Voltage source control of offshore all‐DC wind farm

The fast growth of offshore all-DC wind farm will bring problems such as the weakening of grid frequency stability and the increase of equivalent grid impedance. To overcome this, a coordination control strategy for offshore all-DC wind farm is proposed in this study with two salient features: better performance under weak grid condition, and real-time frequency support from wind farm. This strategy consists of three parts: the inertia synchronising control of receiving end converter, the constant ratio control of DC transformer and the frequency response of wind farm. With the proposed strategy, the all-DC wind farm operates like a synchronous generator to onshore grid, which provides fast frequency support when the onshore grid frequency changes. The effectiveness of the proposed method is validated in PSCAD/EMTDC.


Introduction
The rapid growth of offshore wind farms and the increasing need for long distance transmission accelerate the development of all-DC offshore wind farm [1,2]. Compared with conventional a HVAC transmission system, VSC-HVDC has several superiorities such as lower losses and less capacitor charging effects; moreover, the flexibility of active and reactive power flow control makes VSC-HVDC an attractive means for offshore wind farms integration [3,4]. However, the conventional AC collection of wind turbines is still causing higher power losses, particularly where the distance between the HVDC platform and turbines is likely to be increased. Accordingly, the concept of all-DC wind farm, which utilises both DC collection and DC transmission, becoming the focus of recent studies [5,6].
However, wind farms are immune to grid frequency variation under normal control method due to the decoupled feature of VSC-HVDC and DC transformer; such immunity has no inertial response toward grid, which will deteriorate frequency stability if wind power penetration is large. Therefore, to replace conventional power plants, the all-DC wind farms are required to provide ancillary services such as primary frequency regulation and inertia response to help maintain the stability of power grids.
Recent studies in terms of frequency support usually focused on the AC collection wind farm. Inertial response and primary frequency regulation of wind turbine is discussed in [7,8]. A communication-free coordinate control strategy was proposed in [9] to allow the frequency support of both wind farm and HVDC system. However, few attempts have been made to achieve the frequency control service of all-DC wind farm.
On the other hand, the increasing penetration of wind power has also increased the equivalent grid impedance, thus weakening the grid. Under this circumstance, the control ability may deteriorate when conventional vector-controlled receiving end converter (REC) is utilised to integrate wind power [10,11], thus resulting in the stability issues such as grid voltage distortions and harmonic oscillations. Applying voltage-source control is an effective way to solve this problem. A typical example is the virtual synchronising generator (VSG) [12], which imitates the rotor motion equation of synchronous generator (SG) to realise self-synchronisation to replace PLL. However, it is not suitable for REC which delivers wind power, since the output power of wind turbines are always changing.
Hence, a coordination control strategy of offshore all-DC wind farm is proposed in this paper, including the inertial synchronising control (ISC) of REC, the constant ratio control of DC transformers, and the frequency response of wind turbines. With this strategy, the grid frequency information is transmitted to DC wind turbine with a little time delay. Therefore, the DC wind turbine may realise rapid inertial response and primary regulation. Finally, the all-DC wind farm performs as an SG to the onshore grid. A simulation model of all-DC wind farm is constructed based on PSCAD/EMTDC and the effectiveness of proposed control strategy is validated.

Benchmark of all-DC wind farm and its voltagesource control
A typical offshore all-DC wind farm is shown in Fig. 1. The system mainly consists of three parts: the DC wind turbines, the DC transformers and the onshore REC.
The DC turbines are built up with directly driven permanent magnetic and AC/DC converter. Usually, its output DC voltage is 30-60 kV. A cluster of DC turbines are parallel connected to the low-voltage side a DC transformer. The high-voltage sides of DC transformers are connected to a DC bus (usually ± 150-500 kV). Finally, the wind power are collected by DC transformers and transmitted to onshore converter station by HVDC line.
In the proposed coordination control strategy, a DC voltage is chosen as the medium to transmit frequency information. The variation of onshore grid frequency is reflected on the HVDC voltage by the inertia synchronising control of REC. The equivalent DC capacitor is controlled to simulate rotors of SG by utilising its nature response, achieving the capability of selfsynchronising and accomplishing the real-time link between HVDC voltage and grid frequency. Moreover, the selfsynchronising characteristic of ISC endows it with enhanced performance under weak grid condition.
At the same time, the constant ratio control is applied to DC transformers. The voltage of DC collection bus is regulated by DC transformers according to HVDC voltage, delivering the grid frequency information from HVDC side to DC collection bus. Therefore, the wind turbines are able to obtain grid frequency variation by detecting the voltage of DC collection bus.
For wind turbines, a combined frequency supporting strategy is proposed, including the rotor-speed-based inertial response and the pitch-angle-based primary frequency regulation. Therefore, the all-DC wind farm operates like an SG, which has better performance under weak grid condition, and real-time frequency support to onshore grid.

Inertial synchronising control of REC
Neglecting the loss of DC cable, the natural response of HVDC bus voltage to power variation can then be described as where P WF is the wind power, and P rec_grid is the REC output power. U dc is the DC voltage, and ω is the equivalent DC bus capacitance. U rec is the output RMS voltage of REC (line-to-line), and U g is the RMS voltage of the AC grid (line-to-line). m is the modulation ratio, and δ is the power angle. X is the sum of grid synchronous reactance, the leakage reactance of the transformer, and the transmission line reactance, whereas resistance is neglected because of high voltage and power level conditions. Results indicated that (1) is similar to the motion equation of SG rotors whereas (2) is similar to SG output power equation As observed from (1)-(4), U dc is equivalent to rotor speed m . E f is the electromotive force of SG. Modulation ratio m is equivalent to air-gap flux P WF and P rec_grid are equivalent to SG's mechanical power P m and electrical power P e .
To simulate the natural relationship between rotor speed m and electrical frequency e of SG, a link between U dc and REC output frequency rec is established where U dc_nom and nom are the nominal values of U dc and sec , respectively. K is introduced to scale the coupling strength between DC bus voltage U dc and REC output frequency rec . The substitution of (5) into (1) combined with (2) presents the dynamics of REC with ISC by the following set of equations: Considering a small grid frequency variation, i.e. U dc →U dc_nom has following correlation: Thus grid and U dc are intrinsically coupled. As observed from (6) and (7), several beneficial characteristics are achieved in REC: (i) Similar to SG rotor, DC bus voltage U dc and REC output frequency rec tend to track grid frequency autonomously. Given that the inertia of an equivalent DC bus capacitor is usually minimal, this tracking can be rapid.
(ii) The impedance of REC seen from PCC is purely inductive, and thus, the loop circuit has no resonance as the current-vector-based control method, i.e. enhanced stability performance under weak grid.
Because of the utilisation of DC capacitor physical inertia for synchronising as SG uses its rotor inertia, this control strategy is called inertial synchronisation control (ISC) in this paper. With the developed model in (6), the overall control blocks of REC are presented in Fig. 2.
The reactive power is controlled by manipulating the output AC voltage. In addition, a damping compensation unit is designed to improve the dynamic response performance of the proposed strategy.

Constant ratio control of DC transformer
In the conventional control of all-DC wind farm, the voltage reference of DC collection bus is constant. Therefore, it is decoupled with HVDC voltage, which represents the variation of grid frequency when inertial synchronising control is applied in REC. The proposed constant ratio control of DC transformer will regulate the voltage reference of DC collection bus according to HVDC voltage. Hence, the grid frequency information is delivered to wind turbines.
The block diagram of constant ratio control is shown in Fig. 3. The DC voltage of HVDC side is measured as U* dc , in order to eliminate the influence of wind power fluctuation. The voltage drop on the HVDC transmission line is calculated based on the product of output current I dc and line resistance and line resistance R L , and added to U* dc . The result is then divided by a constant ratio n and become the reference of DC collection bus voltage U dc2 . The control of U dc2 is realised by the bottom control of DC transformer, which is mainly decided by the topology of converter, e.g. two-level or MMC structure. The bottom control will not be introduced in detail since it is not the focus point of this paper.

Frequency response of wind turbine
When the variation of the DC voltage is detected by DC wind turbine, the grid frequency information can be derived by while n is the constant ratio of DC transformer, U dc2 is the DC voltage of DC wind turbine, U dc is the DC voltage of HVDC line. Hence, the inertial response and primary regulation can be realised by DC wind turbines. The capability of wind turbines to provide inertial response is investigated in [7]. An additional value associated with the rate-ofchange-of-frequency (RoCoF) is attached to the active power reference (P MPPT ) given by the MPPT control. Additional power P add is provided by accelerating or decelerating the wind turbine and utilising the kinetic energy stored in rotating blades.
Assuming that the virtual inertia of wind farm is H WF , the value of additional power P add is Substituting (8) into (9), there is Given that the kinetic energy stored in rotating blades is limited, if primary regulation of the wind farm is needed, then power source such as energy storage should be added. Another option is the utilisation of de-loading strategies by preserving a generation margin. Since the extra cost brought by additional power source, especially for offshore all-DC wind farms, de-loading strategies is applied in proposed strategy. Two de-loading strategies have been discussed in [13,14]: pitch-angle-based deloading and rotor-speed-based deloading. In order to decouple with inertial response, which is a rotor-speedbased, the pitch-angle-based deloading strategy is utilised for primary frequency regulation. The deviation of grid frequency can be achieved by (8).
The control block diagram of wind turbines with frequency response capability is shown in Fig. 4. Inertial response is realised by the variation of rotor speed, an extra power P add is calculated by (10) and added to the original power reference PMPPT which is given by the MPPT control.
On the other side, the primary frequency regulation is realised by pitch angle control. Under normal circumstances, the wind turbine works under a small pitch angle to reserve part of the wind power. The amount of reserved power is decided by the demand of local grid (usually 5-10%). When grid frequency variation is detected, wind turbines will change the pitch angle according to the deviation of grid frequency to its rated value.

Simulations
To validate the effectiveness of proposed coordination control strategy, an all-DC wind farm mode is constructed in PSCAD/ EMTDC based on Fig. 1. The parameters of this model are shown in Tables 1-4. The onshore power grid is equivalent to a single SG with a load of 500 + j100 MVA. There are four clusters in this model and each cluster consists of five permanent magnet SGs (PMSGs). The rated power of a wind turbine is 10 MW. 10% of the  rated power is reserved for primary frequency regulation. Therefore, the total output power of wind turbines is 180 MW, i.e. 36% of the total load. Neglecting the voltage drop on the collection lines, wind turbines in each cluster can be equivalent to an aggregated 50 MW PMSG model. The system simulation diagram is shown in Fig. 5.
Based on this model, the capability to provide inertial response and primary frequency regulation of proposed control strategy is validated under two different scenarios.
Scenario I: A step increase of 20% active power and 5% reactive power of Load 1 is simulated at 2.0 s to cause a grid frequency drop. The simulation results are shown in Fig. 6. Scenario II: A step decrease of 20% active power and 5% reactive power of Load 1 is simulated at 5.0 s to cause a grid frequency increase. The simulation results are shown in Fig. 7.
It can be observed from Figs. 6a and 7a that with the proposed control strategy, the grid frequency variation led by the sudden change of load can be delivered to wind turbines timely and precisely through HVDC voltage and DC collection bus voltage.
After detecting the deviation of grid frequency, wind farm may realise fast inertial response and primary frequency regulation with proposed control strategy [see Figs. 6b and 7b]. At the beginning of grid frequency variation, the support power from wind farms is dominated by inertial response and is proportional to RoCoF. After t = 5 s, the grid frequency becomes stable. The support power is dominated by primary frequency regulation, and is proportional to the deviation of grid frequency.    From Figs. 6a and 7a, the frequency nadir/peak and the RoCoF of onshore grid is improved with proposed control strategy, which has validated its effectiveness. However, with conventional control strategy, wind turbines cannot sense grid frequency deviation, thus providing no frequency support.

Conclusion
A multi-timescale coordination control strategy is proposed in this paper, including the inertial synchronising control of REC, the constant ratio control of DC transformers, and the frequency response of wind turbines.
With the proposed control strategy, the grid frequency deviation is delivered to wind turbines through DC-link timely and precisely. Meanwhile, the rotor-speed-based inertial response and pitchangle-based primary frequency regulation is applied in wind turbines. Therefore, the all-DC wind farm operates like an SG to onshore grid, which provides fast frequency support when the onshore grid frequency changes. The effectiveness of the proposed method is also validated by the simulation results.

Acknowledgments
This work was supported by National Natural Science Foundation of China (51707118) and State Key Laboratory of Operation and Control of Renewable Energy & Storage Systems (NYB51201801481).