3.1.2. Operation and Maintenance Costs

*Copex.AC* is usually estimated in the form of percentage *A* of the annual maintenance cost to total investment cost (excluding land occupation cost and offshore platform costs) or percentage *A*<sup>1</sup> of lifetime maintenance costs to total investment cost. The relation between *A* and *A*<sup>1</sup> is

$$A = A\_1 \times \frac{i(1+i)^n}{(1+i)^n - 1} \tag{7}$$

where *i* is the annual interest rate; *n* is the lifetime; Van Eeckhout gives the specific data of *A* equals to 1.2%, *n* is 20 years, *i* is 5% [36]. Then, *Copex.AC* is estimated:

$$\mathbb{C}\_{\text{open}\,\mathcal{AC}} = \mathbb{C}\_{\text{cap}\,\mathcal{AC}} \cdot A \tag{8}$$

#### 3.1.3. Costs of Loss

The loss costs *Closs.AC* comprise of substation loss *Csub.loss* and transmission line loss *Cline.loss*. *Csub.loss* is dependent on the substation loss rate *Psub.loss*, as referred to in the literature [36]. The *Psub.loss* of two substations is 0.8%, that means the loss rate of each substation is 0.4%. *Cline.loss* includes conductor losses *Ccon.loss* and losses of sheath and armor *Cshar.loss*. *Ccon.loss* can be formulated by the current *Icable* of the copper conductor, which can be approximately calculated by

$$I\_{cable} = \frac{P}{\sqrt{3}I I\_{cable} \cos \varphi} \tag{9}$$

where *P* is the active power; the power factor cosϕ is 0.95.

Therefore, with the resistance of conductor *Rcu*, *Ccon.loss* is given by

$$\mathcal{L}\_{con.loss} = 3I\_{cable} \, ^2 \cdot R\_{\mathbb{C}u} \tag{10}$$

The losses of sheath and armor *Cshar.loss* is estimated.

$$
\begin{bmatrix}
\Delta Ul\_{\mathbb{C}} \\
\Delta Ul\_{\mathbb{S}} \\
\Delta Ul\_{A}
\end{bmatrix} = \begin{bmatrix}
Z\_1 & Z\_2 & Z\_3 \\
Z\_4 & Z\_5 & Z\_6 \\
Z\_7 & Z\_8 & Z\_9
\end{bmatrix} \begin{bmatrix}
I\_{\mathbb{C}} \\
I\_{\mathbb{S}} \\
I\_A
\end{bmatrix} \tag{11}
$$

where Δ*Uc*, Δ*Us*, Δ*UA*, *Ic*, *Is*, *IA* are the voltage and current of the copper core, sheath, and armor, respectively; *Z*1–*Z*<sup>9</sup> are the matrix of parameters of the cable.

Moreover, since both ends of the sheath are grounded, the armor layer is linked with the sea, with the assumption of *Us* = *UA* = 0 and *Ic* = *Icable*; so, *Cshar.loss* can be given by the power loss *Par* = 3*IA*<sup>2</sup> × *<sup>R</sup>*, *Psh* = 3*IS* <sup>2</sup> × *<sup>R</sup>*, and *IS* and *IA* are

$$\begin{cases} \ I\_A = \left( Z\_\theta - Z\_8 Z\_5^{-1} Z\_6 \right)^{-1} \left( Z\_8 Z\_5^{-1} Z\_4 - Z\_7 \right) I\_\mathbb{C} \\\ I\_S = -Z\_5^{-1} \left( Z\_4 I\_\mathbb{C} + Z\_6 I\_A \right) \end{cases} \tag{12}$$

The costs of *Carsh* is dependent on the operation time of full generation per year *Tf* and the on-grid price of electricity *Pon-grid*, which are

$$C\_{shar} = (P\_{sh} + P\_{ar}) \times T\_f \times P\_{am-grid} \tag{13}$$

The evaluation of *Closs.ac* is obtained by total *Csh* and *Car.*

$$\mathcal{C}\_{loss.AC} = \mathcal{C}\_{sub.loss} + \mathcal{C}\_{shar} + \mathcal{C}\_{con.loss} \tag{14}$$

### *3.2. Costs Calculation of VSC-HVDC Transmission*

As for the VSC-HVDC transmission concept, the total costs of *CVSC* compose of capital costs *Ccap.VSC*, operation and maintenance costs *Copex.VSC*, and loss costs *Closs.VSC*.

$$\mathcal{C}\_{VSC} = \mathcal{C}\_{cap.VSC} + \mathcal{C}\_{opex.VSC} + \mathcal{C}\_{loss.VSC} \tag{15}$$

#### 3.2.1. Capital Costs

*Ccap.VSC* consists of the converter station foundation cost *Cstation.VSC*, and the cable foundation and installation costs *Ccable.VSC*.

$$
\mathcal{C}\_{cap.VSC} = \mathcal{C}\_{station.VSC} + \mathcal{C}\_{cable.VSC} \tag{16}
$$

#### 1. Converter station foundation cost

*Cstation.VSC* is the total infrastructure investment of each converter station. Furthermore, the additional costs of IGBT, converter controller and reactor, DC capacitor and AC filter, as well as the cost of civil construction of the offshore platform for converter station layout are estimated. Then *Cstation.VSC* is computed as a proportion of the capacity of per converter station *P*.

$$
\mathbb{C}\_{\text{station\\_VSC}} = \mathbb{C}\_{\text{perMWV}} \cdot 2P \tag{17}
$$

2. Cable foundation and installation cost

Similar to HVAC cable, *Ccable.VSC* of DC cable is calculated by the transmission distance.

$$\mathbb{C}\_{\text{cable}\,VSC} = \mathcal{2}(P\_1 + P\_2)L \tag{18}$$

where *P*<sup>1</sup> and *P*<sup>2</sup> are the expense and installation costs of per km DC cable.
