Your SlideShare is downloading. ×
Synchronverters: Inverters that Mimic Synchronous Generators
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

Introducing the official SlideShare app

Stunning, full-screen experience for iPhone and Android

Text the download link to your phone

Standard text messaging rates apply

Synchronverters: Inverters that Mimic Synchronous Generators

1,928
views

Published on

Inverters are made mathematically equivalent to conventional synchronous generators, which considerably facilitates the integration of renewable energy and distributed generation into smart grids. …

Inverters are made mathematically equivalent to conventional synchronous generators, which considerably facilitates the integration of renewable energy and distributed generation into smart grids.

Published in: Technology, Business

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
1,928
On Slideshare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
40
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. 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
  • 2. 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
  • 3. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 3/41
  • 4. 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 knowledgeThese sources are connected to the grid via commonkey devices called inverters so it is possible to tacklethese problems via properly controlling the inverters. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 4/41
  • 5. Our solutionTurning 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) Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 5/41
  • 6. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 6/41
  • 7. 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 - Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 7/41
  • 8. Modelling of synchronous generators Motivation and relevant works Modelling of synchronous generators Electrical part Mechanical part 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. 8/41
  • 9. SG: Electrical partConsider a round rotor (θ = 0 )machine (without dam-per windings), with p Rotor field axispairs of poles per phase Rs , L(and p pairs of poles Rotationon the rotor) and withno saturation effects in M Mthe iron core. The N Field voltagestator windings can be Rs , L Rs , Lregarded as concentra-ted coils having self-inductance L and mu- Mtual inductance −M . Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 9/41
  • 10. NotationDefine     Φa ia Φ =  Φb  , i =  ib  Φc icand     cos θ sin θcos θ =  cos(θ − 2π )  , 3 sin θ =  sin(θ − 2π )  . 3 cos(θ − 4π ) 3 sin(θ − 4π ) 3 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 10/41
  • 11. Flux linkageThe field (or rotor) winding can be regarded as a concentratedcoil having self-inductance Lf . The mutual inductance betweenthe field coil and each of the three stator coils is Mf cos θ. Assumethat the neutral line is not connected, then ia + ib + ic = 0. Thestator 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 secondterm Mf i, cosθ is constant if the three phase currents are sinu-soidal (as functions of θ) and balanced. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 11/41
  • 12. Voltage TThe phase terminal voltages v = va vb vc are dΦ di v = −Rs i − = −Rs i − Ls + e, (3) dt dtwhere Rs is the resistance of the stator windings and Te= ea eb ec is the back emf ˙sin θ − Mf dif cos θ. e = Mf if θ (4) dtThe field terminal voltage, from (2), is dΦf vf = −Rf if − , (5) dtwhere Rf is the resistance of the rotor winding. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 12/41
  • 13. SG: Mechanical partThe 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 rotatingwith the rotor, Tm is the mechanical torque, Te is theelectromagnetic toque and Dp is a damping factor. Tecan be found from the energy E stored in the machinemagnetic 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 13/41
  • 14. Electromagnetic torque Te ∂E ∂E Te = =− . ∂θm Φ, Φf constant ∂θm i, if constantSince 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). 2Note also that if if is constant then (7) with (4) yield ˙ Te θm = i, e . Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 14/41
  • 15. Provision of a neutral lineThe above analysis is based on the assumption that there is noneutral line. If a neutral line is connected, then ia + ib + ic = iN ,where iN is the current flowing through the neutral line. Then, theformula for the stator flux linkages (1) becomes 1 Φ = Ls i + Mf if cos θ − 1 M iN 1and the phase terminal voltages (3) become di 1 diN v = −Rs i − Ls + 1 M + e, dt 1 dtwhere e is given by (4). The other formulae are not affected. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 15/41
  • 16. Real and reactive powerDefine the generated real power P and reactive power Q as P = i, e and Q = i, eq , πwhere 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. 2Then, 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). 2These coincide with the conventional definitions for real power and reactive power. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 16/41
  • 17. Implementation of a synchronverter Motivation and relevant works Modelling of synchronous generators Implementation of a synchronverter Electronic part Power part Interaction between the two parts 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. 17/41
  • 18. The electronic part (without control)It is advantageous to assume that the field (rotor) win-ding of the synchronverter is fed by an adjustable DCcurrent source if instead of a voltage source vf . In thiscase, 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 ignoredif M is chosen as 0, because di 1 diN v = −Rs i − Ls + 1 M + e. dt 1 dt Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 18/41
  • 19. ¨ = 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 . Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 19/41
  • 20. 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 inductors Lg (with series resistance Rg ) anda circuit breaker can be used to interface with the grid. + Circuit Ls , R s va Lg , R g Breaker ia vga ea vb VDC ib vgb eb vc ec ic vgc C - di v = −Rs i − Ls + e. dt Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 20/41
  • 21. 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 Ls , R s va Lg , R g Breaker ia vga - eaTm 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 21/41
  • 22. Operation of a synchronverter Motivation and relevant works Modelling of synchronous generators Implementation of a synchronverter Operation of a synchronverter Operation objectives Regulation of P and frequency drooping Regulation of Q and voltage drooping Complete electronic part Simulation results Experimental setup and results Potential applications Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 22/41
  • 23. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 23/41
  • 24. Frequency droopingThe 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 therequired 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 thebuilt-in frequency drooping mechanism, a synchronverter auto-matically shares the load with other inverters of the same typeand with SGs connected on the same bus. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 24/41
  • 25. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 25/41
  • 26. Voltage droopingThe 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 vnwhere Qn is the nominal reactive power and vn is the nominalamplitude of terminal voltage v. The difference between the refe-rence voltage vr and the amplitude of the feedback voltage vf b isamplified with the voltage drooping coefficient Dq before addingto the difference between the set point Qset and the reactive powerQ. The resulting signal is then fed into an integrator with a gain 1K to generate Mf if . Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 26/41
  • 27. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 27/41
  • 28. Frequency (Hz) 50.2Simulation 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) Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 28/41
  • 29. Experimental setupThe synchronverter is connected to the grid, three-phase 400V50Hz, 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
  • 30. 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 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. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 30/41
  • 31. 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 ©   Time (Second) Time (Second) (b) voltage difference v − vg (d) P and Q Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 31/41
  • 32. Case 2: 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 P (W) and Q (Var) s d v − vg (V) d P Q   ©   Time (Second) Time (Second) (b) voltage difference v − vg (d) P and Q Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 32/41
  • 33. Potential applications 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 33/41
  • 34. 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
  • 35. 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. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 35/41
  • 36. Further detailsFull-text paper:http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5456209BibTex 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.} } Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 36/41
  • 37. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 37/41
  • 38. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 38/41
  • 39. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 39/41
  • 40. 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 Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 40/41
  • 41. Activities in control theoryMainly 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. Q.-C. Z HONG : S YNCHRONVERTERS : I NVERTERS THAT M IMIC S YNCHRONOUS G ENERATORS – p. 41/41