V +V
1d
1q
( 3 . 26 ) ( 3 . 27 )
edsh
Idshref
V1d
Drop caliculator Iqshref
edsh
V1q
Fig. 3.9 Converter voltage calculator
Port 1 voltages are calculated by adding shunt and series currents and from the given sending end voltage. The differential equations for port 1 voltage calculation is
1Q
se
se
dL
se
i
d
dL
+
X i
+V
V
1D
−
qL
b
se
b
dt
d
i
qL
dt
se
ql
X i
−
se
V
x R i ω = −R i − x ω = −
dL
+V
SD
SQ
( 3 . 28 ) ( 3 . 29 )
The dynamical equation for the capacitor is given by
dV
=−
g ω V b cap
cap
b
DC
+
ω b
b
( i dsh − i dse )
( 3 . 30 )
cap
dt
DC
Any real power drawn / supplied by the series branch or by shunt branch (due to real current injection Ipsh) manifests as DC side currents IDCser and IDCsh respectively. Since
we allow variable series voltage injection, and due to losses, the capacitor voltage tends change. To compensate this by IDCsh, we set the real current reference (IPshref ) as the
output of a PI type capacitor voltage regulator.
32
4.1 Introduction To Matlab Simulink [11]
SIMULINK MODELING OF UPFC
Chapter 4
SIMULINK is a software package for modeling, simulating, and analyzing dynamical systems. It supports linear and nonlinear systems, modelled in continuous time, sampled time, or a hybrid of the two; systems can also be multirate, i.e., have
different parts that are sampled or updated at different rates.
For modeling, SIMULINK, provides a graphical user interface (GUI) for
building models as block diagrams, using click- and- drag mouse operations. SIMULINK includes a comprehensive block library of sinks, sources, linear and nonlinear components, and connectors. One can also customize and create his own blocks.
Models are hierarchical, so you can build models using both top-down and bottom-up approaches. You can view the system at a high-level, then double-click on blocks to go down through the levels to see increasing levels of model in detail. After you define a model, you can simulate it, using a choice of
integration methods, either from the SIMULINK menus or by entering commands in MATALAB’s command window. Using scopes and other display blocks, you can see the simulation results while the simulation is running. In addition, you can change the parameters and immediately see what happens, for “what if” exploration.
Two advantages of SIMULINK are: access to sophisticated routines
embedded in MATLAB toolboxes; and circuit equations are solved much faster than PSPICE. Thus SIMULINK requires less CPU run time and memory space.
33
For the performance evaluation of different control strategies, the
numerical simulation is carries out in SIMULINK.
As the model increases in size and complexity, it can specify by grouping
blocks into subsystems. It helps in reduce the number of blocks displayed in model window.
4.2 Modeling 3ph To D-Q Transformation Block:
The transformation subsystem block transforms the three phase quantities
to D-Q quantities in the synchronous reference frame. This transformation has been done in two phases.
1. Transforming the three phase quantities to single phase quantities by using the
transformation matrix [C1] in the stationary reference frame.
2. Transforming the stationary reference frame quantities into synchronously rotating at
System frequency (ωo) quantities by using transformation matrix [C2]. Supply Modeling:
The three phase voltages are modeled using sine wave block in the source library of SIMULINK. The parameters for amplitude set between 0.95-1.05pu and
frequency set as 315 rad/sec. The phase angle parameter is set according to three phase supply, 0, 2.0944, -2.0944 rad for the, b and c phases. Accordingly parameters for lead,
lag and unbalanced voltages are set.
34
using gain and sum blocks available in the linear library.
Modeling Of Transformation Matrices: The transformation matrices are modelled by
Fig.4.1.Transformation block in stationary reference
Fig.4.2.Transformation block in synchronously revolving reference frame
4.3 Modeling of UPFC
The control system described in the previous chapter was derived by
assuming that the series and parallel converters are treated as ideal controllable voltage
sources, that the values of the fundamental components of the line currents are locally available.
35
The UPFC is modeled by combining the shunt and series branches coupled
TRANSMISSION LINE 1 MODEL
TRANSMISS ION LINE2 MODEL
SHUNT CONVERTER CONTROL BLOCK
by the DC voltage control branch. Local load is added at port 1 of the UPFC.
INVERTER DC SIDE MODEL
SERIES INVERTER CONTROL MODEL
LOAD MODEL
Fig 4.3. Organization of UPFC modeling blocks
UPFC was modeled by combining various blocks as shown above. 4.3.1Shunt Converter Control Model: Shunt converter was modeled to inject currents into the port1. Inputs for
the shunt converter block are Vu1Ref , VdcRef. In these two PI control blocks are used. The
PI parameters are tuned accordingly to get required output.
36
Fig 4.4. Unified Power Flow Controller block
37
Fig.4.5 Shunt converter control block
38
The PI values used in port1 voltage control loop are KP= 3, KI =3000.
Large value of integrator gain parameter was set to obtain rapid attainment of steady state without unacceptable oscillations.
The PI values used in DC control loop are KP= 3, KI=0. Normally integral
gain in the capacitor loop set zero to avoid very low frequency oscillations in voltage across capacitor which take a long time to die down.
Rate limiters are used in Idsh and Iqsh loops. The reason is only limited
used are [+2000, -2000]. 4.3.2 Transmission Line 1 Model:
voltage available from the inverter to drive current through Lsh of inverter. The limits
The transmission line 1 model was used to calculate the port1 voltage and the real and reactive power flows (P1 and Q1) from the sending end at port1. Inputs to
this block are sending end voltages (d-q quantities).
In port1 voltage calculator block imperfect differentiators are used to represent line reactances because transmission line are generally made up of aluminium conductor steel reinforced (A.S.C.R) . So the eddy current losses are taken into account
and hence the h.f gain is limited.
Sensing delays are used to sense d-q components of the port1 voltage.
Normally voltages are sensed by potential transformers, it has delay in measurement. The delay time constant set at a representative value of 1ms.These delays also serve to break
the Simulink algebraic loops
Small value (0.00001) is used as a input to the sum block in calculating
V1rms to avoid division by zero or NaN in simulation .
39
Fig 4.6 . Transmission line 1 model
40
4.3.3 Transmission Line 2 Model:
Transmission line 2 was modeled to calculate the series current flowing in
the line from port 2 to the receiving end bus. D-Q power calculator block calculates the
real and reactive power flow from port2 to receiving end. Inputs to this block are
receiving end voltages ( d-q quantities).
Fig 4.7. Transmission line2 model
4.3.4 Inverter DC Side Control Model The capacitor voltage is sensed using the power balance theory [10],
according to which the power at the AC side of the inverter is equal to the power at the
DC capacitor side of the inverter, when the switching losses in the inverter switches are neglected.
41
Fig.4.8. Inverter DC side control model
42
Inverter dc side control model was used to find the shunt converter output
voltages and its RMS value. Power calculator block is used to calculate real and reactive shunt powers.
4.3.5 Load Modeling
Load was connected at the port1 of the UPFC. The real and reactive currents drawn by the load are transformed to calculate the its d-q components. The
inputs to the load model are real and reactive power references.
Fig.4.9. Load modeling
Currents in load will be delayed in practice by reactive energy storage elements. A delay time constant of 10ms is employed to take this into account. 4.3.5 Series Inverter Control modeling: To achieve real power and port 2 control we need to inject series voltage
of appropriate magnitude and angle. The blocks are modeled using
43
Fig.4.10. Series inverter control
44
the product, trigonometric and mathematical functions available from nonlinear library.
VSI Inverter Modeling: The PWM-voltage source inverter was assumed to be
instantaneous and infinitely fast to track the voltage reference template set by the control
strategy, so it was implemented as a voltage amplifier with unity gain.
Inputs to this block are PRef and Vu2Ref. In these two PI controllers was used to get the real and reactive power references at the port1. PI parameters used in real power reference loop are Kp= 1,KI =500, KD =0.001.Derivative control used to limit the
KI=7500.
initial peak overshoot. PI parameters used in voltage control loop are
Kp= 20,
Parameters of saturation blocks are set to [+0.5, -0.5] otherwise the output
Power calculator Block:
of the inverter goes to high values.
Fig.4.11. Power calculator block
45
Chapter 5
5.1 Challenges In Computer Simulation [12]
SIMULATION RESULTS AND DISCUSSIONS
At the outset, we need to realize that there are several factors that make simulation of power electronic systems very challenging. 1.
Solid state switches including Diodes, Thyristors, GTO’s and MOSFETS present
extreme nonlinearity during their transition from one state to the other. The simulation program ought to be able to represent this switching of states in an
2.
appropriate manner.
The simulation may take long time, the time constants, or in otherwords the response time of various parts within the system, may differ by several orders of
3.
magnitude.
Accurate models are not always available. This is specially true for semiconductor devices (even for simple diodes) but is also the case for magnetic components such as inductors and transformers.
The controller in block diagram. Which may be analog and /or digital needs to be
4.
modeled along with the power converters.
5.
Even if only steady state waveforms are of interest, the simulation time is usually long due to unknown values of the initial circuit states at the start of the
simulation.
The challenges listed above dictate that we carefully evaluate the objective
of the simulation. In general, it is not desirable to simulate all aspects of the system in
46
detail. The reason is that the simulation time may be very long and the output at the end
of the simulation may be overwhelming, thus obscuring the phenomena of interest, in this
aspect, the best simulation is the simplest possible simulation that meets the immediate
object.
5.2 Test System
The test system taken for simulation study of UPFC as shown below: P1+ jQ1
Substation bus(port1)
UPFC o/p bus (port2)
Xse
VSI
VSI
Psh+jQsh
PL+jQL
Vs
Local load
Rse
Xse
Rse
P2+jQ2
Fig. 5.1.Test system
Specifications of the system taken for testing the simulation study are:
Xse= 0.075 Rse= 0.0075 Xsh= 0.15
Rsh= 0.01 VDCRef =3.4 p.u
gcap= 0.02
bcap = 2
Vr = 1∠0, Laod 3 p.u with power factor 0.8 (lag). This test system is same as used in Ref []. All the above
quantities are on the UPFC MVA base (33.33 MVA), which is assumed to be 1/3rd of the transmission line MVA base.
47
5.3 Simulation Results and Discussions
Notations used to represent simulated waveforms are: Ese = Series inverter output voltage.
Eshrms= RMS value of series converter output voltage Eserms= RMS value of series converter output voltage
Esh = Shunt inverter output voltage.
P1= Real power flow from sending end to port1 measured at port1.
Q1=Reactive power flow from sending end to port1 measured at port1
P2= Real power flow from port2 to receiving end bus measured at port2 Q2=Reactive power flow from port2 to receiving end measured at port2
Psh = Real power flow from port1 to shunt converter measured at port1 Qsh= Reactive power flow from port1 to shunt converter measured at port1
PL =Real power flow from port1 to load measured at port1 QL=Reactive power flow from port1 to load measured at port1. Pse= Real power flow from series converter to port2 measured at port2. Qse=Reactive power flow from series converter to port2 measured at port2.
VDC= Voltage across DC capacitor V1-A=Port1phase-A voltage.
V2-A= Port 2 phase-A voltage. V1rms = RMS value of port 1 voltage V2rms= RMS value of port2 voltage.
In all the plots below X-axis represents time in seconds.
48
The proposed control strategy was tested for the following cases:
Case (i): Vs = 1∠ 0,load 3p.u with lagging power factor 0.8, initially shunt control is OFF, shunt control ON at T=0.04sec, PRef= 0, load switch on at t=0.08sec, at t=0.25 sec
load throw and subsequently shunt control OFF.
The simulation results are:
Fig. 5.2. Simulation results for case (i) are (a) V1rms, V1d , V2q
(b) V1rms (expanded at T=0.08s) (c) V1rms (expanded at T=0.25s)
49
Fig.5.3. Simulation results for case (i) are (d) V2rms, V2d, V2q
(e)V2rms (expanded at T=0.08s) (f) V2rms (expanded at T=0.25s)
(g) Eshrms, Eserms
50
Fig 5.4 Simulation results for case (i) are (h)V1ang, V2ang (i) V1ph-A, V2ph-A (j) Idse, Iqse (k) P2, Q2.
51
Fig 5.5 Simulation results for case (i) are
(l) P2 (expanded at T=0.08s) (m) P2 (expanded at T=0.3s) (n) P1, Q1 (o) Psh, Qsh
52
Fig 5.6 Simulation results for case (i) are (p) PINV, QINV (q) PL, QL (r) Vdc.
By analyzing the above results for a step change in load at t=0.08sec,
sudden change in q-component of the voltage observed. At that time shunt converter
RMS voltage rises to inject reactive power into the bus. Reactive power shown as
53
negative i.e. shunt converter delivering lagging reactive power to the bus to keep the bus
voltage constant.
When the load is switched on at T=0.08sec reactive power flow in the line
(Q2) increases. So the series converter voltage changes accordingly to supply the reactive power. In the above plots the real power consumed by the shunt converter is not equal to the real power delivered by the series converter. The reason is we are measuring the shunt
converter real power at port1. So, we have to subtract the real power dissipated in the
resistance in the shunt converter path from the shunt real power.
The rise and fall times observed when sudden load change occurred at T=0.08sec and at T=0.25sec in port1 voltage are given by Tr =0.025sec, Tf = 0.02sec.The
load powers given in the figure is that of the commanded powers and are different from the actual power drawn from the bus by the time constant of 1ms.This accounts for the
higher rise time observed. The parameters of the controllers at different locations are tuned to get satisfactory gain when sudden changes in load. Initially there is no power flows from sending end to the receiving end because load angle is zero. When load changes the port1 voltage angle changes with
respect to the receiving end, so there is a real power flow from port1 to receiving end and from sending end to the port1. The rise and fall times observed in real power flow when load suddenly
switched on are Tr= 0.004sec and Tf= 0.0001sec. The rise and fall times observed when
load suddenly switched off at T=0.25sec areTr =0.0001sec,Tf=0.0075sec.
54
Case (ii): Vs = 1∠ 0,load 3 p.u with leading p.f 0.8; initially shunt control is OFF, shunt
and subsequently shunt control OFF, V1ref =1 p.u
The simulation results are:
control ON at T=0.04sec, PRef= 0, load switch on at t=0.08sec, at t=0.25 sec load throw
Fig. 5.7. Simulation results for case (ii) are (a) V1rms, V1d , V2q (b) V1rms (expanded at T=0.08s) (c) V1rms (expanded at T=0.25s)
55
Fig.5.8. Simulation results for case (ii) are (d) V2Rms, V2d, V2q (e)V2rms (expanded at T=0.08s) (f) V2rms (expanded at T=0.25s)
56
(g) Eshrms,
Eserms
Fig 5.9 Simulation results for case (ii) are (h)V1ang, V2ang (i) V1ph-A, V2ph-A (j) Idse, Iqse (k) P2, Q2.
57
Fig 5.10 Simulation results for case (ii) are
(l) P2 (expanded at T=0.08s) (m) P2 (expanded at T=0.3s)
58
(n) P1, Q1 (o) PShj, QSh
Fig 5.11 Simulation results for case (i) are (p) PL, QL (q) Vdc.
In case (ii)-leading load is suddenly switched on initially voltage at port1 decreases and goes up. To maintain port1 voltage constant Shunt converter voltage decreases i.e. it is supplying leading vars to the system. The rise and fall times observed in port1 voltage when load suddenly
switched on are Tr= 0.0035sec,Tf=0.021sec.rise and fall times when load suddenly
switched off are Tr=0.0002sec Tf=0.025sec.
59
The real power flow in the line suddenly goes down ( –
0.06) and rises (0.03) for sudden changes in laod.
Case (iii): Vs = 1∠ 0,load 3p.u with lagging power factor 0.8, initially shunt control is
OFF, shunt control on at T=0.04sec, PRef= 3p.u, load switch on at t=0.08sec, at t=0.25 sec load throw and subsequently shunt control OFF, V1Ref= 1p.u.
The simulation waveforms are as shown below:
Fig. 5.12. Simulation results for case (iii) are (a) V1rms, V1d , V2q (b) V1rms (expanded at T=0.08s) (c) V2rms , V2d , V2q.
60
Fig.5.13. Simulation results for case (iii) are (d)V2rms (expanded at T=0.08s) (e) Eshrms, Eserms (f)V1ang, V2ang (g) V1ph-A, V2ph-A
61
Fig.5.14. Simulation results for case (iii) are (h) Idse, Iqse (i) P2, Q2. (j) P2 (expanded at T=0.08s) (k) P1, Q1
62
Fig.5.15. Simulation results for case (iii) are
(l) PSH, QSH (m) PINV , QINV
In case (iii) PRef set as 3 p.u . so the series inverter responding for changes in PRef . port 2-voltage angle changing correspondingly for change in series converter
output voltage. The angle between port1 and port 2 increases for real power flow in the line.
When load changed at T=0.08sec, sudden change in steady state power
flow in the line observed. Initially power flow in the line goes down and comes to steady
state within one cycle of period.
63
Case (iv): Vs = 1∠ 0,load 3p.u with lagging power factor 0.8, shunt control is ON from the beginning, PRef change at T=0.04sec from 0 to 3p.u, load switch on at t=0.08sec and
The simulation waveforms are as shown below:
.
PRef back to zero at T=0.3 sec.V1Ref=1.
Fig. 5.16. Simulation results for case (iv) are (a) V1rms, V1d , V2q (b) V2rms , V2d , V2q. (c) Eshrms , Eserms
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Fig.5.17. Simulation results for case (iv) are (d)V1ang, V2ang (e) V1ph-A, V2ph-A (f) Idse, Iqse (g) P2, Q2
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Fig.5.18. Simulation results for case (iv) (h) P2 (expanded at
T=0.03s)
(i) P1, Q1 (j) PSH , QSH
Case (iv) was done for step changes in PRef.When step changes in power
reference the current flow in line also changing. Accordingly the series inverter injects inphase voltage at port2 to change the port2 angle. The angle between port 1 and port 2 measured is nearly 15 deg. Reactive
power supplied by the shunt converter increases to keep port 1 voltage at reference value.
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Case (v): Vs = 1.1∠ 20,load 3p.u with lagging power factor 0.8, initially shunt control is
load throw and subsequently shunt control OFF,V1Ref.= 1p.u
The simulation results are:
OFF, shunt control on at T=0.04sec, PRef= 0, load switch on at t=0.08sec, at t=0.25 sec
Fig. 5.19. Simulation results for case (v) are (a) V1rms, V1d , V2q
(b) V1rms (expanded at T=0.08s) (c) V1rms (expanded at T=0.25s)
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Fig.5.20. Simulation results for case (v) are (d) V2rms, V2d, V2q
(e)V2rms (expanded at T=0.04s) (f) V2rms (expanded at T=0.08s) (g) Eshrms, Eserms
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Fig 5.21 Simulation results for case (i) are (h)V1ang, ,V2ang (i) V1ph-A, V2ph-A (j) Idse, Iqse (k) P2, Q2.
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Fig 5.22 Simulation results for case (i) are (l) P2 (expanded at T=0.08s) (m) P2 (expanded at T=0.04s) (n) P1, Q1 (o) PSH, QSH
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In case (v) the sending end voltage makes 20deg-phase angle with
reference to receiving end bus. Under normal conditions, without UPFC the power flow in the line will be nearly 6p.u. The reference set for power reference is zero. To control
inphase voltage with proper polarity and phase angle.
the power flow in the line to reference value series converter has to inject the more
For sudden changes in load the power flow in the line initially decreases and coming to the steady state value. The rise and fall times observed in power flow for
sudden changes in load are Tr=0.0015sec, Tf=0.018sec. By observing the plot (h) port2 phase angle with reference to receiving end is zero. So there is no power flow from port2
to the receiving end bus.
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Case (vi): Vs = 1.1∠ 20,load 3p.u with lagging power factor 0.8, shunt control is ON
from the beginning, PRef change at T=0.04sec from 0 to 3p.u, load switch on at t=0.08sec and PRef back to zero at T=0.3 sec.V1Ref=1.
The simulation waveforms are as shown below:
Fig. 5.23. Simulation results for case (vi) are (a) V1rms, V1d , V2q
(b) V1rms (expanded at T=0.04s) (c) V1rms (expanded at T=0.3s)
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Fig.5.24. Simulation results for case (vi) are (d) V2rms, V2d, V2q
(e)V2rms (expanded at T=0.04s) (f) V2rms (expanded at T=0.08s) (g) Eshrms, Eserms
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Fig 5.25 Simulation results for case (vi) are (h)V1ang, ,V2ang (i) V1ph-A, V2ph-A (j) Idse, Iqse (k) P2, Q2.
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Fig 5.26 Simulation results for case (vi) are (l) P2 (expanded at T=0.08s) (m) P2 (expanded at T=0.04s) (n) P1, Q1 (o) PSH, QSH
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Case (vi) has done for pulse change in power reference at T=0.04 sec from
zero to 3 p.u. Initially power flow in the line rises sharply to a peak value of 3.8 p.u and
take a small dip before coming to the steady state value. The rise and fall times observed
are for pulse in power are Tr =0.0006sec, Tf =0.0025sec.
For controlling the real power flow the series injected voltage and phase angle changes accordingly. Changes in power flow affect the port1 and port2 voltages.
To control the port 1 voltage to 1p.u, shunt converter supplies leading vars to the system.
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Case (vii): Vs = 1∠ 0,load 3p.u with lagging power factor 0.8, shunt control is ON from
the beginning, PRef change at T=0.04sec from 0 to 3p.u, load switch on at t=0.08sec and PRef back to zero at T=0.3 sec.V1Ref=1 p.u.V2Ref=1 p.u (port 2 voltage control included).
The simulation waveforms are as shown below:
Fig. 5.27. Simulation results for case (vi) are (a) V1rms, V1d , V2q
(b) V2rms , Vsd ,V2q (c) Eshrms , Eserms.
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Fig.5.28. Simulation results for case (vii) are (d)V1ang, V2ang (e) V1ph-A, V2ph-A (f) Idse, Iqse (g) P2, Q2
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Fig.5.29. Simulation results for case (vii) are (h)V1abc (i)V2abc (j) P1, Q1 (k) PINV, QINV, PSH, QSH.
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Fig.5.30. Simulation results for case (vii) are (l)VDC
Case (vii) is repeating the case (ii) but with port2 voltage control in action.
All waveforms are similar expect the port2 voltages and reactive power supplied by the series inverter. By comparing this case with case (ii) here port2 RMS voltage controlled to 1 p.u. Series inverter is supplying lagging reactive power to port2 to maintain bus
voltage at the reference value.
The plots in (h) and (i) show the details of the three phase voltage waveforms indicating the effect of sudden change in the d-q voltages at port 2 and
explaining how the rapid rise/fall in d-q currents have been achieved.
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CONCLUSIONS
Chapter 6
1. A MATLAB-SIMULINK model was developed in this work for design and
validation of UPFC control strategy for a UPFC located at a load substation using local measurements only. Control algorithm was implemented in space vector domain (d-q co-ordinates).
2. The developed SIMULINK model was used to arrive at satisfactory control gain settings in various parts of the UPFC controller.
3. Detailed simulation of UPFC system with bus voltage, UPFC second port voltage and line power flow control was carried out using the developed SIMULINK model for various cases involving load switching, step change in voltage reference and power
flow references.
4. Subcycle rise and fall times are achievable for voltage control and power control
using the developed UPFC control strategy. This was verified by detailed simulation.
•
For step change in load , rise and fall times observed in port1 voltage are Tr=0.025 sec, Tf =0.02sec; change in port1 voltage (1-0.975-1). For step change power, rise and fall times observed in power flow are Tr=0.0005sec, Tf=0.001sec.(3-3.6-2.88-3)
•
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in port1 voltage are Tr= 0.0015sec,Tf=0.003sec(1-1.06-1). 5.
For step change in sending end voltage (1-1.05), the rise and fall times observed
•
The developed model can be used for studying the effect of voltage unbalance,
voltage harmonics and load current harmonics on the performance of UPFC control.
This is left as future work.
82
L.Gyugyi,
C.D.
Schauder,
S.L.
Williams,
T.R.Rietman,
D.R.Torgerson,
[1]
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