synchronverters inverters that mimic synchronous generators

SYNCHRONVERTERS: INVERTERS THAT MIMICSYNCHRONOUS GENERATORS

Qing-Chang Zhong

Dept. of Electrical Eng. & Electronics

The University of Liverpool

UK

Email: [email protected]

George Weiss

Dept. of Electrical Eng. Systems

Tel Aviv University

Israel

E-mail: [email protected]

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

Q.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 2/34

MotivationIncreasing share of renewable energy

UK: 20% by 2020EU: 22% target for the share of renewable energy

sources and an18% target for the share of CHP in

electricity generation by2010

Regulation of system frequency and voltage: Currently

most inverters feed currents to the grid and do not take part

in system regulation and there is a need of voltage

controlled inverters to connect with weak grids.Threat to power system stability: Inverters have different

dynamics from conventional synchronous generatorsThe need of smooth transition of knowledge


Our solution

Synchronverters: Inverters that mimicsynchronous generators

Operate voltage source inverters to mimicsynchronous generators

Take part in the power system regulation offrequency and voltage: the same as synchronousgenerators (externally)

Dynamically behave like synchronous generators(internally)


Relevant worksVirtual synchronous machine (VISMA) by Beck and Hesse

The voltages at the point of common coupling with the grid aremeasured 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 synchronousgenerator 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 generatorQ.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 5/34

Some basics about inverters+

-

Rs, Ls va

vb

vc

ia

ib

ic

ea

eb

ec

VDC

C





Electrical partMechanical part



Simulation results


Potential applications


SG: Electrical partConsider a round ro-

tor machine (without

damper windings), with

p pairs of poles per

phase (andp pairs of

poles on the rotor) and

with no saturation ef-

fects in the iron core.

The stator windings can

be regarded as concen-

trated coils having self-

inductanceL and mu-

tual inductance−M .

M

M M

Rs , L Rs , L

Rs , L

Rotor field axis

( 0=θ )

Field voltage

Rotation

N


NotationDefine

Φ =

Φa

Φb

Φc

, i =

iaibic

and

cosθ =

cosθcos(θ − 2π

3)

cos(θ − 4π3)

, sinθ =

sinθ

sin(θ − 2π3)

sin(θ − 4π3)

.


Flux linkageThe field (or rotor) winding can be regarded as a concentrated

coil having self-inductanceLf . The mutual inductance between

the field coil and each of the three stator coils isMf cosθ. Assume

that the neutral line is not connected, thenia + ib + ic = 0. The

stator flux linkages are

Φ = Lsi + Mf if cosθ, (1)

whereLs = L + M , and the field flux linkage is

Φf = Lf if + Mf 〈i, cosθ〉 , (2)

where〈·, ·〉 denotes the conventional inner product. The second

termMf 〈i, cosθ〉 is constant if the three phase currents are sinu-

soidal (as functions ofθ) and balanced.Q.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 10/34

Voltage

The phase terminal voltagesv =[

va vb vc

]T

are

v = −Rsi −dΦ

dt= −Rsi − Ls

di

dt+ e, (3)

whereRs is the resistance of the stator windings and

e =[

ea eb ec

]T

is the back emf

e = Mf if θsinθ − Mf

dif

dtcosθ. (4)

The field terminal voltage, from (2), is

vf = −Rf if −dΦf

dt, (5)

whereRf is the resistance of the rotor winding.Q.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 11/34

SG: Mechanical partThe mechanical part of the machine is governed by

Jθ = Tm − Te − Dpθ, (6)

whereJ is the moment of inertia of all parts rotatingwith the rotor,Tm is the mechanical torque,Te is theelectromagnetic toque andDp is a damping factor.Te

can be found from the energyE stored in the machinemagnetic field, i.e.,

E =1

2〈i, Φ〉 +

1

2ifΦf

=1

2〈i, Lsi〉 + Mf if 〈i, cosθ〉 +

1

2Lf i

2

f .


Electromagnetic torque Te

Te =∂E

∂θm

∣∣∣∣Φ,Φf constant

= −∂E

∂θm

∣∣∣∣i, if constant

.

Since the mechanical rotor angleθm satisfiesθ = pθm,

Te = pMf if

⟨i, sinθ

⟩. (7)

Note that ifi = i0sinϕ then

Te = pMf if i0

⟨sinϕ, sinθ

⟩=

3

2pMf if i0cos(θ − ϕ).

Note also that ifif is constant then (7) with (4) yield

Teθm = 〈i, e〉 .


Provision of a neutral lineThe above analysis is based on the assumption that there is no

neutral line. If a neutral line is connected, then

ia + ib + ic = iN ,

whereiN is the current flowing through the neutral line. Then, the

formula for the stator flux linkages (1) becomes

Φ = Lsi + Mf if cosθ −[

111

]MiN

and the phase terminal voltages (3) become

v = −Rsi − Ls

di

dt+

[111

]M

diN

dt+ e,

wheree is given by (4). The other formulas are not affected.


Real and reactive powerDefine the generated real powerP and reactive powerQ as

P = 〈i, e〉 and Q = 〈i, eq〉 ,

whereeq has the same amplitude ase but with a phase delayed byπ2

, i.e.,

eq = θMf if sin(θ −π

2) = −θMf if cosθ.

Then, the real power and reactive power are, respectively,

P = θMf if

⟨i, sinθ

⟩,

Q = −θMf if 〈i, cosθ〉 . (8)

Note that ifi = i0sinϕ (as would be the case in the sinusoidal steady state), then

P = θMf if

⟨i, sinθ

⟩=

3

2θMf if i0cos(θ − ϕ),

Q = −θMf if 〈i, cosθ〉 =3

2θMf if i0sin(θ − ϕ).

These coincide with the conventional definitions for real power and reactive power.






Electronic partPower partInteraction between the two parts


Simulation results


Potential applicationsQ.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 16/34

The electronic part (without control)It is advantageous to assume that the field (rotor) wind-ing of the synchronverter is fed by an adjustable DCcurrent sourceif instead of a voltage sourcevf . In thiscase, the terminal voltagevf varies, but this is irrele-vant. As long asif is constant, there is

e = Mf if θsinθ − Mf

dif

dtcosθ.

= θMf if sinθ. (9)

Also the effect of the neutral currentiN can be ignoredif M is chosen as0, because

v = −Rsi − Ls

di

dt+

[111

]M

diN

dt+ e.


θ =1

J(Tm − Te − Dpθ),

Te = pMf if

⟨i, sinθ

⟩,

e = θMf if sinθ,

Q = −θMf if 〈i, cosθ〉 .

Te Eqn. (7) Eqn. (8) Eqn. (9)

s

1

Dp

Tm

-

θ θ&

i

e

Mf if

Q

Js

1

-


The power partThis part consists of three phase legs and a three-phase LC filter, which is used to suppress the switchingnoise. If the inverter is to be connected to the grid, thenthree more inductorsLg (with series resistanceRg) anda circuit breaker are needed to interface with the grid.

+

-

Ls , Rs va

vb

vc

ia

ib

ic

ea

eb

ec

VDC

C

vga

vgb

vgc

Circuit Breaker

Lg , Rg

v = −Rsi − Ls

di

dt+ e.


Interaction between the two partsThe switches in the inverter are operated so thatthe average values ofea, eb andec over aswitching period should be equal toe given in(9), which can be achieved by the usual PWMtechniques.

The phase currents are fed back to the electronicpart.

Te Eqn. (7) Eqn. (8) Eqn. (9)

s

1

Dp

Tm

-

θ θ&

i

e

Mf if

Q

Js

1

-

+

-

Ls , Rs va

vb

vc

ia

ib

ic

ea

eb

ec

VDC

C

vga

vgb

vgc

Circuit Breaker

Lg , Rg


Operation of a synchronverterMotivation and relevant works




Operation objectivesRegulation ofP and frequency droopingRegulation ofQ and voltage droopingComplete electronic part

Simulation results


Potential applicationsQ.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 21/34

Operation objectives

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

The output voltage should be maintained, e.g. at230V

The generated/consumed real power should beregulated

The reactive power should be regulated, if con-nected to the grid


Frequency droopingThe speed regulation system of the prime mover for a conven-

tional synchronous generator can be implemented in a synchron-

verter by comparing the virtual angular speedθ with the angular

frequency referenceθr before feeding it into the damping block

Dp. As a result, the damping factorDp actually behaves as the

frequency drooping coefficient, which is defined as the ratioof the

required change of torque∆T to the change of speed (frequency)

∆θ:

Dp =∆T

∆θ=

∆T

Tmn

θn

∆θ

Tmn

θn

,

whereTmn 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.Q.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 23/34

Voltage droopingThe regulation of reactive powerQ flowing out of the synchron-

verter can be realised similarly. Define the voltage drooping co-

efficientDq as the ratio of the required change of reactive power

∆Q to the change of voltage∆v:

Dq =∆Q

∆v=

∆Q

Qn

vn

∆v

Qn

vn

,

whereQn is the nominal reactive power andvn is the nominal

amplitude of terminal voltagev. The difference between the ref-

erence voltagevr and the amplitude of the feedback voltagevfb is

amplified with the voltage drooping coefficientDq before adding

to the difference between the set pointQset and the reactive power

Q. The resulting signal is then fed into an integrator with a gain1K

to generateMf if .Q.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 24/34

Complete electronic part

Js

1

Te Eqn. (7) Eqn. (8) Eqn. (9)

s

1

Dp

Tm

-

θ θ&

i

e

rθ&-

Dq

rv

Qset -

-

Mf if

Ks

1

Q

n

p

θ& Pset

PWM generation

Fro

m\to

the

pow

er

part

fbv

Reset gθ

Amplitude detection

cθ

mv


The synchronverter under simu./exp.

Parameters Values Parameters Values

Ls 0.45 mH Lg 0.45 mHRs 0.135 Ω Rg 0.135 Ω

C 22µF Frequency 50 HzR 1000 Ω Line voltage 20.78 Vrms

Rated power 100 W DC voltage 42VDp 0.2026 Dq 117.88


Simulation results

t = 0: Simulation started to

allow the PLL and

synchronverter to start up;

t = 1s: Circuit breaker on;

t = 2s: Pset = 80W;

t = 3s: Qset = 60Var;

t = 4s: drooping mechanism

enabled;

t = 5s: grid voltage decreased

by 5%.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 649.8

49.9

50

50.1

50.2Frequency (Hz)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60

0.5

1

1.5

2 Amplitude of v-vg (V)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60.95

0.975

1

1.025

1.05Normalised v

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-20

020406080

100120140 P (W)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6-20

020406080

Time (Second)

Q (Var)

50Hz49.95Hz


Experimental setup

The synchronverter is connected to the grid, three-phase 400V50Hz, via a circuit breaker and a step-up transformer.


Experimental resultsThe 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 at2s;

3. turn the circuit breaker on, roughly at6s;

4. apply instructionPset = 70W, roughly at11s;

5. apply instructionQset = 30 Var, roughly at16s;

6. enable the drooping mechanism, roughly at22s;

7. stop data recording, roughly at27s.


Case 1: Grid frequency > 50Hz

Time (Second)

Fre

quen

cy(H

z)

(a) synchronverter frequency

Time (Second)

v−

vg(V

)

(b) voltage differencev − vg

Time (Second)

van

dv

g(a

mpl

itude

,V)

v@I

vg@

@I

(c) amplitude ofv andvg

Time (Second)

P(W

)an

dQ

(Var

)

PXXy

Q

(d) P andQQ.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 30/34

Case 2: Grid frequency < 50Hz

Time (Second)

Fre

quen

cy(H

z)

(a) synchronverter frequency

Time (Second)

v−

vg(V

)

(b) voltage differencev − vg

Time (Second)

van

dv

g(a

mpl

itude

,V)

v@I

vg@

@I

(c) amplitude ofv andvg

Time (Second)

P(W

)an

dQ

(Var

)

P@@I

Q

(d) P andQQ.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 31/34

Potential applicationsDistributed 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

Funding received for building proper

prototypes & commercialisation

Conference paper appeared in

ieeexplore

Journal paper to appear inIEEE

Industrial Electronics

Applied to AC drives — AC Ward

Leonard drive systems (PEMD2010)


SummaryAn 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 frequency

and voltage, via frequency and voltage drooping.

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 transmis-

sion, STATCOM, isolated/distributed power supplies etc.Q.-C. ZHONG & G. WEISS: SYNCHRONVERTERS: INVERTERS THAT MIMIC SYNCHRONOUS GENERATORS– p. 34/34

synchronverters inverters that mimic synchronous generators

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