^{1}

^{1}

This paper presents frequency domain method for harmonic analysis of space vector based STATCOM. Space Vector Pulse Width Modulation (SVPWM) method is an advanced PWM method. It is a best method among all the PWM techniques. It provides a freedom in a switching cycle for placement space vector. In this paper, the SVPWM is used for switching of STATCOM. The harmonic (or frequency) domain is a steady-state form of harmonic analysis method, which represents converters to their harmonic spectra. This paper presents harmonic analysis by means of harmonic domain for space vector based Static shunt converter (STATCOM). Performance of the STATCOM is evaluated in harmonic domain simulation studies in MATLAB environment.

Harmonic in power system is introduced by highly non-linear devices and it degrades its performance. Forced Commutated VSCs are the main building block for low and medium power application. Due to recent development in the semiconductor technology and availability of high power switches e.g. Insulated Gate Bipolar Transistor (IGBT) and Gate Turn off Thyristor (GTO) have widespread acceptance in for high power VSC’s, which are used for HVDC converters and FACTS controllers. The process of calculating the magnitude and phase of fundamental and higher order of system signals means power system harmonic analysis. The generation of harmonics in power system is due to large size of power converter. To reduce the harmonics in the system, filter and modern switching pattern are used. The increasing prevalence of flexible AC transmission system (FACTS) devices makes to have accurate model of these devices. One attracting method for modeling the steady state performance of these devices is frequency domain analysis [

VSC based STATCOM acts as source of harmonic current injection into the system and also interacts with harmonic distortions present within the system. To represent the harmonics interaction between STATCOM and system, as well as its effect on the system, it can be achieved from an accurate model of STATCOM based on VSC [

The Harmonic (frequency) Domain method is used for power system analysis in the steady state to model the coupling between phases and between harmonics. In Harmonic domain, the non-linear components such as converters are converted into Norton equivalents and then combined with the of the system admittance matrix and solved iteratively by the Newton-Raphson technique [

Previous work conducted in harmonic domain has been primarily focus on modeling PWM, multi-module, selective harmonic elimination based STATCOM [

A linear frequency domain model is given in [

To extend the results obtained by other authors in the modeling of STATCOM FACTS device, the proposed SVPWM VSC based STATCOM model is developed in order to be able to obtain the evolution in harmonic components of the STATCOM signal. Harmonic analysis of PWM based STATCOM is shown in [

Consider the non-linear relationship

where x and y are periodic variables, which when determined by infinite Fourier series are expressed as follows

Let X and Y are the vectors of X_{h} and Y_{k} Thus, Equation (1) takes the form

If Equation (1) is differentiable, then for small increments about base values x_{y} y_{b} the following relationship is valid

The linearised, general form of Equation (5) can be written as

Matrix [J] of Equation (6) is the Jacobian associated with Equation (4).

Let us assume that the linearization process takes place about an operation point X_{b} Y_{b} i.e.

From Equations (6), (7) and (8)

From above equation, we conclude that every non-linear component should be amenable to a Norton equivalent representation in the Harmonic Domain [

Pulse Width Modulation (PWM) inverters play a major role in the field of power electronics [

SVM use the combinations of switching states to approximate the locus of V_{ref}. In α-β plane, a hexagon centred at origin of αβ plane, identifies the space vectors shown in

The distinct possible switching states of the 2-level VSC are represented as eight voltage vectors, out of which six are active states (V1-V6) and two are null states (V0, V7). The active states contribute output line voltage as +Vdc or −Vdc, where as null states do not contribute any output voltage for VSC. The eight voltage vectors are shown in

The reference vector is synthesized by the three adjacent switching vectors. For example, when V_{ref} falls into sector I as shown in

where Ts is the period of the switching cycle, T1 and T2 are the switching times of the vectors V1 and V2.

T1 and T2 are calculated as

S. No. | Sa | Sb | Sc | Line to neutral voltage | ||
---|---|---|---|---|---|---|

Van | Vbn | Vcn | ||||

1 | 1 | 0 | 0 | Vdc | 0 | 0 |

2 | 1 | 1 | 0 | Vdc | Vdc | 0 |

3 | 0 | 1 | 0 | 0 | Vdc | 0 |

4 | 0 | 1 | 1 | 0 | Vdc | Vdc |

5 | 0 | 0 | 1 | 0 | 0 | Vdc |

6 | 1 | 0 | 1 | Vdc | 0 | Vdc |

7 | 1 | 1 | 1 | Vdc | Vdc | Vdc |

8 | 0 | 0 | 0 | 0 | 0 | 0 |

Similar calculation is applied to sector II to VI Vector V8 can be used in place of V7. The choice is depend on the requirement to minimize average number of switching per cycle.

The Maximum value of V_{ref} is obtain when θ = 30˚ and V_{ref} is given by

This is the maximum value of line to line voltage injected by the converter. The maximum magnitude of V_{ref} is also the radius of circle inscribed in the hexagon shown in

The General switching function is obtained in time domain for space vector modulation. The harmonic content in switching function is given by Fourier series.

where S_{a}, S_{b}, S_{c} are switching function obtained by using SVPWM algorithm. The line switching vector is defined as

The switching vector for harmonic domain is defined as

A STATCOM consist of VSI, DC capacitor and a coupling transformer.

Capacitor voltage of the STATCOM in the harmonic domain is given by [

where V_{cap} is assembled with the harmonic content of V_{cap}(t) similarly I_{dc} includes the harmonic contain of i_{dc}(t) and E_{dc} contain a DC term, i.e.

Equation (3.1) can be written as

where

The voltage on the DC side its relationship to the AC phase voltages are given in terms of switching function may be expressed in the harmonic domain as

The line current and the direct current relationship in harmonic domain is given by

Therefore, Thevenin equivalent of the three phase converter is given by

Thevenin impedance which is called as equivalent harmonic impedance as seen from AC side of converter is

And Thevenin equivalent voltage is given by Equation (14).

The Thevenin equivalent voltage is a constant three-phase harmonic voltage source which includes the effect of the SVPWM switching functions over the DC voltage. The Thevenin’s equivalent model of STATCOM is shown in _{Th}.

The Thevenin’s equivalent circuit of STATCOM incorporates the switching function. The switching function is obtained by using space vector modulation techniques. Space vector modulation was implemented in MATLAB code to obtain the Thevenin equivalent of the STATCOM.

Three phase circuit shown in

The DC voltage on the capacitor is assume to be 0.7 p.u. Then STATCOM absorb the reactive power.

This paper presents Space Vector based switching strategy for a STATCOM that utilizes the voltage source converter to minimize the harmonic at the point of common contact. The entire design of STATCOM and SVPWM is done in harmonic domain for calculation of harmonic interference in the system and evaluated based harmonic domain algorithms using MATLAB code.

The proposed model can be used to calculate harmonic interference produced by STATCOM. The simulation is fast and gives accurate result as compared to time domain simulation where we have to calculate first the

steady state condition then we can apply the Fourier analysis to calculate the harmonic in the system. The study result shows that when we use the Space vector modulation the power quality of the system is improved.

Devendra Manikrao Holey,Vinod Kumar Chandrakar, (2016) Harmonic Domain Modelling of Space Vector Based STATCOM. Energy and Power Engineering,08,195-203. doi: 10.4236/epe.2016.84018