Comprehensive Evaluation Model and Methodology for Offshore Wind Farm Collection and Transmission Systems

Abstract

With the gradual development of offshore wind farms toward large-scale and long-distance trends, economically efficient methods for correcting and transmitting offshore wind energy have garnered increasing attention. The rational and effective evaluation of offshore wind power collection and transmission methods has become an urgent issue. To address this, a comprehensive evaluation model for collection and transmission systems, considering factors such as network losses, lifecycle costs, and reliability, was established. This proposed model was applied to multiple sets of typical collection and transmission scenarios, utilizing an improved TOPSIS comprehensive evaluation method based on dynamic combination weighting to achieve the comprehensive optimization of collection and transmission schemes. Case studies have validated the feasibility of the comprehensive evaluation model. The results indicate that with an increase in offshore distance, the AC/DC collection and transmission system is superior to the all-AC collection and transmission system, and the all-DC collection system exhibits potential cost advantages.

1. Introduction

As offshore wind farms continue to increase in scale and move further offshore, the adoption of high-voltage direct current (HVDC) transmission technology is an inevitable trend in the development of offshore wind energy [1]. Existing offshore wind farm collection and transmission systems use alternating current (AC) systems, which require multiple rectification, inversion, and voltage-boosting operations, leading to losses and increased investment costs and reducing system reliability. By retrofitting AC wind turbine generators into direct current (DC) units and utilizing DC collection systems to aggregate electricity, with high-voltage DC transmission lines transmitting the energy to the grid, it is possible to address energy losses and reliability issues inherent in AC systems [2,3]. This approach is better suited for collecting and transmitting power over long distances on large-scale offshore wind farms [4]. Therefore, a comprehensive evaluation of collection and transmission systems is of significant importance to the planning, investment, and reliable operation of offshore wind farms.

The collection and transmission system represents a critical electrical component of offshore wind farms, with a high quantity and significant economic cost. Due to the harsh marine environment, including lightning, high salt spray, and high humidity, the probability of equipment failures on offshore wind farms is higher than that on onshore wind farms. Additionally, the accessibility of equipment is lower due to the influence of the wind and waves, resulting in higher operational and maintenance costs for offshore wind farms. In the event of a failure in the collection and transmission system, lengthy repair periods and challenging operational conditions can lead to increased power outage losses, ultimately diminishing the economic viability of the entire system.

Reference [5] evaluated the topology of offshore wind farms with AC collection and DC transmission using a genetic algorithm, demonstrating that the minimum investment cost combined with the shortfall in electricity generation occurs with a ring-shaped collection structure. Only the topology of the collector system was considered, without taking into account the impact of bad weather at sea on it. Reference [6] established a protection zone model and employed a fault enumeration method to assess the reliability of the collection systems at the wind farm level, revealing that chain and large-ring collection system structures exhibit higher reliability. However, only faults up to the second order could be evaluated. Reference [7] developed a total cost model from a full lifecycle perspective and optimized the topology structures of two offshore wind farm collection systems: radial and ring-shaped. Transmission systems for offshore wind farms are not included in the assessment.

Currently, the majority of research focuses on AC collection and DC transmission systems, with limited assessments of DC collection and transmission systems. Reference [8] proposed a reliability assessment model based on a universal generating function, simplifying the evaluation of multi-state systems and concluding that a chain-type centralized boosting and parallel collection structure for a single 10 MW unit is both economically and reliably viable. However, the factor of environmentality was not included in the assessment.

Most studies have traditionally focused on single aspects, such as cost [9,10], efficiency [11], and reliability [12]. Therefore, conducting a rational and effective comprehensive decision-making process for collection and transmission systems holds significant importance in the planning and design of offshore wind farms.

To address the above issues, this paper establishes a comprehensive assessment model for the collection and transmission system that takes into account factors such as loss, life cycle cost, and reliability, and at the same time, it considers the impact of offshore distance on the comprehensive assessment. First, a non-sequential Monte Carlo process was devised for the collection system to conduct reliability assessments at the wind farm level. Second, a full lifecycle cost model for offshore wind farms was developed for economic evaluation, taking into account both losses and environmental factors.

Ultimately, this proposed approach was applied to multiple sets of typical collection and transmission scenarios. It employed an improved TOPSIS comprehensive evaluation method with dynamic combination weighting to achieve the comprehensive optimization of collection and transmission schemes. This method comprehensively assesses the consistency and differentiation of judgment matrices, utilizing dynamic combination weighting based on the magnitudes of characteristic eigenvalues as the measuring standard for scheme ranking. Case studies have validated the feasibility of the comprehensive evaluation model. The primary contributions of this work include:

• The establishment of a comprehensive assessment indicator system tailored for offshore wind farm collection and transmission systems, comprising four primary indicators and sixteen secondary indicators.
• The introduction of an integrated assessment model that takes into account factors such as losses, total lifecycle costs, and reliability while considering the impact of offshore distance on the comprehensive assessment.
• Using a 400 MW offshore wind farm as an example, a comprehensive evaluation is conducted for three collection and transmission methods—full AC, AC collection with DC transmission, and full DC—considering various offshore distances.

2. Reliability Assessment of Offshore Wind Farm Collection and Transmission Systems

2.1. Typical Structures of Offshore Wind Farm Collection and Transmission Systems

The typical structure of offshore wind farm collection and transmission systems is illustrated in Figure 1. From a structural perspective of the power system, the collection and transmission system can be clearly divided into two main components: the offshore wind farm and the long-distance subsea transmission cable. This includes a network of cables and a multitude of components, such as wind turbines, AC/DC converters, circuit breakers, and other equipment.

2.2. Outage Rate Model for Collection and Transmission Systems

The offshore wind farm collection and transmission system, as illustrated in Figure 1, is a complex system comprising a multitude of devices arranged in both series and parallel configurations. The outage rate indicates the probability of fault conditions. The outage rate is as follows:

$$Q_{sys}=1-\left\{1-{\left\{1-\left\{1-{\displaystyle \prod _{j=1}^m\left[1-\left(1-{\displaystyle \prod _{i=1}^n{Q}_{w{t}_i}}\right)\left(1-Q_{brk}\right)\right]}\right\}{\left(1-Q_{brk}\right)}^2\left(1-Q_{trans}\right)\right\}}^2\right\}\left(1-Q_{AC/DC}\right)\left(1-Q_{cable}\right)$$

(1)

where is $Q_{wt}$ the outage rate of wind turbines, $Q_{AC/DC}$ is the outage rate of converters, $Q_{brk}$ is the outage rate of circuit breakers, $Q_{cable}$ is the outage rate of cables, m is the number of feeder lines in each cluster in series, and n is the number of wind turbines per feeder line.

2.3. Reliability Assessment Model for Collection and Transmission Systems

In reliability studies, commonly used reliability indicators describe the ability of an electrical system to provide the required electrical energy stably and abundantly; these include loss of load probability (LOLP) and loss of load frequency (LOLF). However, in the analysis of offshore wind power system interconnection, there is no clearly defined significance of load. Therefore, reliability analyses focus more on the level of effective output provided by the offshore wind power system to the main grid and the level of output variability. Hence, reliability indicators such as expected energy not supplied (EENS), average availability, outage Hours per year, and transmission efficiency are used.

$$\left\{\begin{array}{c}EENS={\displaystyle \sum _{i=1}^N{p}_i}\times \left(P_{OWF\mathrm{m}\mathrm{a}\mathrm{x}}-P_{OWFi}\right)\times 8760\\ H_{\mathrm{AOH}}=\frac{EENS}{P_{OWF\mathrm{m}\mathrm{a}\mathrm{x}}}\\ A_{\mathrm{system}}=1-\frac{H_{\mathrm{AOH}}}{8760}\\ TE=\frac{P_{OWF} - P_{loss}}{P_{OWF}}\cdot 100\%\end{array}\right.,$$

(2)

where $p_i$ is the probability that the entire offshore wind farm collection system is in the i-th power output state, $P_{OWF\mathrm{m}\mathrm{a}\mathrm{x}}$ is the rated capacity of the offshore wind farm, $P_{OWFi}$ is the power output of the entire wind farm collection system when it is in the i-th power output state, N is the total number of power output states for the wind farm, and $P_{loss}$ represents transmission losses.

The steps for calculating reliability indicators of the collection and transmission system using the non-sequential Monte Carlo method are as follows, The flow chart is shown in Figure 2:

Step 1: Input the annual load data for the wind farm, the topological structure of the wind power collection and transmission system, and the corresponding outage rate model.

Step 2: Simulate the annual output sequence of the wind power collection system.

Step 3: Use the outage probability of the collection system to sample and adjust the annual output sequence of the wind power collection system.

Step 4: Calculate the reliability indicators of the wind farm collection system using Equation (2).

3. Economic Evaluation Model for Offshore Wind Farm Collection and Transmission Systems

The full lifecycle cost of the offshore wind farm collection and transmission system can be divided into three stages: the purchase stage, the operation and maintenance stage, and the decommissioning stage. The cost components for each stage are shown in Figure 3 and

Table 1. Composition of LCC for power collection and transmission system.

Composition of Fee Items	Stage
Initial investment cost $C_{P\&I}$	Purchase stage
Operation cost $C_O$	O&M stage
Maintenance cost $C_M$	O&M stage
Failure cost $C_{CM}$	O&M stage
Failure opportunity cost $C_L$	O&M stage
Decommission and disposal cost $C_D$	Decommission stage

[13,14,15].

The costs associated with the purchase and installation of wind turbines, submarine cables, converters, offshore boosting stations, and switches collectively constitute the initial investment cost, which is a one-time investment. The maintenance of submarine cables and circuit breakers is carried out as post-maintenance, with the maintenance time being influenced by factors such as maintenance duration, delays caused by weather and sea conditions, and the time taken for maintenance ships to sail to the location. Operating costs, maintenance costs, failure costs, and opportunity costs for failures collectively constitute the operational and maintenance costs of the offshore wind farm. Submarine cables and other power electronic devices contain a certain amount of non-ferrous metals and have a scrap recovery value, so the cost of their recycling is considered part of the decommissioning cost. Therefore, each cost component can be expressed as:

$$\left\{\begin{array}{l}{C}_{P\&I}=C_{WT}+C_{cable}+C_{conv}+C_{trans}+C_{platform}+C_{brea\mathrm{k}\mathrm{e}\mathrm{r}}\\ C_{O\&M}=C_O+C_M+C_{CM}\\ C_L=opp\times EENS\end{array}\right.,$$

(3)

where $C_{WT}$ is the investment cost of the wind turbines, $C_{cable}$ is the investment and installation cost of the submarine cables, $C_{conv}$ is the cost of the converters, $C_{trans}$ is the cost of the transformers, $C_{platform}$ is the cost of the offshore substation platforms, $C_{brea\mathrm{k}\mathrm{e}\mathrm{r}}$ is the cost of the circuit breakers, opp is the electricity price, and EENS is the expected energy not supplied by the collection and transmission system per year.

3.1. Purchase Stage

The purchase of offshore wind turbines represents one of the most expensive components of capital expenditure. The cost model for DC wind turbines is modified on the basis of the cost model for AC wind turbines of the same capacity since the development of DC wind turbines is still in the research and development stage, and there are no definitive cost data available for DC turbines.

According to the actual investment cost of a specific offshore wind farm in China, a detailed cost breakdown for AC wind turbines based on full-power converters is available. This breakdown includes components such as wind generators, transformers, circuit breakers, tower structures, full-power converters, AC/DC converters, and other specific parts.

In this study, we utilized DAB-based DC wind turbines, which can be considered to have an added AC/DC converter at the front end of an AC wind turbine. The cost is denominated in British pounds (GBP) and amounts to GBP 8.6674/kW.

The costs of AC and DC turbines, cables, reactive power compensation, and circuit breakers can be found in Appendix B,

Table A1. Costs.

Parameters	Costs
AC wind turbine	EUR 776.289/kW
DC wind turbine	EUR 784.505/kW
SVC	EUR 77 k/MVAr
Breaker	230 kv: EUR 0.197 M
	35 kv: EUR 0.0605 M
AC/DC	EUR 0.185 M/MW

.

Offshore wind farms with distances greater than 20 km from the shore often require the installation of offshore substations to reduce cable losses. The general one-line scheme of an MV/HV substation is shown in Figure 4.

The parameter expression linking the cost of offshore substations to the total installed capacity of the offshore wind farm is as follows:

$$\begin{array}{c}{C}_{TR}=n_{TR}·\left(42.688\cdot A_{TR}^{0.7513}\right)\\ C_{SG,MV}=40.543+0.76\cdot V_n\\ C_{DG}=21.242+2.069\cdot P_{WF}\\ C_{offSubst,p{a}_f}=2534+88.7\cdot P_{WF}\\ C_{\mathrm{IS}}=n_{\mathrm{TR}}·C_{TR}+\left(n_{\mathrm{cl}}+n_{\mathrm{TR}}\right)C_{SG,MV}+(n_{\mathrm{HV}}+1)C_{\mathrm{SG},\mathrm{HV}}+\left(C_{DG}+C_{offSubst,p{a}_f}+C_{\mathrm{BB}}\right)\end{array},$$

(4)

where $C_{TR}$, $C_{SG,MV}$, $C_{\mathrm{SG},\mathrm{HV}}$, $C_{\mathrm{BB}}$, $C_{DG}$, $C_{offSubst,p{a}_f}$ are the costs of the main transformer, medium-voltage circuit breaker, high-voltage circuit breaker, high-voltage busbar, station transformer, and substation platform, respectively; $n_{\mathrm{TR}}$ is the number of the transformers; $V_n$ is the rated voltage of the transformers; $A_{TR}^{}$ is the rated power of the transformers; $C_{\mathrm{IS}}$ is the total cost of the offshore substation; $P_{WF}$ represents the total installed capacity of the wind farm; $n_{\mathrm{cl}}$ is the number of MV circuit breakers; and $n_{\mathrm{HV}}$ is the number of HV circuit breakers.

The cost model for the cables is as follows:

$$\begin{array}{c}{C}_{DC}=(402\cdot P^{1.2433})\cdot l\\ C_{AC}=\left[\alpha +\beta e^{(\gamma I_{rated}/{10}^5)}\right]\cdot l\end{array},$$

(5)

where $P=2\cdot U_{DC}\cdot I_{rated}$, $I_{rated}$ represents the current carrying capacity of the cable, l is the length of the cable, and C is the cost. The parameters α, β, and γ are coefficients dependent on the voltage level, and their values can be found in Appendix B,

Table A2. Cable cost parameters.

Voltage	α (kEUR/km)	β (kEUR/km)	γ (1/A)
30–36 kV	52.08	75.51	234.34
220 kV	403.02	13.94	462.1

.

3.2. The Operation and Maintenance Stage

Operation and maintenance (O&M) costs typically account for 14–30% of the full lifecycle cost of offshore wind farms [16]. O&M costs are largely dependent on factors such as vessel costs, leasing duration, working hours, weather conditions, vessel availability, and the availability of electrical equipment. Additionally, these costs are influenced by the offshore distance. The model for O&M costs varying with offshore distance is as follows:

$$OPEX=fixe{d}_{cost}+por{t}_{fees}+d\cdot va{r}_{cost},$$

(6)

where d is the offshore distance, $fixe{d}_{cost}$ is the fixed cost, $por{t}_{fees}$ is the port leasing fee, and $va{r}_{cost}$ is the variable cost. Parameters are shown in

Table 2. O&M cost parameters.

Parameters	Cost
Fixed cost	EUR 20.81/MWh
Variable cost	EUR 0.069/km·MWh
Port leasing fee	EUR 3.47/MWh

.

3.3. Decommissioning Stage

In most countries, approval for decommissioning plans must be obtained before the installation of offshore projects. Because of the absence of actual offshore wind energy projects that have reached this stage thus far, there is considerable uncertainty surrounding decommissioning costs. Considering that submarine cables and other power electronic devices contain non-ferrous metals and have scrap recovery value, the decommissioning costs for offshore wind farms tend to be higher than those for onshore wind farms. A common practice is to estimate decommissioning costs as a percentage of installation costs, as shown in

Table 3. Decommissioning costs.

Components	Decommissioning Costs as a Percentage of Installed Costs
Wind turbine	70%
submarine cable	10%
Substation	90%

[17].

4. Loss Model and Environmental Assessment for Offshore Wind Farm Collection and Transmission Systems

4.1. Losses in the Collection and Transmission System

The losses in the collection and transmission system can be divided into losses in the collection system, losses in the converters, and losses in the transmission cables.

4.1.1. Losses in the Collection System

It should be noted that due to the influence of the internal network topology, different sections of cables in the collection network carry different current intensities, resulting in varying power losses. Therefore, it is necessary to calculate the losses segment by segment and then cumulatively determine the total power loss. Taking the simple circuit shown in Figure 5 as an example, it can be observed that the total power loss in this segment of cable is:

$$P_{cable}=i^2{R}_{cable}+{(2i)}^2{R}_{cable}+\cdots +{(8i)}^2{R}_{cable},$$

(7)

where i is the cable current, $R_{cable}$ represents the resistance value of the cable in each section, $R_{cable}=\frac{\rho }{S}L$, S is the cross-sectional area of the cable, ρ is the resistivity of the cable material, and L is the length of each section of cable.

By employing the method, the losses in the collection systems of offshore wind farms under two different topological structures shown in Figure 6 were calculated. The results are presented in

Table 4. Network loss.

Collection System Structures	Losses
AC Collection	$470i^{2}Rd$
Parallel DC Collection	$700i^{2}Rd$

.

4.1.2. Converter Losses

The losses in the converter are as follows [18]:

$$\begin{array}{c}{P}_{\mathrm{IGBT}}=N_{\mathrm{sw}}\left(V_{\mathrm{CE}0}{I}_{\mathrm{C}\_\mathrm{ave}}+R_{\mathrm{C}}{I}_{\mathrm{C}\_\mathrm{rms}}^2+\left(E_{\mathrm{onT}}+E_{\mathrm{offT}}\right)f_{\mathrm{sw}}\right)\\ P_{\mathrm{FWD}}=N_{\mathrm{sw}}\left(V_{\mathrm{D}0}{I}_{\mathrm{d}\_\mathrm{ave}}+R_{\mathrm{D}}{I}_{\mathrm{d}\_\mathrm{rms}}^2+E_{\mathrm{onD}}{f}_{\mathrm{sw}}\right)\end{array},$$

(8)

where $V_{\mathrm{CE}0}$ is the voltage during IGBT conduction (V), $I_{\mathrm{C}\_\mathrm{ave}}$ is the average current through the IGBT (A), $R_{\mathrm{C}}$ is the on-resistance of the IGBT, $I_{\mathrm{C}\_\mathrm{rms}}^{}$ is the root mean square (RMS) current through the IGBT (A), $E_{\mathrm{onT}}$ is the conduction loss of the IGBT (W), $E_{\mathrm{offT}}$ is the switching loss of the IGBT (W), $f_{\mathrm{sw}}$ is the switching frequency (Hz), $V_{\mathrm{D}0}$ is the voltage during diode conduction (V), $I_{\mathrm{d}\_\mathrm{ave}}$ is the average current through the diode (A), $I_{\mathrm{d}\_\mathrm{rms}}^{}$ is the RMS current through the diode (A), $E_{\mathrm{onD}}$ is the reverse recovery loss of the diode (W), $R_{\mathrm{D}}$ is the on-resistance of the diode, $N_{\mathrm{sw}}$ is the number of switching devices, $P_{\mathrm{IGBT}}$ is the total conduction and switching loss of the IGBT (W), and $P_{\mathrm{FWD}}$ is the total conduction and switching loss of the diode (W).

4.1.3. Transmission Cable Losses

The line losses for AC submarine cables can be obtained through Equation (9):

$$P_{\mathrm{lossAC}}=3\times {\left(\frac{P}{\sqrt{3}U\cos \phi }\right)}^2·RL,$$

(9)

where P is the wind farm transmission power, U is the AC voltage of the AC submarine cable, $\cos \phi$ is the power factor, R is the per-unit length resistance of the AC submarine cable, and L is the length of the AC submarine cable.

The losses for DC submarine cables can be calculated using Equation (10):

$$P_{\mathrm{loss}\mathrm{DC}}=2\times {\left(\frac{P}{U_{\mathrm{DC}}}\right)}^2·RL,$$

(10)

Once the cable losses are calculated, the annual cable losses can be determined by multiplying the cable power losses by the annual utilization hours of the wind farm.

4.2. Environmental Impact of the Collection and Transmission System

As offshore wind farms increase in scale and distance from the shore, there is significant uncertainty regarding their environmental impact. Environmental issues related to offshore wind farms include electromagnetic radiation, collision risk, changes in benthic and pelagic species, alterations to the food web, and pollution from increased shipping traffic. During operation, the transmission cables that transport electrical energy generate electromagnetic radiation, which can affect the movement and navigation of species sensitive to electric or magnetic fields. The magnetic field intensity generated by AC cables ranges from 0.69 to 4.86 μT, while DC cables generate magnetic fields ranging from 56.20 to 105.59 μT [19]. The excavation and burial operations during the installation of submarine cables can disrupt the benthic marine environment, leading to the loss of benthic organisms. Survey reports indicate an average biomass of 45.10 kg/hm² in the eastern coastal areas of Jiangsu Rongcheng. The use of different submarine cable voltage levels and lengths for various collection and transmission methods can also impact the utilization of marine resources.

5. Comprehensive Evaluation Method for Offshore Wind Farm Collection and Transmission Systems

By analyzing the commonalities and differences between offshore wind farm collection and transmission systems, this paper selected evaluation indicators from aspects such as losses, economic viability, reliability, etc., to systematically and scientifically compare the characteristics of collection and transmission system schemes. The comprehensive evaluation indicator system for offshore wind farm collection and transmission systems, as constructed in this study, is illustrated in Figure 7.

5.1. Determination of Indicator Weights

Indicator weighting can be classified into subjective weighting and objective weighting methods. Subjective weighting relies on the subjective preferences or the experience of decision-makers and may lack objectivity. Objective weighting is based on the relationships between the raw data and can be overly dependent on the raw data, leading to limitations in objectivity.

This paper employed a combination weighting method that integrated both subjective and objective approaches. It considered the subjective preferences of decision-makers and objectivity on the basis of data relationships, thus overcoming the limitations of each approach.

The analytic hierarchy process (AHP) is an evaluation method designed for complex multi-objective decision-making problems. Its fundamental concept involves breaking down complex multi-objective problems into several objectives and further decomposing them into multiple levels of indicators. By calculating single rankings at each level and overall rankings, AHP resolves multi-objective decision-making problems. It has the advantages of requiring minimal quantitative data and being straightforward and practical.

The CRITIC method is an improvement on the entropy weighting method. It comprehensively considers the objective weights of indicators by evaluating the strength of comparisons and inherent conflicts among indicators. It also takes into account the variability and correlation between indicators. Therefore, in the subjective weighting approach, the AHP method is used, while the CRITIC method is employed for objective weighting.

5.2. Calculating the Combined Weights

If we use m different methods to calculate weights to indicators and the kth method determines the weights of the indicators as ${\mathit{W}}_k=\left(w_{1k},w_{2k},\dots ,w_{nk}\right),k=1,2,\dots ,m$, the combined weights of the m assignment methods are ${\mathit{W}}_0=\left(w_{10},w_{20},\cdots ,w_{n0}\right)$, and the weight of the combination of the jth indicator for the m assignment methods is:

$$w_{jm}={\displaystyle \sum _{i=1}^m{\mu }_t}{w}_{jt},j=1,2,\dots ,nt=1,2,\dots ,m,$$

(11)

where ${\mu }_t$ is the weighting factor for the tth assignment method.

According to the principle of minimizing variance, an optimization model can be established. This model aims to maximize the dispersion of evaluation values for each indicator while fully considering the differences between the indicators.

$$\left\{\begin{array}{c}\min {\displaystyle \sum _{m=1}^m{\left|{\mathit{W}}_0-{\mathit{W}}_k\right|}^2}\\ {\mathit{W}}_0-{\mathit{W}}_k=\left(w_{10}-w_{1k},w_{20}-w_{2k},\dots ,w_{n0}-w_{nk}\right)\\ {\displaystyle \sum _{i=1}^n{w}_{ik}}=1\\ {\displaystyle \sum _{i=1}^n{w}_{i 0}}=1\end{array}\right.,$$

(12)

To simplify the above equation, we can express it as follows:

$$\begin{array}{c}\left[\begin{array}{cccc}{\mathit{W}}_1{\left({\mathit{W}}_1\right)}^{\mathrm{T}}& {\mathit{W}}_1{\left({\mathit{W}}_2\right)}^{\mathrm{T}}& \dots & {\mathit{W}}_1{\left({\mathit{W}}_k\right)}^{\mathrm{T}}\\ {\mathit{W}}_2{\left({\mathit{W}}_1\right)}^{\mathrm{T}}& {\mathit{W}}_2{\left({\mathit{W}}_2\right)}^{\mathrm{T}}& \dots & {\mathit{W}}_2{\left({\mathit{W}}_k\right)}^{\mathrm{T}}\\ ⋮& ⋮& & ⋮\\ {\mathit{W}}_m{\left({\mathit{W}}_1\right)}^{\mathrm{T}}& {\mathit{W}}_m{\left({\mathit{W}}_2\right)}^{\mathrm{T}}& \dots & {\mathit{W}}_m{\left({\mathit{W}}_k\right)}^{\mathrm{T}}\end{array}\right]\left[\begin{array}{c}{\mu }_1\\ {\mu }_2\\ ⋮\\ {\mu }_m\end{array}\right]=\\ \left[\begin{array}{c}{\mathit{W}}_1{\left({\mathit{W}}_1\right)}^{\mathrm{T}}\\ {\mathit{W}}_2{\left({\mathit{W}}_2\right)}^{\mathrm{T}}\\ ⋮\\ {\mathit{W}}_m{\left({\mathit{W}}_m\right)}^{\mathrm{T}}\end{array}\right]\end{array},$$

(13)

Solving the linear system of equations yields the weight coefficient $\mu$ and thus the combination weights.

In this paper, the subjective weight ${\mathit{W}}_1$ was determined by AHP, the objective weight ${\mathit{W}}_2$ was determined by the CRITIC method, and a linear system of equations was solved to obtain ${\mu }_1,{\mu }_2$.

$$\left[\begin{array}{cc}{\mathit{W}}_1{\left({\mathit{W}}_1\right)}^{\mathrm{T}}& {\mathit{W}}_1{\left({\mathit{W}}_2\right)}^{\mathrm{T}}\\ {\mathit{W}}_2{\left({\mathit{W}}_1\right)}^{\mathrm{T}}& {\mathit{W}}_2{\left({\mathit{W}}_2\right)}^{\mathrm{T}}\end{array}\right]\left[\begin{array}{c}{\mu }_1\\ {\mu }_2\end{array}\right]=\left[\begin{array}{c}{\mathit{W}}_1{\left({\mathit{W}}_1\right)}^{\mathrm{T}}\\ {\mathit{W}}_2{\left({\mathit{W}}_2\right)}^{\mathrm{T}}\end{array}\right],$$

(14)

5.3. Comprehensive Evaluation Based on the Improved TOPSIS Model

To address the issue of the traditional TOPSIS method in which multiple evaluation schemes have the same Euclidean distance to the positive and negative ideal solutions and cannot be ranked, an improved TOPSIS approach was introduced. This method divides the positive and negative ideal solutions into different layers, further calculates rank variable characteristic values, and achieves accurate ranking. Additionally, the classical domain elements and the evaluation elements are normalized in order to handle situations in which the initial data falls outside the range of the domain. This normalization process resolves the problem of the association function being undefined (i.e., the denominator being zero), allowing for the evaluation of the target solution even when it is outside the domain range.

The specific calculation steps are as follows [20]:

When there are m objects ($i=1,2,\cdots ,m$) and n evaluation indicators ($j=1,2,\cdots ,n$), let $M_{ij}$ represent the value of the jth evaluation indicators for the ith evaluation object. These values form the initial decision matrix ${\mathit{M}}_{m\times n}$.

Step 1: Normalize the initial decision matrix ${\mathit{M}}_{m\times n}$ and transform it into a normalized matrix Y:

$$\mathit{Y}=\left[\begin{array}{cccc}{Y}_{11}& Y_{12}& \dots & Y_{1n}\\ Y_{21}& Y_{22}& \dots & Y_{2n}\\ \dots & \dots & \dots & \dots \\ Y_{m1}& Y_{m2}& \dots & Y_{mn}\end{array}\right],$$

(15)

where

$$Y_{ij}=\frac{M_{ij}}{\sqrt{{{\displaystyle \sum _{i=1}^m{M}_{ij}}}^2}},$$

(16)

Step 2: Construct the weighted norm matrix Z.

$$\mathit{Z}=W_i\mathit{Y}=\left[\begin{array}{cccc}{\omega }_1{Y}_{11}& {\omega }_2{Y}_{21}& \cdots & {\omega }_m{Y}_{m1}\\ {\omega }_1{Y}_{12}& {\omega }_2{Y}_{22}& \cdots & {\omega }_m{Y}_{m2}\\ ⋮& ⋮& & ⋮\\ {\omega }_1{Y}_{1n}& {\omega }_2{Y}_{2n}& \cdots & {\omega }_m{Y}_{mn}\end{array}\right],$$

(17)

Step 3: Form the weighted norm matrix $\mathit{Z}$ and find $Z_i^{+}$, $Z_i^{-}$, $L_i^{+}$ and $L_i^{-}$.

Step 4: According to the optimal and the inferior solution distances $L_i^{+}$, $L_i^{-}$, divide the different levels into different classes with the interval $U_{jt}=(u_{jt}^1,u_{jt}^2)$, $t=1,2,\cdots ,N$, and determine the corresponding evaluation level N.

Step 5: Normalize the evaluation levels.

$${\mathit{N}}_t^{\prime }=\left(P_t,C_j,V_{jt}\right)=\left[\begin{array}{ccc}{P}_t& c_1& 〈\frac{u_{1t}^1}{\max u_{1p}^2},\frac{u_{1t}^2}{\max u_{1p}^2}〉\\ & c_2& 〈\frac{u_{2t}^1}{\max u_{2p}^2},\frac{u_{2t}^2}{\max u_{2p}^2}〉\\ & \cdots & \cdots \\ & c_n& 〈\frac{u_{nt}^1}{\max u_{np}^2},\frac{u_{nt}^2}{\max u_{np}^2}〉\end{array}\right] p=1,2,\cdots ,N,$$

(18)

$\mathit{Z}=(z_1,z_2,\cdots ,z_n)$; normalize the weighted norm matrix Z.

$${\mathit{Z}}^{\prime }=\frac{Z_{\mathrm{ij}}}{\max z_j},$$

(19)

Step 6: Calculate the closeness degree $D_{P_i}\left(N_t\right)$ and weighted closeness degree $K_j\left(N_t\right)$ for the relevant evaluation indicators and intervals in the weighted normative matrix.

$$\begin{array}{l}{D}_{P_i}\left(N_t\right)=\left|z_{ij}^{\prime }-\frac{v_{jt}^1+v_{jt}^2}{2}\right|-\frac{v_{jt}^2-v_{jt}^1}{2}\\ K_j\left(N_t\right)=1-{\displaystyle \sum _{j=1}^n{w}_j}D\left(N_t\right)\end{array},$$

(20)

Step 7: Calculate the weighted closeness degree ${\overline{K}}_j\left(N_t\right)$ and the eigenvalue ${\delta }_i$, and achieve the precise ranking of the evaluation objects on the basis of the characteristic values of the ranking variables. The calculation flowchart is shown in Figure 8.

$$\begin{array}{l}{\overline{K}}_j\left(N_t\right)=\frac{K_j\left(N_t\right) - \min \left[K\left(N_t\right)\right]}{\max \left[K\left(N_t\right)\right] - \min \left[K\left(N_t\right)\right]}\\ {\delta }_i=\frac{{\displaystyle \sum _{j=1}^{m}s}{\overline{K}}_j\left(N_t\right)}{{\displaystyle \sum _{j=1}^m{\overline{K}}_j}\left(N_t\right)}\end{array}$$

(21)

6. Case Study

To validate the comprehensive evaluation model for the collection and transmission system proposed in this paper, an example based on a 400 MW offshore wind farm in Jiangsu Province, China, was conducted using the indicator system, as shown in Figure 1. The main parameters for the offshore wind farm case study are presented in

Table 5. Main parameters of offshore wind farm case.

Parameters	Value
Type of wind turbine	AC/DC
Capacity of wind turbine/MW	4
Number of wind turbines	100
Transmission voltage/kV	220/400
Energy transmission methods	HVDC/AC

. The topology of the wind farm is shown in Figure 9.

Under the parameters mentioned above, the specific offshore wind farm topology mentioned in Section 1 can now be specified. To ensure the comparability of the collection and transmission system’s comprehensive evaluation, this study considered different collection and transmission methods (structures shown in Appendix A, Figure A1, Figure A2 and Figure A3) and offshore distances. A total of nine scenarios, as listed in

Table 6. Evaluation cases.

Scenarios	Collection Method	Transmission Method	Offshore Distance/km
1/2/3	AC	AC	63/100/150
4/5/6	AC	DC
7/8/9	DC	DC

, were evaluated.

6.1. The Results of the Reliability Assessment

Among the reliability indicators, the transmission efficiency and average availability were considered positive metrics, while the annual outage hours, equivalent outage rate, and expected energy not supplied were considered negative metrics. The reliability assessment results are depicted in Figure 10.

According to Figure 10, it is evident that as the distance increased, the reliability of all three collection and transmission methods decreased. When the offshore distance was relatively short, both all-AC and all-DC collection and transmission systems exhibited higher reliability. However, as the offshore distance became greater, the reliability of the all-AC collection and transmission system significantly decreased. This is due to the fact that DC circuit breakers and high-capacity, high-voltage ratio DC/DC converters are not yet mature technologies, resulting in higher failure rates. As a result, the reliability of the DC collection and transmission system is slightly lower than that of the AC collection and transmission system.

6.2. The Results of the Economic Assessment

The total cost distribution for the nine collection system scenarios, taking into account the collection and transmission method as well as the offshore distance, is depicted in Figure 11.

6.3. The Results of the Loss Assessment

According to the loss model presented in the third section, the results of the loss assessment are illustrated in Figure 12.

As the all-DC collection and transmission system did not have losses associated with the offshore transformer, and the DC cable losses were lower than those of the AC cables at the same voltage level; the all-DC scheme exhibited the lowest losses. When the offshore distance was relatively close, the AC/DC conversion process in the AC collection and DC transmission system resulted in higher losses compared with the all-AC collection and transmission system. However, as the offshore distance increased, the transmission efficiency of AC cables significantly decreased; the high operating frequency of the transmission lines in the HVAC and the significant capacitive effects of the submarine cables generated significant charging currents and reactive power consumption, limiting the power transfer capability of the cables and making the AC collection and DC transmission system less favorable in terms of losses.

6.4. The Results of the Environmental Assessment

The results of the environmental assessment are illustrated in Figure 13.

In the environmental assessment, marine resource utilization was determined on the basis of local environmental survey reports, providing information about the average biomass in the coastal area. Different wind farm structures occupied varying amounts of land, resulting in different levels of marine resource utilization. Electromagnetic pollution primarily affects the activities of marine organisms and navigation, making it challenging to quantify. Therefore, this study employed the magnitude of electromagnetic radiation as a measurement criterion. As illustrated in Figure 12, it is evident that schemes incorporating DC cables have a more significant impact on the environment due to the higher levels of electromagnetic radiation associated with DC cables.

6.5. Comprehensive Evaluation

6.5.1. Subjective Weights

The development of judgment matrices for the primary and secondary indicators was followed by the computation of the weights of the primary indicators in relation to the goal level and the weights of the secondary indicators in relation to their respective higher-level indicators. By considering the consistency and variations of the judgment matrices, dynamic weighting was performed using Equation (11) to determine the weights of each second-level indicator with respect to the goal level, resulting in subjective weights, as shown in

Table 7. Weight of the second-level index based on AHP.

Indicators	C10	C12	C13	…	C30	C31
Weight	0.055	0.033	0.031	…	0.009	0.008

.

6.5.2. Objective Weights

The information on the indicators was calculated, and the weights of each second-level indicator were determined with respect to the goal level, as shown in

Table 8. Weight of the second-level index based on CRITIC.

Indicators	C10	C12	C13	…	C30	C31
Weight	0.156	0.154	0.160	…	0.015	0.143

.

6.5.3. Combination Weights

Using the optimization model, the combination weights of second-level indicators to the goal level are obtained, as shown in

Table 9. Weight of the second-level indicators.

Indicators	C10	C12	C13	…	C30	C31
Weight	0.152	0.136	0.138	…	0.018	0.111

.

Figure 14 illustrates the comparison of weights for the three algorithms. On the graph, it can be observed that the combined weights, which integrate both subjective and objective weightings, exhibit a similar overall trend to the other two methods. Additionally, they take into account the differences between indicators, enhancing their credibility.

According to the comprehensive assessment method, the evaluation results for each scenario are presented in

Table 10. Comprehensive evaluation results.

Scenarios	Collection and Transmission Method	Offshore Distance	Weighted Closeness
1	All-AC	63	1.6675
2	All-AC	100	1.7699
3	All-AC	150	3.3333
4	AC collection, DC transmission	63	1.7302
5	AC collection, DC transmission	100	1.7413
6	AC collection, DC transmission	150	3.2396
7	All-DC	63	1.7484
8	All-DC	100	1.7642
9	All-DC	150	3.2542

.

According to the comprehensive evaluation model and method described above, the comprehensive assessment results for offshore wind farms with different offshore distances and collection and transmission methods are shown in Figure 15.

For offshore wind farms located 63 km from the coast, the full AC collection and transmission option is the preferred choice regardless of the method.

For offshore wind farms located 150 km from the coast, the AC collection with high-voltage DC transmission is the optimal choice. The full DC collection and transmission option offers lower losses and does not require reactive power compensation. However, due to technical limitations, it requires multiple DC/DC converters connected in series/parallel to build a large-capacity, high voltage conversion ratio DC/DC converter. This significantly increases costs, size, and weight, which may offset the potential cost advantage. Therefore, there is a potential cost advantage.

7. Conclusions

This paper established an evaluation model and methodology suitable for offshore wind farm collection and transmission systems. The proposed model can address cost uncertainties resulting from more complex collection and transmission system structures and longer offshore distances. It also takes into account the reliability, losses, and environmental aspects of offshore wind farm collection and transmission systems. Using the proposed evaluation method, multiple collection and transmission scenarios were established and comprehensively optimized for a 400 MW offshore wind farm under various typical transmission scenarios. The results confirm the validity and effectiveness of the comprehensive evaluation model proposed in this paper for the Hai Shan offshore wind farm collection and transmission system. The results indicate that for offshore wind farms located relatively close to the shore, regardless of the method used, the full AC collection and transmission scheme is the preferred choice. For offshore wind farms located a greater distance from the shore, AC collection and HVDC transmission is the optimal choice.

The proposed decision-making method can be extended to address similar problems, but this study still has several limitations. For instance, offshore wind farm collection and transmission systems are subject to unstable external conditions, for example, the influence of wind speeds in different seasons and the influence of wake effects, so the weights of various decision criteria and their corresponding influencing factors should be updated and adjusted according to specific circumstances and scenarios.

Simultaneously, the environmental assessment within the model is not comprehensive and detailed enough, lacking in-depth research concerning its impact on avian species and marine mammals.

The current assessment model still has room for improvement. Future work will focus on refining the assessment model; enhancing factors that will contribute to its accuracy, such as external environmental considerations and wake effects; and more detailed environmental assessments.