Control strategy resilient to unbalanced faults for interlinking converters in hybrid microgrids

Electrical Power and Energy Systems 119 (2020) 105927

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Control strategy resilient to unbalanced faults for interlinking converters in hybrid microgrids

T

⁎

Amir Eisapour-Moarrefa, Mohsen Kalantara, , Masoud Esmailib a

Center of Excellence for Power System Automation and Operation, Department of Electrical Engineering, Iran University of Science and Technology, Tehran 1684613114, Iran b Department of Electrical Engineering, West Tehran Branch, Islamic Azad University, Tehran, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Hybrid microgrid (HMG) Interlinking converter (IC) Multi-dimensional droop Synchronverter Unbalanced grid faults

Hybrid microgrids (HMGs) consist of AC and DC microgrids (MGs) that are connected through bidirectional interlinking converters (ICs). In order to optimally utilize renewable generations and address their intermittency, efficient control strategies are needed for power management of ICs. The performance of available control strategies for HMGs in case of faults may be limited since the converters are usually set to trip in the event of transient stability related problems to protect converters from being damaged. Also, HMGs may face frequency instability problems due to the lower damping capability of converter-based generations compared with classical synchronous generators. In this paper, an enhanced control strategy based on the concept of 3-D droops is proposed for ICs. The proposed method makes HMGs more resilient against faults at the utility side. It also improves stability of HMGs by mitigating quasi-static active and reactive power oscillations that may be generated by renewable intermittent generations. Also, it ensures a proper transient power sharing without deteriorating the transfer capability of ICs when unbalanced faults, as the most prevalent ones, occur in HMGs. In addition, the synchronverter technology with an adaptive virtual inertia is applied to the control strategy of ICs to enhance frequency stability of HMGs in case of occurring faults or volatile renewable generations. The performance of the proposed features is evaluated by their testing on a typical HMG.

1. Introduction Nowadays, with the ever increasing growth of dc and ac microgrids (MGs), hybrid microgrids (HMGs) have become more popular to reduce power conversions from the dc to ac or vice versa [1]. The ac and dc MGs in HMGs are connected through bidirectional interlinking converters (ICs) [2], which play a crucial role in effective power management between the two subgrids. Without an efficient control strategy for ICs, the stability of HMGs may face critical challenges, especially under unbalanced grid conditions [3]. In literature, power management strategies of ICs are usually classified into droop-based [4] and communication-based [5] control schemes. Although communication-based control strategies may offer more flexibility, they may suffer from security and reliability issues since they may be open to cyber-attacks or the loss of communication links can affect system operation and stability [6]. However, droop-based control approaches are decentralized and act as autonomous controllers and then, they may be more popular to solve HMG-related problems. For instance, authors in [1] have suggested droop characteristics for ICs and sources across both dc and ac

⁎

sides to achieve suitable power sharing in HMGs. In [7], a purposefully droop control strategy is designed for ICs to suppress circulating currents and realize a proper load power sharing between dc and ac subgrids. However, droop-based strategies still have their own concerns. One of challenging issues in droop-based strategies is the accuracy of power sharing among distributed generations (DGs) as well as parallel ICs [8]. Without an appropriate power sharing strategy, some converters may be overstressed, whereas others may have a lower loading. The overstressed converters are likely to trip and thus, the HMG reliability is endangered. One of causes of the inaccurate power sharing is the mismatch between the capacities of dc and ac subgrids. To tackle this, authors in [9] have introduced a droop control strategy to realize proper power sharing among multiple subgrids. Another reason is caused by different impedances of IC lines/cables [10]. The power sharing issue can be studied in ac or dc MGs. In the ac side, since the ac frequency acts as a global variable, the traditional P − f droop can provide a reliable power sharing [11]. Different control strategies are proposed in literature for power sharing at the ac side. For instance, authors in [12] introduced a hierarchical control scheme for power flow

Corresponding author. E-mail address: [email protected] (M. Kalantar).

https://doi.org/10.1016/j.ijepes.2020.105927 Received 26 September 2019; Received in revised form 13 January 2020; Accepted 5 February 2020 0142-0615/ © 2020 Elsevier Ltd. All rights reserved.

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synchronverter technology may be more effective [27]. The synchronverter is a grid-friendly converter which imitates the inertia and damping properties of classical synchronous generators to enhance stability. This can be realized by implementing the mathematical model of synchronous generator in the control system of converters and ICs. Therefore, ICs can act with high virtual inertia to mitigate frequency and power oscillations during grid faults provided that there is a stored energy (similar to kinetic energy of the rotor in synchronous generators). It is worth noting that modern HMGs are usually benefited from energy storage systems (ESSs) in their dc or ac sides and consequently, there is usually no need for an additional ESSs to implement the synchronverter technique for ICs. The idea of multi-dimensional droop is recently proposed by Bunker et al. [28], where a 3-D droop is applied to maximize the power available from wind. It has been realized in [28] that by adding the wind speed as the 3rd axis to the conventional 2-D droop, the maximum power point tracking can be achieved for wind and other non-dispatchable DGs. The advantage of using a 3-D droop is to add an additional degree of freedom to a 2-D droop to improve its flexibility in the control scheme. By utilizing two droop coefficients instead of one, the 3-D droop offers a more flexible operation strategy by purposefully changing its droop surface orientation [29]. That is, it makes possible to adjust the droop surface orientation through optimally tuning droop gains to achieve a more efficient control strategy. Accordingly, the concept of multi-dimensional droop can enhance the control efficacy of ICs while confronting with unbalanced faults or DG volatile generations. Considering the above reviewed context, 3-D droops are proposed for ICs in this paper to simultaneously compensate active and reactive power oscillations without deteriorating power transfer capability of ICs in order to provide a robust control scheme for varying conditions in HMGs. As a result, all parallel ICs contribute to compensating the oscillations, unlike previous works such as [3], without imposing additional cost for the extra IC or operating ICs at lower ratings. Thus, the HMG not only is able to economically use its resources but also becomes more robust against continuously-varying operating states. Using the frequency of dc voltage harmonics (as a global variable), the existing harmonic-based droop in [16] which only contains one PI controller, is modified by adding another inner current control loop to make it applicable in fault conditions. Since the proposed scheme is equipped with two PI controllers (one in the frequency control loop and the other in the current control loop), in addition to steady-state power sharing, its efficiency in transient power sharing is also enhanced and, in the meantime, undesired tripping of dc/dc converters caused by the overcurrent during transient states is prevented. Then, a 3-D droop is proposed using the harmonic-based controller instead of the local dc voltage. Therefore, overstressing of ICs is prevented, especially in case of overcurrent during unbalanced faults. Moreover, an adaptive virtual inertia is proposed for ICs to improve the frequency stability in HMGs. The adaptive virtual inertia does not affect the HMG in steady-state operation, but it damps frequency oscillations during transient phenomena. Accordingly, ICs act as synchronverters so that the HMG is able to absorb more energy from fluctuating renewable generation sources. Concretely, this paper has main contributions as follows:

modeling of islanded MGs, where the P − f droop is employed for active power sharing among DGs in the primary control level. In [13], a decentralized power management scheme based on the P − f droop is suggested to ensure a proper load sharing among voltage source inverters (VSIs). On the other hand, in the dc side of HMGs, the P − V droop is conventionally used to regulate active power generation when the dc voltage changes. However, this droop may not be able to establish an appropriate power sharing in dc MGs. This is due to the fact that it is based on the local dc voltage which may lead to inaccurate power sharing if line resistances are considered. To overcome this drawback, Peyghami et al. in [14] have intentionally imposed a small ac ripple on the dc voltage to create a global variable in the dc side. Although it leads to proper power sharing, it may deteriorate power quality of the dc voltage. The power quality is a vital issue in HMGs and is specifically addressed in the literature; even some works such as [15] just focused on control structures to improve the power quality of the dc voltage. Authors in [16] addressed this drawback by using the frequency of existing harmonics instead of the intentional ac ripple in order to devise a control strategy for the dc side of HMGs. In HMGs, the normalized droop is often employed for power sharing among parallel ICs [17]. Parameters at two sides of ICs (ex., dc voltage and ac frequency) are normalized to decide the amount and direction of IC power. For instance, authors in [18] have used the normalized droop for autonomous operation of parallel ICs to maximize loadability of islanded HMGs under unbalanced ac loading. The normalized droop control has been employed in [19] for proportional power sharing throughout an HMG. However, in the presence of line resistances, these methods may not provide accurate power sharing in HMGs among ICs due to adopting local dc voltages in the dc side. In addition to their limitation in steady-state operation, they may also be limited in transient power sharing among ICs when faults occur at the utility side [20]. If a control strategy fails to establish proper power sharing in transient cases, ICs may trip due to short-term overloading or overshoots. Another vital issue in the control structure of HMGs is the effect of unbalanced faults that are more commonplace than balanced threephase faults at the utility side. These faults have devastating effects on the operation of converters as well as parallel ICs in HMGs [21]. Without a resilient control strategy in HMGs, utility faults challenge stability of HMGs especially by triggering active and reactive power oscillations, dc link voltage ripples, output current fluctuations, and tripping of ICs [22]. To this end, some methods in literature, such as [23] and [24], presented IC control structures that are resilient against grid faults. Among them, although some works, such as [25] and [26], have managed to mitigate power fluctuations and dc link voltage ripples, they limit the power transfer capability of ICs to make them resilient against external faults. This limitation implies that the ICs cannot be used at their rated capacity and then, it may lead to uneconomical solutions. In another approach of dealing with external faults, authors in [3] have added an IC (named as redundant IC) in parallel with other ICs with a higher current rating to ensure an oscillation-free output active power. Although it leads to the elimination of output active power fluctuations among parallel ICs, it imposes the cost of the extra IC with even a higher capacity and also it lacks a mechanism to simultaneously compensate reactive power oscillations. Moreover, since a single redundant IC is responsible to cancel out the fluctuations of all parallel ICs, the reliability of the control strategy may be endangered in case of outage of the redundant IC. Another challenge in the stability of HMGs, where there is a high penetration level of DG-based generation, is the inability of converters including ICs in providing enough inertia unlike synchronous generators. This inherent characteristic of converters makes HMGs more vulnerable against frequency stability problems. To tackle this issue, various control strategies with improved fault ride through (FRT) capability are proposed in literature for ICs, among them the

• Proposing a modified harmonic-based control structure for dc/dc • • 2

converters to make them resilient against disturbances including grid faults. Suggesting a new control strategy for ICs based on 3-D droops to simultaneously suppress active and reactive power fluctuations, establish accurate transient power sharing, and restrain the peak current of ICs during disturbances. Proposing an adaptive virtual inertia for ICs to make them act as synchronverters. Thus, not only the contribution of ICs in suppression of oscillations increases, but also the transient stability of the HMG improves.

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Fig. 1. Overall block diagram of the understudy hybrid microgrid.

for the ac MG, we utilize the control strategy presented in [31].

The rest of this paper is organized as follows. In section 2, the droopbased control structure for dc/dc converters and ICs is developed for satisfactory performance in the presence of unbalanced gird faults. The proposed 3-D droops are also illustrated to simultaneously suppress active and reactive power oscillations as well as to establish an accurate transient power sharing among ICs. The principle of the synchronverter is also applied to the control structure of ICs to improve transient stability. Section 3 presents numerical results obtained from case studies to show the efficiency of the proposed framework. Finally, section 4 concludes the paper.

2.2. Modified droop control for the dc MG Unlike the ac side, the only control variable in the dc side is voltage, which is used to control the active power among dc/dc converters and ICs. Therefore, the conventional P − V droop can be expressed as [32]: max Vdc = Vdc − K vdc Pdc

is where Vdc is the dc voltage at the output of the dc/dc converter; the output dc voltage at no load; Pdc is the output dc power; K vdc is the dc droop gain. In order to have a power sharing in case of parallel dc/dc converters (such as parallel ICs), dc droop gains are set according to the nominal power of converters:

2. Proposed droop control strategy for hybrid microgrids In order to explain the proposed methodology, an HMG is considered with two parallel ICs without loss of generality, as illustrated in Fig. 1, where ICs connect dc and ac MGs through lines/cables and filters. Some types of DGs are connected to the common dc or ac buses through dc/dc converters or VSIs, respectively. Also, the ac MG is connected to the utility grid through a Δ − Y transformer at the point of common coupling (PCC). In order to better convey the proposed ideas, at first, conventional droop control strategies are briefly reviewed in this section. Afterwards, the proposed ideas for the dc/dc converters and ICs are presented.

max min K vdc = (Vdc − Vdc )/ Pndc

is the minimum allowable output voltage of the dc/dc where converter; Pndc is the nominal power of the converter. The conventional P − V droop is only able to monitor the output voltage of the dc/dc converter at its output terminals before dc line ESS EV or Rdc in Fig. 1). However, common dc bus resistances (i.e., Rdc CB voltage Vdc is the main control variable in the dc MG, which cannot be properly estimated by Vdc in the presence of the line resistances. If there is only one converter, this problem may lead to only an error in the voltage of common dc bus, which may be acceptable. However, in case of parallel converters (such as parallel ICs), different resistances and voltage drops across line resistances can adversely affect power sharing accuracy among parallel converters. Thus, some converters may be overstressed, while some others may be loaded lower than their rated power. This problem happens since the dc voltage is not a global variable at the dc side. To tackle this problem, a method is proposed in [16] to employ the frequency of the dominating harmonic in the dc MG as the global variable. Since the harmonic frequency is the same at all dc buses, its efficiency in power sharing is not affected by line resistances. The harmonic-based droop P − fh for the dc MG is expressed as [16]:

The decentralized control of DGs in the ac MG is performed using the following well-known droop characteristics [30]: (1)

max Vac = Vac − K2ac Qac

(2)

where fac and Vac are ac frequency and voltage, respectively, measured max max and Vac represent maximum by the VSI at its output terminals; f ac frequency and voltage at no load, respectively; Pac and Qac are output powers of VSI; K1ac and K2ac are droop gains of the P − f and Q − V droop controls, respectively. In order to establish a proportional load sharing among VSIs, droop coefficients are set according to the rating of VSIs: max min K1ac = (f ac − f ac )/ Pnac

(3)

max min K2ac = (Vac − Vac )/ Qnac

(4)

min f ac

(6)

min Vdc

2.1. Review of droop control for the ac MG

max fac = f ac − K1ac Pac

(5) max Vdc

fh = f hmax − Khdc Pdc

(7)

f hmax

represent the harmonic frequency value and its where fh and maximum permissible value, respectively; Khdc is the P − fh droop gain which can be set as follows using the converter nominal power:

Khdc = (f hmax − f hmin )/ Pndc

min Vac

where and are the minimum permissible frequency and voltage, respectively; Pnac and Qnac represent nominal active and reactive powers of VSIs, respectively. Among the available droop-based schemes

(8)

where f hmin is the minimum harmonic frequency in the dc system. The P − fh droop presented in [16] uses the harmonic frequency fh 3

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−

+

−

+ − − + PIC = (VacIC . IIC + VacIC . IIC ) + (VacIC . IIC + VacIC . IIC ) = Pavr + POSC

(11) +

−

+

−

+

−

+ − − + QIC = (VacIC⊥ . IIC + VacIC⊥ . IIC ) + (VacIC⊥ . IIC + VacIC⊥ . IIC ) = Qavr + QOSC

(12) − + POSC = VacIC . IIC + VacIC . IIC +

(13)

−

− + QOSC = VacIC⊥ . IIC + VacIC⊥ . IIC − + + , where VacIC , VacIC , IIC

and are positive and negative sequence vectors of output voltage and current of the IC; Pavr , POSC , Qavr , and QOSC are average and oscillatory terms of instantaneous active and reactive powers. Without losing generality, we here ignore the zero sequence in the current vectors [22]. In order to prevent the transient violation of current rating limitations of ICs during grid faults, POSC and QOSC should be eliminated by the proposed control strategy. To this end, two scalar coefficients α and γ are defined so that the two terms of (13) counteract each other [3,22]. The same scenario is also applied to (14). By assuming each power fluctuation zero, we can obtain the optimal value of α for each case:

Fig. 2. Modified harmonic-based control structure for dc/dc converters.

as a global variable at the dc side of HMGs. This control strategy includes only one control loop for harmonic frequency, a structure that is able to establish steady-state power sharing among dc/dc converters. This control strategy with only one control loop is not able to establish accurate transient power sharing among dc/dc converters. Therefore, in transient cases, such as faults, the dc/dc converters may be overloaded for a short time and then, their protection isolates them to protect IGBT switches from being damaged. To make the P − fh droop strategy of [16] more versatile and resilient against faults, we here modify it by adding another inner current control loop as illustrated in Fig. 2. This way, the proposed structure is equipped with two PI controllers (the first one for the frequency control loop to wipe out the harmonic frequency error and the second one for the current control loop to eliminate the current error). The advantage of this structure is that an accurate power sharing is established in both steady-state and transient cases. As a result, undesired tripping of dc/dc converters caused by the short-time overcurrent during transient phenomena is prevented. Output parameters of the dc/dc converter at its terminals (Vdc and Idc ) in Fig. 2 are used to determine average power Pdc , through the “Power Calculation” block, as an input to the harmonic-based droop control expressed by (7). Then, the dc voltage is analyzed by an improved fast Fourier transform (IFFT) block [33] in order to extract the dominant harmonic frequency f h' by means of a comparator. Since the IFFT block continuously monitors the dc voltage, it is able to extract the dominating harmonic under time-varying loads/generations and different operation modes [33]. The error fh − f h' is then applied to an outer PI ∗ . In fact, the harmonic regulator to generate the reference dc power Pdc frequency control loop is used in the outer level of Fig. 2 instead of the conventional voltage control loop. Afterwards, the reference dc current ' ∗ ∗ ∗ − Idc Idc is calculated using Pdc and the error Idc is supplied to an inner current regulator. Finally, the transmitted signal from the inner PI regulator is fed into a Pulse-Width Modulation (PWM) module to generate command signals for the converter switch.

+

−

− + If POSC = 0 ⇒ VacIC . IIC = −α. VacIC . IIC , α≥0 p p +

−

and are the positive and negative sequence currents of where the IC obtained from the original abc values. From (11)–(16), the reference current vector of the active power of the IC can be obtained as [22]:

Pavr

∗ + − IIC = IIC + IIC = p p p

αPavr

+

+

VacIC +

−

|VacIC |2 + α |VacIC |2

+

−

|VacIC |2 + α |VacIC |2

VacIC

−

(17) Similarly, the reference current vector of the reactive power of the IC can be expressed as: +

−

− + If POSC = 0 ⇒ VacIC . IIC = −γ . VacIC . IIC , γ≥0 q q +

(18)

−

− + If QOSC = 0 ⇒ VacIC⊥ . IIC = −γ . VacIC⊥ . IIC , γ≥0 q q

(19)

− IIC q

+ IIC q

and are the positive and negative sequence currents of where the IC obtained from the original abc values. From (11), (12) and (18), (19), the reference current vector of the reactive power of the IC can be obtained as [22]: ∗ + − IIC = IIC + IIC = q q q

Qavr

γQavr

+

+

−

|VacIC |2 + γ |VacIC |2

VacIC⊥ +

−

+

−

|VacIC |2 + γ |VacIC |2

VacIC⊥

(20) Considering (17) and (20), the reference current vector of the IC can be found as: ∗ ∗ ∗ IIC = IIC + IIC p q + −⎞ Pavr αPavr ⎛ ⎛ =⎜ VacIC + VacIC ⎟ + ⎜ IC + 2 IC − 2 IC + 2 IC − 2 V + α V + V α V | | | | | | | | ac ac ac ⎠ ⎝ ⎝ ac

(9)

Qavr

QIC =

(16)

− IIC p

+ IIC p

In case of disturbances in the HMG including unbalanced grid faults, active and reactive powers of ICs oscillate. According to instantaneous power theory [3], the instantaneous output active and reactive powers of each IC can be derived as [22]:

VacIC⊥ . IIC

(15)

− + If QOSC = 0 ⇒ VacIC⊥ . IIC = −α. VacIC⊥ . IIC , α≥0 p p

2.3. Power oscillations and proposed droop for interlinking converters (ICs)

PIC = VacIC . IIC

(14)

− IIC

(10)

γQavr

+

+

−

|VacIC |2 + γ |VacIC |2

VacIC⊥ +

+

−

|VacIC |2 + γ |VacIC |2

−⎞ VacIC⊥ ⎟ ⎠

(21)

Considering (11), (12) and (21), the instantaneous active and reactive powers of the IC can be rewritten as:

where VacIC = [VacIC _a, VacIC _b, VacIC _c ] and IIC = [IIC _a, IIC _b, IIC _c ]T are threephase instantaneous output voltage and current vectors of the IC; VacIC⊥ lags VacIC by 90°. By transforming these voltages and currents from the abc to symmetric-sequence framework, (9) and (10) can be rewritten as [22]:

+

PIC = Pavr +

4

+

+

−

Pavr (1 + α )(VacIC . VacIC ) −

|VacIC |2 + α |VacIC |2

+

−

Qavr (1 − γ )(VacIC⊥ . VacIC ) +

−

|VacIC |2 + γ |VacIC |2

(22)

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QIC = Qavr +

−

Pavr (1 − α )(VacIC . VacIC⊥ ) |VacIC

+

|2

+α

|VacIC

−

|2

+

+

−

either ICs may trip or the fluctuations may be transferred from the dc side to the ac side or vice versa with the result of adversely affecting HMG loads. One of the best suited approaches to deal with this issue is to enhance the control strategy of ICs to mitigate active power oscillations and to do accurate transient power sharing among ICs. Since 3-D droops offer a more flexible control strategies [28], we propose a 3-D droop, in which active power fluctuations is added to the modified normalized droop in (27) as the third dimension:

Qavr (1 + γ )(VacIC⊥ . VacIC⊥ ) |VacIC

+

|2

+γ

|VacIC

−

|2 (23)

According to (21)–(23), unbalanced voltage and current terms (negative sequence) contribute in the peak current and power oscillations. Since (21)–(23) are affected by scalar coefficients α and γ , by optimally tuning of which, in addition to suppression of active and reactive power fluctuations, the peak current of ICs can also be controlled. Later in this subsection, a method is proposed to incorporate and adjust the coefficients α and γ into the control structure of ICs as 3D droop gains. One of the most effective droop approaches for bidirectional ICs in HMGs is the normalized droop, in which the amount and direction of IC power is decided by comparing normalized quantities at its dc and ac sides [4]. In the conventional normalized droops, the power of ICs is determined by comparing normalized values of the dc voltage VdcIC (at the dc terminals of ICs as seen in Fig. 1) and the ac frequency fac according to [4]:

VdcIC, pu =

facpu =

PIC = KhIC_3D (fhpu − facpu ) + αPOSC

where and α are droop coefficients in two dimensions, which will be specified later by solving an optimization problem. Although KhIC and KhIC_3D in (27) and (29) represent similar droop coefficients, we use different notations for them to discern numerical values of the 2-D and 3-D droops. POSC represents the oscillatory term of output active power of the IC and can be calculated according to (13). The proposed 3-D droop in (29) creates a droop surface with two degrees of freedom (using the two droop gains) compared with a 2-D droop line that has only one degree of freedom. By properly tuning these coefficients, it is possible to control the orientation of the proposed droop surface and consequently, the performance of the IC. In this way, not only an accurate transient active power sharing is achieved but also the active power oscillations of parallel ICs are mitigated. In addition to active power sharing, it is required to properly share reactive power among parallel ICs. Traditionally, the participation of ICs in supplying reactive power needs of the ac MG is determined using the following conventional 2-D droop [29]:

VdcIC − 0.5(VdcIC, max + VdcIC, min ) 0.5(VdcIC, max − VdcIC, min )

(24)

max min + f ac fac − 0.5(f ac ) max min − f ac 0.5(f ac )

VdcIC, pu

facpu

(25)

VdcIC

and represent the normalized values of and fac , where respectively; VdcIC, min and VdcIC, max are limits of IC voltage at the dc side. Using (24) and (25), both variables VdcIC, pu and facpu are restricted to interval [–1,1]. Eventually, the magnitude and direction of IC active power is decided by [10]:

PIC = KIC (VdcIC, pu − facpu )

−1 k , max QIC = nIC (Vdc − |VacIC|)

k , max QIC = β (Vdc − |VacIC|) + γQOSC

(31)

where β and γ are the two droop gains; QOSC represents the oscillatory term of output reactive power of the IC, which can be calculated according to (14). Through simulation results, we later confirm the superiority of the proposed droop in accurate transient reactive power sharing and suppression of reactive power oscillations. In order to specify optimal droop gains for the proposed 3-D droops in (29) and (31), the following optimization problem is formulated:

(27)

is the droop gain for the modified normalized droop, which where should be set according to the rating of the IC for accurate power sharing; fhpu is the normalized harmonic frequency expressed as [16]:

fhpu =

k , max Vdc

where is the ac voltage amplitude of IC; indicates the maximum permissible dc voltage of IC; nIC is the droop gain of IC for reactive power sharing. As seen in Fig. 1, the positive direction of IC reactive power flow is considered from the dc link of IC to its ac output terminals. The aforementioned 2-D droop is not able to control reactive power oscillations during grid faults or load/generation fluctuations. This in turn may lead to violate current rating limitations of ICs and then result in their trip. In order to add both capabilities of accurate transient reactive power sharing and reactive power oscillation cancellation to the proposed control structure of ICs, we propose the following 3-D droop, in which reactive power oscillations is added as the third dimension:

(26)

KhIC

fh − 0.5(f hmax + f hmin ) 0.5(f hmax − f hmin )

(30)

|VacIC|

where PIC indicates transmitted power by IC from the dc to ac MG (positive or negative); KIC is the IC droop gain. In the conventional normalized droop (26), each IC decides its power based on its local dc voltage. The variable facpu is the same for all ICs since all of them share the same frequency at the ac side as a global variable. However, VdcIC, pu may be different for parallel ICs in the presence of line resistances, which may cause inaccurate power sharing. In fact, to have an accurate power sharing, normalized common dc bus CB IC voltage Vdc , pu rather than Vdc, pu should have been used in (26); however, CB Vdc, pu is not accessible in droop-based approaches. To establish an appropriate power sharing proportional to the rating of ICs, the local dc voltage VdcIC, pu in (26) should be replaced with a global variable, which is the same for all ICs. To this end, we employ the dominant harmonic frequency at the dc side, as proposed in [16], to create a global variable at the dc side as the modified normalized droop:

PIC = KhIC (fhpu − facpu )

(29)

KhIC_3D

,i ,i Min OFitr (Xi ) = ρ1 . ITAE PNr + ρ2 . ITAEQNrOSC OSC

(32)

T

ICi (t )| dt ∫ t |POSC

(28) ,i ITAE PNr = OSC

where f hmin and f hmax are permitted harmonic frequency limits. Since the difference fhpu − facpu in (27) is the same for all parallel ICs, active power is shared among them based on their droop gains even in the case of unequal line resistances at the dc side of ICs. Eq. (27) ensures an accurate power sharing among parallel ICs in the steady-state. However, the stability of the HMG is also affected by grid faults and transient power oscillations caused by loads/DGs. Accordingly, ICs should be able to resist the fluctuations without losing their transient stability. Also, an accurate power sharing during transient periods prohibits ICs from short-term overstressing. Otherwise,

0

PnICi

(33)

T

ICi (t )| dt ∫ t |QOSC ,i ITAEQNrOSC

=

0

QnICi

s. t. Ximin ≤ Xi ≤ Ximax Y. V = I

(34)

∀i

(35) (36)

where ρ1 and ρ2 are weighting factors to make a tradeoff between 5

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A. Eisapour-Moarref, et al. ,i elimination of active and reactive power oscillations; ITAE PNr and OSC ,i ITAEQNrOSC represent the Integral Time Absolute Error (ITAE) [31] for IC i active and reactive power oscillations, respectively, normalized by their power rating; PnICi and QnICi indicate nominal active and reactive powers of IC i , respectively; Xi = [KhIC_3,iD, αi, βi , γi ]T is the vector of transient droop gains used in (29) and (31); Y is the network admittance matrix; I and V are nodal current injections and nodal voltages, respectively. Eq. (35) constrains droop gains. Constraint (36) models the HMG and it can be implemented by solving the HMG in a time-domain simulation software such as MATLAB/Simulink. ICi ICi (t ) have a time-varying nature, we have uti(t ) and QOSC Since POSC lized their ITAE to determine the average value of power oscillations in the time interval T . In fact, (33) and (34) calculate the area under the curve of the power fluctuations multiplied by t . By minimizing the fitness function (32), the obtained optimal droop gains make the area approach zero and consequently, the active and reactive power oscillations are suppressed. There are several ways to solve the optimization problem presented by (32)–(36). In this paper, we used the particle swarm optimization (PSO) algorithm [31] without loss of generality. The PSO is a heuristic algorithm employing the social intelligence of particles that have their own initial position and speed. Each particle, as a candidate solution in the defined solution space, modifies its speed and position over iterations to explore the optimal solution. Mathematically, the velocity and position of particles are updated as [31]:

2.4. Proposed synchronverter-based control for ICs Unlike power plants where synchronous generators are often used, DG-based HMGs are free of rotational mass and damping properties due to the inertia-less feature of converters including ICs [27]. This may challenge the frequency stability of the HMG and intensify power oscillations when faults occur. One solution to enhance frequency stability and restrain active and reactive power ripples is to improve control strategy of ICs to enable them using the synchronverter technology. Mathematically, the synchronverter-based ICs can be modeled by mechanical and electrical equations of synchronous generator [34]:

J

dω = Tm − Te + DP (ωn − ω) dt

Te = Mf . i f 〈iIC , sinθ〉 ∗

(37) (38)

VacIC = ω. Mf . i f sinθ

(39)

Q = −ω. Mf . i f 〈iIC , cosθ〉

(40)

where θ is the rotor angle; 〈x , y〉 denotes the conventional inner product of x and y ; J and DP are virtual inertia and damping, respectively; ωn , ω = dθ / dt , Tm , Te , and Q represent reference angular frequency, synchronverter angular frequency, virtual mechanical torque, virtual electromagnetic torque, and the reactive power of the synchronverter, respectively; i f indicates the field-excitation current; Mf is the maximum mutual inductance between stator and field windings. The aim of ∗ (37)–(40) is to calculate VacIC . The proposed combined control structure for ICs equipped with the synchronverter technology and multi-dimensional droops is depicted in Fig. 3. As seen, the dominant harmonic frequency fh is extracted from droop using (7). Also, a phase-locked loop (PLL) is used to determine the ac frequency fac at the ac side of the IC. Then, fac and fh are normalized by (25) and (28), respectively. After calculating the difference fhpu − facpu and the oscillatory term POSC [3], the IC active power PIC is produced by the proposed 3-D droop (29). Likewise, the IC reactive power QIC is extracted by the proposed 3-D droop using (31). Afterwards, through adopting the mechanical and electrical quantities of the synchronverter expressed by (37)–(40), the damping and virtual inertia properties are implemented. An adaptive virtual inertia is considered for a higher efficiency: only in transient states, where there are higher frequency fluctuations, the virtual inertia should be more effective. Conversely, in steady-state operation points, the virtual inertia should be ineffective to increase system performance. In Fig. 3, we implement the adaptive virtual inertia by defining K = |ωn − ω|/Δωmax , which lies in range [0,1]. Parameter K is a dynamic parameter and is zero when the frequency ω is at its rated value ωn . By increasing the frequency deviation, K becomes closer to unity. As the virtual inertia in Fig. 3 is multiplied by K , it more affects the control strategy at larger frequency deviations as the imitation of synchronous generator inertia. As a result, the adaptive virtual inertia improves frequency stability of HMG in case

Vi(k + 1, j) = w kVi(k, j) + c1 r1 (Xilbest (k, j) − Xi(k, j) ) + c2 r2 (Xigbest (k ) − Xi(k, j) )

Xi(k + 1, j) = Xi(k, j) + Vi(k + 1, j) i = 1, 2, ⋯, D , j = 1, 2, ⋯, N where Vi(k, j) and Xi(k, j) are the velocity and position of entry i of particle j produced in iteration k , respectively; Xilbest (k, j) and Xigbest (k ) represent the best local and global positions, respectively; N and D indicate the size of population and number of decision variables, respectively; w k is a parameter called inertia constant; r1 and r2 are random numbers produced uniformly at each iteration within the [0,1] interval; c1 and c2 are constants. In the beginning of the algorithm (iteration zero), the initial population is randomly generated within the specified limits. All particles consist of the vector of transient droop gains Xi = [KhIC_3,iD, αi, βi , γi ]T . Then, these particles are fed into the block diagram of the proposed control strategy in Fig. 3 leading to different outputs for active and ,i ,i reactive power oscillation curves with their own ITAE PNr and ITAEQNrOSC OSC for each particle. Next, the fitness function (32) is calculated for each individual particle to detect local and global best solutions. Afterwards, the velocity and position of particles are updated. This process repeats until the fitness function converges to a steady value or the maximum number of iterations is achieved. It is worth noting that in real-time applications, where enough time may not be available to solve the optimization problem, the optimal coefficients can be set in an offline basis and stored in a lookup table [16] for different operating points.

Fig. 3. Proposed control strategy for ICs. 6

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of disturbances/faults. The ultimate result of Fig. 3 is to produce the ∗ reference voltage VacIC as an input to the space vector PWM (SVPWM) in order to generate command signals for IC switches.

Table 1 System specifications and control parameters. Item

Parameter

Symbol & value

DC/DC converter

DC inductor & capacitor Inner current regulator

Ldc = 200 μH , Cdc = 500 μF Kp _i = 0.05 , Ki _i = 1

Outer harmonic frequency regulator P − Vdc droop gain

Kp _h = 0.45 , Ki _h = 20

P − fh droop gain

Khdc = 0.00024 Hz/W

Nominal power

Pndc = 6 kW Ls = 2 mH , Cs = 30 μF

3. Case studies and numerical results The steady-state and transient performance of the proposed framework is evaluated in this section using different case studies as follows:

• The first case study explains the 3-D droop, the optimal gains of •

• •

VSI

which are obtained by the optimization problem described by (32)–(36). In the second case study, the efficiency of the proposed method is evaluated in eliminating active and reactive power oscillations, establishing an accurate transient power sharing, and stabilizing ac and dc common bus voltages when a two-phase to ground unbalanced fault occurs. Also, the ac current of ICs is investigated to clarify the active and reactive power transfer capability of ICs under the unbalanced grid fault. In the third case study, the effectiveness of the proposed mechanism is examined in restricting the peak current of ICs under a single lineto-ground unbalanced fault. In the fourth case study, it is shown that the proposed method using the virtual inertia is able to absorb more renewable energy from a volatile photovoltaic (PV) source compared to the conventional method due to the fact that it is able to mitigate renewable generation oscillations and establish a more robust frequency. The dynamic frequency stability of the proposed approach is also compared with some recent works.

ICs

Filter inductor & capacitor Inner current regulator

Without loss of generality, the HMG is considered with two parallel ICs as shown in Fig. 1. System specifications and control parameters are given in Table 1. All simulations are implemented using MATLAB/Simulink. Converters are modeled using IGBTs with the sampling and switching frequency of 100 kHz and 20 kHz, respectively. Impedances VSI = 0.02 + j 0.16 Ω, as indicated in Fig. 1 are assumed as ZacL1 = Zac RdcIC1 = 0.2 Ω, RdcIC2 = 0.5 Ω, ZacL2 = 0.03 + j 0.2 Ω , Zu = 1 Ω, RdcLoad = 1 Ω, and RdcEV = RdcESS = 0.2 Ω [10,16,22]. The dc and ac loads are assumed as PLdc = 2500 W and SLac = 1000 + j500 VA , respectively. At first, the HMG is studied in the grid-connected mode. Then, its behavior is studied after occurring a fault at the utility side and islanding the HMG. Practically, the total time required to detect whether the fault is transient or persistent and to operate the circuit breaker is considered 100 ms [35] in simulations. We used the PSO algorithm [31] to solve our optimization problem expressed by (32)–(36).

Kpi = 10 , Kii = 15300

Outer voltage regulator

Kpv = 0.076 , Kiv = 372

Frequency droop gain

K1ac = 0.000133 Hz/W

Voltage droop gain

K2ac = 0.00133 V/Var ωc = 30 rad/s H = 0.68 Pnac = 4 kW , Qnac = 2 kVar

Filter cutoff frequency Feedforward gain Nominal active & reactive power Filter inductor & capacitor Inertia coefficient

Grid

Kvdc = 0.005 V/W

L f1 = L f2 = 2 mH , C f1 = C f2 = 560 μF J IC1 = 2.814 , J IC2 = 1.267

(Kg. m2 ) Damping coefficient (N. m. s/rad ) Integrator controller gain Nominal power of ICs (kW) Utility voltage level

VnU = 110 V

Nominal ac MG voltage

Vnac = 200 V

Nominal dc MG voltage

Vndc = 400 V

Nominal ac frequency

fnac = 50 Hz

DpIC1 = 50 , DpIC2 = 12.67 KI = 7854 Var/(V. rad)

PnIC1 = 2 , PnIC2 = 1

3.2. Case 2: Transient stability under a two-phase to ground unbalanced fault A two-phase to ground unbalanced fault (between phases B and C) with a fault resistance 1 Ω [22] is applied to the utility bus at t = 1 s CB and cleared at t = 1.1 s . The common ac bus voltage Vac is depicted in Fig. 4 as a result of employing conventional and proposed methods. Before occurring fault in t < 1 s , three-phase common ac bus voltages are balanced at their nominal value. After applying the fault at t = 1 s , three-phase voltages become unbalanced. During period 1 < t < 1.1 s , the amplitude of three-phase voltages depends on the transformer connection since the fault is unbalanced. According to [3], if the transformer in Fig. 1 is a Δ-Y transformer, the positive and negative sequence components of the voltage are obtained as 2/3 and 1/6 of the nominal value, respectively, with a phase angle difference of 180 degrees. Accordingly, the voltage amplitude for phase A is obtained as 1/2 of the nominal voltage in 1 < t < 1.1 s in Fig. 4, whereas it is 0.7638 of the nominal value for phases B and C. Note that both conventional and proposed methods in Fig. 4 have similar voltages before clearing the fault since the voltages are governed by the fault conditions. At t = 1.1 s , the fault is cleared by opening the breaker at PCC. As seen in Fig. 4(a), the conventional method is not able to restore voltage of the three phases to their normal status after clearing the fault in period t > 1.1 s and therefore, the common ac bus experiences low voltages that are not acceptable. Thus, the entire ac MG may trip due to unstable voltages. In contrast, if the proposed method is employed, as seen in Fig. 4(b), voltage of the three phases are recovered to their normal values shortly after clearing the fault (at about t =1.16 s implying 60 ms after clearing the fault). The better performance of the proposed method lies in its more efficient power management of ICs. Using the conventional control strategy, ICs are not able to sufficiently support the ac MG by managing exchanged power between ac and dc MGs. To

3.1. Case 1: Optimal tuning of the proposed 3-D droop surface The number of particles in the PSO algorithm and iterations is set to 50. Inertia and cognitive constants are assumed 0.5 and 1, respectively, for droop gains [31]. Also, the search space for the droop gains KhIC_3,iD , αi , βi , and γi are set to [0.5,2.5] kW, [0.05,0.25], [200,1000] Var/V and [0.02,0.12], respectively. In Table 2, the optimal gains of the 3-D droop for two ICs are reported for the fault applied (shown in Fig. 1). In order to equally minimize the active and reactive power oscillations, the weighting factors in objective function (32) are considered as ρ1 = ρ2 = 0.5. It is noted that the proposed strategy is feasible under different fault types, including unbalanced and balanced conditions. In Table 2, the optimal gains obtained for some fault types are reported. However, in order to evaluate the performance of the proposed method under unbalanced conditions, which may be more challenging for control approaches, we consider single line-to-ground and two-phase to ground faults, which are reported in Table 2, in the ensuing subsections.

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Table 2 Optimal gains for the proposed 3-D droops considering different fault types. Fault type

KhIC_31D , KhIC_32D (kW )

α IC1, α IC2

Single line-to-ground Line-to-line Two-phase to ground Symmetrical (three-phase)

1.9906, 0.9948 1.9832, 0.9910 1.9971, 0.9983 2, 0.9996

0.09859, 0.10127, 0.09623, 0.09105,

(a)

0.19703 0.20247 0.19106 0.18192

β IC1, β IC2 (Var/V )

γIC1, γIC2

679.03, 645.11, 683.27, 717.41,

0.04857, 0.04983, 0.04792, 0.04472,

328.91 304.50 340.67 352.38

0.09796 0.10045 0.09618 0.08951

more investigate this behavior, active powers transferred by ICs are presented in Fig. 5. As seen in Fig. 5, since prior to fault in t < 1 s , the HMG is in the grid-connected mode and the utility provides demands of loads, active powers of ICs are negative implying that they are transmitted from the ac side to the dc side through ICs. Positive flow directions of IC powers are assumed from the dc to ac side (see Fig. 1). As the rating of IC1 is two times of IC2, if an accurate power sharing is established, the power of IC1 should be two times of IC2. As seen in Fig. 5(a), the conventional droop fails to establish a proper steady-state power sharing as the ratio of IC powers is not 2:1 prior to occurring fault in t < 1 s . The reason is that the power of each IC is decided by its local dc voltage, which is different for ICs in the presence of line resistances. However, the proposed control strategy is able to establish an accurate power sharing between ICs as seen in Fig. 5(b) for t < 1 s . The reason is that it uses the harmonic frequency fhpu as a global variable instead of local dc voltage of ICs. During the fault in 1 < t < 1.1 s , the conventional control method in Fig. 5(a) fails to establish an accurate transient power sharing between the two parallel ICs (power values are shown by data tips in Fig. 5 for convenience). Thus, IC2 may trip because it is overloaded. However, the proposed method in Fig. 5(b) is able to establish a better transient power sharing between the two ICs as the power of IC1 is about two times of IC2 in this period. This ensures that ICs are not overstressed during the fault and then, their undesired overload and trip is prevented. In the post-fault period t > 1 s , the conventional method fails to stabilize active power oscillations in Fig. 5(a) and IC powers become unstable. As seen, active power of IC2 exceeds its rating (1 kW) and it may ultimately trip. However, the proposed control strategy is able to stabilize active power of ICs in Fig. 5(b) shortly following fault clearing. Due to employing virtual inertia and damping characteristics, the proposed method is able to efficiently mitigate active power oscillations. Reactive power oscillations of ICs using the conventional and proposed schemes are also illustrated in Fig. 6. Before occurring fault in period t < 1 s in Fig. 6, reactive power is not transmitted by the ICs. This is because of the fact that the ac MG does not need to import reactive power from ICs due to its connection to the utility. However, during the fault in period 1 ≤ t ≤ 1.1 s , the reactive power is transmitted from the dc link of ICs to the ac MG since the ac voltage drops due to the fault. As seen in Fig. 6(a), the conventional control strategy is not able to do accurate transient reactive sharing proportional to the rating of ICs. However, since the proposed method employs the 3-D droop to eliminate reactive power oscillations using the synchronverter technology, it has been able in Fig. 6(b) to damp reactive power oscillations even during the fault. Ripple percentage of active and reactive powers of IC1 at the first cycle after fault clearing time in Fig. 5(b) and Fig. 6(b) is 4.3% and 0.8%, respectively, implying almost constant powers. In addition, the proposed control strategy is able to establish a proper transient reactive power sharing in Fig. 6(b) as shown by data tips. It is worth noting that the reactive power rating of IC1 and IC2 is assumed QnIC1 = 968.6 Var and QnIC2 = 426 Var , respectively [22]. After clearing the fault at t = 1.1 s , the HMG is islanded from the utility. Then, the ac MG needs reactive power in period t > 1.1 s as shown in Fig. 6(b). The conventional method has made the voltages of the ac MG

(b)

Fig. 4. Common ac bus voltage under the unbalanced grid fault, (a) conventional method, (b) proposed method.

(a)

(b)

Fig. 5. Active power of ICs under the unbalanced grid fault, (a) conventional method, (b) proposed method.

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(a)

(b)

Fig. 6. Reactive power of ICs under the unbalanced grid fault, (a) conventional method, (b) proposed method. Fig. 8. AC current of ICs under the unbalanced grid fault using the proposed strategy, (a) IC1, (b) IC2.

(a)

proportional to their ratings even prior to fault occurrence. For instance, in t < 1 s , the per-phase peak current of IC1 and IC2 is 5 A and 4 A, respectively; whereas the power rating of IC2 is one half of IC1. As a result, an improper current sharing is obtained among parallel ICs using the conventional control strategy. Compared to the conventional method in Fig. 7, the ac current of ICs using the proposed scheme is depicted in Fig. 8. For t < 1s in Fig. 8, the per-phase peak current of IC1 and IC2 is about 6 A and 3 A, respectively, which are proportional to their ratings (2:1 ratio). In period 1 ≤ t ≤ 1.1s , the virtual inertia damps oscillations. As seen, in addition to establishing an accurate current sharing among parallel ICs, the adaptive virtual inertia makes the proposed method able to restore equal currents among the three phases shortly after clearing the fault in period t > 1.1s . The peak values of the three-phase currents in the first cycle after clearing fault in Fig. 8(a) and (b) are equal to [6.358, 6.092, 6.061](A) and [3.179, 3.046, 3.031](A) , respectively, implying almost balanced currents. As a result, not only three-phase ac currents of ICs are approximately balanced, but also their current rating limitations are not violated implying an enhanced transient stability. This is due to the fact that the inertia-less feature of ICs in the HMG is compensated by adopting virtual inertia in the proposed control structure. One of undesirable effects of unbalanced voltages at the ac side of ICs is that they deteriorate dc link ripple adversely affecting the dc side voltage. The variation of the common dc bus voltage is plotted in Fig. 9 for both methods. As seen, prior to fault in t < 1 s , the common dc bus voltage equals to 1 pu for both conventional and proposed methods. After the unbalanced fault at t = 1 s , the common dc bus voltage using the conventional method significantly drops to unacceptable levels which makes it unstable. However, using the proposed control strategy, the dc link ripple is wiped out even before clearing the fault and the common dc bus voltage is stabilized at 0.9613 pu , which is in the permissible range [0.95, 1.05] pu . This is due to the fact that the power transferred by ICs is more robust using the proposed control scheme and consequently, the common dc bus voltage is able to stabilize around its nominal value.

(b)

Fig. 7. AC current of ICs under the unbalanced grid fault using the conventional strategy, (a) IC1, (b) IC2.

unstable due to varying reactive powers in Fig. 6(a). The currents at the ac side of ICs are depicted in Figs. 7 and 8 using the conventional and proposed methods, respectively. During the fault in 1 ≤ t ≤ 1.1 s , the current of IC2 in Fig. 7(b) exceeds its rating and probably trips in real applications. Afterwards, its load is transferred to IC1, which also trips due to being overloaded. For t > 1.1 s in Fig. 7, the voltage drop, as shown in Fig. 4(a), leads to a further increase in the ac current of ICs and consequently, it makes the currents unstable. In addition, as a result of employing the conventional droop in Fig. 7, the steady-state and transient current sharing between ICs is not 9

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(a)

Fig. 9. Common dc bus voltage under the unbalanced grid fault using the conventional and proposed schemes.

(b)

3.3. Case 3: Transient stability under a single line-to-ground unbalanced fault In order to investigate the applicability of the proposed mechanism in another type of unbalanced grid faults, we have applied a single lineto-ground fault, as the most prevalent unbalanced fault [36] with the same conditions as assumed in the previous subsection. In this case, the optimal droop coefficients relevant to single line-to-ground fault, as reported in Table 2, are used in the proposed control structure. As verified in [36], voltages and currents in case of unbalanced faults depends on transformer winding connections. Assuming the transformer in Fig. 1 is a Δ-Y transformer, the currents at the ac side of ICs under the single line-to-ground fault are depicted in Figs. 10 and 11 using the conventional and proposed methods, respectively. The single line-to-ground fault is inserted at t = 1 s and cleared at t = 1.1 s . For 1 ≤ t ≤ 1.1 s in Fig. 10, the peak current of ICs is not significantly reduced with the conventional control strategy. This is due to the fact that the conventional method is not able to compensate the oscillatory term of active and reactive powers, which are expressed in (22)–(23). For t > 1.1 s in Fig. 10, due to the inertia-less feature of the conventional structure, the peak current of ICs increases again and makes the currents unstable. As the rating of IC2 is one half of IC1, at first IC2 trips in real applications. Afterwards, its load is transferred to

Fig. 11. AC current of ICs under the single line-to-ground grid fault using the proposed strategy, (a) IC1, (b) IC2.

IC1 leading ultimately to tripping of IC1. Compared to the conventional approach in Fig. 10, the ac current of ICs using the proposed scheme is illustrated in Fig. 11. For 1 ≤ t ≤ 1.1 s in Fig. 11, the peak current of ICs during the single line-to-ground fault has been restricted to around their ratings. This is due to the fact that by optimally tuning the 3-D droop gains in the proposed method, not only the suppression of the power fluctuations is achieved, but also the peak current of ICs can be restrained. In period t > 1.1 s in Fig. 11, since the proposed control strategy is equipped with the adaptive virtual inertia, the oscillations are damped and, in the meantime, the three-phase ac currents of ICs are eventually balanced. As a result, an effective FRT capability is established by the proposed control strategy. In addition, an appropriate current sharing proportional to the rating of ICs is achieved in all periods of Fig. 11.

(a)

3.4. Case 4: Dynamic stability analysis In this case study, the impact of high penetration level of renewable energy is investigated on the HMG stability. To this end, it is assumed that most of generated power at the ac side is supplied by the PV system as a non-dispatchable and volatile source (see Fig. 1) that may challenge HMG stability. Therefore, power and frequency oscillations are expected at the ac side of the HMG due to the variable nature of sun irradiation. In order to evaluate the robustness of the closed-loop system in this situation, the trace of eigenvalues is depicted in Fig. 12 for both conventional and proposed methods as the PV output increases. The eigenvalues can be calculated from the state matrix of state equations as explained in the Appendix. As mentioned in Fig. 12, the maximum absorbable PV power in the stable operation is obtained as max max PPV = 1.597 kW and PPV = 3.969 kW for the conventional and proposed schemes in Fig. 12(a) and (b), respectively. These results indicate that the proposed method is more resilient against volatile renewable generation and it is able to absorb more renewable generation as much as (3.969 − 1.597)/1.597 = 148.5% than the conventional method without losing HMG stability. This improvement is achieved due to using the 3-D droop and adaptive virtual inertia that enhance the

(b)

Fig. 10. AC current of ICs under the single line-to-ground grid fault using the conventional strategy, (a) IC1, (b) IC2. 10

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(a)

(a)

(b)

(b)

Fig. 13. Frequency stability with volatile solar irradiation using the control strategy of A ([3]) and the proposed strategy, (a) original PV output, (b) curtailed PV output.

the frequency, the proposed method needs a lower settling time, which is more preferred. If the energy of the two PV generation curves in Fig. 13(a) and (b) is compared, it is observed that the proposed method is able to absorb more PV energy by 139.3% compared with the method of [3]. Consequently, one of tangible advantages of the proposed method is its higher flexibility that results in capturing a higher level of renewable energy.

Fig. 12. Trace of eigenvalues for the closed-loop system as a function of increasing PV output using the (a) conventional and (b) proposed schemes.

control strategy performance by mitigating power oscillations. The non-dispatchable PV generation can also challenge the frequency stability of the ac MG as the frequency is a function of the injected volatile generation. In order to evaluate the dynamic frequency stability of the proposed scheme compared with a previous work [3], a real-world solar irradiation curve is utilized [37]. For a fair comparison, both control methods (the proposed and [3]) are run on the understudy HMG with the same conditions. Results are depicted in Fig. 13 for both methods. As seen in Fig. 13(a), there is a high level of PV power volatility reaching 3.969 kW (as also shown in Fig. 12(b)). Under these circumstances, the control strategy of [3] has failed to mitigate frequency variations and then, the frequency at the ac side of HMG cannot be stabilized after even 15 s. However, the proposed method (indicated by facPro.) has managed to reach a stable frequency. This ability owes to using the 3-D droop and virtual inertia features in the proposed method making it able to continuously adapt the droop surface and to damp oscillations by the virtual inertia imitating synchronous generators. If the volatility of PV generation is reduced, the control scheme of [3] can make the HMG stable. The maximum threshold of volatility, under which the control scheme of [3] is able to keep the HMG stable, is shown in Fig. 13(b). That is, if the control scheme of [3] is used, we have to curtail the peak of PV generation to 1.667 kW as shown in Fig. 13(b). This curtailment in PV generation implies that we cannot use the maximum power point tracking of the PV arrays due to the stability limitation of the control strategy of [3]. Under this curtailed PV generation, although both methods in Fig. 13(b) have managed to stabilize

4. Conclusions In this paper, a novel control strategy is proposed for parallel operation of ICs to simultaneously eliminate active and reactive power oscillations and establish an accurate transient power sharing under unbalanced grid conditions. Besides effective transient performance, the proposed control strategy provides a more robust control than available techniques and, in the meantime, it improves frequency stability. Furthermore, the proposed scheme enhances the power transfer capability of ICs with damped oscillations using an adaptive virtual inertia and 3-D droop control. According to obtained results, the proposed synchronverter-based strategy is able to improve renewable PV energy utilization 139.3% higher than existing methods. Also, under the unbalanced fault, the proposed control approach, unlike the conventional method, has been able to stabilize the common dc bus voltage at the permissible value of 0.9613 pu. CRediT authorship contribution statement Amir Eisapour-Moarref: Conceptualization, Software, Validation, Data curation, Writing - original draft. Mohsen Kalantar: Investigation, Writing - review & editing. Masoud Esmaili: Methodology, Visualization, Supervision.

Appendix A In view of the fact that our understudy HMG consists of three parts (the dc and ac sides as well as ICs in Fig. 1), we extract state space equations for each part individually. Afterwards, we present the state space equation for the entire HMG. Without loss of generality, we assume one dc/dc converter and IC for this purpose. 11

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A.1. State space equations of the dc side The following time domain equations describe the proposed harmonic-based control structure for the dc/dc converter in Fig. 2:

Ki _h d ΔPdc = (Δf hmax − Khdc ΔPdc − Δf h' ) dt 1 + Kp _h Khdc

(41)

Kp _i Ki _h Ki _i ΔV DG − ΔV1 ⎞ d ΔV1 ' = ∗ ⎡ (Δf hmax − Khdc ΔPdc − Δf h' ) ⎤ + ∗ ΔPdc − Kp _i ⎜⎛ dc ⎟ − K i _i ΔIdc dc ⎢ ⎥ dt Vdc ⎣ 1 + Kp _h Kh Ldc Vdc ⎝ ⎠ ⎦

(42)

d ΔVdc 1 (1 − D) ' = − dc ΔVdc + ΔIdc dt Cdc RL Cdc

(43)

' d ΔIdc (1 − D) ΔVdc + ΔVdcDG =− dt Ldc

(44)

RLdc

PLdc

is the load resistance of (see where Δ denotes perturbation variable and can be omitted when it comes to the linearized small signal system; Fig. 1); D indicates the duty cycle of the dc/dc converter. Other parameters are defined in Fig. 2. According to (41)–(44), the small-signal stability model of the dc/dc converter can be established by choosing the state variable matrix ' T Xdc = [ΔPdc , ΔV1, ΔVdc , ΔIdc ] . If we consider the state equation as Ẋdc = Adc Xdc + Bdc Wdc , only the state matrix Adc is sufficient to calculate eigenvalues of the dc side. By rearranging (41)–(44), the state matrix Adc can be extracted as: −Ki _h

⎡1 + K p _h ⎢ ⎢ −1 Kp_i Ki _h ⎢ V ∗ 1 + Kp_h − Ki _i = ⎢ dc ⎢0 ⎢ ⎢0 ⎢ ⎣

(

Adc

0

)

K p _i Ldc

0 0

0

−1 RLdc Cdc

0

−(1 − D) Ldc

0

⎤ ⎥ ⎥ − Ki _i ⎥ ⎥ (1 − D) ⎥ Cdc ⎥ ⎥ 0 ⎥ ⎦

(45)

A.2. State space equations of the IC According to Fig. 3, the following time-domain equations describe the synchronverter-based IC:

dθ =ω dt

(46)

dω 1 = [Tm − Te + DP (ωn − ω)] dt J

(47)

di f dt

1 1 k , max [QIC − Q] = [β (Vdc − |VacIC|) + γQOSC − Q] KI Mf KI Mf

=

(48)

dVacIC 1 1 CB = (Vac − VacIC ) + iIC dt Cf Cf ZacL

(49)

diIC 1 out = − (VacIC − Vac ) dt Lf

(50)

where

Tm =

PIC ω

(51)

Te = Mf . i f 〈iIC , sinθ〉 = Mf . i f [iIC _asinθ + iIC _bsin(θ − 120) + iIC _c sin(θ + 120)]

(52)

Q = −ω. Mf . i f 〈iIC , cosθ〉 = −ω. Mf . i f [iIC _acosθ + iIC _bcos(θ − 120) + iIC _c cos(θ + 120)]

(53)

denotes the output voltage of the IC before its LC filter (see Fig. 1); iIC _a , iIC _b , and iIC _c are the IC currents at the terminals a , b , and c , where respectively. Other parameters are defined in Fig. 3.Then, the linearized model can be represented by: out Vac

d Δθ = Δω dt

(54)

d Δω 1 = [ΔTm − ΔTe + DP (Δωn − Δω)] dt J

(55)

d Δi f dt

=

1 k , max [β (ΔVdc − |ΔVacIC|) + γ ΔQOSC − ΔQ] KI Mf

(56)

d ΔVacIC 1 1 CB (ΔV ac = − ΔVacIC ) + ΔiIC dt Cf Cf ZacL

(57) 12

Electrical Power and Energy Systems 119 (2020) 105927

A. Eisapour-Moarref, et al.

d ΔiIC 1 out = − (ΔVacIC − ΔVac ) dt Lf

(58)

In the steady-state, ω is equal to ωn . Therefore, (51)–(53) can be expressed as: IC

ΔPIC 1 ⎡ Kh _3D ⎛ pu Δω − 0.5(ωmax + ωmin ) ⎞ Δωh − = + α ΔPOSC⎤ ⎥ 2 0.5( ) ωn ωn ⎢ π ω − ω max min ⎝ ⎠ ⎣ ⎦

(59)

ΔTe = 〈i IC0 , sinθn 〉ΔMf . i f + 〈i IC0 , cosθn 〉Mf . i f0 Δθ + Mf . i f0 〈ΔiIC , sinθn 〉

(60)

ΔQ = ωn . Mf . i f0 〈i IC0 , sinθn 〉Δθ − ωn 〈i IC0 , cosθn 〉ΔMf . i f − ωn . Mf . i f0 〈ΔiIC , cosθn 〉

(61)

ΔTm =

⎜

⎟

By substituting (59)–(61) into (55) and (56), the stability model of the IC can be found by choosing the state variable matrix XIC = [Δθ , Δω, Δi f , ΔVacIC _a, ΔVacIC _b, ΔVacIC _c , ΔiIC _a, ΔiIC _b, ΔiIC _c ]T . If the linearized state space equations of the IC is considered as ̇ = AIC XIC + BIC WIC , only the state matrix AIC is needed to calculate eigenvalues of the model. By rearranging (54)–(61), the state matrix AIC can XIC be extracted as:

AIC

⎡0 ⎢ −〈iIC0, cosθn 〉Mf i f0 ⎢ J ⎢ ⎢ −ωn i f0 〈iIC0, sinθn 〉 KI ⎢ ⎢ 0 ⎢ ⎢ = ⎢0 ⎢ ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢ ⎢0 ⎣

1 −

0 1⎛ DP J

⎝

KhIC _3D

+ πω (ω − ω ) ⎞ min n max ⎠

0

−〈iIC0, sinθn 〉Mf J

0

ωn 〈iIC0, cosθn 〉

0

0

0

0

KI

0

0

0

0

0

−Mf i f0 sinθn

−Mf i f0 sin(θn − 120)

−Mf i f0 sin(θn + 120) ⎥

J

J

0

0

0

−β KI Mf

−β KI Mf

−β KI Mf

ωn i f0 cosθn

ωn i f0 cos(θn − 120)

KI

KI

0

0

1 Cf

0

0

0

0

1 Cf

0

0

0

1 Cf

−1 L Cf Zac

0

−1 L Cf Zac

−1

J ωn i f0 cos(θn + 120) KI

0

0

0

0

0

0

−1 Lf

0

0

0

0

0

0

0

0

0

−1 Lf

0

0

0

0

0

0

−1 Lf

0

0

0

0

L Cf Zac

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(62)

A.3. State space equations of the ac side As addressed in Section 2, we have utilized the droop-based control strategy presented in [31] for the ac MG. Since the small signal model of the ac side is provided in [31] with full detail, we refer the reader to [31] for this stability model. A.4. State space equations of the entire HMG The dc MG in our HMG model in Fig. 1 has two dc/dc converters. Then, it needs eight state variables and its state matrix is doubled with respect to (45) resulting in a 8 × 8 matrix. Also, we have two ICs in Fig. 1 with a doubled dimension of (62) resulting in a 18 × 18 state matrix. The ac side has a single converter resulting in a 6 × 6 state matrix [31]. The state matrix of the entire HMG in Fig. 1 can be constructed by putting the obtained submatrices as [38]:

⎡ A11 A12 ⎤ AHMG = ⎢ A21 A22 ⎥ ⎢ A31 A32 ⎥ ⎣ ⎦32 × 32

(63)

where A11 and A21 represent the submatrices dimensioned 8 × 8 and 18 × 18, respectively; A31 denotes the 6 × 6 submatrix [31]. The number of rows in (63) is 32. Then, A12 , A22 , and A32 are zero submatrices to make them the AHMG square matrix [38]. By analyzing the eigenvalues of AHMG , it is possible to study the small signal stability of the HMG in Fig. 1.

References [1] Baharizadeh M, Karshenas HR, Guerrero JM. An improved power control strategy for hybrid AC-DC microgrids. Int J Electr Power Energy Syst 2018;95:364–73. https://doi.org/10.1016/j.ijepes.2017.08.036. [2] Hu J, Shan Y, Xu Y, Guerrero JM. A coordinated control of hybrid ac/dc microgrids with PV-wind-battery under variable generation and load conditions. Int J Electr Power Energy Syst 2019;104:583–92. https://doi.org/10.1016/j.ijepes.2018.07. 037. [3] Sun K, Wang X, Li YW, Nejabatkhah F, Mei Y, Lu X. Parallel operation of bidirectional interfacing converters in a hybrid AC/DC microgrid under unbalanced grid voltage conditions. IEEE Trans Power Electron 2017;32:1872–84. https://doi.org/ 10.1109/TPEL.2016.2555140. [4] Mortezapour V, Lesani H. Hybrid AC/DC microgrids: a generalized approach for autonomous droop-based primary control in islanded operations. Int J Electr Power Energy Syst 2017;93:109–18. https://doi.org/10.1016/J.IJEPES.2017.05.022. [5] Pourbehzadi M, Niknam T, Aghaei J, Mokryani G, Shafie-khah M, Catalão JPS.

[6]

[7]

[8]

[9]

[10]

13

Optimal operation of hybrid AC/DC microgrids under uncertainty of renewable energy resources: a comprehensive review. Int J Electr Power Energy Syst 2019;109:139–59. https://doi.org/10.1016/j.ijepes.2019.01.025. Unamuno E, Barrena JA. Hybrid ac/dc microgrids – Part II: Review and classification of control strategies. Renew Sustain Energy Rev 2015;52:1123–34. https://doi. org/10.1016/j.rser.2015.07.186. Yang P, Xia Y, Yu M, Wei W, Peng Y. A decentralized coordination control method for parallel bidirectional power converters in a hybrid AC-DC microgrid. IEEE Trans Ind Electron 2018;65:6217–28. https://doi.org/10.1109/TIE.2017.2786200. Tummuru NR, Manandhar U, Ukil A, Gooi HB, Kollimalla SK, Naidu S. Control strategy for AC-DC microgrid with hybrid energy storage under different operating modes. Int J Electr Power Energy Syst 2019;104:807–16. https://doi.org/10.1016/j. ijepes.2018.07.063. Xia Y, Wei W, Yu M, Wang X, Peng Y. Power management for a hybrid AC/DC microgrid with multiple subgrids. IEEE Trans Power Electron 2018;33:3520–33. https://doi.org/10.1109/TPEL.2017.2705133. Peyghami S, Mokhtari H, Blaabjerg F. Autonomous operation of a hybrid AC/DC microgrid with multiple interlinking converters. IEEE Trans Smart Grid

Electrical Power and Energy Systems 119 (2020) 105927

A. Eisapour-Moarref, et al.

2018;9:6480–8. https://doi.org/10.1109/TSG.2017.2713941. [11] Tayab UB, Bin Roslan MA, Hwai LJ, Kashif M. A review of droop control techniques for microgrid. Renew Sustain Energy Rev 2017;76:717–27. https://doi.org/10. 1016/J.RSER.2017.03.028. [12] Agundis-Tinajero G, Segundo-Ramírez J, Visairo-Cruz N, Savaghebi M, Guerrero JM, Barocio E. Power flow modeling of islanded AC microgrids with hierarchical control. Int J Electr Power Energy Syst 2019;105:28–36. https://doi.org/10.1016/j. ijepes.2018.08.002. [13] Jayachandran M, Ravi G. Predictive power management strategy for PV/battery hybrid unit based islanded AC microgrid. Int J Electr Power Energy Syst 2019;110:487–96. https://doi.org/10.1016/j.ijepes.2019.03.033. [14] Peyghami S, Mokhtari H, Blaabjerg F. Autonomous power management in LVDC microgrids based on a superimposed frequency droop. IEEE Trans Power Electron 2018;33:5341–50. https://doi.org/10.1109/TPEL.2017.2731785. [15] Wu M, Niu X, Gao S, Wu J. Power quality assessment for AC/DC hybrid micro grid based on on-site measurements. Energy Procedia, vol. 156, Elsevier Ltd; 2019, p. 396–400. doi: 10.1016/j.egypro.2018.11.105. [16] Eisapour-Moarref A, Kalantar M, Esmaili M. Power sharing in hybrid microgrids using a harmonic-based multi-dimensional droop. IEEE Trans Ind Inform 2019;16:109–19. https://doi.org/10.1109/tii.2019.2915240. [17] Ordono A, Unamuno E, Barrena JA, Paniagua J. Interlinking converters and their contribution to primary regulation: a review. Int J Electr Power Energy Syst 2019;111:44–57. https://doi.org/10.1016/j.ijepes.2019.03.057. [18] Allam MA, Hamad AA, Kazerani M, El-Saadany EF. A novel dynamic power routing scheme to maximize loadability of islanded hybrid AC/DC microgrids under unbalanced AC loading. IEEE Trans Smart Grid 2018;9:5798–809. https://doi.org/10. 1109/TSG.2017.2697360. [19] Loh PC, Li D, Chai YK, Blaabjerg F. Autonomous control of interlinking converter with energy storage in hybrid AC-DC microgrid. IEEE Trans Ind Appl 2013;49:1374–82. https://doi.org/10.1109/TIA.2013.2252319. [20] Liu J, Miura Y, Bevrani H, Ise T. Enhanced virtual synchronous generator control for parallel inverters in microgrids. IEEE Trans Smart Grid 2017;8:2268–77. https:// doi.org/10.1109/TSG.2016.2521405. [21] Allam MA, Hamad AA, Kazerani M, El-Saadany EF. A steady-state analysis tool for unbalanced islanded hybrid AC/DC microgrids. Electr Power Syst Res 2017;152:71–83. https://doi.org/10.1016/J.EPSR.2017.06.027. [22] Nejabatkhah F, Li YW, Sun K. Parallel three-phase interfacing converters operation under unbalanced voltage in hybrid AC/DC microgrid. IEEE Trans Smart Grid 2018;9:1310–22. https://doi.org/10.1109/TSG.2016.2585522. [23] Liu J, Hossain MJ, Lu J, Rafi FHM, Li H. A hybrid AC/DC microgrid control system based on a virtual synchronous generator for smooth transient performances. Electr Power Syst Res 2018;162:169–82. https://doi.org/10.1016/j.epsr.2018.05.014. [24] Rahman MS, Hossain MJ, Lu J, Pota HR. A need-based distributed coordination strategy for EV storages in a commercial hybrid AC/DC microgrid with an improved interlinking converter control topology. IEEE Trans Energy Convers 2018;33:1372–83. https://doi.org/10.1109/TEC.2017.2784831. [25] Jin N, Guo L, Gan C, Hu S, Dou Z. Finite-state model predictive power control of

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

14

three-phase bidirectional AC/DC converter under unbalanced grid faults with current harmonic reduction and power compensation. IET Power Electron 2018;11:348–56. https://doi.org/10.1049/iet-pel.2017.0209. Vo T, Ravishankar J, Nurdin HI, Fletcher J. A novel controller for harmonics reduction of grid-tied converters in unbalanced networks. Electr Power Syst Res 2018;155:296–306. https://doi.org/10.1016/j.epsr.2017.10.019. Serban I, Ion CP. Microgrid control based on a grid-forming inverter operating as virtual synchronous generator with enhanced dynamic response capability. Int J Electr Power Energy Syst 2017;89:94–105. https://doi.org/10.1016/j.ijepes.2017. 01.009. Bunker KJ, Weaver WW. Multidimensional droop control for wind resources in dc microgrids. IET Gener Transm Distrib 2017;11:657–64. https://doi.org/10.1049/ iet-gtd.2016.0447. Malik SM, Sun Y, Huang W, Ai X, Shuai Z. A generalized droop strategy for interlinking converter in a standalone hybrid microgrid. Appl Energy 2018;226:1056–63. https://doi.org/10.1016/j.apenergy.2018.06.002. Gao Y, Ai Q. Distributed cooperative optimal control architecture for AC microgrid with renewable generation and storage. Int J Electr Power Energy Syst 2018;96:324–34. https://doi.org/10.1016/j.ijepes.2017.10.007. Sedighizadeh M, Esmaili M, Eisapour-Moarref A. Voltage and frequency regulation in autonomous microgrids using hybrid big bang-big crunch algorithm. Appl Soft Comput 2017;52:176–89. https://doi.org/10.1016/J.ASOC.2016.12.031. Salem Q, Xie J. Decentralized power control management with series transformerless H-bridge inverter in low-voltage smart microgrid based P/V droop control. Int J Electr Power Energy Syst 2018;99:500–15. https://doi.org/10.1016/j.ijepes. 2018.01.047. Zeng B, Teng Z, Cai Y, Guo S, Qing B. Harmonic phasor analysis based on improved FFT algorithm. IEEE Trans Smart Grid 2011;2:39–47. https://doi.org/10.1109/ TSG.2010.2078841. Shuai Z, Huang W, Shen C, Ge J, Shen ZJ. Characteristics and restraining method of fast transient inrush fault currents in synchronverters. IEEE Trans Ind Electron 2017;64:7487–97. https://doi.org/10.1109/TIE.2017.2652362. Gashteroodkhani OA, Majidi M, Fadali MS, Etezadi-Amoli M, Maali-Amiri E. A protection scheme for microgrids using time-time matrix z-score vector. Int J Electr Power Energy Syst 2019;110:400–10. https://doi.org/10.1016/j.ijepes.2019.03. 040. Aung MT, Milanović JV. The influence of transformer winding connections on the propagation of voltage sags. IEEE Trans Power Deliv 2006;21:262–9. https://doi. org/10.1109/TPWRD.2005.855446. Shan Y, Hu J, Chan KW, Fu Q, Guerrero JM. Model predictive control of bidirectional DC-DC converters and AC/DC interlinking converters – a new control method for PV-wind-battery microgrids. IEEE Trans Sustain Energy 2019;10:1823–33. https://doi.org/10.1109/TSTE.2018.2873390. D’Arco S, Suul JA, Fosso OB. Small-signal modeling and parametric sensitivity of a virtual synchronous machine in islanded operation. Int J Electr Power Energy Syst 2015;72:3–15. https://doi.org/10.1016/j.ijepes.2015.02.005.