Different control methods of hybrid AC/DC microgrids have been presented in the literatures. Droop control scheme was employed in [11], where the controllable loads with different capacities were taken into account. A coordinate control method for a hybrid microgrid composed of various kinds of renewable energy sources was proposed in [31], where detailed models of PV modules, batteries and wind turbines were derived and the energy management strategy for whole system was developed. A configuration with both DC- and AC-links and the corresponding control method were presented in [32], where the DC-link could integrate the local converters with DC couplings and connect to the common AC-link through DC–AC interfacing converters. A power quality enhancement method was proposed in [33], where the unbalanced and nonlinear loads were taken into account and the control strategies were developed for a multi-bus microgrid. The above-summarized methods can effectively enhance the performance of a hybrid microgrid. But they mainly focus on the AC side performance and the corresponding control schemes.
For the islanding operation of hybrid AC/DC microgrid, the control schemes mentioned in Sections 3 and 4 allow the distributed sources to share the load demands in their respective sub-microgrid. But sharing the load demands in both AC and DC sub-microgrids simultaneously cannot be simply realized by means of droop controlled distributed sources. The power sharing in both sub-microgrids would heavily depend on the control strategy of interlinking converter. References [30] and [34–36] proposed an autonomous control scheme for the interlinking converter whose responsibility was to link AC and DC sub-microgrids together to form the hybrid AC/DC microgrid, where the distributed AC and DC sources were classified into two consolidated sources tied to the same interlinking converter, as shown in Fig. 1. Generally, the interlinking converter consists of a standard DC-DC boost converter and a standard DC-AC inverter, as shown in Fig. 4. V, \( V^{{\prime }} \) and \( V^{{\prime \prime }} \) are the voltages measured at the AC and DC terminals of interlinking converter, and the DC-link capacitor or storage, respectively. P, Q and \( P^{{\prime }} \) are the power flow through the interlinking converter between AC and DC microgrids, respectively. Such topology allows the AC and DC voltages in both sub-microgrids to be flexibly controlled, meanwhile allows bidirectional real power flow between both sub-microgrids. At the common DC-link, either capacitor or energy storage can be added for buffering, filtering or storage. According to the configuration of interlinking converter, the control scheme of interlinking converter can be classified as general control scheme, control scheme with DC-link capacitor and control scheme with energy storage.
General control scheme
In AC sub-microgrid, the real power sharing is influenced by the controlled frequency as already addressed in Section 3, however, the real power sharing in DC sub-microgrid is affected by the controlled voltage as mentioned in Section 4. It is obvious that the droop variables assumed in two sub-microgrids are totally different. Therefore, both droop variables should be properly merged before using them to control the real power across the interfacing converter. A normalized expression has been proposed to normalize the frequency in AC sub-microgrid and the voltage in DC sub-microgrid so that their respective ranges of variations commonly span from −1 to 1 [30], i.e.:
$$ \left\{ \begin{gathered} f_{pu} = \frac{{f - 0.5(f_{\hbox{max} } + f_{\hbox{min} } )}}{{0.5(f_{\hbox{max} } - f_{\hbox{min} } )}} \hfill \\ V^{\prime}_{pu} = \frac{{V - 0.5(V^{\prime}_{\hbox{max} } + V^{\prime}_{\hbox{min} } )}}{{0.5(V^{\prime}_{\hbox{max} } - V^{\prime}_{\hbox{min} } )}} \hfill \\ \end{gathered} \right. $$
(7)
where subscripts max and min represent the maximum and minimum values of AC side frequency f and DC side voltage \( V^{{\prime }} \), and subscript pu represents their normalized per-unit values.
As shown in Fig. 5, the AC terminal voltages of interlinking converter are measured to give a phase locked loop (PLL), whose outputs are the AC side frequency f, voltage amplitude V and phase angle θ for d-q transformation. Then, the AC side frequency from PLL and the measured voltage of DC side are normalized by (7). The error of normalized variables \( \left( {f_{pu} - V_{pu}^{{\prime }} } \right) \) can be fed to a proportional-integral (PI1) controller to produce the control reference. In the steady state, the two normalized variables will be forced to be equal, thus the error would be zero [34]. Based on such equalization, the two sub-microgrids would share real power according to their respective overall ratings as illustrated in Fig. 6. This proposal is similar to have a common frequency in the aforementioned AC sub-microgrid, upon which the AC sources can share power proportional to their individual power ratings. The output of PI1 controller is the real power reference P* that should be transferred from DC to AC sub-microgrid through the interfacing converter when it is positive and vice versa. In order to produce the current reference for both sides of interlinking converter, the determined real power reference P* from PI1 controller is converted to a real current reference I
*
d
for AC side and another current reference I’* for DC side, as depicted in Fig. 5 by (8).
$$ \left\{ \begin{gathered} I^{*}_{d} = \frac{{2P^{*} }}{3V} \hfill \\ I^{{{\prime } *}} = \frac{{{ - }P^{*} }}{{V^{{\prime }} }} \hfill \\ \end{gathered} \right. $$
(8)
where V and V′ are the voltage amplitudes measured at the AC and DC terminals of interlinking converter, respectively.
At the same time, this control scheme can realize reactive power control. The reactive power Q* and the reactive current reference I
*
q
are calculated by measuring the AC terminal voltage V of interlinking converter generated from PLL and using below expressions.
$$ \left\{ \begin{gathered} Q^{ *} = \frac{{(V - V_{\hbox{max} } )}}{n} \hfill \\ I^{ *}_{q} = \frac{{ - 2Q^{ *} }}{3V} \hfill \\ \end{gathered} \right. $$
(9)
where n is the droop coefficient for reactive power sharing.
It is noted that only AC sub-microgrid needs the reactive power, which means the reactive current reference I
*
q
calculated by (9) is not applicable when the power transfer from AC sub-microgrid to DC sub-microgrid through the interlinking converter. In the above control scheme, therefore, the nonzero \(I_{q}^{\ast} \) calculated by (9) should only be used when real power reference P* is positive. When the real power reference P* is negative, which means the power transfers from AC sub-microgrid to DC sub-microgrid, the reactive current reference I
*
q
should be set to zero for unity power factor operation [35], as shown in Fig. 5. The current references generated for the AC and DC terminals of interlinking converter can be formed as (I
*
d
+ jI
*
q
) and \(I^{\prime \ast}. \)
For the AC side, together with the phase angle θ from PLL, the measured AC terminal currents are transformed from the stationary frame into the synchronous frame by means of the Park transformation. The combined d-q current references, together with the measured d-q currents, are delivered to proportional-integral (PI2) controller, which can achieve proper tracking performance in the synchronous reference frame. On the other hand, a proportional-integral (PI3) controller is adopted to force the DC side current to track the current reference from (8) exactly. The output of PI2 and PI3 are the desired modulation signals, which are used to generate the pulse width modulation (PWM) sequences for both side converters.
It is noted that the distributed sources within each sub-microgrid still can share the real or reactive power proportionally since they are controlled by the established droop control method reviewed in Section 3 and 4, respectively. The interlinking converter only functions as an energy buffer to control the power flow between AC and DC sub-microgrids.
Control scheme with DC-link capacitor
In the case of a DC-link capacitor added to the interlinking converter the same as the general AC-DC conversion circuits, the above general control scheme should be further specified. A proportional-integral (PI4) controller is introduced to the general control scheme to keep the DC-link voltage constant by generating a real current reference \( I^{{{\prime\prime }*}} \) for compensating the losses in the power conversion circuit, as depicted in Fig. 5. This current reference can be added to the DC current reference of DC side drawn by the DC-DC boost converter from the DC sub-microgrid. Meanwhile, the current reference for AC terminal of the interlinking converter remains unchanged.
Control scheme with energy storage
For case, where the energy storage instead of a capacitor is added to the DC-link of interlinking converter, the control scheme of interlinking converter should be revised to fully utilize the energy storage capacity. It means that the energy storages should be charged only when the sources can generate additional energy after meeting the load demands. On the other hand, it should discharge only when the sources cannot fully satisfy the load demands.
The two operation modes require sensing the additional generation capacities of sources. This task can be realized by calculating the DC terminal voltage \( V_{pu}^{{\prime }} \) and AC side frequency f
pu
as shown in (7) [36], whose values reflect the power flow in AC and DC sub-microgrids. Their mean value of v
ave
can then be calculated by (10) before substituting it into (11) to generate the charging or discharging power reference P
*
S
. Figure 7 illustrates the designed behavior of charging or discharging power of energy storage according to (11).
$$ v_{ave} = \frac{{f_{pu} { + }V_{pu}^{{\prime }} }}{2} $$
(10)
$$ \left\{ \begin{gathered} P_{S}^{ * } = \left\{ \begin{array}{l} P_{S\_\hbox{min} } ,v_{ave} \ge v_{t} \hfill \\ h(v_{ave} - v_{\text{z}} ), - 1 \le v_{ave} \le v_{t} \hfill \\ P_{S\_\hbox{max} } ,v_{ave} < - 1 \hfill \\ \end{array} \right. \hfill \\ P_{S\_\hbox{min} } < 0,\;{\text{Charging}} \hfill \\ P_{S\_\hbox{max} } > 0,\;{\text{Discharging}} \hfill \\ h = \frac{{P_{S\_\hbox{min} } - P_{S\_\hbox{max} } }}{{1 + v_{t} }} \hfill \\ v_{z} = \frac{{P_{S\_\hbox{min} } + P_{S\_\hbox{max} } v_{t} }}{{P_{S\_\hbox{max} } - P_{S\_\hbox{min} } }} \hfill \\ \end{gathered} \right. $$
(11)
where h is the droop coefficient; v
t
is a boundary value and v
z
is a middle value at which the energy storage will not absorb or generate real power; P
*
S
, PS_min and PS_max are the real power reference, maximum charging and discharging power of energy storage, respectively. These parameters should be properly set according to the state of charge of energy storage.
The charged/discharged real power of energy storage should be shared in proportion to their rated power or equally in both sub-microgrids. With the energy storage, the AC and DC side real current references calculated by (8) should be changed to those calculated from (12), as shown in Fig. 5. At the same time, the reactive current reference remains unchanged.
$$ \left\{ \begin{gathered} I^{*}_{d} = \frac{{2P^{*} + \frac{{P^{*}_{AC\_tol} }}{{P^{*}_{DC\_tol} + P^{*}_{AC\_tol} }}P_{S}^{*} }}{3V} \hfill \\ I^{{{\prime } *}} = \frac{{{ - }P^{*} + \frac{{P^{*}_{DC\_tol} }}{{P^{*}_{DC\_tol} + P^{*}_{AC\_tol} }}P_{S}^{*} }}{{V^{\prime}}} \hfill \\ \end{gathered} \right. $$
(12)
or
$$ \left\{ \begin{gathered} I^{*}_{d} = \frac{{2P^{*} + 0.5P_{S}^{*} }}{3V} \hfill \\ I^{{{\prime } *}} = \frac{{{ - }P^{*} + 0.5P_{S}^{*} }}{{V^{\prime}}} \hfill \\ \end{gathered} \right. $$
where I
*
d
and \(I^{\prime \ast}\) are the real current reference for AC side converter and the current reference for DC side converter of interlinking converter; P* is the real power reference transferred between AC and DC sub-microgrids; P
*
S
is the energy storage real power reference; P
*DC_tol,
P
*AC_tol
are the total real power ratings of DC and AC microgrids, respectively.