Scientific Journal of Impact Factor (SJIF): 4.72 …ijaerd.com/papers/special_papers/EE026 MATHEMATICAL...Keywords - HVDC, Voltage Source Converter, Back to Back Topology, Vector Control

International Journal of Advance Engineering and Research Development

Scientific Journal of Impact Factor (SJIF): 4.72 Special Issue SIEICON-2017,April -2017

e-ISSN : 2348-4470 p-ISSN : 2348-6406

@IJAERD-2017, All rights Reserved 1

MATHEMATICAL MODELING OF BACK TO BACK TOPOLOGY VSC'S

FOR HVDC SYSTEM

Desai Pooja1, Mihir Kuvadiya2, Stefee Siroya3, Bhavik Prajapati4

1Electrical Engineering, Sigma Institute of Engineering, Vadodara 2Electrical Engineering, Sigma Institute of Engineering, Vadodara 3Electrical Engineering, Sigma Institute of Engineering, Vadodara

4Assistant Professor, Electrical Engineering, Sigma Institute of Engineering, Vadodara

Abstract - There have been a lot of developments in the field of semiconductors devices. There has been recent research

and developments on the High Voltage Direct Currents based on Voltage Source Converters. The advantages of using the

VSC Technology and PWM Techniques have several advantages, namely; reduction in short circuit current; rapid and independent control of active and reactive power, etc. One converter will be used for the control of active power and the

other converter will be used for the control of reactive power. Based on these benefits, this technology will be widely used

in the transmission line for transmitting bulk amount of power. This project will focus on the control of HVDC based on

VSC. The main objective of this project is to understand the control of the VSC-HVDC system, and the process of tuning of

the PI controllers of the converter controlling system.

Keywords - HVDC, Voltage Source Converter, Back to Back Topology, Vector Control Method, Pulse Width Modulation,

Mathematical Modeling.

I. INTRODUCTION

The main requirement in a power transmission system is the precise control of active and reactive power flow to maintain

the system voltage stability. The VSC operating with the specified vector control strategy can perform independent control

of active/reactive power at both ends. This ability of VSC makes it suitable for connection to weak AC networks or even dead network. A Need of high voltage power in power system has been increasing dramatically in recent years. So, for

improvement of controllability of system and reliability, HVDC system is more preferred as compare HVAC. The line

commutated converters based high voltage direct current system is conventional technology but it has some disadvantages

like problems related to voltage/power stability and Low-order harmonic resonance is another issue of concern in line-

commutated HVDC system. Innovation about voltage source converter based high voltage direct current system is

relatively used for weak or passive alternating current network which can transmit large power over long distance and

supply the reactive power to system. Insulated Gate Bipolar Transistor (IGBT), Gate Turn off (GTO), Metals Oxide

Semiconductor Field Effect Transistors (MOSFET), high frequency devices are used as converter switching. For

maintaining continuous flow of HVDC power, the operation of voltage source converter is control of alternating current of

output voltage, phase angle and controlled frequency is requiring without any type of rotary machine. The main

requirement in a power transmission system is the precise control of active and reactive power flow to maintain the system voltage stability. The VSC operating with the specified vector control strategy can perform independent control of

active/reactive power at both ends. This ability of VSC makes it suitable for connection to weak AC networks.

A. Configuration of VSC-HVDC system

The configuration of a VSC-HVDC system shown in Figure (1) consists of ac filters, transformers, converters, phase

reactors, dc capacitors and dc cables.Figure (1) shows the typical arrangement for voltage source converter based HVDC

system which is interconnected between two alternating network systems at the same frequency operated with DC link.

The VSC-HVDC system consists of various equipment such as: voltage source converter, phase reactor, shunted ac filters

(R-L-C), converter transformer, DC capacitors and DC overhead or underground or submarine cables. The detail

explanations of this equipment are given in below.

International Journal of Advance Engineering and Research Development (IJAERD)

Special Issue SIEICON-2017, April -2017,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406


Figure 1. Single Line Diagram of Voltage Source Converter Based HVDC

1. AC Filters

High frequency switching is used on both sides of the converter which leads to generation of higher order voltage and

current frequency as an output. Generally, the harmonics of current are dependent upon the switching frequency of

pulse width of generator. The AC filters comprise of the both low-pass and high-pass filters, which eliminate

harmonics of current generated by the voltage source converters at both end.

2. Converter Transformer

The converter transformer is used to step-up and step-down the AC voltages at both end of transmission lines. The

converter transformers also provide insulation between converter and AC network. The power ratings of transformer are

decided according to the configuration of converter and system specifications.

3. Phase Reactors

Phase reactors are connected in series with transformer, which used to control the active and reactive power with help of

current passing though reactors. Main function of Phase reactor is prevention of the discontinuous current which depends

on load voltages and control of the dc fault currents in DC-link.

4. DC Capacitors

For the smoothing of DC voltage, two series capacitors of the same ratings are connected with DC-link and they are

neutrally grounded. DC voltage of line is dependent on the value of capacitors. These Capacitors will eliminate the

distortions which are produced by the converters. Charging and discharging energy of capacitor depends upon time

constant ( )

5. Voltage Source Converter The main equipment of HVDC system is voltage source converter. The number of converter valves depends upon the

operating characteristics and level of voltages required in system. Voltage source converter has different types of

topologies. Which topology to use is decided according to the purpose of application and multilevel configuration for

output voltage. Every topology has different methodology, circuit network and semiconductor device for switching.

5.1. Classification of Voltage Source Converter

The Different configuration are invented for voltage source converter, each and every configuration has different types of

methods and working.

Converter

1

Transformer

Transformer

c

2

Converter

2

Ac

Filters Ac

Filters

Phase

reactor

c

2

c

2

c

2




Figure 2. Classification of VSC Configuration

6.Two Level Voltage Source Converters

The two-level voltage source converters are used in VSC-HVDC system to make analysis simple. As shown in “Figure 3”,

two level configurations consist of two pair of switches, each having 3 switches connected in anti-parallel manner. Two

converters are connected with one single DC-link which is known as back to back topology of system. Three phase

transmission line are connected with two level voltage source converters at both ends. With the help of different types of

pulse modulation, the switches are triggered. IGBT switches are used at converter valve in VSC-HVDC system, these

switches have high switching frequency of 1 KHz to 2 KHz, voltage and current are rated up to 4000 to 6000v, 800A and power ratings are up to 200Mw.

Figure 3. Two Level VSC Configuration

II.CONTROL SYSTEM

A.Vector Control

The control of a VSC-HVDC system is basically the control of the transfer of energy. The aim of the control in VSC based

HVDC transmission is thus, the accurate control of transmitted power and independent control of active and reactive

power. Widely used method for control of VSC-HVDC is the vector control method. Vector control method uses

modelling of three phase systems by using axis transformations. Vector theory is most widely used in the control of three

phase PWM converters these days. In PWM converters for ac applications, vector control systems can be utilized to obtain

independent control of the active and reactive powers. One of the most advantageous characteristics of vector control is

that vectors of ac currents and voltages occur as constant vectors in steady state, and hence static errors in the control system can be avoided by using PI controllers.

A.1.Vector Control Principle

Voltage Source Converter

Two Level Three Level

NCP-conveter Topology

Flying Capacitor Converter Topology

ANCP Converter Topology

Five Level

Cascade H Bridge Converter Topology




Vector control system involves simplified representation of three phase systems known as DQ transformation.

A.2 DQ Transformation

DQ transformation is the transformation of coordinates from the three-phase stationary coordinate system to the d-q

rotating coordinate system. This transformation is made in two steps.

transformation from the three-phase stationary coordinate system to the two-phase, α-β

stationary coordinate system and

transformation from the α-β stationary coordinate system to the d-q rotating coordinate system

Clark and Inverse-Clark transformations are used to convert the variables (e.g. phase values of voltages and currents) into

stationary α-β reference frame and vice-versa. Similarly, Park and Inverse-Park transformations convert the values from

stationary α-β reference frame to synchronously rotating d-q reference frame, and vice versa.The reference frames and

transformations are shown in Figure 4.

Figure 4. Control Stages and Respective Reference Frames

The stationary α-axis is chosen to be aligned with stationary three phase a-axis for simplified analysis. The d-q reference

frame is rotating at synchronous speed ω with respect to the stationary frame α-β, and at any instant, the position of d-axis

with respect to α-axis is given by θ=ωt. The transformation of axes in different control stages is shown in Figure 5.

Figure 5. Phasor Diagram of D-Q Transformation

For analysis of the voltage source converter using vector control, three phase currents and voltages are described as

vectors in a complex reference frame, called α-β frame. A rotating reference frame synchronized with the ac-grid is also

introduced, as in Figure4. As the d-q frame, is synchronized to the grid, the voltages and currents occur as constant

vectors in the d-q reference frame in steady state. For the analysis of the system, basic equations describing the system

3- Φ

To

2- Φ

Stationary To

Rotating Modulation

Rotating

To

Stationary

Con

trol

pro

cess

AC DC

Rotating Reference Frame

2- Φ system

AC

3-Φ system

Stationary Reference Frame

d

q

d

q

α

β

α

β

Stationary Reference Frame

3-Φ System




behavior are presented based on analysis done in [9]-[11]. Considering the converter system connected to grid, and defining grid voltages as vabc, currents iabc, and converter input voltages vabc conv, and resistance (R) and

inductance(L) between the converter and the grid, as shown in the system of Figure 6, the voltage at the grid side of the

converter can be expressed as,

Figure 6. Equivalent Model of System

Using the a-b-c to d-q transformations, the converter 3-phase currents and voltages are expressed in 2-axis d-q reference frame, synchronously rotating at given ac frequency, ω.

Vd

Vq =

vdcon

vqcon +R

id

iq +L

d

dt id

iq +ωL

0 − 1

1 0

id

iq

Similarly the current on output side of converter ( ) can be expressed as,

Idc = CdVdc

dt+ IL

The power balance relationship between the ac input and dc output is given as,

P = 3

2 (Vd id+Vq iq) = Vdc Idc

where

Vdc and Idc are dc output voltage and current respectively.

The grid voltage vector is defined to be along the d-axis direction, and then a virtual grid flux vector can be assumed to be

acting along the q-axis. With this alignment, vq = 0 and the instantaneous real and reactive power injected into or absorbed

from ac system is given by,

P = 3

2Vd id

Q = - 3

2Vd iq

Vc

Vb

𝑉a R L

R L

R L

ia

ib

ic

Vacon

Vbcon

Vccon




A.3 Inner Control loop

The inner current control loop can be implemented in the dq-frame, based on the basic relationship of the system model.

The control loop consists of PI controllers, decoupling factors and feed-forward terms as will be described further. The

current control block is represented by the following general block diagram figure 8.

Figure 8. Inner control loop

Inside the current control block, there are two PI regulators, respectively for d and q axis current control. They transform

the error between the comparison of d and q components of current into voltage value. With help of modulus optimum

tuning criteria Output transfer function of inner loop is define follows.

G(s)= Kp pu .1+τi .S

τi .S .

1

1+Ta .S.(

1

Rpu .

1

1+τpu .S)

A.4 The Outer Controller

In this loop the dc voltage and active/reactive power will be controlled right now this paper will focus on only dc voltage

control. the dc voltage controller is discussed as the outer controller. Dimensioning of the dc link voltage controller is

determined by the transfer function between the current reference value to be given and the dc link voltage. The general

block diagram of the external controller can thus be given as in Figure 7.

PI

Controller

PWM

convertor System +

Iref V′conv Vconv I

-

PI

Controller

PWM

convertor System +

𝑉𝐷𝐶 𝑟𝑒𝑓

𝐼𝑑𝑟𝑒𝑓 𝐼𝑑 𝑉𝐷𝐶

-




Figure 9. Outer control loop

Gv(s)=KP(pu ).1+Tiv

Tiv .S.

1

1+Teq .S .(

Vdpu

Vdcpu .

ωb Cpu

S )

III.CONCLUTION

We conclude that we will conclude that demand of more power can be fulfilled by reducing the transmission losses with

help of HVDC and can achieve independent control of active and reactive power using VSC-HVDC system.

IV. REFERENCES

[1] V Kamaraju & S Kamakshaiah, on“HVDC Transmission” published by Mcgraw hill education (india)Pvt Ltd. copy

right 2011, page:1,40,53,62,106

[2] D P Kothari & I J Nagrath, on“Modern Power System Analysis” published by Mcgraw hill education (india)Pvt Ltd.

copy right 2011,2003,1989,1980,page:520 to 528

[3]Muhammad H. Rashid Ph.D., Fellow IEEE, on“Power Electronics”published by ACADEMIC PRESS Copyright 2001

,page:101 to 113,307,575 to 579

[4] Chandra Bajracharya, Marta Molinas, Jon Are Suul, Tore M Undeland “Understanding Of Tuning Techniques Of

Converter Controllers For VSC-HVDC” Chandra Bajracharya, Marta Molinas, Jon Are Suul, Tore M Undeland

[5] Se-kyo Chung, Member, IEEE Transactions On Power Electronics, Vol. 15, No. 3, May 2000 “A Phase Tracking

System For Three Phase Utility Interface Inverters”

[5] Ms. Manali Kshirsagar, Dr. Archana Thosar ,“HVDC Light Transmission Technology Simulation Study & Application

To Indian Grid “ International Journal Of Scientific & Engineering Research, Volume6,issue7,july-2015, ISSN 2229-5518

[6]Chandra Bajracharya. “Control of VSC-HVDC for wind power” Norwegian University of Science and Technology,

June 2008

[7] Tatjana Kalitjuka “Control of Voltage Source Converters for Power System Applications” Norwegian University of

Science and Technology, July 2011

[8] MD ROKIBUL HASAN. “Development, calibration and simulation of generic VSC-HVDC high level controls for DC

grid Simulation” School of Electrical Engineering, KTH Royal Institute of Technology, Sweden 2014

[9]Agust Egea-Alvarez, Adria Junyent-Ferre and Oriol Gomis-Bellmunt. A”ctive and reactive power control of grid

connected distributed generation systems”

Scientific Journal of Impact Factor (SJIF): 4.72 …ijaerd.com/papers/special_papers/EE026 MATHEMATICAL...Keywords - HVDC, Voltage Source Converter, Back to Back Topology, Vector Control

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