The document discusses the relationship between the P-Q circle of a DG (distributed generation) unit and its P-f and Q-E droops. It presents the classic droop control scheme block diagram and equations that model how active power P and reactive power Q are related to frequency f and voltage magnitude E based on the droop coefficients. It also shows circuit diagrams for a droop controlled inverter connected to a microgrid and the structure for multiple parallel connected inverters.

1. 1/250
Relationship between the P-Q circle of a DG unit and P-
f and Q-E droops
Voltage
loop
Current
loop
PWM +
Inverter
P/Q CalculationVoltage reference
E-sin(2𝜋𝑓𝑡)
Virtual Impedance loop
( )DZ s
*ov
ov
oI
P
*P
*Q
Q
E
f
refv
Inductive
Q<0
Capacitive
Q<0
S P jQ 
Storage
P<0
Generation
P>0
P
Q
Q
*
Q
maxQ
maxQ
f
f
E
*
E
P
PmaxP maxP
Primary
response
Primary
response
E
f

2. Decoupled Droop Control Techniques
J. Quesada, J.A. Sainz, R. Sebastian, and M. Castro, “Decoupled droop control techniques for inverters in low-voltage AC microgrids,” IEEE
11th International Multi-Conference on Systems, Signals & Devices (SSD), pp. 1-6, 11-14 Feb. 2014.
(a) Droop controlled inverter (b) Simplified model of
the droop controlled inverter.
(c) Control diagram for classic droop.
(d) Droop control with an RL coupling impedance.
(d) Droop control with decoupling term kc in the
feedback matrix.
Droop
Control
Vbus
Bridge
Basic controlled inverter(BCI)
fL
fC
cV
gi
Li
p
qPQ
d qE E jE  
refe
reff
Droop
Control
p
q
refe
reff
d qE E jE  
Microgrid
MicrogridLZ R j X   g d qi i j i  
coupling
point1
Reference syntetizer
coupling
point
 
E
(a)
(b)
Internal
Controller
PQ
g
V
( )G s0
1 0
0
S

 
 
 
 
0
0
q
p
k
k
 
 
 
0
0
0
0
0
0
S
S S
S
S S
 
 
 
 
  
e
f
e
reff
refe

p
q
( )G s0
1 0
0
S

 
 
 
 
0
0
q
p
k
k
 
 
 
L
L
X R
Z Z
XR
Z Z
 
 
 
  
e
f
e
reff
refe

p
q
p
q
( )G s0
1 0
0
S

 
 
 
 
0
c q
p
k k
k
 
 
 
0
0
0
0
0
0
S
S S
S
S S
 
 
 
 
  
e
f
e
reff
refe

p
q

3. 3/250
Block Diagram for Classic Droop Scheme
( )G s0
1 0
0
S

 
 
 
 
0
0
q
p
k
k
 
 
 
0
0
0
0
0
0
S
S S
S
S S
 
 
 
 
  
e
f
e
reff
refe

p
q
0
0
1 00
0
0
b
d d d
o
bq q q
b
b
ZR
i i vdELd L
E
Zi i vRdt
V
VL



                                                 
1 03
0 12
do b
qb
ip V I
iq S
    
          

4. 4/250
Circuit structure for the n-parallel connected inverters
2015.Line and grid impedance impact on the performances of a parallel connected modular inverter system.pdf
Inverter
Inverter
Inverter
1 1 1, ,a a ai R L
2 2 2, ,a a ai R L
, ,an an ani R L
1 1 1, ,c c ci R L
, ,cn cn cni R L
,a aR L
1 1 1, ,b b bi R L
 ae
V
Cgv
inL
ini