Process for controlling low voltage microgrids
This technology is a process for controlling low voltage microgrids (MGs) with centralized communication, based on the “Power-Based Control” (PBC) technique adapting the same to a modified PBC (MPBC) process. The technology provides the following technical effects: 1) sharing of active power and reactive power proportionally to the capacity of distributed energy resources (DERs) of the MG; 2) power unbalance compensation at the point of common coupling (PCC or PAC in Portuguese); 3) the process can be implemented without knowing the parameters and topology of the power grid; 4) ability to handle the arbitrary connection of inverters in the MG; 5) it makes possible to distinguish between DERs connected to the MG in both types of connection: phase-phase and phase-neutral, wherein single-phase DERs connected arbitrarily between the phases share the amounts of balanced power, while the unbalanced and homopolar powers are steered only to the inverters connected between phase and neutral; 6) it allows the connection of the MG to multiple PCCs and also the operation in isolated mode (“islanded”). The technology is applied in the technical field of equipment and infrastructure for the development of MGs.
1 . A process for controlling low voltage microgrids, characterized in that it comprises the following steps:
a) Temporarily delimiting a control cycle l, with the next control cycle defined as l 1 =l+1;
b) Assigning the following vectors P PCC x (l) and Q PCC x (l), which are vectors that indicate the active and reactive powers exchanged with the main grid from the three phases of the microgrid (MG) and the respective references
P
_
PCC
x
*
(
l
1
)
and
Q
_
PCC
x
*
(
l
1
)
,
where the terms with the subscript ( PCC x ) are provided by the grid at the controlled point of common coupling (PCC) and terms with superscript (*) indicate the power references for the respective ( PCC x ) where x is the numeric identification of the PCC in which the control process is applied, and the indices m or mn indicate the phases of the three-phase system in the context of the phase-neutral and phase-phase connection types, respectively;
c) Steering the power references
[
P
_
PCC
x
*
(
l
1
)
and
Q
_
PCC
x
*
(
l
1
)
]
using the central control, located in the secondary control layer, which transmits command instructions to the distributed energy resources (DER) according to their connection types in the MG, which can be phase-phase or phase-neutral to determine the powers to be generated individually, wherein the powers are calculated by sub-steps i to iv, namely:
i. Homopolar powers
P
_
PCC
x
ho
(
l
)
and
Q
_
PCC
x
ho
(
l
)
:
the power components for these vectors are calculated for each phase of the PCC considering only the homopolar components (ho) of current that are calculated by expression (1);
i
ho
=
1
3
∑
m
=
1
3
i
m
(
1
)
ii. Expression 2 is used to equate the characteristics inherent to homopolar currents, expressions 3 and 4 calculate the vectors of non-homopolar powers (nho) in each phase of the PCC;
∑
m
=
1
M
P
PCC
x
m
ho
=
∑
m
=
1
M
Q
PCC
x
m
ho
=
0
(
2
)
P
_
PCC
x
nho
(
l
)
=
P
_
PCC
x
(
l
)
-
P
_
PCC
x
ho
(
l
)
(
3
)
Q
_
PCC
x
nho
(
l
)
=
Q
_
PCC
x
(
l
)
-
Q
_
PCC
x
ho
(
l
)
(
4
)
where M is the number of phases of the P CC x (in general, M=3);
iii. Balanced powers
(
P
_
PCC
x
b
(
l
)
and
Q
_
PCC
x
b
(
l
)
)
:
these vectors represent the portions of power consumed by a balanced load whose total powers are equivalent to the non-homopolar total powers in the PCC x , that is:
∑
m
=
1
M
P
PCC
x
m
b
=
∑
m
=
1
M
P
PCC
x
m
nho
,
∑
m
=
1
M
Q
PCC
x
m
b
=
∑
m
=
1
M
Q
PCC
x
m
nho
(
5
)
where the powers of the vectors
P
_
PAC
x
b
and
Q
_
PAC
x
b
are calculated as:
P
PAC
x
m
b
=
∑
n
=
1
N
P
PAC
x
n
nho
∑
n
=
1
N
V
n
2
·
V
m
2
,
Q
PAC
x
m
b
=
∑
n
=
1
N
Q
PAC
x
n
nho
∑
n
=
1
N
V
^
n
2
·
V
^
m
2
,
(
6
)
where V and {circumflex over (V)} are the root mean square (rms) values of the phase-neutral voltages measured at the PCC x and the rms values of the respective voltage integrals, calculated by discounting their average value over time;
iv. The difference between the balanced portion of the power and the non-homopolar portion of the power is calculated, which results in the amount of “unbalanced” power (u) by expressions 7 and 8.
P
_
PCC
x
u
=
P
_
PCC
x
nho
-
P
_
PCC
x
b
(
7
)
Q
_
PCC
x
u
=
Q
_
PCC
x
nho
-
Q
_
PCC
x
b
(
8
)
wherein, based on equations (5), (7) and (8), it is possible to deduce that:
∑
m
=
1
M
P
PCC
x
m
u
=
∑
m
=
1
M
Q
PCC
x
m
u
=
0
;
(
9
)
d) Generating power transformation matrices: for DERs connected to the MG with phase-phase connection, the powers in the phase-phase configuration are converted into their respective phase-neutral values by a transformation that uses matrices A and B, detailed by expressions 10 and 11, and this conversion is made based on the Y−Δ transformations defined for impedance, generalized here in the form of matrices valid for any voltage conditions
A
_
=
[
V
1
2
-
〈
v
1
,
v
2
〉
0
V
1
2
-
〈
v
3
,
v
1
〉
V
2
2
-
〈
v
1
,
v
2
〉
V
2
2
-
〈
v
2
,
v
3
〉
0
0
V
3
2
-
〈
v
2
,
v
3
〉
V
3
2
-
〈
v
3
,
v
1
〉
]
(
10
)
B
_
=
[
V
^
1
2
-
〈
v
^
1
,
v
^
2
〉
0
V
^
1
2
-
〈
v
^
3
,
v
^
1
〉
V
^
2
2
-
〈
v
^
1
,
v
^
2
〉
V
^
2
2
-
〈
v
^
2
,
v
^
3
〉
0
0
V
^
3
2
-
〈
v
^
2
,
v
^
3
〉
V
^
3
2
-
〈
v
^
3
,
v
^
1
〉
]
(
11
)
where (v 1 , v 2 , v 3 ), ({circumflex over (v)} 1 , {circumflex over (v)} 2 , {circumflex over (v)} 3 ), (V 1 , V 2 , V 3 ), ({circumflex over (V)} 1 , {circumflex over (V)} 2 , {circumflex over (V)} 3 ) are, respectively, the phase-neutral voltages and the corresponding homo-integrals and the respective rms values of the voltages and their homo-integrals, while the operator , corresponds to the internal product of two quantities that are functions of time, and, thus, with these matrices in hand, the powers between phases
(
vectors
P
_
ff
and
Q
_
ff
)
can be converted to phase values
(
vectors
P
_
fn
and
Q
_
fn
)
and vice versa using equations 12 and 13:
P
_
fn
=
A
_
·
(
diag
(
V
_
ff
)
)
-
1
·
P
_
ff
↔
P
_
ff
=
diag
(
V
_
ff
)
·
A
_
-
1
·
P
_
fn
(
12
)
Q
_
fn
=
B
_
·
(
diag
(
V
^
_
ff
)
)
-
1
·
Q
_
ff
↔
Q
_
ff
=
diag
(
V
^
_
ff
)
·
B
_
-
1
·
Q
_
fn
(
13
)
where the vectors
V
_
ff
and
V
^
_
ff
contain the rms values of the voltages between phases and the respective homo-integrals of the phase-phase voltages, and the function diag( ) represents the transformation of a vector with m elements into a square matrix of order m whose elements of the main diagonal correspond to the elements of the original vector and the other elements are null;
e) Considering that J distributed generators are in operation in the MG during control cycle l, the quantities of interest of the j-th DER for the control algorithm are:
Active and reactive powers injected into the microgrid during cycle l:
P
Gj
(
l
)
,
Q
Gj
(
l
)
;
Maximum active and reactive powers that the DER can inject into the grid during the cycle l:
P
G
j
max
(
l
)
and
Q
G
j
max
(
l
)
;
In the case of energy storage systems, there is the minimum active power that can be absorbed from the microgrid in the cycle l:
P
G
j
min
(
l
)
;
f) Performing the steps described below during the control cycle l, considering all information received from the distributed generators in operation and controllable PCCs:
Step 1: sums of active and reactive powers of the J DERs in operation and the X controllable PCCs for each phase m=1,2,3 and pair of phases mn=12,23,31:
P
Gfn
m
(
l
)
=
∑
j
=
1
J
P
Gj
m
(
l
)
,
Q
Gfn
m
(
l
)
=
∑
j
=
1
J
Q
Gj
m
(
l
)
(
14
)
P
Gff
mn
(
l
)
=
∑
j
=
1
J
P
Gj
mn
(
l
)
,
Q
Gff
mn
(
l
)
=
∑
j
=
1
J
Q
Gj
mn
(
l
)
(
15
)
P
Gfn
m
max
(
l
)
=
∑
j
=
1
J
P
Gj
m
max
(
l
)
,
Q
Gfn
m
max
(
l
)
=
∑
j
=
1
J
Q
Gj
m
max
(
l
)
(
16
)
P
Gff
mn
max
(
l
)
=
∑
j
=
1
J
P
Gj
mn
max
(
l
)
,
Q
Gff
mn
max
(
l
)
=
∑
j
=
1
J
Q
Gj
mn
max
(
l
)
(
17
)
P
PCC
m
(
l
)
=
∑
x
=
1
X
P
PCC
x
m
(
l
)
,
Q
PCC
m
(
l
)
=
∑
x
=
1
X
Q
PCC
x
m
(
l
)
(
18
)
P
PCC
m
*
(
l
1
)
=
∑
x
=
1
X
P
PCC
x
m
*
(
l
1
)
,
Q
PCC
m
*
(
l
1
)
=
∑
x
=
1
X
Q
PCC
x
m
*
(
l
1
)
(
19
)
P
PCC
m
ho
(
l
)
=
∑
x
=
1
X
P
PCC
x
m
ho
(
l
)
,
Q
PCC
m
ho
(
l
)
=
∑
x
=
1
X
Q
PCC
x
m
ho
(
l
)
(
20
)
P
PCC
m
nho
(
l
)
=
∑
x
=
1
X
P
PCC
x
m
nho
(
l
)
,
Q
PCC
m
nho
(
l
)
=
∑
x
=
1
X
Q
PCC
x
m
nho
(
l
)
(
21
)
P
PCC
m
b
(
l
)
=
∑
x
=
1
X
P
PCC
x
m
b
(
l
)
,
Q
PCC
m
b
(
l
)
=
∑
x
=
1
X
Q
PCC
x
m
b
(
l
)
(
22
)
P
PCC
m
u
(
l
)
=
∑
x
=
1
X
P
PCC
x
m
u
(
l
)
,
Q
PCC
m
u
(
l
)
=
∑
x
=
1
X
Q
PCC
x
m
u
(
l
)
(
23
)
calculates the reference values of active and reactive powers for the generators
P
PCC
m
*
(
l
1
)
=
∑
x
=
1
X
P
PCC
x
m
*
(
l
1
)
,
Q
PCC
m
*
(
l
1
)
=
∑
x
=
1
X
Q
PCC
x
m
*
(
l
1
)
(
19
)
P
PCC
m
ho
(
l
)
=
∑
x
=
1
X
P
PCC
x
m
ho
(
l
)
,
Q
PCC
m
ho
(
l
)
=
∑
x
=
1
X
Q
PCC
x
m
ho
(
l
)
(
20
)
distributed in control cycle l 1 :
If only the DERs connected between phases are in operation, the power references for the pairs of phases mn=12,23,31 contained in the vectors
P
_
Gff
(
l
1
)
and
Q
_
Gff
(
l
1
)
are calculated using:
P
_
Gff
(
l
1
)
=
diag
(
V
_
ff
)
·
A
_
-
1
·
(
P
_
PCC
b
(
l
)
-
P
_
PCC
*
(
l
1
)
)
+
P
_
Gff
(
l
)
(
24
)
Q
_
Gff
(
l
1
)
=
diag
(
V
^
_
ff
)
·
B
_
-
1
·
(
Q
_
PCC
nho
(
l
)
-
Q
_
PCC
*
(
l
1
)
)
+
Q
_
Gff
(
l
)
(
25
)
where the elements of vectors
P
_
Gff
(
l
)
,
Q
_
Gff
(
l
)
,
P
_
PCC
*
(
l
1
)
,
Q
_
PCC
*
(
l
1
)
,
Q
_
PCC
nho
(
l
)
and
P
_
PCC
b
(
l
)
are calculated by equations (15), (19), (21) and (22), respectively;
If only the DERs connected between phase and neutral are in operation, the power references for the phases m=1,2,3 contained in the vectors
P
_
Gfn
(
l
1
)
and
Q
_
Gfn
(
l
1
)
are calculated using:
P
_
Gfn
(
l
1
)
=
P
_
PCC
(
l
)
-
P
_
PCC
*
(
l
1
)
+
P
_
Gfn
(
l
)
(
26
)
Q
_
Gfn
(
l
1
)
=
Q
_
PCC
(
l
)
-
Q
_
PCC
*
(
l
1
)
+
Q
_
Gfn
(
l
)
(
27
)
where the elements of the vectors
P
_
Gfn
(
l
)
,
Q
_
Gfn
(
l
)
,
P
_
PAC
(
l
)
and
Q
_
PAC
(
l
)
are calculated by equations (14) and (19), respectively;
If distributed generators with both types of connection (phase-phase and phase-neutral) are in operation, a criterion for sharing some portions of active and reactive power is established based on the following coefficients:
c
_
P
(
l
)
=
(
diag
(
P
_
Gfn
max
(
l
)
+
P
_
Gfn
max
′
(
l
)
)
)
-
1
·
P
_
Gfn
max
(
l
)
(
28
)
c
_
Q
(
l
)
=
(
diag
(
Q
_
Gfn
max
(
l
)
+
Q
_
Gfn
max
′
(
l
)
)
)
-
1
·
Q
_
Gfn
max
(
l
)
(
29
)
where the elements of the vectors
P
_
Gfn
max
(
l
)
and
Q
_
Gfn
max
(
l
)
are calculated by equations (16), while the elements of the vectors
P
_
Gfn
max
′
(
l
)
and
Q
_
Gfn
max
′
(
l
)
are calculated by using:
P
_
Gfn
max
′
(
l
)
=
A
_
·
(
diag
(
V
_
ff
)
)
-
1
·
P
_
Gff
max
(
l
)
(
30
)
Q
_
Gfn
max
′
(
l
)
=
B
_
·
(
diag
(
V
^
_
ff
)
)
-
1
·
Q
_
Gff
max
(
l
)
(
31
)
where the elements of the vectors
P
_
Gff
max
(
l
)
and
Q
_
Gff
max
(
l
)
are calculated by equations (17), and,
P
_
fn
sh
(
l
)
=
diag
(
c
_
P
(
l
)
)
·
(
P
_
PAC
b
(
l
)
-
P
_
PAC
*
(
l
1
)
)
(
32
)
Q
_
fn
sh
(
l
)
=
diag
(
c
_
Q
(
l
)
)
·
(
Q
_
PAC
b
(
l
)
-
Q
_
PAC
*
(
l
1
)
)
(
33
)
P
fn
sh
′
(
l
)
=
(
I
_
-
diag
(
c
_
P
(
l
)
)
·
(
P
_
PAC
b
(
l
)
-
P
_
PAC
*
(
l
1
)
)
(
34
)
Q
_
fn
sh
′
(
l
)
=
(
I
_
-
diag
(
c
_
Q
(
l
)
)
·
(
Q
_
PAC
b
(
l
)
-
Q
_
PAC
*
(
l
1
)
)
(
35
)
therefore, the power sharing is defined as:
where l is the identity matrix, and, finally, the power references for the phases and pairs of phases are calculated as a function of the vectors
P
_
fn
sh
(
l
)
,
Q
_
fn
sh
(
l
)
,
P
_
fn
sh
′
(
l
)
and
Q
_
fn
sh
′
(
l
)
:
P
_
Gff
(
l
1
)
=
(
diag
(
V
_
ff
)
·
A
_
-
1
·
P
_
fn
sh
′
(
l
)
)
+
P
_
Gff
(
l
)
(
38
)
Q
_
Gff
(
l
1
)
=
(
diag
(
V
^
_
ii
)
·
B
_
-
1
·
Q
_
fn
sh
′
(
l
)
)
+
Q
_
Gff
(
l
)
;
(
39
)
Step 3:
calculation of power coefficients:
For phases m=1,2,3:
α
_
fn
P
=
(
diag
(
P
_
Gfn
max
(
l
)
)
)
-
1
·
P
_
Gfn
(
l
1
)
(
40
)
α
_
fn
Q
=
(
diag
(
Q
_
Gfn
max
(
l
)
)
)
-
1
·
Q
_
Gfn
(
l
1
)
(
41
)
For the pairs of phases mn=12,23,31:
α
_
ff
P
=
(
diag
(
P
_
Gff
max
(
l
)
)
)
-
1
·
P
_
Gff
(
l
1
)
(
42
)
α
_
ff
Q
=
(
diag
(
Q
_
Gff
max
(
l
)
)
)
-
1
·
Q
_
Gff
(
l
1
)
(
43
)
where the values of the coefficients contained in the vectors
α
_
fn
P
,
α
_
fn
Q
,
α
_
ff
P
and
α
_
ff
Q
are limited between 0 and 1, and these coefficients are used to control the injection of active and reactive power of each DER in operation in the microgrid, so that:
The references of active and reactive power for the control cycle l 1 of the j-th DER connected between phase m and neutral are calculated by:
P
Gj
*
(
l
1
)
=
α
fn
m
P
·
P
Gj
max
(
l
)
,
Q
Gj
*
(
l
1
)
=
α
fn
m
Q
·
Q
Gj
max
(
l
)
;
(
44
)
The references of active and reactive power for the control cycle l 1 of the j-th DER connected between phase m and n are calculated by:
P
Gj
*
(
l
1
)
=
α
ff
mn
P
·
P
Gj
max
(
l
)
,
Q
Gj
*
(
l
1
)
=
α
ff
mn
Q
·
Q
Gj
max
(
l
)
.
(
45
)