Reduction of DC-link Voltage Oscillations during Unbalanced Conditions by Utilizing

Converter Terminals

As mentioned in section 3.5.1, it can be a relevant option to synchronize the control system to the Virtual Flux estimated at the terminals of the converter, as labelled

“Converter Flux Oriented Control” in [156], [201]. This approach was also shown to have a positive influence on the performance of the particular current control strategy applied in [156]. The approach of synchronizing to the converter terminals will however have further relevant implications in the case of control under unbalanced grid voltage conditions.

One of the major objectives in many publications related to operation of VSCs during unbalanced conditions is to limit voltage oscillations in DC-link of the converter by eliminating second harmonic oscillations in the active power flow as discussed in [34], [31], [89], [98], [206], [207], [221]. For zero average reactive power reference, this corresponds to active power control by the PNSC strategy. Elimination of power oscillations at the grid side of the filter inductor, usually labelled as “Input-Power-Control” (IPC), will however reduce but not entirely eliminate the DC-link voltage oscillations, since the unbalanced currents flowing in the filter inductance will cause active power oscillations that will be reflected in the DC-link voltage of the converter.

Therefore, a simple method for current reference calculation with the objective of compensating for the influence of the filter inductors by that achieving elimination of DC-link voltage oscillations during unbalanced conditions have been proposed [222].

This approach is usually labelled as “Output-Power-Control” (OPC). More advanced methods have also been proposed with the purpose of controlling the active power flow to be constant at the terminals of the converters while at the same time achieving zero or controllable average reactive power flow at the grid side of the filter inductor and by that unity displacement power factor at the point of connection to the grid [31], [99], [223]. Such methods are usually labelled as Input-Output-Power-Control (IOPC).

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Iterative methods for achieving current references that causes elimination of double frequency active power oscillations at the converter terminals have also been recently proposed [224].

For Virtual Flux-based operation, the Output-Power-Control (OPC) strategy mentioned above is corresponding to the case of active power control by PNSC with zero as reference for the average reactive power and with Virtual Flux estimation at the grid side of the filter inductor as described and illustrated by experimental results in section 4.4.4.

By utilizing the possibility to estimate the Virtual Flux at the converter terminals, Virtual Flux-based Input-Power-Control (IPC) can also be easily achieved in a simpler way than for voltage-based grid synchronization and power control. The Virtual Flux at the converter terminals is as mentioned easily estimated by specifying the resistance r1

and the inductance l1 to be zero, and the elimination of the double frequency active power oscillations is then easily achieved by using the PNSC strategy. A set of experimental results illustrating such a case is shown in Fig. 4-14.

Among the results plotted in the figure, Fig. 4-14 (a) and (b) are showing the three-phase voltages and currents measured at the grid side of the filter inductor, while Fig. 4-14 (c) is showing the active and reactive powers calculated from these signals. The PNS Virtual Flux signals used for the current reference calculation are however estimated at the grid side of the filter inductor, and the active and reactive powers calculated from these signals and the PNS current components are shown in Fig. 4-14 (d). From the curves in Fig. 4-14 (d), it can be clearly seen that a constant value of 1.0 pu active power at the converter terminals is achieved in steady state conditions for both balanced and unbalanced operation. The average reactive power flow is also kept at the reference value of 0, although the expected double frequency oscillations are occuring under the unbalanced conditions.

Studying Fig. 4-14 (c), it can be seen that the active power flow at the grid side of the filter inductor is slightly below the 1.0 pu at the converter terminals, due to the losses in the filter inductor. Similarly, it can be seen that a negative reactive power is flowing, since the reactive power consumption of the filter inductor must be covered from the grid side when the converter is controlling zero reactive power flow. When the unbalanced voltage sag occurs, the differenced between the average active and reactive powers at the converter side and at the grid side is increased, since the current is increased to keep the average active power at its reference value. During the unbalanced conditions, a small double frequency oscillation can also be observed in the active power flow at the grid side of the filter inductor, as expected due to the unbalanced currents required to eliminate double frequency active power oscillations at the converter terminals.

The results from Fig. 4-14 verify how the objective of Output-Power-Control during unbalanced conditions can be easily achieved by DSOGI-VF-based voltage-sensor-less control. The same characteristics could also be achieved for simultaneous control of active and reactive power at the converter terminals by using the AARC strategy corresponding to kq = 1 for the calculation of the reactive current reference. Input-Output-Power-Control could also be achieved by Virtual Flux-based voltage-sensor-less control by simultaneously estimating the PNS Virtual Flux signals at the converter terminals and at the grid side of the filter inductor by using the extended DSOGI-VF

4.5 Further Application Examples of the Developed Strategies for Virtual Flux-based Active and Reactive Power Control

Jon Are Suul 97

estimation method shown in Fig. 3-16. This approach is however not further investigated in this setting.

It is however important to note that strategies for eliminating double frequency oscillations in the active power flow can only be applied for limited degree of grid voltage unbalance. This can be seen from the equations for current reference calculation in (4.28), since an amplitude of the negative sequence Virtual Flux component that is approaching the amplitude of the positive sequence component will cause the current amplitude to increase towards infinity. Strategies for limiting the current references will therefore be necessary to protect the converter during severe unbalanced conditions, as will be discussed in the next chapter.

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

-1 -0.5 0 0.5 1

Response to unbalanced voltage dip - Virtual Flux-based PNSC

v f [pu]

v_f,a v_f,b v_f,c

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

-1.5 -1 -0.5 0 0.5 1 1.5

i c [pu]

i_c,a i_c,b i_c,c

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

-1 -0.5 0 0.5 1 1.5

p v,i, q v,i [pu]

p - measurements q - measurements

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

-1 -0.5 0 0.5 1 1.5

Time [s]

p ,i, q ,i [pu]

p from PNS Virtual Flux q - from PSN Virtual Flux

(a)

(b)

(c)

(d)

Fig. 4-14 Experimental results with p = 1.0 pu, Virtual Flux estimation at the ^* converter terminals and active current reference calculation by PNSC (kp = 1) for

elimination of active power oscillations

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4.5.2 Control of Active and Reactive Power at a Remote Location