Evaluation and Comparison of the Low-Frequency Oscillation Damping Methods for the Droop-Controlled Inverters in Distributed Generation Systems

Abstract

The droop-based control strategy is widely applied in the interfacing inverters for distributed generation. This can be a problem since low-frequency stability issues may be encountered in droop-based microgrid. The objective of this paper is to classify, evaluate and compare various low-frequency damping methods. First, low-frequency stability problems are analyzed and an equivalent model of a droop-controlled inverter is investigated to classify the damping methods into the source-type damping strategies and the impedance-type damping strategies. Moreover, the lead-lag compensation network insertion control is proposed as a beneficial part of the source-type damping strategies. Then, the advantages and disadvantages of the different types of damping methods are theoretically evaluated and experimentally tested. Furthermore, the damping methods are comprehensively compared to illustrate the application field of each method. Finally, the synthesis of different damping methods to enhance the low-frequency stability is discussed and experimental validation is presented.

I. INTRODUCTION

The application of renewable energy sources and micro-sources keeps growing in recent years [1]. Distributed generation (DG) is a promising form to integrate these resources into the grid. With the development of DG, the concept of microgrid, which contains a number of systematically organized DG units, has been proposed [2]-[5]. In order to provide enhanced reliability and power quality, microgrid should be able to operate in both grid-connected (GC) mode and islanding (IS) mode. Moreover, the droop control method is often applied to avoid circulating currents among the parallel inverters without the use of any critical communication among them [4]-[8].

However, low-frequency oscillation which destabilizes the microgrid and influences the safety of power electronics elements may be introduced with droop-based control [9]-[12]. Low-frequency stability issues are mainly caused by the coupling between active power and reactive power [13], the interaction between the droop loops, and inner voltage and current loops in high droop coefficients [12], [13], and the constant power loads or constant power generators [9], [17]-[21]. In order to solve the stability problems, many active damping methods have been proposed to mitigate the low-frequency oscillation of droop-based microgrid [4], [13]-[16], [22]-[36].

In [22]-[25], power derivative terms are inserted into both the conventional active power-frequency and the reactive power-voltage magnitude droop loops. The low-frequency stability and dynamic performance can be improved with the derivative terms. However, under non-ideal operation conditions, low-frequency noise may be amplified because of the derivative terms if the cut-off frequency of the power calculation low-pass filter (LPF) is not very low. Since dynamic response is sacrificed with a low cut-off frequency, the determination of the cut-off frequency needs a tradeoff. The reactive power-voltage magnitude derivative droop is applied in [26] instead of the conventional reactive power-voltage magnitude droop to improve the reactive power sharing among parallel inverters. Moreover, this method can indirectly enhance the low-frequency stability while a complicated restoration mechanism of the voltage magnitude derivative is needed. In order to ensure the low-frequency active damping under different load conditions, the power derivative terms are inserted into the droop loops with adaptive transient droop gains in [27]. Nevertheless, the low-frequency noise problem in [22]-[25] can also be encountered. Moreover, the adaptive droop gains are obtained via small-signal analysis of the power sharing mechanism along the loading trajectory of each DG unit, which significantly increases the computational burden. Furthermore, it is very difficult to guarantee the accuracy of the small-signal analysis. In [28], [29], the feedforward of output current or an increment of active power is inserted into the reference of output voltage. However, the design methods for the feedforward gain and compensation controller are complicated. The feedforward of active power is introduced to accurately link the microgrid frequency dynamics to the motor dynamics in [16] to ensure robust stability under a wide range of droop coefficients. In addition, power system stabilizer (PSS) is an effective method to damp the generator rotor oscillations by controlling the excitation with an auxiliary stabilizing signal, such as speed deviation [30]-[33]. Similarly, low-frequency stability might be improved with the feedforward of the frequency deviation in droop-controlled inverters. In [34], since only the active power droop loop is modified through inserting different compensation networks, the stability improvement is limited. Consequently, the above methods are all implemented by inserting supplementary control loops into the droop loops to enhance the low-frequency stability.

As analyzed in [13]-[15], virtual impedance is a popular method to decouple active power and reactive power, along with improving the low-frequency stability. However, the dynamic response is degraded. In [36], the impacts of inverter output impedance on stability and dynamic performance are investigated, and an inverter current feedforward scheme is proposed to enhance the low-frequency stability. In addition, the output current feedforward scheme can also mitigate the impacts of inverter output impedance on low-frequency stability [11], [37]. However, extra sensors for output current are needed. In conclusion, the low-frequency stability can also be enhanced through changing the low-frequency characteristics of the output impedance.

As mentioned above, many active damping methods have been proposed to solve the low-frequency stability issues in droop-based microgrid. However, there is a lack of systematic evaluation and comparison for different active damping methods. In this paper, the classification, evaluation and comparison for state-of-the-art low-frequency active damping strategies are addressed to give an insightful cognition. The low-frequency stability problems are analyzed and an equivalent model of the droop-controlled inverter is explored to classify the damping methods into the source-type damping strategies and the impedance-type damping strategies. The source-type damping strategies are realized by inserting supplementary control loops into the droop loops, while the impedance-type damping strategies are implemented through changing the low-frequency characteristics of the output impedance. The lead-lag compensation network insertion control is also proposed as a beneficial part of the source-type damping strategies. Then, the advantages and disadvantages of different damping methods are theoretically evaluated and experimentally tested. Moreover, a comprehensive comparison is implemented to illustrate the application field of each method. Finally, the synthesis of different damping strategies to enhance the stability is discussed, and experimental validation is also presented.

The paper is organized as follows. The low-frequency stability of the conventional control strategy and a classification of the existing damping methods are investigated in section II. The source-type damping strategies are introduced in section III. The impedance-type damping strategies are evaluated in section IV. Experimental validation of different damping methods is illustrated in section V. The comparison and synthesis of different damping strategies are discussed in section VI. The last section summarizes the investigation.

 

II. LOW-FREQUENCY STABILITY OF THE CONVENTIONAL CONTROL STRATEGY

In general, voltage source inverter (VSI) is applied as the interface to connect DG units to the grid. A simplified system configuration, as shown in Fig. 1, is used to implement the theoretical analysis. A three-phase VSI with an LCL filter is considered in this paper. Lc is the inverter-side filter inductor and Rc is the equivalent series resistor (ESR). Cf is the filter capacitor. Lg consists of the grid-side inductor of the LCL filter, the leakage inductor of the isolation transformer and the line inductance, and Rg is the ESR. Lf is the feeder inductance and Rf is the ESR. iLabc, ucabc, igabc and ugabc are the inverter-side current, the voltage of the filter capacitor, the grid-side current (or output current) and the grid voltage in GC mode or the load voltage in IS mode. Since droop-based microgrid can operate in both GC mode and IS mode, the stability analysis in both operation modes needs to be considered. In this paper, one inverter is considered in GC mode to simplify the analysis while two parallel inverters are analyzed in IS mode.

Fig. 1.Structure of the system configuration.

The conventional control strategy for the DG interfacing VSIs is shown in Fig. 2 [5], [36], [38]. As shown, the control strategy consists of active power-frequency and reactive power-voltage magnitude droop loops, initial virtual impedance, and inner voltage and current loops. The detailed explanations of the three parts can be found in [11], [36], [38], which is not introduced here.

Fig. 2.Block diagram of the conventional control strategy.

In order to further investigate the low-frequency stability of the conventional control strategy, the analysis is implemented. (Note that the low-frequency range is mainly below 10Hz in this paper.) Meanwhile, the classification of the existing low-frequency oscillation damping methods is also given in this section.

A. Low-frequency Stability Issues

The small-signal representation as shown in (1) can be achieved from the droop loops, while (2) can be achieved by combining the inner loops with power calculation [36].

where Δ denotes the perturbed value, δand E are the phase and amplitude of the output voltage reference, E0 is the nominal amplitude, P and Q are the active and reactive power, P0 and Q0 are their references, and kp and kq are the droop coefficients, respectively. In addition, the derivation of B1 and B2 can be found in [36], which is not introduced in this paper.

Substituting (1) into (2), (3) can be obtained.

Finally, closed-loop transfer functions of the active power-frequency and reactive power-voltage magnitude droop loops in GC mode can be manipulated as (4) and (5), respectively.

Bode diagram of both Gpc(s) and Gqc(s) is given in Fig. 3 with the parameters listed in Table I and Table II. As shown in Fig. 3(a), low-frequency resonance peak appears in both Gpc(s) and Gqc(s), even with a small active power droop coefficient kp, which can induce instability. Instability occurs if kp is increased to the rated value as presented in Fig. 3(b), and the phase lead happens in the presence of right-half plane poles, which can be verified through Fig. 4.

Fig. 3.Bode diagram of closed-loop transfer function of droop loops for conventional control strategy in GC mode. (a) kp=0.94×10-3. (b) kp=1.57×10-3.

Table IPOWER STAGE PARAMETERS

Table IICONTROL PARAMETERS

Fig. 4.Root locus diagram of the low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes.

Low-frequency dominant eigenvalues in GC mode can be obtained by calculating the poles of the closed-loop transfer functions of the droop loops. In IS mode, the state variables can be defined as (6):

where is the reference of the inner current loop and:

Following the modeling approach in [11], the complete system model can be obtained:

where ΔiLoadDQ denotes the small-signal perturbation of the load current in the common reference frame, ΔXinv1 and ΔXinv2 are small-signal perturbations of the state variables for inverter 1 and inverter 2. The stability in IS mode can be judged through analyzing the low-frequency eigenvalues of Asys. Therefore, low-frequency dominant eigenvalues in different operation modes can be acquired as presented in Fig. 4. As shown, stability margin of the conventional control strategy is very low since the dominant low-frequency eigenvalues are very close to the imaginary axis. (Note that stability is mainly influenced by the value of kp in droop-controlled inverters [11], and stability margin is specially defined as the difference between the value of kp at the critical stable state and the rated value in this paper.) Moreover, the system becomes unstable with a small droop coefficient kp, which significantly limits the adjustment range of energy management in autonomous microgrid [12], [36].

B. Classification of Low-frequency Oscillation Damping Methods

In order to mitigate the low-frequency resonance and improve the stability, many oscillation damping methods have been proposed [4], [13]-[16], [22]-[36]. In this paper, the classification of the existing damping methods is implemented according to the equivalent model of the droop-controlled VSI in [36], [38]. From [36] and [38], (9) can be derived.

where Gclu(s) is the closed-loop transfer function of the voltage loop, Zov(s) is the equivalent output impedance matrix, ucdq and igdq are the filter capacitor voltage and grid-side current in synchronous rotating frame (SRF), and urdq is the reference for the voltage loop which is shown in Fig. 2.

From (9), it can be seen that the output voltage ucdq is mainly determined by the controlled voltage source Gclu(s)urdq and the output impedance Zov(s). Thus, low-frequency oscillation damping can be carried out by changing the low-frequency characteristics of the controlled voltage source and the output impedance. Since the control bandwidth of Gclu(s) is determined by the switching frequency and the control bandwidth of the inner current loop, the low-frequency function of the controlled voltage source is dominated by urdq, which is decided by the droop loops. Consequently, the existing low-frequency oscillation damping methods can be classified into two categories, i.e., the source-type damping strategy and the impedance-type damping strategy. The source-type damping strategy is mainly implemented through inserting supplementary control loops into the droop loops, while the impedance-type damping strategy is mainly realized by introducing current feedforward to alter the low-frequency characteristic of the output impedance. Although both methods can enhance the low-frequency stability, their detailed impacts on the inverter performance are different. Therefore, the analysis, evaluation and comparison of different low-frequency active damping methods are discussed in this paper to better illustrate the diversity of performance impacts. In order to establish a fair comparison among the different active damping methods, the design for the control parameters of the damping methods is based on a common target which is to reduce the values of the resonant peak in Gpc(s) and Gqc(s) to be both lower than 5dB.

 

III. EVALUATION OF THE SOURCE-TYPE DAMPING STRATEGIES

As mentioned in section II, the source-type active damping methods are implemented with supplementary control loops to change the voltage reference urdq. As seen in [4], [16], [22]-[33], there are two kinds of implementations. The one is to introduce the feedforward of active power, the increment of angular frequency, or the increment of active power. The other is to insert compensation networks into the droop loops and introduce the feedforward of output current. The closed-loop transfer functions of the source-type damping methods can be achieved with the same derivation method in section II-A by modifying (1) according to the corresponding structure of the droop loops. The detailed investigation is given as follows.

A. Active Power Feedforward Control (APFC)

The feedforward item can be active power [16], the increment of active power [29], or the increment of angular frequency [30]-[33]. All the feedforward methods listed above can be equivalent to the feedforward of active power, but with different feedforward compensation networks Gpδ(s) and GpE(s), as shown in Fig. 5. In this paper, Gpδ(s) and GpE(s) are given as:

where k1=5×10-2, τ=1/(2π∙50), T1=2π∙15 and T2=2π∙0.5. The design of the parameters is from reference [29].

Fig. 5.Block diagram of the APFC scheme.

Similarly, the closed-loop characteristics of the droop loops and the root locus of the low-frequency dominant eigenvalues are shown in Fig. 6. As seen in Fig. 6(a), the resonance peak is effectively mitigated with the APFC scheme. Meanwhile, the stability margin is obviously enhanced in both GC and IS mode through comparing Fig. 6(b) with Fig. 4. However, the feedforward compensation networks need to be carefully designed since stability is very sensitive to the parameters and structure of the compensation networks. Moreover, the coupling between active power and reactive power may be strengthened for introducing the active power into the reactive power droop loop.

Fig. 6.APFC scheme. (a) Closed-loop characteristics of droop loops in GC mode. (b) Root locus of low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes.

B. Compensation Network Insertion Control (CNIC)

The compensation network insertion control scheme is presented in Fig. 7. Typically, the compensation networks Hp(s) and Hq(s) are proportional terms [4]. Nevertheless, proportional-derivative (PD) compensation networks [22]-[27] are beneficial for improving stability. In addition, lead-lag (LL) compensation networks are proposed in this paper to enhance the stability. Actually, the feedforward of output current to enhance stability in [28] can also be classified as a CNIC scheme. Two typical compensation network insertion control schemes are evaluated below.

Fig. 7.Block diagram of the CNIC scheme.

1) Proportional-derivative Compensation Network Insertion Control (PD-CNIC): The PD compensation networks are shown as (11):

where kpd=2×10-3 and kpd=4×10-2. The design process of the control parameters can be seen in [24].

As shown in Fig. 8(a), the resonance peak can be suppressed with the PD-CNIC scheme. Moreover, the control bandwidth of the droop loops is increased. Therefore, the interaction with the inner loops in high droop coefficients may deteriorate the stability. As seen in Fig. 8(b), the value of kp in the stability boundary is only 2.5 times larger than that in the conventional control strategy and the stability margin is worse than the APFC scheme. Therefore, the stability margin and the adjustment range are still limited with the PD-CNIC scheme since there is only one degree of freedom in the PD compensation networks. Meanwhile, low-frequency noise might be introduced with the derivative terms under non-ideal operation conditions. Although low-frequency noise can be suppressed by reducing the cut-off frequency of the power calculation LPFf, the dynamic response would be degraded. Consequently, a tradeoff needs to be considered when designing the cut-off frequency with the PD-CNIC scheme.

Fig. 8.PD-CNIC scheme. (a) Closed-loop characteristics of droop loops in GC mode. (b) Root locus of low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes.

2) Proposed Lead-lag Compensation Network Insertion Control (LL-CNIC): As illustrated by the PD-CNIC scheme, one-order proportional-derivative controllers are effective for realizing active damping. However, low-frequency noise may be induced by the derivative terms under non-ideal conditions.

In addition, the frequency of the low-frequency oscillation in the unstable state is often close to the cut-off frequency of the power calculation LPF. Therefore, an additional LPF structure can be combined with the proportional-derivative controller to filter out the low-frequency noise and the low-frequency oscillation. Moreover, the cut-off frequency of the LPF should be lower than that of the power calculation LPF. Essentially, the combination of a LPF and a proportional-derivative controller forms a lead-lag controller. Consequently, the lead-lag controller is effective for improving the stability. One-order LL compensation networks are adopted in this paper to illustrate the impacts of the LL-CNIC scheme and the compensation networks are given as (12).

where Tp1=1.257, Tp2=0.314, Tq1=5.027 and Tq2=1.257. The design is based on the closed-loop characteristics and the low-frequency root-locus as shown in Fig. 9.

Fig. 9.Proposed LL-CNIC scheme. (a) Closed-loop characteristics of droop loops in GC mode. (b) Root locus of low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes.

Compared with the PD-CNIC scheme, there are two degrees of freedom in the LL compensation networks with the LL-CNIC scheme. Therefore, the adjustment of stability margin is more flexible than PD-CNIC scheme. As shown in Fig. 9, the resonance peak can be effectively suppressed and the stability margin is also improved compared with the PD-CNIC scheme. In addition, high order LL compensation networks can also be applied to realize more control degrees of freedom. Meanwhile, the adjustment range of the stability and dynamic performance is also expanded with high order LL compensation networks. Therefore, the proposed LL-CNIC scheme can be a good choice to improve the stability.

 

IV. EVALUATION OF THE IMPEDANCE-TYPE DAMPING STRATEGIES

According to (9), low-frequency stability is also influenced by the output impedance. Therefore, low-frequency oscillation damping methods can be realized by changing the output impedance characteristics. Moreover, these implementations are divided into two types in this paper. The first type is to insert virtual impedance [13]-[15]. The second type is to introduce output current or inverter current feedforward to mitigate the impacts of inverter output impedance [36], [37]. The closed-loop transfer functions of the impedance-type damping methods can be achieved with the derivation method discussed in section II-A through modifying B1and B2 in (2) according to the corresponding structure of the current feed-forward control. The detailed analysis is given as below.

A. Virtual Impedance Control (VIC)

The original purpose of virtual impedance is to decouple the active power and the reactive power [4], [5], [13]-[15]. Nevertheless, active damping is also reinforced along with introducing virtual impedance. The VIC scheme is implemented by introducing the feedforward of the grid-side current as presented in Fig. 10. The difference between Fig. 10 and Fig. 2 is the larger value of the virtual impedance for the VIC scheme, which means better damping. The voltage drops across the virtual impedance in SRF shown in Fig. 10 can be expressed as (13):

where Rv and Lv are the virtual resistance and inductance, and ω is the angular frequency of the inverter. In this paper, Rv and Lv are set to 2Ω and 30mH for the VIC scheme. The design process of the virtual impedance is described in reference [13].

Fig. 10.Block diagram of the VIC scheme.

As shown in Fig. 11, the resonance peak is mitigated and the stability is enhanced through introducing virtual impedance. Nevertheless, the control bandwidth is reduced and the dynamic response is degraded. In addition, the harmonic performance and voltage unbalance compensation are also influenced by the virtual impedance [38], [39]. Therefore, a tradeoff needs to be made when designing the virtual impedance. Since high-frequency noise might be introduced with the derivative term sLv, sLv is often ignored in practical applications.

Fig. 11VIC scheme. (a) Closed-loop characteristics of droop loops in GC mode. (b) Root locus of low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes without sLv.

B. Mitigation of Inverter Output Impedance Impacts (MIOII)

As analyzed in [36], the inverter output impedance with the conventional control strategy can be expressed as (14):

where Guc(s) is the PI controller for the voltage loop, and Gcli(s) is closed-loop transfer function of the current loop.

If virtual impedance is not introduced, the equivalent output impedance Zov(s) is equal to Zo(s). As illustrated in [36], the stability margin is enhanced with a reduced inverter output impedance. Meanwhile, the dynamic performance is improved since the dominant eigenvalues moves from right to left. However, with small output impedance, the in-rush current can’t be effectively mitigated during start-up or when plugging in different DG units [40]. Moreover, the harmonic performance and voltage unbalance compensation are also influenced by the inverter output impedance [36].

The MIOII scheme can be classified into the output current feedforward control strategy [37] and the inverter current feedforward control strategy [36]. The evaluation and comparison of these two methods are given in this subsection.

1) Output Current Feedforward Control (OCFC): When the OCFC scheme presented in Fig. 12 is adopted, the equivalent output impedance can be obtained as (15):

Fig. 12.Block diagram of the OCFC scheme.

where Rv0 and Lv0 are the initial virtual resistance and inductance, and kcg is the feedforward gain which is set to 0.7 in this paper. The detailed design method of the feedforward gain kcg can refer to [36] since the OCFC scheme is basically equivalent to the inverter current feedforward control strategy as verified with the analysis and experiment results below.

As shown in Fig. 13, the resonance peak can be suppressed and the stability margin can be enhanced with the OCFC scheme. Moreover, the control bandwidth is guaranteed and the dynamic performance can be improved. However, the promotion of stability margin mainly depends on the feedforward gain kcg. Since the previously listed performance listed before may be influenced by the inverter output impedance, the design of kcg needs to be compromised.

Fig. 13.OCFC scheme. (a) Closed-loop characteristics of droop loops in GC mode. (b). Root locus of low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes.

2) Inverter Current Feedforward Control (ICFC): To avoid the current sensor requirement for igabc with the OCFC scheme, the ICFC scheme can be applied to realize the similar performance as OCFC scheme. As shown in Fig. 14, the inverter current iLdq with a low-pass filter LPF1 substitutes for igdq. The feedforward gain kcL is chosen to be the same as kcg. Moreover, LPF1 is a one-order LPF and the cut-off frequency is 1kHz. The detailed design process of the control parameters can be seen in [36].

Fig. 14.Block diagram of the ICFC scheme.

As shown in Fig. 15(a), the closed-loop characteristics of the ICFC scheme basically coincide with the OCFC scheme as displayed in Fig. 13(a). Therefore, the control bandwidth and dynamic performance are equivalent to the OCFC scheme. Nevertheless, the stability margin of the ICFC scheme is slightly worse than the OCFC scheme in both operation modes as shown in Fig. 15(b). Moreover, the LPF1, which is used to eliminate the current ripple of iLdq, also has an important impact on stability [36].

Fig. 15.ICFC scheme. (a) Closed-loop characteristics of droop loops in GC mode. (b) Root locus of low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes.

 

V. EXPERIMENTAL VALIDATION

In order to verify the correctness of the above analysis, experiments based on a 2kVA prototype as shown in Fig. 16 are implemented. The controller is realized in the RT-LAB environment. The power stage parameters and control parameters of the prototype are listed in Table I and Table II, respectively. As seen in the root locus of the different methods, the trend of low-frequency stability in IS mode is very similar to that in GC mode. Therefore, it is concentrated on GC mode in this subsection to avoid unnecessary details. The experimental results are given as follows. In order to avoid triggering overcurrent protection which can be induced by the overshoot when P0 steps or the low-frequency oscillation when kp steps in GC mode, the step of P0 and the value of P0 when kp steps are both set as 500W in the experimental validation.

Fig. 16.Picture of the experimental prototype.

A. Conventional Control Strategy

The low-frequency dominant eigenvalues with the conventional droop control strategy can be obtained through the small-signal model adopted in this paper. The boundary values of kp with the conventional control strategy are 1.095×10-3 in GC mode and 1.280×10-3 in IS mode as shown in Fig. 4. Note that the boundary value is the value in which the system is under the critical stable state. Moreover, it can be illustrated from Fig. 17(b) and Fig. 17(c) that the practical boundary values in the experiments are 1.1×10-3 in GC mode and 1.34×10-3 in IS mode. Comparing the modeling results with the experimental results, it can be concluded that the theoretical analysis of the adopted small-signal model in this paper basically coincides with the experimental results.

Fig. 17.Experimental results of active power P and reactive power Q with the conventional strategy in GC mode, respectively: (a)P0 steps from 0 to 500W when kp=0.63×10-3, (b)kp increases from 0.63×10-3 to 1.1×10-3 with P0=500W. (c)kp increases from 1.1×10-3 to 1.34×10-3 with 800W load in IS mode.

In GC mode, the transient process is activated by stepping the power instruction P0. As shown in Fig. 17(a), stability is guaranteed in both GC mode and IS mode with a small kp, which is lower than the rated value. Moreover, low-frequency oscillation is activated with a kp step as presented in Fig. 17(b). Therefore, stable operation can’t be satisfied with the rated value of kp, and stability margin is very limited with the conventional control strategy.

B. The Source-type Damping Strategies

As seen in Fig. 18(a), the low-frequency oscillation is mitigated with the APFC scheme. Note that in case of triggering the over-current protection for the coupling between the active power and the reactive power, the power step instruction is reduced in the experiment. Moreover, the stability margin is also significantly enhanced since stability is still ensured with a kp that is three times larger than the rated value as presented in Fig. 18(b). Nevertheless, a large overshoot occurs in the reactive power when a small active power step is implemented. Meanwhile, the overshoot increases with a larger kp. Hence, the coupling between the active power and the reactive power is obviously strengthened with the APFC scheme.

Fig. 18.APFC strategy in GC mode: (a)P0 steps from 0 to 300W when kp=1.57×10-3, (b)P0 steps from 0 to 100W when kp=4.71×10-3.

As shown in Fig. 19(a)-(b), stability is enhanced with the PD-CNIC scheme while the promotion of stability margin is much lower than the APFC scheme due to the lack of enough control degree of freedom. In addition, the low-frequency noise which can trigger the overcurrent protection is also introduced in IS mode as seen in Fig. 19(c)-(d). Since the isolation transformer is not ideal in the experiment, the voltage control is easy to be degraded in IS mode. However, in GC mode, voltage is mainly clamped by the stiff grid and the impact of a non-ideal isolation transformer can be mitigated. Consequently, the low-frequency noise is more serious in IS mode.

Fig. 19.PD-CNIC strategy. (a) P0 steps from 0 to 500W when kp=1.57×10-3 in GC mode, (b) kp increases from 2.04×10-3 to 2.67×10-3 with P0=500W in GC mode. (c) Steady-state waveforms when kp=1.57×10-3 with 400W load in IS mode. (d) kp increases from 2.98×10-3 to 3.61×10-3 with 400W load in IS mode.

Since the degree of freedom is larger than that in the PD-CNIC scheme, the adjustment range turns to be wider with the proposed LL-CNIC scheme. As presented in Fig. 20(a), stability can be guaranteed with the LL-CNIC scheme at the rated value of kp. Moreover, when kp is three times larger, stability is still ensured as displayed in Fig. 20(b). Therefore, stability can be effectively enhanced with the LL-CNIC scheme, and it is a very good choice when attempting to improve stability.

Fig. 20Proposed LL-CNIC strategy in GC mode: P0 steps from 0 to 500W when (a)kp=1.57×10-3, (b)kp=4.71×10-3.

C. The Impedance-type Damping Strategies

As shown in Fig. 21(a), the low-frequency oscillation is effectively mitigated and stability is ensured with the VIC scheme at the rated value of kp. Moreover, stability is still guaranteed with a kp that is four times larger as presented in Fig. 21(b). In addition, the VIC scheme is immune to high-frequency noise when neglecting the derivative terms in practical applications.

Fig. 21.VIC strategy in GC mode: P0 steps from 0 to 500W when (a)kp=1.57×10-3, (b)kp=6.28×10-3.

Compared with the conventional control strategy, stability is guaranteed at the rated value of kp with the OCFC scheme as presented in Fig. 22(a) although low-frequency damped oscillation exists. Nevertheless, since low-frequency oscillation occurs with a slightly higher kp than the rated value as shown in Fig. 22(b), stability margin is still limited because of the restraint of feedforward gain kcg.

Fig. 22.OCFC strategy in GC mode. (a) P0 steps from 0 to 500W when kp=1.57×10-3. (b) kp increases from 1.89×10-3 to 2.36×10-3 with P0=500W.

With the ICFC scheme, stability is ensured with the rated kp as displayed in Fig. 23(a) in spite of the damped oscillation. Nevertheless, stability margin is still limited as in the OCFC scheme as presented in Fig. 23(b). Hence, the ICFC scheme is basically equivalent to the OCFC scheme when ignoring this minor difference.

Fig. 23.ICFC strategy in GC mode. (a) P0 steps from 0 to 500W with kp=1.57×10-3. (b) kp increases from 1.89×10-3 to 2.36×10-3 with P0=500W.

 

VI. COMPARISON AND DISCUSSION

Different damping strategies have been evaluated and analyzed in section III and section IV. The comparison and synthesis of different damping methods are discussed below.

A. Comparison between Different Damping Methods

Although the low-frequency stability can be improved with both types of damping methods, the individual impacts on the system performance are different.

The comparison between the source-type damping methods and the impedance-type damping methods is shown in Fig. 24(a). As can be seen, the source-type damping methods may introduce side-effects in the low-frequency range, such as power coupling and low-frequency noise. Moreover, the performance relies heavily on the structure and parameters of the compensation networks. The high frequency performance, such as harmonic performance, voltage unbalance performance and transient current-limiting performance, is influenced by the impedance-type damping methods because the impedance characteristics are changed. Therefore, the source-type damping methods should be applied in fields where high frequency performance is not expected to be changed. However, the impedance-type damping methods can be applied in fields where the high frequency performance is compatible and low-frequency side-effects are intolerable.

Fig. 24.(a) Comparison between different types of damping methods. (b) Comparison between APFC scheme and CNIC scheme. (c) Comparison between VIC scheme and the MIOII scheme.

In addition to the function of enhancing the low-frequency stability, the impacts of the source-type damping methods and the impedance-type damping methods are different. Therefore, the comparison between the constituent parts of each method is implemented as follows:

1) Since the source-type damping strategies consist of the APFC scheme and the CNIC scheme, the comparison between these schemes is shown in Fig. 24(b). As shown, intensive power coupling is introduced by the APFC scheme while the CNIC scheme has no impact on the power coupling. In addition, both schemes are significantly influenced by the structure and parameters of the compensation networks. Meanwhile, the adjustment range of both schemes is often determined by the control degrees of freedom of the compensation network. Therefore, with properly designed compensation networks, the CNIC scheme may be a good choice.

2) The impedance-type damping methods include the VIC scheme and the MIOII scheme. Since the output impedance is increased by the VIC scheme and reduced by the MIOII scheme, the characteristics of the VIC scheme are basically contrary to the MIOII scheme as shown in Fig. 24(c). In addition, the adjustment range of the MIOII scheme is limited by the feedforward gain since the stability might be degraded by negative impedance. However, a wide adjustment range can be guaranteed by changing the virtual impedance with the VIC scheme. Therefore, the VIC scheme can be applied in fields demanding a high output impedance, while the MIOII scheme should be applied in low output impedance fields.

Consequently, different damping methods have different advantages and disadvantages. Fortunately, there are no conflicts among different damping strategies. Therefore, these damping strategies can also be combined to enhance stability.

B. Synthesis of Different Damping Methods

Three types of combinations between different damping methods can be achieved: the synthesis of source-type damping strategies, the synthesis of impedance-type strategies and the synthesis of the source-type damping strategy and the impedance-type damping strategy. To better illustrate the effect of these combinations on stability, one possible combination for each type is given and analyzed in this subsection.

For the source-type damping strategies, the APFC scheme and the CNIC scheme can be combined to improve stability. For example, the root locus of low-frequency dominant eigenvalues with the synthesis of the APFC scheme and the PD-CNIC scheme is presented in Fig. 25(a). Compared with Fig. 6(b) and Fig. 8(b), the stability margin is significantly enhanced. Moreover, the low-frequency noise introduced by the PD-CNIC scheme can be suppressed with the feedforward of active power in the APFC scheme. However, the effect of the coupling between active power and reactive power introduced by the APFC scheme can’t be avoided.

Fig. 25.Root locus of low-frequency dominant eigenvalues for 0.785×10-3≤kp≤31.4×10-3 in different operation modes: (a) with the synthesis of APFC scheme and PD-CNIC scheme, (b) with the synthesis of VIC scheme and OCFC scheme and (c) with the synthesis of LL-CNIC scheme and OCFC scheme.

For impedance-type damping strategies, stability is also enhanced through synthesizing the VIC strategy and the MIOII strategy as shown in Fig. 25(b). Compared with Fig. 11(b) and Fig. 13(b), the stability is further strengthened. However, output impedance is often changed by the impedance-type damping strategies. Moreover, harmonic performance, voltage unbalance and dynamic response are significantly influenced by the output impedance [36], [38]-[39]. Consequently, the controller design in the case of synthesis should comprehensively weigh the impacts on stability and high-frequency performance.

In addition, the synthesis of the source-type damping strategy and the impedance-type damping strategy is also very helpful in the promotion of stability margin. As displayed in Fig. 25(c), the stability margin is significantly enhanced through the combination between LL-CNIC scheme and the OCFC scheme.

Based on the above analysis, it can be concluded that stability can be further enhanced with the synthesis of different damping methods. Nevertheless, the disadvantages of each method may be introduced through the synthesis. Therefore, trade-off and comprehensive evaluation are needed when considering the synthesis of different damping methods.

C. Experimental Validation

In order to verify the theoretical analysis for the synthesis of different damping methods, experimental validation is presented in this subsection.

As shown in Fig. 26(b), when kp=8.32×10-3, which is larger than the boundary value of the APFC scheme and the PD-CNIC scheme, stability is still guaranteed. However, the coupling of active power and reactive power introduced by the APFC scheme also exists. In addition, comparing Fig. 26(a) with Fig. 18(b), better low-frequency damping and smaller overshoot of reactive power also signify the reinforce of stability through the synthesis of the APFC scheme and the PD-CNIC scheme.

Fig. 26.Experimental results of the synthesis of APFC scheme and PD-CNIC scheme when P0 steps from 0 to 500W in GC mode with: (a) kp=4.71×10-3 and (b) kp=8.32×10-3.

Comparing Fig. 27(a) with Fig. 21(b), low-frequency oscillation in the same value of kp is better mitigated with the combination of the VIC scheme and the OCFC scheme. Meanwhile, as presented in Fig. 27(b), stability is ensured when kp=10.36×10-3, which is larger than the boundary value of the VIC scheme as shown in Fig. 11(b).

Fig. 27.Experimental results of the synthesis of VIC scheme and OCFC scheme when P0 steps from 0 to 500W in GC mode with: (a) kp=6.28×10-3 and (b) kp=10.36×10-3.

Better low-frequency damping presents in Fig. 28(a) through the comparison with Fig. 20(b). Moreover, as shown in Fig. 28(b), stability is guaranteed with a larger value of kp than the boundary value of the LL-CNIC scheme. Therefore, better low-frequency damping performance is achieved through the synthesis of the LL-CNIC scheme and the OCFC scheme.

Fig. 28.Experimental results of the synthesis of LL-CNIC scheme and OCFC scheme when P0 steps from 0 to 500W in GC mode with: (a) kp=4.71×10-3 and (b) kp=6.28×10-3.

 

VII. CONCLUSION

In this paper, low-frequency oscillation issues are analyzed for the conventional droop control strategy and the oscillation damping strategies are classified into two categories: the source-type damping strategy and the impedance-type damping strategy. The source-type damping strategy consists of the APFC scheme and the CNIC scheme, while the impedance-type damping strategy includes the VIC scheme and the MIOII scheme. The advantages and disadvantages of each damping strategy are theoretically evaluated and experimentally validated. Moreover, comparison among different methods is implemented to illustrate the suitable application fields of each method. Finally, the synthesis of different damping methods is discussed to significantly improve the low-frequency stability, and experiment results verify the stability improvement.