Virtual machine controller performance

Considering a converter connected to a strong grid, the performance of the virtual machine controller described in Section 5.4 will be verified via simulation in this section. For this, the

parameters of the system are set similar to the one in Table 5.1. A constant DC-link voltage is assumed and a PWM scheme with a switching frequency of 5 kHz is used for the converter control similar to the discussion in Section 5.5.1 .

Before testing the dynamic performance of the virtual machine controller for a step in the active and reactive power reference, the converter should be synchronized to the grid similar to the case in an actual synchronous machine. This is achieved by using a vector current controller and a PLL. Once the converter is connected to the grid with zero current injection, the grid frequency and angle outputs from the PLL will be used to initialize the speed and angle of the virtual machine controller, respectively.

The first test involves designing a virtual machine controller according to the description in Section 5.4 to verify if the design requirements are met in a time-domain simulation. For this purpose, a damping ratio of 0.1 and a natural frequency of 12.6 rad/s are chosen for the active power controller, which yields KDv = 17 and Hv = 3.38 s. For the reactive power controller,

the integrator gain is chosen as KQc = 18.5 to get a bandwidth of αQc = 62.8 rad/s. For this

choice of parameters, the dynamic performance of the virtual machine controller for a step in the active and reactive power reference is shown in Fig. 5.12. As it can be observed from the results, active and reactive power control are achieved with the desired design requirements through variation of the virtual angle and converter voltage magnitude, respectively.

Fig. 5.12 Dynamic performance of the virtual machine controller; (a) reference (gray) and actual (black) injected active power; (b) reference (gray) and actual (black) injected reactive power; (c) vir- tual angle deviation; (d) change in converter voltage magnitude.

As shown in the results in Fig. 5.12, the active and reactive power controllers work with a rea- sonably small coupling between them. Hence with zero reactive power injection, the impact of various parameters such as KDv and Hv on the dynamic performance of the active power

controller will be investigated next. The first set of tests is performed using a natural frequency ofωn = 12.6 and three different values of the damping coefficient, KDv = [67.9, 118.8, 169.8]

damping ratio ofς = 1.0 and three different values of the virtual inertia, Hv= [3.38, 0.54, 0.14]

corresponding to a natural frequency ofωn = [12.6, 31.4, 62.8], respectively. The dynamic re-

sponse of the active power controller for the various cases when a step in the reference active power is applied at 0.5 s is shown in Fig. 5.13.

Fig. 5.13 Impact of parameters on the active power controller; Injected active power (plot a), virtual speed deviation (plot b) and virtual angle deviation (plot c) withωn = 12.6 and ς = 0.4 (gray

dashed), ς = 0.7 (black solid) and ς = 1.0 (black dashed); Injected active power (plot d),

virtual speed deviation (plot e) and virtual angle deviation (plot f) withς = 1.0 and ωn = 12.6

(black dashed), ωn = 31.4 (black solid) and ωn = 62.8 (gray dashed); Gray solid curves

represent the injected active power reference.

As the results in Fig. 5.13 show, a higher damping ratio gives a well damped response. By choosing a damping ratio close to 1, an overshoot in the response of the injected active power can be avoided. On the other hand, the choice of the natural frequency is a compromise between response speed and emulated inertia. A higher choice of the natural frequency, correspondingly a lower virtual inertia, results in a faster response. However, this could be a disadvantage if the purpose of the converter is to provide some inertia support to the power system. Based on the requirement from the converter, the controller parameters can be selected.

A final test is made to investigate the performance of the virtual machine controller versus the classical cascade controller. For this purpose, the active power controller parameters are chosen as ς = 1.0 and ωn = 62.8 rad/s whereas the bandwidth of the reactive power controller is

chosen asαQc= 62.8 rad/s for the virtual machine controller. For comparison, an integral outer

loop active and reactive power controller that gives a bandwidth of 62.8 rad/s is selected for the classical cascade controller. The dynamic performance of the two controllers for a step in the active and reactive power reference is shown in Fig. 5.14.

Fig. 5.14 Comparison of the virtual machine controller versus the classical cascade controller; Injected active power (plot a) and reactive power (plot b) using virtual machine controller; Injected active power (plot c) and reactive power (plot d) using classical cascade controller; Gray curves represent reference power and black curves represent actual power.

The results in Fig. 5.14 show that the two control structures provide the required power reference tracking based on the design requirement. However, the virtual machine controller is slightly slower for this choice of parameters, due to the fact that the active power controller in (5.22) is a second-order system unlike the classical cascade controller, which is characterized by a first- order transfer function. If a similar performance as the classical cascade controller is required from the virtual machine controller, it can be achieved by adjusting the parametersHvandKDv.

One advantage with the classical cascade controller is that a reliable control of the converter current is possible during fast transients such as power system faults. On the other hand, the virtual machine controller has the capability of providing inertia support to the power system, where the added inertia value (Hv) can be calculated directly.

5.6

Experimental Verification

The obtained simulation results have been verified experimentally in the laboratory. A descrip- tion of the setup together with the experimental results will be presented in this section.

5.6.1

Laboratory setup

A single line diagram of the actual laboratory setup for the tests in this section is shown in Fig. 5.15. The setup consists of a VSC system connected to an AC grid. The grid voltage eg

contains about 0.015 pu5th_and7th_{order harmonics among others as shown in Fig. 5.16, where}

the FFT of the phase-to-ground voltage (phase a) is depicted.

Fig. 5.15 Single line diagram of the laboratory setup.

Fig. 5.16 FFT of measured phase-to-ground grid voltage.

The VSC system consists of a two-level converter connected to the AC grid though an L-filter. The parameters of the laboratory setup together with the controller parameters are the same as the ones in the simulation in Section 5.5. The VSC is controlled from a computer with a dSpace 1103 board [50]. The DC-link of the VSC is connected to a DC machine rated 700 V and 60 A, which gives the VSC active power injection capability. The terminal voltage of the DC machine is controlled to a constant value of 650 V and this has been used for all the tests. Moreover, PWM with a switching frequency of 5 kHz is used to generate the pulses for the VSC valves.

Fig. 5.17 Dynamic performance of vector-current controller for a step in current reference (dashed curves); conventional current controller response for d-component current (plot a) and q-component current (plot b); harmonic compensated current controller response for d-

component current (plot c) andq-component current (plot d).