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Control Techniques for Active Power Filters 1 Abstract There have been many variants of the active power filter proposed and these variations cover both the…

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Control Techniques for Active Power Filters 1 Abstract There have been many variants of the active power filter proposed and these variations cover both the circuit topology and the control system employed. Some of the control variants reflect different control objectives but there are still many variants within similar objectives. This paper describes and contrasts the available control techniques in a structured way to identify their performance strengths. Objectives are classified by the supply current components to be corrected and by the response required to distorted grid voltage. The various signal transformations are described in terms of their impact on the distortion identification problem. Time-domain, frequency-domain, instantaneous power and impedance synthesis methods are examined. Additional control functions such as DC-bus voltage and current reference following are also discussed. It is found that a key difference between control methods is way in which current distortion is treated in the presence of distorted grid voltage. 2 Introduction The idea of active filtering of distortion found in power distribution lines appears in the literature from the 1970s [1,2,3,4]. The terms active filter and active power filter (APF) are both in common use. Here active power filter is preferred to distinguish filter that must process instantaneous power from active filters for signal processing. Since the early schemes, many Active Power Filter (APF) variants have been proposed and the literature has been reviewed from several stand points. An early review was [5]. It categorises active power line conditioners according to whether time or frequency domain signal processing is used and whether current or voltage type converters are used. Akagi reviewed the emerging APF technologies [6] in terms of their objectives, configuration and controllers and discussed the unified power quality conditioner (a combination of a shunt and a series APF). 1 In [7], Peng reviewed the literature regarding shunt versus series forms of APF and articulated clearly the need to match the form of filter to the form of distortion. Thus, shunt APFs are effective against current-stiff (inductive) non-linear loads that inject distortion current whereas series APFs are effective against voltage-stiff (capacitive) non-linear loads that inject distortion voltage. While it is possible to use the other combinations, the ratings required of a shunt APF when used to compensate a current-stiff non-linear load can become large if the line impedance is small [7, 8]. In [9] Peng develops the theme and expands the discussion to the several forms of hybrid active/passive power filters (Hybrid APFs) appearing in the literature. The paper uses the idea of duality to fully populate the matrix of possible combinations of shunt and series impedances and controlled sources. The features and operating characteristics of each combination are examined. Another categorisation of topologies for hybrid filters was presented in [10]. Singh et al. [11] categorise a large number of reported active filters under headings of Converter, Topology, Supply Lines, Signal Conditioning and Compensation Derivation. El-Habrouk et al. [12] categorise published work under headings of Power Rating; Circuit Configuration; Compensation Quantity, Control Method and Reference Identification. The assessment under each heading is necessarily brief but the reviews are comprehensive. There are several papers that compare certain control schemes for the quality of the results they produce such as [13, 14]. Execution speed and time response of three harmonic identifiers were reviewed in [15]. This paper draws together the various control schemes reported and identifies their characteristics. The literature on APFs contains reports of many different circuit topologies but these are not a focus of this review. To simplify the discussion here, attention is focused on the case of a shunt active filter injecting compensating current into a line. A control method for a shunt filter can normally be applied to a series compensation case using the ideas of duality discussed in [9]. Only where a control method is tailored to a different circuit topology, is that topology example used. APF control includes subtasks such reference generation, current control and DC-bus voltage control. Each of these topics is covered. The focus is on three-phase methods as the more general situation. Where a method can be applied with modification to a single-phase APF this is discussed. 2 3 APF Structure Figure 1 shows the shunt connected APF used as the principal example and illustrates the five basic elements of an APF: 1. Distortion Identifier – a signal processing function that takes the distorted waveform (the line current or voltage), d(t), and forms a reference waveform, r(t), which will reduce the distortion. 2. Inverter – a power converter (and coupling inductance/transformer) able to reproduce the reference waveform at suitable amplitude, IAPF (or VAPF). 3. Inverter Controller – a pulse-width modulator and, in the case of a voltage source inverter used to inject current, a local current control loop that ensures that IAPF tracks r(t) 4. Synchroniser – a signal processing block based on phase-locked loop techniques that ensures that the cancellation waveforms are correctly synchronised to the mains voltage. Certain methods do not require explicit synchronisation. 5. DC-Bus – an energy store that supplies the fluctuating instantaneous power demand of the inverter. Errors and losses that cause the energy store to engage in long term real power flows must be compensated for by additional action of the inverter controller. An example series APF is shown in figure 2. It uses the same basic elements but the inverter is configured to inject series voltage. According to the classification in [6], Figure 1 would be described as current injecting and load current sensing. Figure 2 would be described as voltage injecting and load current sensing. Voltage detecting configurations are also possible and can be used with voltage or current injection. The system shown in Figure 1 has been described as open-loop in the discussion in [16]. It is open-loop in that id (not is ) is measured. The distortion generated by the load is then identified and a correction term fed-forward to correct the distortion in the supply. There may be errors in the calculation process or inaccuracy in the current injection that result in imperfect correction. There may also be some coupling such that the injected current perturbs the source or the load such that the distortion changes and the correction is unstable. The calculation of the feed-forward correction is subject to processing delay and so the transient response is a concern. (Although Figure 1 contains a control loop, it is a local loop to operate the voltage-source inverter as a current source.) In contrast, the closed-loop approach measures is, identifies any remaining distortion and updates the injection reference. In some cases this update will be a low sample rate process with perhaps one update per mains period. 3 This requires that the update coefficient (gain) is low so that a stable approach is made to the zero-distortion target [16]. Slow convergence of this loop provides a degree of smoothing in the compensation current of a fluctuating distortion load. Continuous versions of closed loop control have also been reported but with a relatively slow adjustment of the target [17]. 4 Choice of Cancellation Objective In principle, an APF is capable of correcting a wide variety of power quality problems such as: ã Harmonic Distortion (of any phase sequence) ã Fundamental-Frequency Reactive Power (non-unity displacement factor) ã Negative Sequence Fundamental Components (unbalance components) ã Zero-Sequence Fundamental Components (neutral line current) ã Flicker (low frequency modulation of power flow) Correction of harmonic distortion is taken as a core function present in all APFs. Displacement factor correction with fundamental frequency reactive power is often also included [18]. Correction of the fundamental frequency negative-sequence component can be provided and will balance unbalanced load currents in a three-wire system [19]. With a four-wire system, zero-sequence harmonics and zero-sequence fundamental can flow as a result of single-phase distorting loads and a four-wire APF can be used to correct these terms. Flicker correction is normally a function of a Dynamic Voltage Restorer (DVR) but can fall within the remit of an APF [20]. Functions such as combating voltage sag and swell are considered to be DVR functions. The use of an APF in response to various power quality problems is discussed in [21]. It is tempting to consider that all of the various power quality issues can be dealt with by simply adding control functions to the basic APF power converter circuit. However, each corrective action contributes to the volt- ampere rating of the power converter and hence to the cost of the equipment. Compensation of unbalance and flicker also has implications for the DC-side energy store since the energy flows represented by peaks in the instantaneous power can be large. With this acknowledged, it is important to note that a control scheme designed to correct harmonic distortion might provide unintentional action to correct flicker and thereby cause the APF to exceed its rating when faced with large flicker components. Control schemes need to be assessed for their effectiveness in correcting the problems they were explicitly designed for and assessed for any unintended 4 additional action. The largest energy exchanges with the DC-side are likely to arise from fundamental frequency unbalance and low frequency power variation (flicker). Any discussion of APF control rests on the definition of the distortion that is to be corrected. Viewed from the standpoint of an ideal power system with balanced sinusoidal voltages, the ideal load current is also a balanced sinusoid set. A non-sinusoidal current or an unbalanced current can be decomposed and the distortion terms identified. This identification of distortion can also be approached from an analysis of the instantaneous power. For the case of a sinusoidal voltage and distorted current, identification of the active power is equivalent to identification of the in-phase fundamental component of current. For the general case of an unbalanced, non- sinusoidal voltage and an unbalanced non-sinusoidal current there is still debate over the most appropriate form of decomposition. There are two long standing approaches. Fryze [22] defined active current, iA(t) as being responsible for the real power flow and having the same form as the voltage, (1). The active current is the minimum RMS current required to transmit the active power. The remaining current was defined as non-active current, iN(t) (2) and is found to be orthogonal to the active current (3). P i A (t ) = 2 v(t ) ( 1) v where ã is the RMS value and P is the real (average) power. i N (t ) = i(t ) − i A (t ) ( 2) 2 2 2 i = iA + iN ( 3) The Fryze non-active power, QF and the apparent power, S are defined by multiplying the current equation by the RMS voltage (4) 2 S 2 = P 2 + QF ( 4) Budeanu used a frequency domain decomposition of voltage and current to define the active (5) and reactive powers (6). N cos(φ n ) ( 5) P= ∑V I n =1 n n N sin (φ n ) ( 6) QB = ∑V I n =1 n n A third power term, D needs to be introduced to complete the apparent power equation (7). 5 2 S 2 = P 2 + QB + D 2 ( 7) Enslin and Van Wyk surveyed possible approaches to decomposing power into terms that can be separate out for compensation (or not) [23, 24]. There are several other views of this topic [25] and much debate [26]. Peng [27] has shown the relationship between the definition of active power and the definitions of instantaneous active and reactive power that become popular in APF applications (to be reviewed in Section 6) The shunt current-correcting APF will often be placed in the low voltage distribution network where there is significant degree of existing voltage distortion caused by distant non-linear loads and their common-impedance coupling to the APF site. A significant question to address is what is the most desirable response of the combined APF+load to the distortion components of the supply voltage. As will be shown in section 5, many of the reported methods set an objective of achieving sinusoidal current flow. This can be interpreted as presenting a very high impedance to harmonic voltages (and a moderate impedance to the fundamental term). In contrast, the instantaneous power method (to be described in Section 6) draws significant harmonic current in response to harmonic voltages. The response is complex and as will be shown in section 6, the process is non-linear and results in current harmonics at different frequencies to the voltage excitation. The non-sinusoidal current has been noted and several attempts have been made to force sinusoidal current. However, [28] and [29] argue (from differing starting points) that the APF should respond to voltage distortion but should do so with a resistive characteristic. Harmonic currents will be drawn in phase with the harmonic voltage excitation and the power extracted by the APF+load will provide damping of the excitation. If the same resistance is presented at all frequencies then the current waveform will have the same shape as the voltage waveform. This matches the definition of active current discussed by Fryze and used in [23]. Three categories of compensation can be defined. 1. Waveform Compensation. Commonly the objective is to achieve a supply current with fundamental active current only. In impedance terms, the APF+load is resistive at fundamental frequency and open circuit at harmonic frequencies. 2. Instantaneous Power Compensation. Commonly the objective is to achieve a constant instantaneous power drawn from the supply. The APF+load present a complex, non-linear response to distorted excitation and can not be described in terms of an impedance. 6 3. Impedance Synthesis. Commonly the objective is to present a resistive characteristic. Power is absorbed at all frequencies present in the excitation and APF+load can be made to closely approximate a passive system. 5 Waveform Compensation Waveform correction can be approached in many ways. There are many signal processing techniques that can decompose the current waveform into various components and separate those that should remain from those that should be cancelled (the cancellation reference). This is essentially a filtering task and the non-ideal properties of real filters must be recognised. In addition to the analytical approaches, there are pattern learning techniques such as neural networks. 5.1 Filter-based methods Distortion identification is a signal filtering task and can be conducted with time domain filters or by Fourier based frequency decomposition. As with all filtering tasks, the filters need to be considered in terms of the following: ã Attenuation: it is important that the identified components have their magnitude preserved, that the other components are heavily attenuated and that the transition band between the pass and stop bands is narrow ã Phase-distortion: because the cancellation relies on injecting cancellation signals in phase-opposition, it is important to preserve the phase of the identified components ã Time-response: the (distorted) load current will be subject to change and the filter should respond rapidly without large overshoot. These three performance considerations are inextricably linked for time-domain filters: flatness of magnitude response has to be traded off against phase-response (at least for causal filters) and a well-damped transient response is in conflict with a narrow transition region. Applying a filter to determine directly the distortion means that the cancellation process is subject to the transient response of the filter. The alternative is indirect identification, i.e., use the filter to determine the fundamental signal f(t) that should remain and subtract that from the instantaneous distorted signal d(t) to form 7 the reference r(t) (illustrated in Figure 3). There are two stages of inversion in achieving the desired component: first it is subtracted from the measured current to form the reference and then the reference is subtracted from the actual line current. The difference between the direct and indirect methods is apparent during a transient. Real-time filters are causal and during a transient, there is a time lag between the output of the filter and the component to be identified. Thus, the direct method will have an out-of-date distortion term and the distortion cancellation will be in error. The indirect method will have an out-of-date fundamental term and, while the distortion terms will be cancelled, real power will also be exchanged through the inverter. Real power exchange disturbs the DC-bus voltage and requires that the inverter be rated to cope with a real power component which might be large. When considering unintended action of a distortion identifier it must be borne in mind that for a direct identifier, only those components specifically separated by the signal filter will be compensated by the APF whereas for an indirect identifier, any component not specifically identified by the signal filter for retention will be compensated by the APF. Most APF implementations opt for indirect distortion identification since it yields the best distortion cancellation during transients. The inadvertent exchange of real power (caused by incomplete separation of the real power component in an indirect identifier) can be corrected as explained in section 8. Direct identification is used where different groups of harmonics are to be treated differently or where only a specific range of harmonics are to be compensated [19]. This might be desirable where this allows the rating of the filter to be kept within a limit or where interaction with a system resonance is a danger if cancellation is attempted in a certain frequency band. The well known transformations of three-phase systems are widely used in APF controllers to facilitate separation of a current or voltage term for cancellation. The transform to orthogonal components in a stationary reference frame (the αβ0 reference frame) and the transform to a rotating reference frame (the dq0 reference frame) are both useful. The choice of reference frame in which to operate has an important impact on the filter design; in particular: ã The width of the transition band between pass-band and stop-band is different in different domains 8 ã The decomposition of the fundamental into various components depends on the domain used and gives choice over what type distortion is cancelled. Both of the transforms separate out the zero-sequence component into a separate term (or axis). The αβ0-transform does not separate sequence-sets (although the sequence can be determined from whether the α or β component leads). The rotation transformation shifts fundamental frequencies to DC and separates out the active and reactive components. Components of the same harmonic order but of opposite rotation (phase sequence), i.e., +n and -n, are separated from each other because positive sets are shifted to order n-1 and negative sets to order –n-1. An early example of using the synchronous frame is [30, 31]. In [32] it is argued that, especially for high sample rate systems, the overhead in performing αβ0 and rotation transformations is too much of a burden. A method is demonstrated of transforming a filter designed in a rotating frame to an exact equivalence in the stationary frame. Importantly, the method preservers the ability of a synchronous frame filter to distinguish between negative and positive s

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