无功功率补偿-中英文资料外文翻译文献本科本科毕业论文.doc

无功功率补偿毕业论文中英文资料外文翻译文献

HARMONIC DISTORTION AND REACTIVE POWER COMPENSATION IN SINGLE
PHASE POWER SYSTEMS USING ORTHOGONAL TRANSFORMATION TECHNIQUE

W. Hosny(1)and B. Dobrucky(2)

(1) University of East London, England (2) University of Zilina, Slovak Republic

ABSTRACT

This paper reports a novel strategy for analysing a single phase power system feeding a non-linear load. This strategy is based on a new theory to transform the traditional single phase power system into an equivalent two-axis orthogonal system. This system is based on complementing the single phase system with a fictitious second phase so that both of the two phases generate an orthogonal power system. This would yield a power system which is analogous to the three phase power system but with the phase shift between successive phases equal to л/2 instead of 2л/3.

Application of this novel approach makes it possible to use the complex or Gauss domain analytical method in a similar way to the well known method of instantaneous reactive power for three phase power system instigated by Akagi et al in 1983. Thus, for the fictitious two-axis phase power system, the concept of instantaneous active and reactive power could be instigated. Moreover, the concept of instantaneous power factor could be defined.

The novel strategy of power system analysis outlined in this paper is applied to a single phase power system feeding a non-linear load in conjunction with an active power filter. The latter serves the purpose of compensating for either of the instantaneous reactive power or the harmonic current distortion in the single phase power system under investigation or for compensating of both.

Experimental results demonstrated the effectiveness of the novel single phase power system analysis reported in this paper.

Keywords: single phase power systems, orthogonal transformation technique, harmonic distortion and reactive power compensation

1 INTRODUCTION

In this section the orthogonal transformation technique applied to a single phase power system instigated by Akagi et al, reference [1], is described. By adopting this technique expressions for the reference currents used in an active power filter for the compensation of harmonic distortion or reactive power or both, are derived.

Consider a single phase power system which is defined
by its input voltage and input current as follows:

vRe(t) = V Cos ωt
(1)
iRe(t) = I Cos (ωt – Ф)

Where V and I respectively are the peak values of the voltage and current, ω is the angular frequency of the power supply and Ф is the phase shift between voltage
and current.

The power system described by Eq.(1) is termed as the real part in a complex power system and is

complemented by a fictitious/imaginary phase defined as follows:
Vim(t) = V Sin ωt
(2)
Iim(t) = I Sin ( ωt – Ф)

Comparing Eqs (1) and (2), it is obvious that the imaginary or fictitious phase of the voltage or current in a single phase power supply can be created in the time domain by shifting the real component on the time axis to the right by an equivalent phase shift of л/2.

According to Eqs(1) and (2), the α-β orthogonal co-ordinate systems for both of the voltage and current are defined as follows:

vα = vRe(t) and vβ = vim(t)
(3)
iα = iRe(t) and iβ = iim(t)

According to reference [1], each of the α and β components of the voltage and current are combined to form a vector, x(t).

This vector can be represented by the following equation:

This vector is represented in the Gaussian complex domain as a four sided symmetrical trajectory, Fig.1.

Because of the symmetry of the x(t) trajectory shown in Fig.1, it is evident that the voltage and current investigation for the complex power system (including both of real and imaginary voltage and current components), could be carried out within quarter of the periodic time of the voltage and current waveforms (T/4). Thus, Fourier transforms applied for the harmonic analysis of non-sinusoidal waveforms could be carried out during this time interval only as it will be shown later. Fig.2 shows the arrangement of the real and fictitious/imaginary circuits of the complex single phase power system under investigation. As it is shown on this Figure, the real and fictitious circuits should be synchronised by the so called “SYNC” signal. This implies that the x(0) is a priori zero.

2 p-q-r INSTANTANEOUS REACTIVE POWER

In this section the use of the p-q-r instantaneous reactive power method, described in references [2], [3] and [5], for compensating of the reactive power and harmonic filtering is explained.

Consider a single phase power system with a cosinusoidal voltage supplying a solid state controlled rectifier, thus yielding a non-sinusoidal supply current waveform. The supply current is assumed to have a square waveform. Thus, the supply voltage and the fundamental component of the supply current could be written as:

vRe(t) = V Cos ωt
(5)
i1Re(t) = I1 Cos (ωt –л/3)

The supply voltage and current waveforms as well as the fundamental current waveform are depicted in Fig.3.

The voltage and fundamental current components are given as:
vim(t) = V Sin ωt
(6)
iim(t) = I1 Sin (ωt – л/3)

The instantaneous active and reactive power equations for the complex power system under consideration are given in the α-β domain, as described in references [1],
[3] and [5], as follows:

Fig.5 depicts the time variation of p and q for the complex single phase power system under consideration. In this figure PAV and QAV respectively are the average values of the active and reactive power.

The instantaneous power factor, Ф, is defined as:

It is important to point out that the values of p, q and Ф in Eqs (7) and (8) are instantaneous values.

The p-q-r theory is introduced in reference [3], where the current, voltage and power equations are projected in p-q-r rotating frame of reference. Fig.6 shows the voltage components in both of the fixed α-β and rotating p-q frame of reference for a single phase power system.

The r-axis is considered to be identical to the zero axis, hence the voltage transformation equation from the fixed frame of reference α-β to the rotating frame of reference p-q-r, can be written as:

The currents in the rotating frame of reference, ip, iq and ir are related to the currents in the stationary frame of reference, iα and iβ by similar equations as the voltage equations in Eq.11.

Moreover, the following relations can be derived in the p-q-r rotating frame of reference:

3 DERIVATION OF REFERENCE CURRENT
EXPRESSIONS FOR THE ACTIVE FILTER

In this section instantaneous expressions for the reference currents for an active power filter to
compensate for the harmonic distortion or reactive power or both in the single phase power system under investigation are derived.

Because of the symmetry of the complex voltage and current vectors trajectories, Fig.1, the average value of the active and reactive powers for both of the real and imaginary/fictitious phases can be evaluated from Eq.7 as follows:

According to reference [1], the instantaneous expressions for the active and reactive power in the real phase of the single phase power system under analysis are given as:

The real phase average value, fundamental and ripple components of the active and reactive power are extracted from Eqs (12) and (13) and are depicted in Fig .7 and Fig.8 respectively.

The real phase current, iα, can be derived from Eq.7 as follows:

In Eq.14, p~ and q~ respectively are the ripple active and reactive power components.

Reference current for the active filter of the single phase system under consideration can assume different expressions depending on the special requirements of compensating for the reactive power or filtering the distortion harmonics. Three special cases are listed below:

i) Reference current for distortion harmonic filtering
and reactive power compensation

ii) Reference current for average reactive power
compensation

iii) Reference current harmonic distortion compensation

4 EXPERIMENTAL RESULTS

A test rig was set up to verify the theoretical derivations above. An active power filter is implemented with the current reference of Eq.(15) used as an input to the filter and the digital signal processing of the voltages and currents is implemented using a 32 bit floating point DSP, TMS 320C31. The configuration of the experimental setting is shown in Fig.9.

The non-linear of the single phase power system under experimentation is a diode bridge rectifier with an RL load connected to the dc side. The ac to dc converter is rated at 25 kVA. An inductor, L, with a value of 1.2 mH and a capacitor with a value of 10,000 µF are used as dc output filter.. The output current of the active power filter is controlled by a hysteresis comparator to confine
the switching frequency to 15 kHz.

Fig.10 shows the waveforms of the load current, the compensating current of the active power filter and the

supply current. It is clear that active power filter performed its task of compensating for the harmonic distortion as the supply current is converted to a pseudo-sinusoidal waveform from its original square shape waveform. The top waveform in Fig.10 shows the original supply current waveform and the bottom waveform shows the supply current wave form after the implementation of the active power filter. The middle wave form is the compensating current of the active power filter.

5 CONCLUSIONS

A novel strategy, orthogonal transformation technique, is used to yield reference current expressions for the active power filter of a single phase power supply feeding a solid state power converter, in terms of the supply voltage and current. The power active filter control strategy could compensate for either the harmonic distortion of the supply current or the reactive power or both.

Experimental results demonstrated the effectiveness of the novel active power filter control strategy.

6 REFERENCES
1. Akagi, H., Kanazawa, Y. and Nabae, A., Generalized Theory of the Instantaneous Reactive Power in Three Phase Circuits, Proceedings IPEC83 Conference, Tokyo (J8), Sept. 1983, pp 1375-1386.
2. Dobrucky, B., Analysis and Modelling of Power Semiconductor in Steady and Transient States, PhD Thesis, University of Zilina, Slovak Republic, 1985.
3. Kim, H. and Akagi, H., The Instantaneous Power Theory on the Rotating p-q-r Reference Frame, Proceeding of PEDS’99 Conference, pp.422-427.
4. Kim, H., Blaabjerg, F., Bak-Jensen, B. and Choi J., Novel Instantaneous Compensation Theory in Three Phase Systems, Proceedings of EPE’01 Conference, Graz (Austria), Aug.2001.
5. Akagi, H., Kanazawa and Nabae, Instantaneous reactive Power Compensators Comprising Switching Devices Without Energy Storage Components, IEEE Transactions on AI, vol.20, 1984, No.3, pp 625-630.

Power System Harmonic Fundamental Considerations: Tips and Tools for
Reducing Harmonic Distortion in Electronic Drive Applications
Larry Ray, PE; Louis Hapeshis, PE December 2005
Abstract
This paper provides an overview of harmonic considerations for designing industrial and commercial electric power distribution systems. These power systems must serve a combination of loads, many of which produce non-sinusoidal current when energized from a sinusoidal ac voltage source. While conventional power distribution systems accommodate a significant amount of non-sinusoidal current, the design engineer can utilize existing IEEE guidelines and basic software tools to avoid some special circuit and load configurations that exacerbate harmonic distortion problems.
Introduction
Power system harmonic distortion has existed since the early 1900’s, as long as ac power itself has been available. The earliest harmonic distortion issues were associated with third harmonic currents produced by saturated iron in machines and transformers, so-called ferromagnetic loads. Later, arcing loads, like lighting and electric arc furnaces, were shown to produce harmonic distortion as well. The final type, electronic loads, burst onto the power scene in the 1970’s and 80’s, and has represented the fastest growing category ever since.
A better understanding of power system harmonic phenomena can be achieved with the consideration of some fundamental concepts, especially, the nature of non-linear loads, and the interaction of harmonic currents and voltages within the power system.
Harmonic Distortion Basics

What’s Flowing on the Wire?

By definition, harmonic (or non-linear) loads are those devices that naturally produce a non-sinusoidal current when energized by a sinusoidal voltage source. Each “waveform” on the right, for example, represents the variation in instantaneous current over time for two different loads each energized from a sinusoidal voltage source (not shown on the graph). For each load, instantaneous current at some point in time (at the start of the graph, for example) is zero. Its magnitude quickly increases to a maximum value, then decreases until it returns to zero. At this point, the current direction appears to reverse – and the maximum-to-zero-magnitude trend repeats in the negative direction. This pattern is repeated continuously, as long as the device is energized, creating a set of largely-identical waveforms that adhere to a common time period.

Both current waveforms were produced by turning on some type of load device. In the case of the current on the left, this device was probably an electric motor or resistance heater. The current on the right could have been produced by an electronic variable-speed drive, for example. The devices could be single- or three-phase, but only one phase current waveform is shown for illustration. The other phases would be similar.
How to Describe What’s Flowing on the Wire?
Fourier Series
While the visual difference in the above waveforms is evident, graphical appearance alone is seldom sufficient for the power engineer required to analyze the effects of non-sinusoidal loads on th