A Unified Active Damping for Grid and Converter Current Feedback in Active Front End Converters

The Active Front End (AFE) is interconnected to the grid with an LCL filter to reduce the switching harmonics. Possible resonances induced by the LCL filter can be damped using Active Damping (AD). In AFE applications, the current sensor can be placed on either the grid-side or the converter-side, resulting in different frequency responses. This paper presents a novel active damping approach that is universally applicable to all active front end converters regardless of whether the current sensor is placed on the grid side or the converter side. At the heart of the proposed approach is a practically implementable fourth-order filter that dampens the resonance whilst being capable of mitigating the challenges associated with both grid current feedback and converter current feedback. These include amplifications associated with derivatives in active damping term with grid current feedback and high susceptibility to instability with converter current feedback due to digital delay. The proposed active damping is thoroughly investigated in terms of practical implementation issues such as different LCL filter parameters, different sampling methods, grid impedance, and digital delay. The approach is experimentally validated on motor drives consisting of 2 two-level three-phase converters interfaced with a dSPACE rapid control prototyping system across a wide range of resonant frequencies and PWM sampling methods. Stability analysis is performed on both current control methods to validate that active damping assures stable operation for a wide range of resonant frequencies and grid impedance.


I. INTRODUCTION
In recent years, power electronics technology development has had a significant impact on renewable energy [1] and the motor drive industry, however, with the penetration of non-linear elements, new problems are emerging. Mainly, the growth of non-linear loads has a magnifying effect on the current distortion [2] and voltage waveforms (THD), consequently, polluting the grid [3], [4]. Therefore, one of the main goals for researchers is to reduce THD injected into the grid [5].
The industrial motor drives [6] even though not as attractive topics as renewable energy [7] and electric vehicle [8], have a critical role in global industries and world suitability. A typical industrial motor drive consists of a front-end rectifier The associate editor coordinating the review of this manuscript and approving it for publication was Jiefeng Hu . (either passive or active) connected to the grid, 2-level voltage source inverter supplying a three-phase current to the motor, and a controller associated with it as shown in Figure 1. Desirably, if an active front-end converter is used as a front end of the drives, then THD requirements can be fulfilled due VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ to AFE's capability to draw sinusoidal currents. As an active front-end converter operates as a PWM converter, L or LCL filters are required to provide attenuation for high switching frequency. The combination of PWM converter and low pass filter produces an advantageous alternative to diode rectifiers, which in regards to diode rectifier improve THD drastically. The objective of AFE is to control the DC-link capacitor voltage as per a set reference value independent of connected load while also controlling grid current to a reasonable THD, thereby delivering THD improvements relative to the diode bridge used in the past. The use of active switches such as IGBTs rather than diodes are the main difference between AFE and diode bridge rectifiers. In addition to the ability to draw sinusoidal currents, the active solution provides controllable DC-link voltage, bidirectional power flow, and unity power factor. The most common type of filter used in combination with AFE is the LCL filter due to the inherent −60 dB/dec attenuation property. However, the LCL filter introduces resonance which has to be properly damped by either passive [9], active [10] or hybrid damping [11]. Active damping can provide advantages over passive damping in terms of efficiency at the cost of additional sensors and implementation complexity. Generally, passive damping is implemented by adding a resistor in series with a filter capacitor, however, the resistor will add extra zero into the transfer function, inherently reducing LCL filter attenuation to −40 dB/Decade after resonant frequency. This is undesirable due to the high switching frequency of PWM, which requires filtering. Aside from simple passive damping techniques that use a resistor in series or parallel with the LCL filter components [12], there are also more complex other options, such as a split capacitor with series resistor [13], which optimizes power loss and size, but is parameter-sensitive and inherently amplifies switching harmonics, thus, active damping is necessary for many applications.
Many active damping solutions focus on additional capacitor current [14] or voltage sensors [15] to implement active damping due to simplicity. However, the current control objective can be used as a feedback method for active damping, removing additional sensors that are required in conventional active damping techniques [16].
Recent advances in current controller research suggest that controls such as multi-frequency current controllers [17] and model predictive controllers [18] do not suffer from the same stability issues as traditional PI or PR in different frames due to resonance and active damping is not necessary. However, the drawback of recent controls is the high computational burden. Conventional control as voltage-oriented control, on the other hand, remains popular and widely used in industry due to its simplicity and lower computational cost.
Mainly, two different types of current feedback are used for AFE voltage-oriented control. In industry, converter current feedback is usually implemented due to easier execution of circuit protection, while grid current can generally provide better performance. Considering that the resonance is the dominant frequency in frequency response for both control techniques, it is feasible to design active damping capable of damping resonance for both control mechanisms. Thus, a reduction in the number of sensors while not sacrificing system performance is a control objective for any practical motor drive system. In a desire to reduce the number of sensors, this paper considers AFE universal active damping method for both converter and grid current feedback control methods.
This paper is an extension of the previous paper presented in [19]. This comprehensive active damping proposal contains a number of important novelties. The main difference and additional novelty is the inclusion of the converter side control active damping and the unification of the active damping method to fit both control techniques. There is no research that the authors are aware of that proposes a unified damping approach for the two main feedback methods used in voltage-oriented control AFE. The discrete investigation of stability, which shows proposed active damping robust behavior under various LCL filter parameters, is also a key novelty. Grid impedance and various sampling methods have also been investigated, demonstrating the versatility of proposed active damping under various conditions. The proposed active damping is implemented and validated in experiments conducted by stabilizing unstable systems and evaluating their response under transients. A summary of the novelties presented in this paper is as follows: • A unique unified active damping approach for both grid and converter side current feedback independent on LCL filter resonant frequency and sampling method • Discrete domain analysis of the proposed active damping under a diverse selection of LCL filter parameters.
• In-depth stability analysis taking into account various grid impedances and resonant frequencies.
• Experimental validation on motor drive consisting of 2 two-level three phase converters interfaced with a dSPACE rapid control prototyping system. The paper is organized as follows. Section II analytically describes the system of interest. Section III introduces proposed active damping control. Stability analysis is investigated in section IV while section V provides simulation and experimental results of the proposed control. Finally, the conclusion is presented in section VI.

II. SYSTEM DESCRIPTION
The system diagram is shown in Figure 1. A conventional three-phase two-level voltage source converter is interfaced to the grid through an LCL filter. Either grid or converter current measurements are needed for the implementation of the control. If properly designed, the AFE converter provides stable low ripple DC-link voltage, low grid current THD, and close to unity power factor.

A. CONVERTER AND GRID SIDE CURRENT CONTROL
The advantage of LCL filters over conventional L filters is that they offer much better harmonic attenuation characteristics for the smaller footprint. Therefore, to improve current harmonic attenuation and economical cost, the LCL filters are increasingly used when connecting voltage source converters to the grid.
Considering both control feedback and LCL filter, openloop transfer functions are derived where equation (1) relates to grid current control while (2) relates to converter side control. AFE LCL filter per phase is derived from the block diagram in Figure 2 as an output control objective grid current I g or converter current I con and input PWM voltage U afe . Aside from the two control methods, depending on the single or double update PWM sampling method used, delay can inherently change the system frequency response.
Assuming no resistance is included in series with filter components, LCL-filter introduces resonance in both of the control types shown in Figure 3 a) that has to be properly damped to ensure system stability. Two main differences seen from bode plots in the figure are converter side anti-resonance introduced by second-order zero, and reduced attenuation to −40dB/dec after resonant frequency poles. However, apart from the frequency response differences, both controls have different inherent stability. Grid side current control (G g ) is inherently unstable while converter side current control (G c ) is stable considering ideal characteristics. However, taking into consideration the digital delay introduced by sampling and PWM, additional phase lag is added to the system that causes phase margin to decrease, making the converter control system unstable as seen in Figure 3 Grid side current control, on the other hand, can become stable in some resonant frequency regions with enough delay without the need for active damping [20]. However, as controllers become faster, delays decrease, necessitating the use of active damping. Table 1 summarises the effect of delays on stability for various control methods, where: where f critical is defined as f res f samp . The frequency between 10 f line and critical frequency is defined as Low f res while High f res is a frequency between critical frequency and half of the switching frequency. Critical frequency compared to investigated switching frequency (10 kHz) is 0.167 as a ratio f res f samp or in terms of frequency (3.34 kHz) for double update, and 1.67 kHz for single update similarly as in [20]. Critical frequency is the threshold frequency where each control method passes the stability criterion shown in Table 1. Considering that delays will be different depending on if the PWM sampling is single or double update [21], they affect control stability differently at different resonant frequencies.
Lower resonant frequencies are usually chosen for better filtering performance, which, as shown in the table, makes grid current control unstable. In applications where filter size is crucial, high resonant frequencies are dominant, making the converter current control method more susceptible to instability. However, even if the system is stable due to delays, damping the resonance to improve THD is still desirable. Thus, both control techniques are equivalently susceptible to instability due to the LCL filter resonance depending on values of digital delay and LCL filter resonant frequency, and active damping is needed.

B. ACTIVE DAMPING
The papers [10] and [22] provide a thorough examination of passive and active damping techniques. The most intuitive active damping method is the virtual resistor. The virtual resistor active damping method modifies the controller to simulate the frequency response of the real damping resistor. Based on the findings of the previous papers, a virtual resistor in parallel with the filter capacitor provides excellent damping characteristics while having no effect on lower or higher frequency attenuation. Therefore, this paper focuses on the virtual resistor in parallel with the capacitor technique as seen in Figure 4 using a novel implementation approach for both of the current control methods.
The resistor value can be found in (6), where ζ d is desired damping ratio of open-loop transfer function in (1) and (2). Active damping can be achieved by modifying the control diagram to simulate a virtual resistor in parallel with the filter capacitor. Figure 5 shows a block diagram of inner current control for both feedback controls, where the red color denotes the parallel virtual connection of the resistor. By using the block diagram modification technique, active damping terms in (4) and (5) can be obtained. As seen from damping transfer functions, both terms contain the same information in numerator L afe L g s 2 , while denominator  consists of virtual resistor R v gain coupled with additional derivative in converter side feedback control.
In fact, when active damping terms are implemented in the feedback loop shown in Figure 5, numerators of (4), (5) become damping poles of the open-loop transfer function mentioned in (1), (2), thus, they contain crucial information needed for implementation of active damping. However, the issue arises for practical implementation of (4), as s 2 term in (4) is not possible to implement due to not being strictly proper transfer function. This paper presents a close approximation of (4) and (5) by keeping the good characteristics as damping of the resonance and negating undesired characteristics of (4) transfer function as a higher gain for frequencies outside of the zone of interest. This way s 2 issue is addressed, and at the same time, damping equivalent for both grid and converter side feedback is developed. LCL filter is designed based on the trade-off between filter size and current ripple and switching ripple attenuation [23], [24]. In fact, as the resonant frequency decreases in value, the filter's attenuation increases, increasing the physical size of the filter, whereas, for higher values of resonance, the opposite is true. However, stability will also vary depending on the resonant frequency. This has been investigated in [20] where active damping is needed for grid current feedback in low resonant frequency, while not needed in for higher resonant frequency term of stability. In addition to that, grid inductance can also reduce resonant frequency below the critical frequency, making it unstable. Thus, active damping and the control should be stable for a broad range of resonant frequencies.
Many papers have addressed LCL filter resonance damping by analysing two types of current feedback separately, but no universal damping method capable of damping resonance in both cases has been developed. This paper proposes a universal active damping solution that unifies various current control objectives.

C. AFE CONTROL
AFE control is based on voltage-oriented control where the system frame is in a synchronously rotating d-q reference frame. The synchronous rotating frame allows the decoupling of three-phase current into 2-dc components. This way, through controlling I d , the system is indirectly controlling active power, while through I q , reactive power can be controlled allowing control of power factor. Desired DC link voltage is accomplished assuming power balance between DC link and AC side. A phase-locked loop is utilized to obtain the phase angle, used in d-q transformation. AFE control seen in simplified control diagram in Figure 6 is represented by following equations Equations (7)- (11).
30916 VOLUME 10, 2022  I q reference is set to 0 in order to achieve unity power factor.
where Ud, Uq are: where M d , M q are modulation indices, while other parameters, later used in simulation and stability analysis are defined in Table 2. To make this controller equivalent for both control methods, in case of the converter feedback, the measured current is multiplied with a gain of −1. Also, for the converter feedback control method, I * q quadrature current reference set to ω o C f U g instead of to 0 as in grid current feedback control. The reason is that grid current is not directly controlled in the converter feedback method. Tuning of PI controller parameters can be done using modulus optimum technique for the inner current loop and symmetrical optimum technique for the outer DC voltage loop [25]. Additionally, the PI controller parameters can be optimized through frequency response analysis or through a heuristic approach. VOLUME 10, 2022

III. PROPOSED ACTIVE DAMPING FILTER
This section proposes a novel 4 th order filter for both feedback control mechanisms and a systematic step-wise design procedure for the practical implementation of grid and converter side current active damping. The primary goal of active damping is to simulate the frequency behaviour of the LCL filter as if it had a resistor in parallel with the filter capacitor. To do so, the s 2 term in (4) has to be implemented correctly so that it keeps all the required characteristics while negating problematic ones. Due to the nature of s 2 and infinite gain at a higher frequency, practical implementation is not achievable as a result of unwanted noise amplification in addition to not being a strictly proper transfer function. Therefore, s 2 needs to be approximated so that approximation replicates low and mid-range frequency responses while also attenuating higher frequencies. Therefore, the damping term is desired to have low magnitude at low and high frequencies, high magnitude at the LCL filter resonant frequency. Different approximation techniques have already been introduced as 1 st and 2 nd order high pass filter [16], [26], however, 1 st order high pass filter does not meet the specification of the same slope as s 2 since it introduces only 20 dB/dec which changes the low-frequency response of the system. The second-order high pass filter satisfies low-frequency response but has flat gain after resonant frequency and does not attenuate high-frequency noise in addition to non intuitive tuning. Thus, as an alternative to G d as per (4), (5) a new filter is introduced in (12) to solve the mentioned problems.
Overdamped pole pairs ( s 2 ω 2 res + 2ζ 2 s ω res +1) Underdamped pole pairs (12) Active damping term in (12) introduces 2 pairs of overdamped and slightly underdamped poles. Damping coefficients ζ 1 and ζ 2 govern system stability. If both pairs of poles are critically damped, depending on virtual resistor value, the system would not satisfy phase frequency response requirements and would become unstable. However, by overdamping 1 pair of poles, and slightly under damping other pair of poles, the system satisfies phase margin and provides stability. Depending on the current control method used, a plus or minus sign is placed in front of the filter to satisfy either phase lead or phase lag at resonant frequency introduced by LCL resonance. The systematic approach to stabilize the arbitrary system is proposed in the following subsections.

A. STEP WISE DESIGN PROCEDURE
To reproduce damping frequency behavior as there is a resistor in parallel with the filter capacitor, the active damping term from (12) is introduced. The following steps ensure a damped stable system:

1) SELECTION OF THE ω res
According to specification, firstly, ω res in (12) is set to resonant frequency (13) of the LCL filter. This will assure that the active damping term approximately follows +40 dB/dec until the resonant frequency, after which it drops off by −40 dB/dec.
By setting ω res to the resonant frequency, active damping will closely satisfy two requirements, accurate magnitude response of s 2 to resonant frequency and noise attenuation after resonant frequency.

2) SELECTION OF THE DAMPING TERMS ζ 1 AND ζ 2
Damping term ζ 2 in (12) is set to 0.707, and ζ 1 is varied. Figure 7 shows the LCL filter grid current feedback open-loop transfer function with implemented active damping and how the system is unstable due to phase-frequency response mismatch if over-damped pair of poles are not damped enough. For comparison purposes, Figure 7 also includes a system with no active damping implemented. As seen in the figure, an increase in damping constant ζ 1 leads to a stable system due to earlier roll-off frequency. However, overdamping can lead to resonance damping degradation as the filter due to earlier roll-off does not follow the active damping term in (4) accurately enough. Therefore, ζ 1 should be selected to be high enough to satisfy phase response characteristics, and low enough so that early roll-off frequency does not deteriorate the damping of the resonance. It is important to note, swooping through different resonant frequencies shows that ζ 1 between 2 and 3 provides the best damping performance and stability margins, however, this is only by ignoring the digital delay effect on stability. In the later section, consideration of digital delay will introduce the additional term to compensate for the digital delay in active damping.

3) SELECTION OF THE VIRTUAL RESISTOR R v AND PHASE-SHIFTING
As a final step, two unknowns need to be determined to properly implement active damping. The virtual resistor value is calculated based on the equation presented in (6). After determining the virtual resistor value, the active damping sign is left to determine. As mentioned previously, the active damping sign depends on the type of control used. If grid current active damping is used, based on the bode diagram shown in Figure 3, phase lag at resonant frequency needs to be compensated, therefore, a negative sign in front of the active damping is used for grid current control. In the case of converter current control, it will be exactly the opposite, therefore, plus sign is added in front of active damping. As seen in step by step design procedure, tuning of the active damping is relatively simple and intuitive. As long as LCL filter parameters and ω res are known, good damping performance is achievable as it will be shown in later sections.

B. COMPARISON OF PROPOSED FILTER VS EXISTING METHODS
To highlight the advantages of the proposed active damping control, a comparison with existing methods for grid current feedback control is shown in the following Figure 8. Grid current feedback control method is considered in the low resonant frequency ω res range where the system is least stable. 1st and 2nd order filters are tuned based on the heuristic approach presented in [26]. As shown, proposed active damping offers the best attenuation of the resonant frequency, better harmonic rejection at 150 Hz, a much bigger phase margin, and a better gain margin. The reason for this is that more poles provide a higher degree of freedom, which increases robustness when parameters change. In addition to the advantages seen in the figure, proposed active damping offers more intuitive tuning based on LCL filter resonant frequency compared to existing methods. Proposed active damping also assures stability for the wide range of resonant frequencies. In summary, the main goal of the virtual resistor technique is to simulate resistor in parallel with the filter capacitor, and the proposed filter offers a closer approximation of the passive resistor frequency response.

C. SENSITIVITY TO SWITCHING AND LOW-ORDER HARMONICS
The impedance of the AFE LCL filter changes when active or passive damping is used. This can make the system more sensitive to specific harmonics, which can be harmful. The optimum damping technique should have no effect on harmonics other than the resonant frequency, which is the frequency of interest. As mentioned previously, this is one of the inherent advantages of using proposed active damping. In Figure 9, the grid current admittance magnitude for the proposed active damping represented in purple color is compared to passive damping with a resistor in series with the capacitor shown in orange color, as well as the worst-case scenario with no damping in green color. For low order and switching harmonics, the proposed active damping has little to no effect on frequency response, as shown in the figure. Passive damping, for example, increases sensitivity to switching harmonics, which can be detrimental to the system. As can be seen from the analysis, active damping only affects the frequency of interest.

D. DISCRETIZATION OF THE PROPOSED FILTER
As control algorithms are employed on the digital controller, there is a concern with the effect of digital delays. Considering that the current is sampled at the beginning of each switching period, the conversion time of the A/D converter and calculation time of the digital controller will introduce delays in the control loop. Digital delays could weaken system stability margin, and possibly induce system instability [27], [28]. In the previous section, the system has been analyzed considering only for continuous domain, and ignoring the effect of a digital delay. Additional phase delay will, in fact, have an extensive negative effect on system stability depending on LCL filter resonant frequency. Therefore, to analyze system stability, it is necessary to discretize both systems shown in Figure 5 starting from the main contribution VOLUME 10, 2022 of this paper, proposed active damping. Proposed 4 th order filter from (12) is discretized using Tustin method.
where, a = 4 L afe L g T 2 s w 4 res z 4 − 8 L afe L g T 2 s w 4 res z 2 , b = 4 L afe L g T 2 s w 4 res , c = R v ( 4 ζ 2 T s w res z 2 − 1 + T 2 s w 2 res (z + 1) 2 + 4 (z − 1) 2 ), d = T 2 s w 2 res (z + 1) 2 + 4 T s w res z 2 − 1 ζ 1 + 4 (z − 1) 2 Delay G dz is approximated to a z − 1 considering worst-case scenario for computational, PWM and transport delay. However, bearing in mind the digital delay introduced by sampling, computation, and PWM, for specific resonant frequencies, the phase will be shifted into an unstable region, resulting in a frequency response that differs from that of continuous systems in the discrete domain. Thus, to keep with the requirements stated in previous sections, the additional term will be added into active damping to assure stable performance in a wide range of LCL filter resonant frequencies.
The term added is a simple zero (s T s ) in continuous domain adding 90 degrees of phase lead, when discretized becomes the following term: For grid and converter current feedback control, both transfer functions (1), (2) are discretized using zero order hold, thus, including sampling delay.
where, a = L g + L afe , b = L g L afe C f and c = L g C f . Lastly, the PI controller is discretized using the Tustin transformation method in (18).
Combining all discrete transfer function yields system shown in Figure 10. The closed-loop transfer function of the system in the mentioned figure is analyzed for stability in the following section.

IV. STABILITY ANALYSIS
The main concern with LCL filter resonance is the stability. The magnitude peak at resonance will include phase lag or lead (depending on control method) that drives the system to instability. To compensate for phase lag or lead, active damping is used to dampen the magnitude peak. However, depending on the application, LCL filter and grid impedance can change, which will affect the stability and performance of active damping on current control. As a result, the following section investigates the impact of changes in LCL filter parameters and grid impedance on stability margin under double update PWM sampling.

A. EFFECT OF DIFFERENT RESONANT FREQUENCY ON STABILITY
Active damping that can damp resonance and keep the system in a stable region for a wide range of resonant frequencies is critical. The selection of the resonant frequency depends on a designer and LCL filter, however, resonance can drift from expected values, depending on grid impedance. Thus, active damping should be able to stay stable for a broad spectrum of resonant frequencies. Figure 11 represents the root loci of the system in Figure 10. Root loci is plotted for 3 different resonant frequencies by changing filter capacitor value. The most prominent conclusion is that proposed active damping assures stability for both control strategies as poles are inside of the unit circle with adequate stability margins. In the case of the grid current control, Figure 11 a), especially for frequencies above 1500 Hz system guarantees sufficient gain and phase margin, and damping performance, however, for the low range of resonant frequencies, poles are moving to the boundaries of the unit circle, resulting in the lower gain margin. As critical frequency for double update PWM for the investigated system is 3.34 kHz, without active damping, the region below critical frequency is unstable.
In the case of the converter current control, Figure 11 b), it is obvious that active damping offers sufficient stability margins. Poles at the highest resonant frequency are closest to becoming unstable, but still with high enough safety margins. As shown in Table 1, a system with that resonant frequency and no active damping is usually unstable. Thus, from the stability point of view, it can be concluded that the proposed active damping helps in damping resonant poles for a wide range of resonant frequencies, therefore, it provides a robust active damping method that is independent of LCL filter parameters.

B. GRID IMPEDANCE EFFECT ON STABILITY
In practical industrial applications, weak grid, grid impedance unpredictability, or LCL-filter degradation can lead to model uncertainty. Specifically, the grid side filter inductor, L g parameter will be combined with the grid inductance value L gpar which in practical operations cannot be identified. Therefore, it is important that active damping  can provide robustness to grid inductor parameter variation. As active damping depends on model accuracy in (12), it is important to investigate the performance of the proposed control considering total L g uncertainty. Grid impedance effect on stability based on double update PWM and resonant frequency of 2500 Hz can be seen in Figure 12. Figure a) shows grid current control impedance effect on complex resonant poles on the right of the unit circle. As grid inductance is increased, complex poles are moving closer to the unit circle, reducing the stability margin associated with the poles. However, even in the presence of excessive grid impedance, for a reasonable proportional gain, the system remains in the stable region. The grid impedance effect on stability increases as the resonant frequency decreases. However, this is an expected drawback for most of the control well known in power electronics control engineering. Despite these facts, the proposed active damping provides excellent resistance to external effects such as grid impedance. Figure 12 b) illustrate poles movement for the converter current control due to grid impedance. Grid impedance has no significant effect on stability margins. Thus, from the provided analysis, grid impedance affects stability, however, even under a weak grid, stability can be assured.

A. SIMULATION
To evaluate the proposed filter (14), a system in Fig. 6 with parameters values in Table 2 is simulated in MATLAB/Simulink. As the system in Table 2 is inherently unstable, simulations validations verify filter effectiveness of the proposed filter in damping resonant frequency. In the simulation, the effect of delay and sampling is included to replicate real system behavior.
Measured grid current waveforms can be seen in Fig. 13. At the start, the proposed active damping method is connected to the inner current control until 0.49 s, when active damping is disconnected, the system immediately becomes unstable due to resonance until the 0.51 s when active damping is connected again, and resonance is properly damped through modified control. This simulation evaluates stabilizing grid VOLUME 10, 2022 current control, however, the same result is obtained when active damping is implemented for converter current control.

B. EXPERIMENTS
To validate the simulations, proposed active damping had to be tested on real hardware. The hardware seen in Figure 14 consists of dSPACE MicroLabBox as a controller, 2 level AFE and inverter boards, LCL filter boards for each phase, required voltage and current sensors, and grid simulator as a voltage source. As shown in the figure, hardware has grid side and converter side current sensors. This way, both controls can be easily implemented.

1) GRID AND CONVERTER CURRENT CONTROL DAMPING PERFORMANCE
Firtsly, the proposed active damping is put to the test in terms of the grid current control method. Due to the LCL filter resonance, lack of passive damping, and double update PWM sampling where the sampling frequency is ( f s = 2f SW ) system is inherently unstable which is also verified before the implementation of active damping (as shown in Table 1). The reason for system instability is f res which is lower than critical frequency (3) for grid current double update control, therefore, the currents are unstable if no damping is implemented. Figure 15 depicts measured grid current at 2 different states. At the beginning, active damping is not connected, and only damping is provided by parasitic resistances in the LCL filter, thus, currents are unstable due to high resonance. The proposed active damping is turned on at 90 milliseconds, and the system instantly stabilises, confirming previous simulations. As shown in the figure, the proposed active damping reacts very quickly, providing sufficient damping in a matter of milliseconds. For the converter side current control, similar to grid current control, firstly, the system has to be unstable without active damping. This happens for the same hardware when the sampling frequency is changed to single update sampling ( f s = f SW ). For a single update, the same value of f res is now above critical frequency, and the system is inherently unstable. However, active damping is more than capable of damping the resonance induced in the current. To avoid repetition, the reader can refer to Figure 15 as the performance is exactly the same.

2) TRANSIENT RESPONSE OF THE PROPOSED ACTIVE DAMPING
The importance of transient response in power electronics cannot be overstated. Different grid conditions can induce transients in the AFE system. Unexpected transients caused by load changes can jeopardise system stability. Particularly in motor drives, where the power flow from the grid is dependent on the varying motor load. Grid voltage abnormalities such as voltage sags and interruptions can also cause transients. When there is a power imbalance between the AC and DC sides due to a short-term grid voltage reduction, the controller adjusts the current reference to keep the DC-link equal to the setpoint reference, resulting in grid current increase and induced transients. Thus, the inherent AFE ability to ride through different grid voltage irregularities is due to the controller's fast reaction to step-change current. Therefore, proposed active damping is investigated under transients. Figure 16 shows grid current control damped by proposed active damping under transients. As can be seen, at −1.21 milliseconds, the controller increases the current, however, induced transients are properly damped. As a result, the proposed active damping has no negative effects on the control during transients.
As a result, it is clear that the proposed active damping can dampen the resonance induced in both control methods.

VI. CONCLUSION
As the power electronics industry is focusing on economical and robust control solutions, this paper considers an AFE system where sensor number is minimized, and, at the same time, improves the system performance. In the grid current feedback AFE, and the converter current feedback AFE, active damping is implemented using control objective current measurements to remove the LCL filter resonance issue. This paper proposes a novel filter for the practical active damping implementation removing the impracticality of implementing s 2 term derived in equation (4) and presents a unifying approach for two different possible control methods.
A novel filter design procedure is presented to stabilize and damp any arbitrary LCL-filter resonance. As LCL filter parameter choice is up to the designer, it is crucial that active damping can assure the stability for different LCL filter resonant frequencies. This study explores the stability region and displays that proposed active damping is capable of keeping the system stable for a spectrum of different resonant frequencies.
In addition to that, the proposed active damping performance is verified through extensive simulation. Simulations provide a comprehensive analysis of the proposed control and demonstrate satisfying damping characteristics of the novel active damping proposed in this paper. Further, through experimental validation it is shown that both inherently unstable systems can be damped using the proposed active damping filter. Thus, it can be concluded that the proposed active damping can be used in either converter or grid-side current feedback control mechanism and provide good damping performance independent of LCL filter parameters.