Inverters that mimic synchronous generators

S YNCHRONVERTERS : I NVERTERS THAT M IMIC
S YNCHRONOUS G ENERATORS
Qing-Chang Zhong, Fellow of IET, SMIEEE
ZhongQC@ieee.org

Chair in Control and Systems Engineering
Dept. of Automatic Control and Systems Engineering
The University of Shefﬁeld
United Kingdom

http://zhongqc.staff.shef.ac.uk

(Joint work with George Weiss, Tel Aviv University

Outline
Motivation and relevant works
Modelling of synchronous generators
Implementation of a synchronverter
Operation of a synchronverter
Simulation results
Experimental setup and results
Potential applications
An overview of other research activities

Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 2/41

Motivation
Transition from centralised generation to distributed
generation
Wind power
Solar energy
Tide and wave energy
CHP
Increasing share of renewable energy
UK: 20% by 2020
EU: 22% target for the share of renewable energy
sources and an 18% target for the share of CHP in
electricity generation by 2010


Challenges
Regulation of system frequency and voltage
Currently most inverters feed currents to the grid and
the grid cannot control these sources. Inverters will
have to take part in the regulation of power systems in
the near future.
There is an increasing need of voltage controlled
inverters to connect with weak grids
Threat to power system stability: Inverters have different
dynamics from conventional synchronous generators
The need of smooth transition of knowledge
These sources are connected to the grid via common
key devices called inverters so it is possible to tackle
these problems via properly controlling the inverters.

Our solution
Turning inverters into synchronous generators, mathe-
matically. Such inverters are called synchronverters.
Operate voltage source inverters to mimic
synchronous generators
The energy ﬂow between the DC bus and the AC
bus changes direction automatically according to
the grid frequency
Take part in the power system regulation of
frequency and voltage: the same as synchronous
generators (externally)
Dynamically behave like synchronous generators
(internally)

Relevant works
Virtual synchronous machine (VISMA) by Beck and Hesse

The voltages at the point of common coupling with the grid are measured to
calculate the phase currents of the VISMA in real time.
These currents are used as reference currents for a current-controlled inverter. If the
current tracking error is small, then the inverter behaves like a synchronous
machine, justifying the term VISMA. However, a synchronous generator is a
voltage source.
The grid integration using control algorithms for SG was left as future work

Virtual synchronous generator (VSG) by VSYNC

Add a short-term energy storage system to provide virtual inertia
The inverter itself does not have the dynamics of a synchronous generator

Frequency/voltage drooping

e.g. by De Brabandere, Bolsens, Van den Keybus, Woyte, Driesen, Belmans
and by Sao and Lehn
The inverter itself does not have the dynamics of a synchronous generator

Some basics about inverters
+
Circuit
Ls , R s va Lg , R g Breaker
ia vga
ea vb
VDC ib vgb
eb
vc
ec ic vgc

C
-


Electrical part
Mechanical part
Simulation results

SG: Electrical part
Consider a round rotor (θ = 0 )

machine (without dam-
per windings), with p Rotor field axis

pairs of poles per phase
Rs , L
(and p pairs of poles
Rotation
on the rotor) and with
no saturation effects in M M
the iron core. The
N
Field voltage
stator windings can be
Rs , L Rs , L
regarded as concentra-
ted coils having self-
inductance L and mu- M

tual inductance −M .

Notation
Deﬁne    
Φa ia
Φ =  Φb  , i =  ib 
Φc ic
and
   
cos θ sin θ
cos θ =  cos(θ − 2π )  ,
3
sin θ =  sin(θ − 2π )  .
3
cos(θ − 4π )
3 sin(θ − 4π )
3


Flux linkage
The field (or rotor) winding can be regarded as a concentrated
coil having self-inductance Lf . The mutual inductance between
the field coil and each of the three stator coils is Mf cos θ. Assume
that the neutral line is not connected, then ia + ib + ic = 0. The
stator flux linkages are

Φ = Ls i + Mf if cos θ, (1)

where Ls = L + M , and the field flux linkage is

Φf = Lf if + Mf i, cos θ , (2)

where ·, · denotes the conventional inner product. The second
term Mf i, cosθ is constant if the three phase currents are sinu-
soidal (as functions of θ) and balanced.

Voltage
T
The phase terminal voltages v = va vb vc are

dΦ di
v = −Rs i − = −Rs i − Ls + e, (3)
dt dt
where Rs is the resistance of the stator windings and
T
e= ea eb ec is the back emf

˙sin θ − Mf dif cos θ.
e = Mf if θ (4)
dt
The ﬁeld terminal voltage, from (2), is
dΦf
vf = −Rf if − , (5)
dt
where Rf is the resistance of the rotor winding.

SG: Mechanical part
The mechanical part of the machine is governed by
¨ ˙
J θ = Tm − Te − Dp θ, (6)
where J is the moment of inertia of all parts rotating
with the rotor, Tm is the mechanical torque, Te is the
electromagnetic toque and Dp is a damping factor. Te
can be found from the energy E stored in the machine
magnetic ﬁeld, i.e.,
1 1
E = i, Φ + if Φf
2 2
1 1 2
= i, Ls i + Mf if i, cos θ + Lf if .
2 2

Electromagnetic torque Te
∂E ∂E
Te = =− .
∂θm Φ, Φf constant ∂θm i, if constant
Since the mechanical rotor angle θm satisﬁes θ = pθm ,

Te = pMf if i, sin θ . (7)

Note that if i = i0 sin ϕ then
3
Te = pMf if i0 sin ϕ, sin θ = pMf if i0 cos(θ − ϕ).
2
Note also that if if is constant then (7) with (4) yield
˙
Te θm = i, e .


Provision of a neutral line
The above analysis is based on the assumption that there is no
neutral line. If a neutral line is connected, then

ia + ib + ic = iN ,

where iN is the current ﬂowing through the neutral line. Then, the
formula for the stator ﬂux linkages (1) becomes
1
Φ = Ls i + Mf if cos θ − 1 M iN
1

and the phase terminal voltages (3) become
di 1 diN
v = −Rs i − Ls + 1 M + e,
dt 1 dt
where e is given by (4). The other formulae are not affected.

Real and reactive power
Deﬁne the generated real power P and reactive power Q as

P = i, e and Q = i, eq ,

π
where eq has the same amplitude as e but with a phase delayed by 2
, i.e.,

˙ π ˙
eq = θMf if sin(θ − ) = −θMf if cos θ.
2

Then, the real power and reactive power are, respectively,
˙
P = θMf if i, sin θ ,
˙
Q = −θMf if i, cos θ . (8)

Note that if i = i0 sin ϕ (as would be the case in the sinusoidal steady state), then

˙ 3˙
P = θMf if i, sin θ = θMf if i0 cos(θ − ϕ),
2
˙ 3˙
Q = −θMf if i, cos θ = θMf if i0 sin(θ − ϕ).
2
These coincide with the conventional deﬁnitions for real power and reactive power.

Electronic part
Power part
Interaction between the two parts
Simulation results

The electronic part (without control)
It is advantageous to assume that the ﬁeld (rotor) win-
ding of the synchronverter is fed by an adjustable DC
current source if instead of a voltage source vf . In this
case, the terminal voltage vf varies, but this is irrele-
vant. As long as if is constant, there is
˙sin θ − Mf dif cos θ.
e = Mf if θ
dt
˙
= θMf if sin θ. (9)
Also the effect of the neutral current iN can be ignored
if M is chosen as 0, because
di 1 diN
v = −Rs i − Ls + 1 M + e.
dt 1 dt

¨ = 1 (Tm − Te − Dpθ),
θ ˙
J Dp

-
Te = pMf if i, sin θ , Tm 1 θ& 1 θ
Js s
-
Te
Eqn. (7)
˙
e = θMf if sin θ, Q Eqn. (8)
Eqn. (9) e
Mf if i

˙
Q = −θMf if i, cos θ .


The power part
This part consists of three phase legs and a three-
phase LC ﬁlter, which is used to suppress the switching
noise. If the inverter is to be connected to the grid, then
three more inductors Lg (with series resistance Rg ) and
a circuit breaker can be used to interface with the grid.
+
Circuit
ia vga
ea vb
VDC ib vgb
eb
vc
ec ic vgc

C
-

di
v = −Rs i − Ls + e.
dt

Interaction between the two parts
The switches in the inverter are operated so that
the average values of ea , eb and ec over a
switching period should be equal to e given in
(9), which can be achieved by the usual PWM
techniques.
The phase currents are fed back to the electronic
part.
+
Dp
Circuit
ia vga
- ea
Tm 1 θ& 1 θ vb
VDC ib vgb
Js s eb
- vc
ec ic vgc
Te
Eqn. (7)
Q Eqn. (8)
Eqn. (9)
C
e
-
Mf if i


Operation objectives
Regulation of P and frequency drooping
Regulation of Q and voltage drooping
Complete electronic part
Simulation results

Operation objectives
The frequency should be maintained, e.g. at 50Hz

The output voltage should be maintained, e.g. at
230V

The generated/consumed real power should be re-
gulated

The reactive power should be regulated, if connec-
ted to the grid


Frequency drooping
The speed regulation system of the prime mover for a conventio-
nal synchronous generator can be implemented in a synchronver-
˙
ter by comparing the virtual angular speed θ with the angular fre-
˙
quency reference θr before feeding it into the damping block Dp .
As a result, the damping factor Dp actually behaves as the fre-
quency drooping coefﬁcient, which is deﬁned as the ratio of the
required change of torque ∆T to the change of speed (frequency)
∆θ:˙
∆T ˙
∆T θn Tmn
Dp = = ,
∆θ˙ Tmn ∆θ ˙ θn
˙
where Tmn is the nominal mechanical torque. Because of the
built-in frequency drooping mechanism, a synchronverter auto-
matically shares the load with other inverters of the same type
and with SGs connected on the same bus.

Complete electronic part
Dp θr
&
-
Reset θg

Pset p Tm 1 θ& 1 θ
θ&
n Js s
-
θc

Fromto the power part
Te
Eqn. (7)
Q Eqn. (8)
PWM
Eqn. (9)
e generation
- Mf if
Qset 1 i
Ks

Dq
- Amplitude v fb
vm detection
vr


Voltage drooping
The regulation of reactive power Q flowing out of the synchron-
verter can be realised similarly. Define the voltage drooping co-
efficient Dq as the ratio of the required change of reactive power
∆Q to the change of voltage ∆v:
∆Q ∆Q vn Qn
Dq = = ,
∆v Qn ∆v vn
where Qn is the nominal reactive power and vn is the nominal
amplitude of terminal voltage v. The difference between the refe-
rence voltage vr and the amplitude of the feedback voltage vf b is
amplified with the voltage drooping coefficient Dq before adding
to the difference between the set point Qset and the reactive power
Q. The resulting signal is then fed into an integrator with a gain
1
K
to generate Mf if .

The synchronverter under simu./exp.

Parameters Values Parameters Values
Ls 0.45 mH Lg 0.45 mH
Rs 0.135 Ω Rg 0.135 Ω
C 22 µF Frequency 50 Hz
R 1000 Ω Line voltage 20.78 Vrms
Rated power 100 W DC voltage 42V
Dp 0.2026 Dq 117.88


Frequency (Hz)
50.2

Simulation results 50.1
50
50Hz
49.95Hz

49.9
49.8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

t = 0: Simulation started to 2
Amplitude of v-vg (V)

1.5
allow the PLL and 1
0.5
synchronverter to start up; 0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Normalised v
1.05
t = 1s: Circuit breaker on; 1.025
1

t = 2s: Pset = 80W; 0.975
0.95
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
P (W)
t = 3s: Qset = 60Var; 140
120
100
80
60
t = 4s: drooping mechanism 40
20
0
-20
enabled; 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Q (Var)
80

t = 5s: grid voltage decreased 60
40
20
by 5%. 0
-20
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Time (Second)


Experimental setup

The synchronverter is connected to the grid, three-phase 400V
50Hz, via a circuit breaker and a step-up transformer.
Q.-C. Z
HONG :S :I
YNCHRONVERTERS M S G – p. 29/41
NVERTERS THAT IMIC YNCHRONOUS ENERATORS

Experimental results
The experiments were carried out according to the fol-
lowing sequence of actions:
1. start the system, but keeping all the IGBTs off;
2. start operating the IGBTs, roughly at 2s;
3. turn the circuit breaker on, roughly at 6s;
4. apply instruction Pset = 70W, roughly at 11s;
5. apply instruction Qset = 30 Var, roughly at 16s;
6. enable the drooping mechanism, roughly at 22s;
7. stop data recording, roughly at 27s.


Case 1: Grid frequency > 50Hz

v and vg (amplitude, V)
s
d
Frequency (Hz)

dvg

s
dv

Time (Second) Time (Second)

(a) synchronverter frequency (c) amplitude of v and vg

y
ˆ
ˆ

P (W) and Q (Var)
P
v − vg (V)

Q
©


(b) voltage difference v − vg (d) P and Q

Case 2: Grid frequency < 50Hz

v and vg (amplitude, V)
s
d
Frequency (Hz)

dvg

s
dv


(a) synchronverter frequency (c) amplitude of v and vg

P (W) and Q (Var)
s
d
v − vg (V)

d
P
Q

©


(b) voltage difference v − vg (d) P and Q

Distributed generation and renewable energy, allowing
these sources to take part in the regulation of power system
frequency, voltage and overall stability.
Uninterrupted power supplies (UPS), in particular, the
parallel operation of multiple UPSs
Isolated/distributed power supplies, e.g. to replace rotary
frequency converters
Static synchronous compensator (STATCOM) to improve
power factor
HVDC transmission (at the receiving end)
Induction heating


Current status of the technology
Patent application ﬁled, entered into
the PCT stage and the national phase.
A Senior Research Fellowship
(one-year) was awarded by the Royal
Academy of Engineering to further
develop this technology for 2009-2010.
Conference paper appeared
Journal paper appeared in IEEE Trans.
on Industrial Electronics
Applied to AC drives — AC Ward
Leonard drive systems
Numerous requests from worldwide
researchers Q.-C. Z :S
HONG YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 34/41

Summary
An approach is proposed to operate inverters to mimic synchronous
generators after establishing the mathematical model of synchronous
generators. Such inverters are called synchronverters.

Synchronverters can be operated in island mode or grid-connected
mode. When it is connected to the grid, it can take part in the regulation
of power system via frequency and voltage drooping.

No external communication is needed for parallel operation.

The energy ﬂow between the DC bus and the AC bus changes direction
automatically according to the grid frequency.

It can disconnect from the grid and can automatically re-synchronise
and re-connect with the grid.

Potential applications include grid connection of renewable energy
sources, parallel operation of UPS, HVDC transmission, STATCOM,
isolated/distributed power supplies etc.

Further details
Full-text paper:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&
arnumber=5456209

BibTex entry:
@ARTICLE{ZhongW.IEEE:09, author = {Q.-C.
Zhong and G. Weiss}, title = {Synchronverters:
{I}nverters that mimic synchronous generators}, jour-
nal = {{IEEE} Trans. Ind. Electron.}, year = {2011},
volume = {58}, pages = {1259–1267}, number = {4},
month = {Apr.} }


Other activities in PE
DC grid/bus
AC bus

G G
~
Generic Topology

…
~ Grid
or
Load
G Energy
~

…
Storage
System
~

1. MPPT 5. Energy management 7. Power quality improvement
Technologies

2. AC drives 6. Bi-directional DC/DC conversion 8. Parallel operation of inverters
3. DC/DC conversion 9. Grid-friendly connection
4. DC drives 10. Power flow control
11. Synchronisation
12. Provision of a neutral line


Activities in automotive engineering
Rapid control prototyping (RCP) and
Hardware-in-the-loop (HIL) simulation
dSPACE systems
MicroGen systems
Developing a powerful HIL system

Hybrid electrical vehicles
HEV driver model
AC Ward Leonard drive systems
Charging systems with grid support
EPSRC Future project: Energy ﬂow/storage/management
systems

Initial work done on engine control

Activities in chemical engineering
Control of integral processes with dead-time: A research monograph, Control of Integral
Processes with Dead Time, jointly with Antonio Visioli from Italy, is to appear in 2010.

Disturbance observer-based control strategy

Dead-beat response

Stability region on the control parameter space

Achievable speciﬁcations etc

Practical experience with a production line
Advances in Industrial Control

16 reactors, controlled by 3 industrial computers
Antonio Visioli
Qing-Chang Zhong
Effective object code > 100 KB (Intel 8086 assembler)
1 Control of
Analogue control variables and measurements etc. Integral Processes
with Dead Time
Continuous Stirred Tank Reactor (CSTR) System


Activities in control theory
Mainly three threads:

Robust control of time-delay systems: A series of fundamental problems in this area have
been solved:

Projections

J-spectral factorisation

Delay-type Nehari problem

Standard H ∞ problem of single-delay systems

Unified Smith predictor

Realisation of distributed delays in controllers
Infinite-dimensional systems: applied the generic theory of infinite-dimensional systems
to time-delay systems and solved problems about feedback stabilizability, approximate
controllability, passivity etc
Uncertainty and disturbance estimator (UDE)-based robust control: can be applied to li-
near or nonlinear, time-varying or time-invariant systems with or without delays; attracted
several Indian groups to work on this.

Inverters that mimic synchronous generators

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