2.1. The Generalized Current-Based Control Strategy
First we suppose that a number
J (i.e.,
j = 1, 2, 3, …, J) of DERs exist in the grid-connected MG. Moreover, as long as the DERs present remote control capabilities, they can be controlled by the GCBC. Now, to explain the GCBC strategy, let us consider that the peak value (
I) of current components from a DER and from the MG PCC will be denoted by
and
, respectively. Additionally, one fundamental definition is highlighted: supposing a time-domain current (
) composed of
H harmonic components (i.e.,
h = 1, 2, 3, …, H),
can be rewritten at any time by Equation
1. Such a definition considers an AC time-domain signal of unity amplitude that determines the in-phase (
) or quadrature (
) synchronism of the current components, respectively, in relation to the voltage of that same node of the circuit.
The GCBC strategy relies on three main tasks to coordinate DERs, being: (
i) the local evaluation of electrical quantities at DERs and PCC; (
ii) the processing of the GCBC algorithm at the MGCC; and (
iii) the local current reference setting at DERs. The scheme shown in
Figure 3 illustrates how these tasks compose the GCBC strategy. Note that, given a control cycle “
k”, the GCBC tasks are processed sequentially at different locations of the MG, using communication links to adjust the currents injected by the DERs at the final step.
Consequently, load changes and uncertainty in generation capabilities can be handled by the GCBC strategy, steering DERs to achieve the intended MG operational goals respecting their nominal capabilities. Let us now present a more detailed explanation about each of these tasks.
- (i)
Local Evaluation of Electrical Quantities
This task processes the electrical quantities (i.e., voltage and currents) at the nodes of interest. It occurs at each coordinated DER as well as at the MGCC. Such a procedure is required to detect the peak values of the currents flowing through the DERs’ PoCs and the PCC. For instance, taking the time-domain local output current of a DER,
, in which
m stands for the respective phase of a generic circuit (e.g.,
m = a, b, or
c, for three-phase topology). The scheme demonstrated in
Figure 4a extracts the magnitude of the in-phase (
) and quadrature (
) currents components from
. Because such calculations occur at the DERs and the PCC, one finds that
for each
j-th DER, and
for the PCC.
The decomposition of current components should be conducted for all harmonic orders (h) aimed to be controlled. By managing the fundamental in-phase component, , active current control is obtained, whereas reactive current control relates to . The components of higher harmonic orders (i.e., for h = 2, 3, 4, 5, …, H), , and , are responsible for the regulation of non-fundamental currents. As a result, at this point, it is evident that a per-phase analysis of currents is performed by the GCBC at selected harmonic orders. It is important to reinforce that both even and odd harmonics can be considered in the GCBC formulation. Hence, the set of controlled harmonic orders is defined by the MGCC according to the MG’s desired goals of operation.
The GCBC’s local evaluation task first measures the local currents and voltages (
) of a PoC or PCC, as seen in
Figure 4a (i.e.,
for DERs, or
for the PCC). Later, the voltage feeds a PLL algorithm, allowing to obtain the fundamental synchronization angle
, which is also used for calculating the synchronization angles
that provide the references for the harmonic frames. By feeding such angles to cosine and sine functions, the unity reference signals,
and
, can be obtained for the in-phase and quadrature orientations. Assuming that the adopted PLL algorithm is robust, the GCBC can endure operation under non-ideal voltage conditions. Hence, the PLL algorithm discussed in [
51] is herein considered for the GCBC implementation.
Knowing
and
, as well as the node current
, a discrete Fourier transform (DFT) [
52] allows to calculate the peak values of the targeted current components. The adopted DFT is devised in
Figure 4a by means of moving average filters (MAFs) that act as low-pass filters (LPFs), allowing simple digital implementation. Consequently, due to the feature of this implementation, the peak current terms
and
are average quantities that could assume either positive or negative values, depending on how
and
interact with
. For instance, attaining a positive value for
would indicate an injection of active power. On the other hand, power absorption (i.e., storage) would result in a negative value for
. (The negative magnitude of a periodic current component does not present mathematical meaning. Such a definition is an abstraction, given that the peak detection scheme from
Figure 4 can indicate if a current component is either in phase or 180
o shifted in relation to
or
. For the case of having a 180
o-shifted current signal, a negative peak value is obtained.) It is remarked that other approaches for the calculation of the peak currents [
53,
54] could be devised if desired, guaranteeing compatibility with the following steps of the GCBC strategy. Finally, note that in
Figure 4b, a graphical representation of the discussed local evaluation is presented to further clarify how the peak currents are calculated.
By having all the peak currents calculated (i.e.,
and
), they are gathered to compose a data packet, which is sent to the MGCC, as shown in
Figure 4a. Along with the decomposed terms, other peak current terms are inserted into this data packet. Such quantities are the nominal current rating for each
j-th DER (
), the maximum active current that it can generate (
), and the maximum active current that it can store (
) if an ESS exists.
The term
relates to the nominal apparent power of that DER. Moreover, the term
indicates
j-th DER’s capability to inject active current, either considering the implementation of MPPT algorithms for its RES (i.e., if it is an nd-DER) or based on the usage of stored power (i.e., if it is a d-DER). On the other hand, the term
relates to the SoC of the ESS, as typically adopted for battery systems [
55], indicating that such a variable is only applied to d-DERs.
As a final remark, it is highlighted that and are only used locally by the MGCC. This occurs because they are obtained from quantities measured at the PCC and are not required to be transmitted to DERs at any moment.
- (ii)
Processing of the GCBC Algorithm at the MGCC
The second task relates to the operation of the GCBC algorithm at the MGCC. Such an algorithm needs to be periodically processed, taking into account the data packets transmitted by the DERs. In addition, the GCBC algorithm processing occurs at each control cycle “k” triggered at the beginning of a periodic window of the MG management, which operates between milliseconds and minutes, according to the control needs and physical topology of the system. Consequently, “k” is only updated at the next control cycle “k = k + 1”. By starting a new control cycle, after processing task “(i)”, the MGCC pulls the data packets processed by DERs and attains the results from the evaluation of the PCC currents.
By determining the
H harmonic orders that need to be controlled, the following calculation is performed at the MGCC. The total current contribution of the
J DERs is computed first, for each harmonic order
h, being given by Equations (
2) and (
3). Note that the in-phase (
) and quadrature (
) current components are processed independently. In addition, the superscript “
t” herein stands for the total quantities of the MG (i.e., with relation to all
J DERs being coordinated).
Similarly, the nominal capabilities of the DERs (
) need to be computed, along with their maximum generation (
) and storage (
) currents, as given by Equations (
4)–(
6), respectively. The GCBC processing at this stage allows to identify the actual participation of DERs in the overall status of the MG operation.
Because the MGCC also has the information about the currents flowing through the PCC (i.e.,
and
), the summed current contribution (
and
) of all MG elements, including the passive or non-controlled ones, can be devised by Equations (
7) and (
8). For that, Kirchhoff’s current law can be applied at the MG PCC as presented in
Figure 5.
Additional remarks are made with regard to
and
. First, note that they not only comprise the currents drawn by the loads that may exist within the MG, but they also incorporate all the power losses occurring in line impedances and other dissipative elements. Moreover, DERs not being coordinated by the GCBC strategy are also considered within these terms. Yet, Equations (
7) and (
8) are only valid due to the limited size of the considered MG, its homogeneous characteristic, and the low
X/R feature of its line impedances, which guarantees that voltage shifts are not significant [
43]. As a last remark, note that if the DERs share
and
completely, the current flow through the PCC will become null. Therefore, if
and
for all significant harmonic orders, the MG operates under full self-consumption mode [
56] in a steady state, not depending on the upstream grid (i.e., aside from the fact of forming the grid by imposing the voltages and frequency at the PCC).
Now, the controllable power dispatchability through the PCC provided by the GCBC is further explained. Such a desired power flow can be translated into current signals that must be drawn or dispatched by the MG, considering that it is interpreted as single entity from the upstream grid perspective. Such reference signals refer to each harmonic order “
h” at the PCC, namely
and
, and they establish the amount of peak current that must circulate at the PCC, even after fulfilling the MG internal current needs (i.e.,
). Consequently,
and
are usually set by the DSO. For example, if
is a non-null positive quantity, the upstream grid interprets the MG behaving as a single entity acting as a load drawing active currents. On the other hand, if
is a negative quantity, it means energy export (i.e., the MG dispatching active power). In addition, as typically adopted in MG contracts, active and reactive power is limited [
57]. Consequently, such PCC reference terms are constrained to upper and lower bounds (i.e.,
and
and Equations (
9) and (
10) must be considered.
The GCBC algorithm then allows to define the currents that need to be shared by the DERs, at the next control cycle “
k + 1”, namely
and
. Such references can be calculated according to Equations (
11) and (
12), which are expanded to Equations (
13) and (
14).
Hence, to coordinate DERs to achieve current sharing over multiple harmonic orders,
and
are used to calculate scaling coefficients (i.e., namely
and
), by means of Equations (
15) and (
16). The term
is the overall peak current capability of the MG, and it provides proportional current sharing among DERs, while respecting their current ratings. This term must be adjusted iteratively according to the calculation of each scaling coefficient, as demonstrated in
Figure 6.
Such a correction of
follows a sequential order, having active current control processed first, reactive control next, and the in-phase and quadrature harmonic orders processed last. Particular attention must be given to active current control because active current injection or absorption must be related to
and
, respectively. Note that, because each step of this procedure is based on orthogonal subtractions, by using the DERs’ estimated currents (i.e., given by
or
) at “
k + 1”, overcurrents are prevented. Additionally, such phasorial calculations also guarantee that their current capabilities are respected. The scheme in
Figure 6 uses two auxiliary variables (
and
), which hold the quadratic value of the overall current capability at the actual and previous calculation steps, respectively. It should ultimately be remarked that, if desired, for whatever MG management reason, the sequence of the iterative calculation of
can be flexibly readjusted.
Finally, further explanations are given about the scaling coefficients, and . These coefficients are within the range of , and if they are equal to +1 or −1, it indicates that all the DERs’ current capacity, at a given harmonic order h, is used. As expected, if these coefficients are null, no current control is performed at the respective harmonic order. In particular, when looking into the coefficients of the fundamental order, one can generally understand the coordination purpose of the DERs.
For instance, the term
relates to active current control, and it indicates that power injection is demanded by the DERs (i.e., if
), or that absorption/storage is commanded (i.e., if
). On the other hand, the term
implies that inductive or capacitive behavior is provided by the DERs, if
or
, respectively. Yet, by using the non-fundamental scaling coefficients (i.e,
and
, for
), the MG manager has a means to implement distributed and selective compensation of harmonic currents. Of course, for the case of nd-DERs not comprising ESS,
cannot assume negative values, as
is null. In addition, because the GCBC algorithm can also be employed to coordinate active filters [
58], a similar idea would apply, resulting in
being always null, as
.
This task of the GCBC strategy terminates by gathering, in a data packet, the scaling coefficients of all harmonic orders to be controlled. Sequentially, this data packet is broadcast to all participating DERs within the MG, so they can adjust their output currents as given by the next step of the GCBC approach.
- (iii)
Current Reference Setting at DERs
The final procedure of the GCBC strategy is responsible for setting the right current references to be injected by the DERs. This task occurs only at each DER, and it uses the scaling coefficients transmitted by the MGCC. Let
be the time-domain current reference of the phase
m, for each
j-th DER participating in the coordination strategy. Such a reference can then be constructed similarly to Equation (
1), in which the unity reference signals (i.e.,
and
) come from the local evaluation of the electrical quantities realized by that
j-th DER. Thus, the final current reference used for that DER is given by Equations (
17) and (
18), which can be summed up to result in Equation (
19), similarly to Equation (
1).
In such equations, the current capability of each respective DER (
) is used. This variable is calculated in the same way as for the total current capability of the MG (
), following the same iterative scheme presented in
Figure 6. However, for
, only the local quantities of that specific
j-th DER must be used (i.e.,
,
, and
).
A final remark is made with regard to the per-phase controllability provided by the GCBC strategy. Note, from Equation (
19), that the current reference for a DER is locally constructed based on the evaluations performed at each phase
m, even for the three-phase topology. This indicates that, for the case of single-phase MGs, the GCBC is performed only for one phase. On the other hand, for three-phase MGs, the GCBC application depends on the topology of the inverters. For instance, if three-leg DERs exist, only two phases need to be controlled [
59], being the modulation of the third leg obtained from Kirchhoff’s current law. Hence, the GCBC needs to be implemented considering two phases to adequately coordinate such DERs. For the case in which three-phase four-leg DERs exist (i.e., in a three-phase four-wire MG) [
44], the GCBC is applied to three phases, controlling the DER’s neutral leg by Kirchhoff’s current law.