**1. Introduction**

Jeju Island is one of the biggest islands in South Korea with a peak and average power demand of 944 and 627 MW, respectively, and consists of thermal power plants, renewable energy sources, two static synchronous compensators (STATCOMs) and two current source converter high voltage direct current (CSC-HVDC) transmission systems connected to the mainland. This small power system is being supplied with over 40% of the demand load by high voltage direct current transmission systems (HVDCs) from the power system on the mainland. However, the local governmen<sup>t</sup> of this island has proceeded with the renewable energy promotion policy, namely "Carbon Free Island Jeju by 2030" [1]. Thus, an o ffshore wind farm (OWF) with a total capacity of 100 MW will be constructed in the near future in the north of Jeju Island. To achieve this plan successfully, the entire Jeju Island power system should be analyzed, including the large scale wind farm by using a detailed simulation model because this large scale wind farm will have a 16% average power load.

According to advanced research about HVDC with wind farm, voltage sourced HVDC can suitably deliver output power from wind farms to a weak grid such as the Jeju Island power system [2–7]. However, its application might increase the installation cost of an OWF. To deal with the economic challenge, [8–10] presented a new topology of HVDC, which changes conventional modular multilevel converter (MMC) to the uncontrolled diode rectifier at the o ffshore platform, as illustrated in Figure 1. Although the controllable converter will disappear in this new grid connection method, the diode rectifier HVDC (DR-HVDC) has many advantages, including reduced installation costs, low losses, easy management, and high reliability, among others.

From this perspective, this study analyzed the Jeju Island power system with a 100 MW OWF, which is connected to DR-HVDC via a 50 km submarine DC (Direct current) cable. To verify the effectiveness of DR-HVDC, a simulation model of the Jeju Island power system with a new OWF was conducted for steady and transient situations by using the PSCAD/EMTDC program. First, the Jeju Island power system, which was made by using actual parameters, operated without the new OWF. In this case, a comparison was made between the results of the simulated model and the measured data to check the accuracy of the simulation model. Second, a new OWF was linked to the Jeju Island power grid by DR-HVDC under normal operation. Third, the disconnection fault occurred to the OWF of the DC transmission line. Finally, the single line ground fault occurred to the OWF.

**Figure 1.** Conceptual design of high voltage direct current transmission systems (HVDC) for an offshore wind farm (OWF): (**a**) Conventional HVDC; (**b**) diode rectifier HVDC (DR-HVDC).

#### **2. Modeling of the OWF System**

#### *2.1. Onshore MMC Station*

An MMC is a type of voltage sourced converter (VSC), as shown in Figure 2. Using this concept, it is possible to make a huge capacity VSC [11]. In this case, the MMC plays a role as an onshore station of the new OWF by converting DC to AC (Alternative current), Figure 3. To transfer, MMC has three controllers, which are a current, a circulation current, and a capacitor balancing controllers [12–20]. Using the Park's transformation theory to control that, the terminal voltage of MMC in the dq axis can be calculated as

$$vvtd = -Rid - pLid + vsd + \alpha Liq \tag{1}$$

$$
\sigma tq = -Riq - pLiq + \nu sq - \alpha Lid \tag{2}
$$

where *vt* and *vs* are the terminal and grid voltage. *i* is the three-phase current. *R* and *L* are the resistance and inductance, respectively. p is the di fferential operator. ω is the grid angular frequency. If the PI controller is used, the current controllers will be expressed as

$$
\upsilon^\* td = -\left(\mathbb{K}p + \mathbb{K}\dot{\mathbb{y}}\,\right)\left(\mathbb{i}^\* d - \mathrm{id}\right) + \upsilon\text{sd} + \alpha\,\mathrm{L}iq\tag{3}
$$

$$
\sigma^\* t q = -\left(Kp + K\dot{\iota}/\dot{s}\right)\left(\dot{\iota}^\* q - iq\right) + vsq - \alpha \text{L}\dot{\iota} d\tag{4}
$$

where superscript of \* denotes reference mark. Then, *i\*d* and *i\*q* are decided by

$$i^\*d = 2Q^\*/\text{(3 vsq)}\tag{5}$$

$$i^\*q = 2P^\*/(\Im \ vs q) + k\left(V^\*dc - Vdc\right) \tag{6}$$

where *P\** and *Q\** are the real and reactive power, respectively. In this simulation, *P\** will be the summation of the generated power from the OWF. *Q\** will be zero to make the unity power factor. *k* is the coefficient for the *dc* link voltage control to maintain a stable range of it, as illustrated in Figure 3.

**Figure 2.** Basic structure of a modular multilevel converter (MMC): (**a**) Topology; (**b**) Submodule.

**Figure 3.** Current controller of MMC in an onshore station.

The MMC needs a circulation current controller to suppress it because it always occurs from the difference of capacitor voltages among phases. To mitigate circulation current, the differential voltage of the MMC in the dq frame can be written as

$$r\text{-}v\text{diff}d = \text{R0}\text{icird} + p\text{L0}\text{icird} - \text{2}\alpha\text{L0}\text{ictir}q\tag{7}$$

$$
vid\overline{g}\overline{q} = R\text{0}\text{ic}\text{ir}\eta - pL\text{0}\text{ic}\text{ir}\eta + 2\omega vL\text{0}\text{ic}\text{ir}d\tag{8}$$

where *vdi*ff is the differential voltage. *R*0 and *L*0 are the resistance and inductance of arm inductors, respectively. *icir* is the circulating current. If the PI controller is adapted to the circulating current controller, as shown in Figure 4, it will be expressed as

$$\text{cv}^\* \text{d} \text{jfd} = - \left( \text{Kp} + \text{Kj/s} \right) \left( \text{i}^\* \text{cird} - \text{icird} \right) - 2\omega \text{L0} \text{bicirq} \tag{9}$$

$$
\sigma^\* \text{d} \text{f} \text{f} \text{\"} q = - \left( \text{K} p + \text{K} \text{j/s} \right) \left( \text{i}^\* \text{circ} - \text{i} \text{circ} \right) + 2 \omega \text{L} \text{0} \text{i} \text{circ} \text{d} \tag{10}
$$

**Figure 4.** Circulating current controller of MMC in an onshore station.

The final reference value will be generated as a PWM (Pulse width modulation) switching signal, then it will be decided by a capacitor balancing controller depending on sorted capacitor voltages. The parameters of the MMC are as described in Table 1.



#### *2.2. O*ff*shore Diode Rectifier Station*

To convert AC power from the wind power generator to DC power, an offshore DR station should be connected to the DC link of the onshore MMC station, as shown in Figure 5. It consists of a DR, AC filter, and phase-shifting transformers. The phase-shifting transformer can reduce the ripple voltage of the DC link. Through a series connection with them, the DC voltage will be increased to rated voltage. The parameters of the DR station are shown in Table 2.

**Figure 5.** Simulation model of diode rectifier (DR) (Offshore side rectifier).

**Table 2.** Parameters of diode rectifier (DR) station.


#### *2.3. Wind Turbine*

In this analysis case, the simulation model of the offshore wind farm will be used as equivalent models to simplify the simulation model, i.e., 20 MW 2 level VSC, as illustrated in Figure 6, is assumed as four wind turbines each with a capacity of 5 MW. Although the wind turbines are replaced with the equivalent models, its controller will be quite similar to the detailed model, i.e., the current controller, which is similar to the MMC model, will be applied to the equivalent model. There is one problem of the controller in a wind turbine because the uncontrolled DR station cannot generate reference voltage signals and phase angle. It means that it is impossible to perform voltage transforming to dq from a 3-phase frame from the DR side converter of a wind turbine. Thus, [8–10] proposed the method as known as FixRef control, as illustrated in Figure 7, which uses GPS signal instead of space phasor angle of grid voltage. This study will also use a steady increased time signal, which is an assumed GPS signal.

**Figure 6.** Equivalent simulation model of wind turbines in the new OWF.

**Figure 7.** Equivalent simulation model of a wind turbine in the new OWF.

#### *2.4. Whole OWF System*

Figure 8 shows the whole simulation model of OWF with DR-HVDC. This system will be attached to the Jeju Island power system as the new OWF, then it will be simulated by parallel computing method in PSCAD/EMTDC program.

**Figure 8.** Simulation model of OWF with DR-HVDC.

#### **3. Configuration and Modeling of the Jeju Power System**
