The Synchronverter Control Technique
3.1 Grid Side - Inverter Control strategy
The Synchronverter control technology is based on the mathematical model of a synchronous machine, and a Synchronverter is thus defined in [27] and [28] as a converter that mimics a synchronous machine. It is therefore considered as a way of implementing a Virtual Synchronous Machine. The power part of a typical three-phase inverter is depicted in Figure 3.1, where the inverter is connected to a stiff grid.
Figure 3.1: Power part of a typical controllable inverter[27].
From Figure 3.1 it can be seen thatLsand Rsrepresents the inductance and resistance of the stator windings of the imaginary synchronous generator[27]. This means that the terminal voltages of the Synchronverter VSM are the capacitor voltages in Figure 3.1, and the output of the actual inverter will represent the back-Electromotive Force (EMF)eof the VSM due to the imaginary rotor movement. LsandC in additions functions as a filter to attenuate ripples due to the PWM switching.
The Synchronverter controller is located in the electronic part of the power electronic converter, where the mathematical model used is derived in Section 2.3.1. More specifically equations (2.16), (2.18) and (2.19b) will constitute the core of the controller along with the swing equa-tion[27]. Ultimately the control system will generate the reference for the PWM signals used to control the physical IGBTs in the power part of the converter. The objective of the grid side converter is to inject the correct amount of power to the grid when taking into account both the MPPT set-point from the turbine and the grid voltage and frequency. This should be achieved for the entire operating range of the wind turbine.
The control topology of the grid side controller in the Laplace domain is depicted in Figure 3.2. As can be seen, the inputs to the controller are the active power referencePref, the reactive power referenceQref, the converter currentic,grid, and the voltagevpcc, which will be the voltage at the Point of Common Coupling (PCC). When the Synchronverter is utilised in a WECS,Pref will be set by the MPPT of the turbine and thus follow (2.8) which gives the maximum power delivered by the wind turbine for a given wind speed. Usually, the power reference is set slightly below maximum to account for losses[30]. It is also possible to operate the turbine in a de-rated mode and thus further decrease the power set-point to an even lower percentage of the MPPT.
Pref is divided by the nominal speed of the system,ωn, to obtain the mechanical torque reference.
Note thatωncan be used in this division instead of the virtual frequency of the converterωas the relative difference between them is negligible[27]. Qref can be set based on the operator’s needs, making the utility achieve reactive power support if needed. ic,gridandvpcc are obtained through measurements using sensors. For easy interpretation of the control system depicted in Figure 3.2, the equations constituting the core of the controller are repeated here, using that the number of pole pairs in the imaginary machine is 1:
˙ ω = 1
J(Tm−Te−Dpω) (3.1a)
e=Mfifωsinfθ (3.1b)
Te=Mfifhic,grid,sinfθi (3.1c)
P =ωMfifhic,grid,sinfθi (3.1d)
Q=−ωMfifhic,grid,cosf θi (3.1e)
3.1.1 Active Power Control and Frequency Droop
It is clear that the controller consists of two control channels; one for the active power and one for the reactive power[29]. The Active Power Loop (APL) is the upper loop in Figure 3.2 and is governed by the swing equation using the mechanical torque reference, electrical torque and drooping torque. The mechanical torque reference is calculated as
Tm,ref = Pref
ωn (3.2)
Ca c a f
S ch A
A de
de ec S ch B
PWM ge e a
2 1 MPPT
Figure 3.2: Synchronverter control topology for inverter, modified from [27].
wherePref is slightly below the value calculated by (2.8) as explained above. The electromag-netic torque is calculated using (3.1c). The frequency drooping is implemented by comparing the virtual frequency of the converter ω to the system frequency reference ωn, yielding∆ω which is then multiplied with the frequency droop coefficientDp.Dp is here representing both the mechanical friction coefficient, i.e. the damping, and the drooping coefficient of a real synchronous generator[29], and is in [27] defined as
Dp =−∆T
∆ω (3.3)
where∆T is the change in mechanical torque applied to the imaginary rotor and∆ω is the change in frequency. The deviation between (Tm,ref + ∆T) and Te is then fed through an integrator via the inertia gain J1, yielding the speed of the converter.
Using this implementation method it can be seen that if the active power consumption decreases in the grid, resulting in a lowerTe, the speed of the converter will initially increase. However, by comparing the increased speed of the converter to the frequency reference, the drooping feedback will be negative and thus result in a reduced net mechanical torque set-point for the VSM. Thereby achieving the desired frequency control.
The active power loop ultimately controls the speedωof the VSM which again, by integration, yields the phase angleθof the back-EMFeof the VSM.eis the control signal used as reference for the PWM.
3.1.2 Reactive Power Control and Voltage Droop
The Reactive Power Loop (RPL) is the lower loop in Figure 3.2 and consists of the reactive power reference, actual reactive power injected and the voltage drooping. The reactive power reference is set by the operator, and the actual reactive power is calculated by use of (3.1e).
The voltage drooping is implemented by comparing the amplitude of the voltage at the Point of Common Coupling (PCC),Vm,pcc, to the grid voltage referenceVm,g, giving the voltage error
∆V which is then multiplied with the voltage droop coefficientDq. This term is then added to the reactive power deviation and fed through an integrator via the gain K1
q, creating the virtual Mfif of the VSM.Dq is in [27] defined as
Dq =−∆Q
∆V (3.4)
where∆Qis the required change in reactive power needed to change the voltage∆V volts. Note that the voltage droop in Figure 3.2 can be disabled by opening switch B.
Using this method it can be seen that if the grid voltage decreases, the drooping term will be positive and thus add to the net reactive power reference. This will, in turn, increase the reactive power injected to the grid by the converter, increasing the grid voltage. The desired voltage support is thus achieved.
The reactive power loop ultimately controls the amplitude E of e by adjusting the virtual Mfif. This means thate, which is used as reference signal for the PWM signals, now can be fully computed using (3.1b) as the controls governing both the amplitude and angle have been described. This completes the Synchronverter control technique for inverters.
3.1.3 Amplitude Detection
To successfully implement the control technique described above, some additional functionality needs to be introduced. In Section 3.1.2 the voltage drooping was implemented by comparing the amplitude ofvpcc to the grid voltage reference. However, to do this, an amplitude detector have to be implemented. Different methods exists in the literature to obtain the amplitude of the voltage, such as utilising a Phase Locked Loop (PLL), or the fact that in balanced systems we can write[47][27]:
vavb+vbvc+vcva=−3 4vm
whereva,b,care the phase voltages andvm is the amplitude.
However, for the application in this thesis the Clarke transformation, also known asα−β trans-formation, will be used to determine the amplitude of the grid voltage. The Clarke transformation is a mathematical transformation that transforms theabccomponents in the time domain of the three phase system intoαβγcomponents, and is given as[48]:
vαβγ =
When assuming a balanced three phase system it is known thatva+vb +vc = 0yielding the result thatvγ = 0[48]. Equation (3.5) can therefore be rewritten as
vαβ =
ultimately yielding the following definitions of theα- andβcomponents:
vα = 2 3va−1
3(vb+vc) (3.7a)
vβ = 1
√3(vb−vc) (3.7b)
It is now possible to calculate the amplitude of the voltage,vm, using (3.8), and this will be the method used to obtainVm,pccin Figure 3.2.
vm =q
vα2 +vβ2 (3.8)
3.1.4 Self Synchronisation
Another functionality that needs to be introduced is a way of synchronising the inverter controller with the grid before connection. This is important to avoid large transients that can damage the converters and to ensure a stable and secure connection.
The synchronisation is usually achieved by implementing a dedicated synchronisation unit, and many different methods for obtaining synchronisation exists in the literature. For example [49]
outlines the use of Zero-Crossing detection, PLLs and Sinusoidal Tracking Algorithms (STA).
However, in almost all power electronic equipment connected to the grid today, a basic PLL is used to obtain an accurate synchronisation[50]. The objective of the synchronisation unit is to provide the frequency, phase and amplitude of the fundamental component of the grid voltage, for which the PLL is well suited.
However, synchronisation units can have a negative impact on controller performance[51], and the PLL is in addition non-linear, making it difficult and time-consuming to tune the PLL parameters. It is therefore preferable, if possible, to omit the synchronisation unit altogether and instead implement the synchronisation functionality into the core of the controller. The method that will be used in this thesis was first proposed in [51] and utilises the inherent capabilities of the synchronous machine to synchronise with the grid. A slightly modified version will be explained here.
The active and reactive powers delivered to the grid by a synchronous machine can be approxim-ated, using amplitudes instead of RMS values, as[51]:
P = 3VgE
2X sin(θ−θg) (3.9a)
Q= 3Vg
2X[Ecos(θ−θg)−Vg] (3.9b) whereVgis the amplitude of the grid voltage,Eis the amplitude of the synchronous machines back-EMF,θis the angle of the machine andθg is the angle of the grid.X is the synchronous reactance of the machine. The objective is to synchronise the converter with the grid, i.e.:
E∠θ =Vg∠θg =⇒
(E =Vg
θ =θg (3.10)
and from (3.9a) and (3.9b) it can quickly be deduced that if the criteria in (3.10) is fulfilled, the active and reactive power injected into the grid will both be zero. This can be utilised in the synchronisation procedure for the Synchronverter as it will implye = vg. Setting the power set-points Pref = 0and Qref = 0during the initial synchronisation therefore means that the Synchronverter will control itself into synchronisation with the grid. As the synchronverter will be connected at the Point of Common Coupling the voltage at the PCC will be the voltage that the converter should be synchronised with, and thereforevpccwill be used in the procedure.
However, during the synchronisation process, i.e. before the converter is connected to the grid, the circuit breaker will be open, meaning the currentic,grid will be zero. The Synchronverter will therefore not be able to achieve synchronisation usingic,gridas feedback current to the controller as no regulation process is possible when the current is zero. Therefore, to overcome this problem, a synchronising loop will be implemented, injecting a virtual current into the controller so that the desired synchronisation is achieved. This means that during the synchronisation process the virtual current
is = e−vpcc Lsync·s+Rsync
(3.11) will be the input to the control system[51]. Here,Lsyncis a virtual inductor, sis the Laplace operator andRsync is a virtual resistor used to create the virtual current.iscan then be used in (3.1c) and (3.1e), along withPref = 0andQref = 0so thateis controlled to be synchronised with the grid voltage. This will also imply thatisis controlled to be zero and that the converter can be connected to the grid, i.e. the breaker can be closed, without large transients. After connection to the grid the real currentic,gridwill be fed into the controller instead of the virtual current by switching switch A in Figure 3.2 from position 1 to position 2. The active and reactive power set-points will also be changed to reflect the desired operation. The part of the controller implementing the synchronisation capability is depicted in the far right of Figure 3.2. Using this type of synchronisation greatly reduces controller complexity and increases overall efficiency and performance[51].
3.1.5 Set-Point Limiter and Saturation
To ensure that the control system does not operate the system at an operating point beyond the capabilities of the converters, limitations and saturation should be implemented to limit the active- and reactive power set-points. This will be done using a strategy which is prioritising
active power over reactive power. The power set-points are based on the reference power and the drooping so that
Pset =Tsetωn=
Tm−Dp(ω−ωn)
ωn (3.12a)
Qset =Qref +Dq(Vm,g−Vm,pcc) (3.12b)
Firstly, the set-points are saturated so thatTset ∈[0,Sωn
n]andQset ∈[0, Sn], whereSnis the rated apparent power. In addition, the total apparent power set-point of the inverter should not exceed the rated apparent power, i.e.
pPset2 +Q2set ≤Sn (3.13)
A check is therefore implemented so verify that the criterion in (3.13) is satisfied. If this is not the casePset remains unchanged whileQsetis set as
Qset = q
Sn2−Pset2 (3.14)
Note that if the originalQset is negative, i.e. the voltage at the PCC is sufficiently high so that the voltage drooping brings the reactive power set-point below zero, the check in (3.13) may give a wrong result. Therefore, ifQset <0,Qset = 0is used. The actual set-point limiter implemented into the Simulation model can be found in Appendix C.1, Figure C.6.