Offshore Network Development to Foster the Energy Transition

Abstract

A growing interest in offshore wind energy in the Mediterranean Sea has been recently observed thanks to the potential for scale-up and recent advances in floating technologies and dynamic cables: in the Italian panorama, the offshore wind connection requests to the National Transmission Grid (NTG) reached almost 84 GW at the end of September 2024. Starting from a realistic estimate of the offshore wind power plants (OWPPs) to be realized off the southern coasts in a very long-term scenario, this paper presents a novel optimization procedure for meshed AC offshore network configuration, aiming at minimizing the offshore wind generation curtailment based on the DC optimal power flow approximation, assessing the security condition of the whole onshore and offshore networks. The reactive power compensation aspects are also considered in the optimization procedure: the optimal compensation sizing for export cables and collecting stations is evaluated via the AC optimal power flow (OPF) approach, considering a combined voltage profile and minimum short circuit power constraint for the onshore extra-high voltage (EHV) nodes. The simulation results demonstrate that the obtained meshed network configuration and attendant re-active compensation allow most of the offshore wind generation to be evacuated even in the worst-case scenario, i.e., the N1 network, full offshore wind generation output, and summer line rating, testifying to the relevance of the proposed methodology for real applications.

1. Introduction

The increase in renewable energy capacity reached around 507 GW in 2023 alone, almost 50% higher than in 2022. Renewable capacity additions will continue this trend in the upcoming years, with solar photovoltaics and wind being able to represent the record amount of 96% due to generation costs being lower than both fossil and non-fossil options in most countries due to policies in their support [1].

The European Union (EU) energy policies [2,3], aimed at achieving carbon neutrality by 2050 and reducing net greenhouse gas emissions by at least 55% compared to 1990 levels by 2030, are guiding the transition towards a decarbonized energy system in the EU.

To meet the ambitious targets set by future energy scenarios [4], a substantial increase in renewable wind and solar capacity is foreseen. In particular, offshore wind is expected to represent a crucial resource, benefiting from enhanced performance due to larger, more powerful turbines; stronger and more consistent winds at sea compared to on land; and a lower environmental impact [5,6]. On the other side, grid connection costs are significantly higher offshore than onshore [7]. From a social point of view, the public perception could benefit from appropriate distances from the coast, such as locations in suitable sea areas defined in maritime spatial plans. Higher maintenance costs and difficulties are further aspects to be considered.

The offshore wind sector is projected to expand rapidly in the coming years, driven by recent advancements in floating wind technologies. These new technological solutions will unlock new markets previously limited by seabed constraints while introducing new technical and operational challenges to Transmission System Operators (TSOs) [8,9].

In fact, the seabed structure and the seawater depth are crucial factors for the viability of offshore wind power plants (OWPPs) [10]. Currently, most of Europe’s offshore wind installations are concentrated in the northern seas, with the North Sea hosting 80% and the Irish Sea and the Bay of Biscay each hosting 10% of European offshore wind installations. Also, the Baltic Sea seems to be very attractive as an offshore reservoir thanks to the proper water surface at a short distance from the coast and a low average water depth [10,11].

Furthermore, in recent years, offshore wind initiatives have been experiencing significant growth, particularly in the Mediterranean Sea. In Italy, the number of offshore wind connection applications has risen sharply, increasing from 4.5 GW in December 2020 to over 84 GW by September 2024. This value far exceeds the national target of 2.1 GW set by the most recent “National Energy and Climate Plan” (“NECP”) policy scenario for 2030 [4].

Figure 1 illustrates the evolution of offshore wind connection applications to the National Transmission Grid (NTG) [12] across various market zones in the Italian power system [13,14]. As depicted, most OWPPs are concentrated in southern Italy (33%) and the main islands (31% and 18%, respectively, in Sicily and Sardinia) [12]. This concentration is attributable to the higher wind availability, which results in improved load factors. However, these regions face significant challenges because of infrastructure transmission deficiencies [15] and lower electricity demand (registered and expected) when compared to the northern and central northern areas of the country, exacerbating TSO’s transmission planning complexities [16].

Furthermore, given that most of these plants have particularly relevant sizes, typically in the range of power between 500 and 1000 MW, along with the variable nature of the primary energy source, it is essential to establish suitable grid infrastructure sizing, particularly in light of the expected relevant power injections. In this context, the Italian TSO, Terna, has recognized the need to conduct extensive technical surveys on an international scale to gather valuable information for developing appropriate connection solutions, as noted previously [5,8]. In principle, there are three alternative transmission approaches for offshore wind farms (OWFs), namely HVDC, HVAC, and LFAC [17,18,19,20]. At this time, the latter is purely theoretical, with contrasting evaluations of the expected benefits, and is not generally regarded as an optimal fit for OWF connections [21]. Of the other two solutions, HVDC allows for longer transmission distances and, in a broader perspective, is seen as the gateway to a future multiterminal DC “supergrid” [22,23]. On practical grounds, however, HVAC technology has been identified as the most suitable option for distances up to 100–120 km from the shore and for OWFs with a rated power capacity of less than 1 GW [8,9,24], with studies pointing to an even broader power–distance envelope [25,26]. However, novel connection alternatives could be developed to accommodate greater distances from the shore, higher rated capacities, and deeper water depths, along with updates to the Network Grid Code [27,28].

Currently, based on the technological maturity of the required components and the characteristics of OWPPs, such as distances from shore and rated power, Terna has identified two HVAC-technology-based options as the most suitable for connecting OWFs to the nearest robust Extra High Voltage (EHV) onshore node (400 or 230 kV), as illustrated in Figure 2: (i) Option 1, for distances of less than 40–60 km and a rated power of up to 300 MW, consists of the direct interconnection from the OWPP to the onshore network connection node using the same inter-array 66 kV voltage level; (ii) Option 2 involves an offshore substation for the step-up transformer 66 kV/EHV and an HVAC link from the OWPP to the onshore EHV NTG bay [5,8,29]. To facilitate the development and management of the offshore connection infrastructure, Terna has adopted a “Developer Build Model,” similar to the UK model. In contrast, the “TSO Build Model” (used in France, Germany, the Netherlands, Belgium, and Denmark) places the development and operation of offshore transmission infrastructure under the responsibility of the TSO. This model often includes centralized definition and planning (at the institutional level) of areas for offshore installations.

Existing literature on AC-connected OWFs primarily focuses on point-to-point systems. This paper specifically addresses the meshed AC configurations of potential offshore NTG stations to harness the production from future wind farm clusters off the southern coast of Italy, identified as the most representative case study. An optimization procedure based on DC power flow approximation has been developed and applied to determine the optimal meshed offshore grid configuration for integrating the OWPPs under study. The test grid is modeled using the power transfer distribution network (PTDF) matrix, considering all planned network developments [30] in place by 2040, as well as the detailed connection solutions provided to the OWPPs under evaluation.

Reactive power control of the HVAC OWPPs’ interconnection links is a critical issue for ensuring voltage stability and minimizing power losses. OWPPs present significant challenges for power system operation due to their distance from the onshore network, variable wind speed, and the complexity of the electrical infrastructure.

As is well known, AC submarine cables exhibit significant charging currents, which increase with cable length. This necessitates managing substantial amounts of capacitive reactive power surpluses [31,32].

To this purpose, the reactive compensation requirements for marine cables and offshore substations are evaluated using the optimal power flow (OPF) method. The AC operation of the complete system (onshore and offshore grid) is then verified over a full year through an optimization procedure to ensure a minimum level of short-circuit power at EHV onshore connection nodes.

The remainder of the paper is organized as follows: Section 2 presents the novel methodology developed. Section 3 illustrates the system under study. Section 4 presents the results obtained. Finally, Section 5 concludes the paper.

2. Methodology

2.1. Architecture of the Procedure

Starting from a realistic estimate of the offshore windfarms to be built off the southern coast, and assuming the 2040 scenario for the central and southern portion of the Italian NTG, the procedure is articulated into the following steps:

• Aggregation of the individual OWPPs into larger clusters based on a combined distance/capacity constraint;
• Individuation of an optimal EHV AC offshore network configuration connecting the aforementioned clusters and the shore network using a DC security constrained optimal power flow (DC-SCOPF). This step incorporates an (N − 1) security constraint on the whole onshore and offshore network, considering only the active power flows;
• Determination of the shunt compensation requirements for the resulting EHV AC submarine cable network;
• Determination of the optimal size and location of reactive compensation devices for the complete onshore and offshore network through an AC OPF algorithm. This step incorporates a combined voltage profile/minimum short-circuit power constraint.

A more detailed description of Steps 2, 3, and 4 is provided in the following subsections.

2.2. Optimal Offshore Network Configuration

The optimization problem formulated to assess the offshore network configuration is based on a DC-SCOPF type optimization model. The nomenclature of sets, parameters and variables is described in

Table 1. Summary of the nomenclature: sets and parameters.

Sets	Description
K	Set of AC branches
KDC	Set of DC branches
KS	Set of branches of the offshore network, all switchable
NB	Set of buses
NOWF	Set of buses of the offshore network
NSTO	Set of buses with a storage system installed
S	Set of scenarios
Parameters	Description
PTDFS	|K| × |NB| PTDF matrix in scenario s
Φs	|K| × |K| Φ matrix in scenario s
DCDFS	|K| × |KDC| DCDF matrix in scenario s
I	|KS|×|KS| identity matrix, independent of scenario s
P0	|NB\NOWF| vector of nodal power injections of onshore buses at t = Tdim (P0(i) > 0 if power is generated), independent of scenario s
POWF	|NOWF| vector of generated power in offshore buses at t = Tdim, independent of scenario s
PSTO	|NSTO| vector of rated power of storage systems installed in the onshore network, independent of scenario s
FMAX	|K| vector of AC branch capacities, independent of scenario s
FMAXDC	|KDC| vector of DC branch capacities, independent of scenario s
EOWF	Aggregate power generated at offshore buses at t = Tdim
CurtMAX	Maximum allowed curtailment of offshore wind farms, in p.u. of EOWF
M	Large enough number

and

Table 2. Summary of the nomenclature: variables.

Linear Variables	Description
PNOD	|NB| × |S| matrix of bus injected powers in each scenario s
vT	|KS| × |S| matrix of “flow-canceling transactions”
PDC	|KDC| × |S| matrix of power flows through HVDC branches
Binary Variables	Description
z	|KS| × |S| matrix referred to switchable line status: z(i,s) = 0 if branch i is switched off in scenario s, z(i,s) = 1 if branch i is connected in scenario s

. In the following subsection, |A| denotes the cardinality of set A.

2.2.1. Network Representation

The network is represented using the DC power flow approximation and the power transfer distribution factors (PTDF) matrix. In the PTDF formulation, power flows F are calculated as follows:

$$F=PTDF\cdot P_{NOD}$$

(1)

If HVDC lines are installed in the network, they are modeled as nodal injections at their bus terminals. Their effect on F can be included using the direct current distribution factors (DCDF) matrix according to

$$F=PTDF\cdot P_{NOD}+DCDF\cdot P_{DC}$$

(2)

Since both PTDF and DCDF strongly depend on the network topology, this formulation would require the recalculation of PTDF and DCDF for each branch removal/addition, leading to a significant computational burden. This can be overcome by using the formulation described in [33], which simulates branch connection/disconnection through appropriate nodal injections, named “flow-canceling transactions”, without altering the network topology. In this approach, the PTDF and DCDF matrices are calculated only once, considering all branches connected. Following [33] and denoting the set of switchable branches with superscript S and the set of non-switchable branches with superscript N, the power flows F^N through non-switchable branches are calculated as

$$F^N=PTD{F}^N\cdot P_{NOD}+{\Phi }^{N,S}\cdot v_T+DCD{F}^N\cdot P_{DC}$$

(3)

Whereas the power flows F^S through switchable branches are calculated as

$$F^S=PTD{F}^S\cdot P_{NOD}+\left({\Phi }^{S,S}-1\right)\cdot v_T+DCD{F}^S\cdot P_{DC}$$

(4)

In (3) and (4), Φ is the “selfPTDF” matrix, calculated as $\Phi =PTDF·{Cft}^T$, where Cft is the connection matrix. Cft(i,j) = 0 if branch i is not connected to bus j, Cft(i,j) = 1 if bus j is the “from” node of branch i, and Cft(i,j) = − 1 if bus j is the “to” node of branch i.

2.2.2. Structure of the Optimization Procedure

The DC-SCOPF procedure aims at optimally configuring the offshore network topology in the following steps:

(1)

Read input data;

(2)

Calculate all the parameters required by the optimization problem;

(3)

Implement and solve the optimization model in a representative time-stamp T_dim. This step includes all N_S scenarios, with N_S = 1 + K + K_DC, i.e., in N condition (all branches in operation) and applying the N − 1 security criterium considering the contingency of each branch of the network (both onshore and offshore);

(4)

Check the solution in other representative time-stamps. If in any time-stamp at least one branch capacity is exceeded, go to Step 2 and include the time-stamp in the optimization problem;

(5)

Provide the solution, i.e., the optimal offshore network topology.

2.2.3. The Optimization Model

The mathematical formulation of the optimization model is described below. The symbol ⸰ refers to the Hadamard product between two arrays.

Objective function

$$\min \left(E_{OWF}-{\displaystyle \sum _{n\in N_{OWF}}{P}_{NOD}\left(n,1\right)}\right)$$

(5)

Constraints

$$P_{NOD}\left(n,s\right)=P_0\left(n\right), \forall n\in N_B\backslash \left(N_{OWF}\cup N_{STO}\right), \forall s$$

(6)

$$P_0\left(n\right)-P_{STO}\left(n\right)\le P_{NOD}(n,s)\le P_0\left(n\right)+P_{STO}\left(n\right), \forall n\in N_{STO}, \forall s$$

(7)

$$0\le P_{NOD}(n,1)\le P_{OWF}\left(n\right), \forall n\in N_{OWF}$$

(8)

$$-M\cdot \left(1-z\left(i,s\right)\right)\le v\left(i,s\right)\le M\cdot \left(1-z\left(i,s\right)\right), \forall i\in K_S, \forall s$$

(9)

$$\begin{array}{l}-F_{MAX}\left(i\right)\le PTD{F}^N\left(i,n\right)\cdot P_{NOD}\left(n,s\right)+{\Phi }^{N,S}\left(i,j\right)\cdot v_T\left(j,s\right)+\\ DCD{F}^N\left(i,w\right)\cdot P_{DC}\left(w,s\right)\le F_{MAX}\left(i\right), \forall i\in K\backslash \left(K_S\cup K_{DC}\right), \\ \forall j\in K_S, \forall n,\forall s, \forall w\in K_{DC}\end{array}$$

(10)

$$\begin{array}{l}-F_{MAX}\left(i\right)\circ z\left(i,s\right)\le PTD{F}^S\left(i,n\right)\cdot Pnod\left(n,s\right)+\left({\Phi }^{S,S}\left(i,j\right)-I\left(i,j\right)\right)\cdot v_T\left(i,s\right)\\ +DCD{F}^S\left(i,w\right)\cdot P_{DC}\left(w,s\right)\le F_{MAX}\left(i\right)\circ z\left(i,s\right), \\ \forall i\in K_S, \forall j\in K_S, \forall n,\forall s, \forall w\in K_{DC}\end{array}$$

(11)

$$P_{NOD}\left(n,s\right)=P_{NOD}\left(n,1\right), \forall n\in N_{OWF}, \forall s>1$$

(12)

$$z\left(i,s\right)=0, \forall \left(i\in K_S\cap i=s-1\right), \forall s>1$$

(13)

$$z\left(i,s\right)=z\left(i,1\right), \forall \left(i\in K_S\cap i\ne s-1\right), \forall s>1$$

(14)

$$-F_{MAXDC}\left(i\right)\le P_{DC}\left(i,1\right)\le F_{MAXDC}, \forall i\in K_{DC}$$

(15)

$$P_{DC}\left(i,s\right)=P_{DC}\left(i,1\right), \forall i\in K_{DC}, \forall (s>1)\cap \left(s<N_S-\left|K_{DC}\right|\right)$$

(16)

$$P_{DC}\left(i,s\right)=0, \forall i\in K_{DC}, \forall s=N_S-i$$

(17)

$${\displaystyle \sum _{n\in N_{OWF}}{P}_{NOD}\left(n,1\right)}\ge \left(1-Cur{t}_{MAX}\right)\cdot E_{OWF}$$

(18)

Equations (5)–(18) describe a mixed integer linear programming (MILP) problem, due to the presence of the binary variables z representing the state of the switchable lines. The objective is to minimize the reduction in offshore wind generation over the time period T_dim, calculated as the sum of the power generated at all equivalent nodes in the offshore grid, as defined in Equation (5).

In all scenarios, nodal power injections at onshore nodes and at nodes where storage is not installed are constrained by (6) to the injections P₀. On the other hand, nodal injections at storage buses may vary within the range ±P_STO, as described by (7): note that the constraint (7) allows P_NOD to differ in each scenario, enabling each storage unit to adjust its power injection based on the contingency. Nodal injection at each offshore bus is limited between 0 and P_OWF, as stated by (8), allowing for wind curtailment.

In the case where the switchable branch i is on, i.e., z(i,s) = 1, the constraint (9) enforces a zero flow-canceling transaction; on the other hand, if the switchable branch i is off, i.e., z(i,s) = 0, the flow-canceling transaction can range between -M and M. In the case of both non-switchable and switchable branches, respectively, the constraints (10) and (11) limit power flows to the branch capacity. Moreover, in the case where a switchable branch is off, (11) imposes a zero active power flow.

Offshore wind generation is forced to be the same in all scenarios by (12), thus ensuring that wind offshore generation dispatch meets N − 1 security requirements.

Regarding the status of switchable offshore branches in contingency scenarios, the constraint (13) switches off the branch i when scenario s corresponds to the contingency of branch i itself, whereas (14) enforces the same status for branch i in all other scenarios. Due to (13) and (14), an offshore branch is either always switched off, and therefore not installed by the procedure, or is always switched on (i.e., is installed by the procedure) except during its own contingency scenario.

HVDC lines’ operation is considered by the constraints (15)–(17). The constraint (15) imposes that in Scenario 1, i.e., without contingencies, the active power set-point of each HVDC line is limited by the line capacity. On the other hand, in a contingency scenario the constraint (16) imposes the same active power set-point of Scenario 1, except for the scenario corresponding to the contingency of the HVDC line itself: in this case, the constraint (17) imposes a zero active power flow through the HVDC line.

Lastly, the constraint (18) limits the maximum curtailment of aggregate wind generation to Curt_MAX.

The output of the model is the optimal status of each offshore switchable line at the time-stamp t = T_dim. After this step, a simple DC power flow is applied in other significant time-stamps to verify whether the grid topology provided at T_dim remains valid, i.e., no branch overload occurs. If the check is successful, the procedure stops and returns the optimal topology, otherwise the first time-stamp with branch overloads is added to the model and the optimization procedure restarts. This iterative process continues until no further overloads are found at any significant time-stamp.

The DC-SCOPF procedure for offshore network configuration is a home-made procedure implemented in MATLAB R2019b and coupled with an external solver for the solution of the MILP formulation.

2.3. Shunt Compensation of the Offshore Grid

The study of the steady-state operation of underground AC cable lines can be approached through an equivalent positive-sequence circuit model, analogous to that obtained for overhead lines; compared to the latter, cables constitute a special case in terms of charging current and reactive power balance. One of the peculiar characteristics of cables, especially EHV cables (in the case under consideration, at 400 kV–50 Hz), is the value of the surge impedance Z_c, generally included in the interval of 30–60 Ω, significantly lower than that of a typical 400 kV overhead line (250–320 Ω). This is for two fundamental reasons:

• For the same voltage level, the positive-sequence capacitance per unit length (p.u.l.) of cables is much higher than that of overhead lines (roughly an order of magnitude greater). This is attributed to the value of the relative dielectric constant of the insulator (ε_r = 2.4 for XLPE, universally adopted for 400 kV AC cables), and the reduced distance between the phase conductor and the metallic screen. In submarine applications, the metallic screen is invariably connected to earth at both ends of the connection, according to the solid bonding technique.
• The positive-sequence longitudinal reactance per unit length (p.u.l.) of cables is lower than that of overhead lines, due to the smaller distance between the phases; the (X_OHL/X_CL) ratio between the reactance of an overhead line (X_OHL) and the reactance of a cable line (X_CL) varies significantly based on the operating voltage level and the laying method of the cable itself. In 400 kV transmission networks, overhead lines are equipped with bundled conductors, or more rarely double, while cables are generally laid flat with phases spaced 1–2 m apart; under these conditions, the X_OHL/X_CL ratio can be estimated around 1.5 [34].

Especially for the 400 kV level, the ampacity of XLPE-insulated cables with a large cross-section is, however, lower than that of a typical bundled conductor overhead line, essentially due to the greater difficulty of dissipating the heat generated by internal losses. Consequently, unless more than one cable per phase is installed, the transfer capacity of an EHV overhead line cannot be achieved by a cable line. For the same conductor cross-section, the ampacities of submarine AC cables are slightly higher than those of underground cables; this is largely due to the lower values of thermal resistance encountered by the heat flux.

The consistently capacitive nature of cables results in two primary issues: excessive reactive power generation, causing voltage rises at interconnection points, and substantial capacitive charging currents that circuit breakers must interrupt during no-load conditions. To mitigate these problems, shunt reactors are commonly employed to compensate for long cable lines (typically exceeding 10–15 km). These reactors are directly connected to the cable terminals to reduce the reactive power surplus and minimize the capacitive current burden on circuit breakers. Typical compensation levels for long EHV cables range from 90% to 97%.

Major global manufacturers do not currently offer three-phase 400 kV–50 Hz cables. However, significant demand from large-scale clients could likely stimulate rapid growth in the availability of such cables. A credible estimate of the electrical characteristics of potential 400 kV–50 Hz submarine cables with XLPE insulation, both in three-phase and single-phase configurations, is given in

Table 3. Electrical data for projected 400 kV–50 Hz XLPE submarine cables.

Cable Type	S (mm2)	z’ (Ω/km)	c’ (nF/km)	Iz (A)	Pc (MVA)	Sz (MVA)
Single core	2000 Cu	0.023 + j0.100	240	1660	4395	1150
Three-core	1600 Cu	0.019 + j0.120	200	1070	3660	740

.

Even considering the different conductor cross-sections, the values reported in Table 3 highlight the clear superiority of the single-core solution in terms of the current carrying capacity I_z, and therefore the maximum power transmission at the thermal limit, S_z, which is 1150 MVA for the single-core cable versus 740 MVA for the three-core solution. For a 400 kV line, these are not particularly high values, especially for the three-core cable. In view of these considerations, the use of single-core submarine XLPE cables at 400 kV–50 Hz may deserve some attention, at least as a study hypothesis. It may also be interesting, for a given configuration, to compare the two solutions (single-core and three-core), carrying out a technical–economic evaluation that also considers the cost of the offshore platform. Given the upper limit on the practical cable cross-section S reported in Table 3, the only viable approach to increase the maximum transmittable power is to increase the number of circuits. In addition to the obvious increase in the cost of the line, this involves multiplying the shunt reactors to be installed, both in the terrestrial station and on the offshore platform, with a significant impact on weight and therefore cost.

The shunt compensation of the offshore grid is achieved using an in-house, deterministic algorithm based on the formulation presented in [32] and implemented within the MATLAB environment.

2.4. Optimization of the Reactive Compensation of the Whole Onshore and Offshore Grid

The devices used to perform the reactive compensation of the whole network are synchronous condensers (SCs), whose optimal size and location are chosen by an optimization procedure based on a specific class of genetic algorithms, namely NSGA-II [35,36]. This algorithm is a benchmark for evaluating the performance of new optimization algorithms and is widely used by the scientific community.

The purpose of the optimization is to minimize both the number of nodes with short-circuit power below a certain threshold and the costs of SC installation, resulting in a bi-objective optimization problem. The operation begins by initializing a population with the characteristics of random individuals. Then, the short-circuit power at all nodes and the cost of SCs are evaluated. Next, the stopping criterion is checked. If this is not satisfied, a new iteration is performed. A rank and crowding distance are first assigned to the solutions. Then, a binary tournament is run to select the solutions that will serve as parents to create the new population. Once the parents are chosen, crossover operations are performed to generate the chromosomes of the offsprings and finally the mutation operator is applied. A flow chart of the optimization procedure is provided in Figure 3.

In the optimization procedure, nodal injections of active power are derived from the DC-SCOPF procedure outlined in Section 2.1 except for borders nodes, i.e., nodes interconnecting the portion of the Italian onshore grid under study with the rest of the NTG. At border nodes, generators are simulated to account for joule losses, which are not considered in the DC load flow approximation. Regarding nodal injections of reactive power, all loads are simulated with a 0.98 lagging fixed power factor, whereas the power factor of all of the distributed generators may vary between 0.95 leading and 0.90 lagging. SCs may be installed at any bus and may inject a reactive power between the limits in under-excitation and in over-excitation. Bus voltages are kept in the 0.95–1.05 range per unit of the rated voltage and currents flowing through branches are limited by ampacity.

The optimization of the reactive compensation of the whole onshore and offshore grid is performed using a home-made procedure developed in Python implementing a metaheuristic algorithm based on NSGA-II.

3. Case Study

3.1. System Under Study

In this paper, a test grid portion located in the south of the country, encompassing the Calabria, South, and Center-South bidding zones of the Italian power system has been studied under a very long-term horizon taking into consideration all planned network developments.

The system under study comprises 218 power lines and 156 nodes (both existing and planned) focusing on the EHV transmission network (i.e., 400/230 kV voltage levels). Consequently, equivalent sub transmission power injections/withdrawals were assessed at the 400/150 kV and 230/150 kV transformers. Furthermore, since the purpose of the study is to identify the optimal offshore grid topology that minimizes the expected generation curtailment of the EHV-connected OWFs within the analysis perimeter, the latter are explicitly modeled. In contrast, onshore wind and solar photovoltaic plants, expected to be connected to the 150 kV sub transmission grid, are represented as equivalent power injections at appropriate nodes.

The network limits in “N” and “N − 1” in both summer and winter condition are considered with a maximum accepted load of 80% in the N condition, increased to 120% in the N − 1 condition [37,38].

The Terna 2040 network scenario includes a vast array of reactive compensation devices, namely 5 STATCOMs (each rated ±125 MVAr), 10 synchronous condensers (each rated −125/+250 MVAr), and 25 controllable shunt reactors, with an aggregate rating of 5500 MVAr. STATCOMs and synchronous condensers are assumed to be fully controllable within their capability, whereas shunt reactor outputs can vary between 40% and 100% of the rated power.

Existing and planned HVDC links are simulated as equivalent generators with variable output within their respective capacity limits. Power transfers between the system under consideration and adjacent network parts are modeled as equivalent exchanges, depending on the capability of the boundary power lines.

3.2. Data and Scenarios

The analysis has been carried out considering the “Distributed Energy” (“DE”) 2040 policy scenario [39]. The storage and onshore renewable energy sources (“RES”) generation capacity, as well as the expected load, align with the target objectives.

The distribution of the future onshore wind (15 GW) and solar photovoltaic (50 GW) targets for the Calabria, South, and Center-South bidding zones was determined based on the connection request solutions provided by the TSO and their progress [12]. The same approach was adopted for the nodal distribution of the future storage quota, which amounts to approximately 91.2 GWh.

A distinct approach was employed to define the OW target, as it does not directly correspond to the DE 2040 target. Based on the connection request data, a multi-criteria analysis was performed using the Technique for Order Preference by Similarity to an Ideal Solution (“TOPSIS”) [40,41,42] to select the OWPPs with the highest probability of concretization. This analysis considered three key criteria identified through technological surveys: (i) distance from shore, (ii) water depth, and (iii) rated power. The analysis resulted in the selection of 22 OWPP initiatives, representing 10.9 GW, as the most likely to be realized.

The DE 2040 electrical demand per market zone was distributed with regional detail based on available historical data [43] and provisions regarding load evolutions. The regional target was then further divided between network nodes depending on specific power withdrawals expected at the 400–230/150 kV transformers. The total electrical load within the system under study amounts to approximately 110 TWh. For the sake of clarity, all assumptions regarding RES and storage capacity, as well as load consumption, implemented within the system under study are summarized in

Table 4. Summary of assumptions about RES technology capacity [GW], storage capacity [GW], and load [TWh] for the system under study.

RES Technology	[GW]
Solar photovoltaic	50
Onshore wind	15
Offshore wind	11
Storage capacity	[GWh]
	91.2
Load	[TWh]
	110

.

The analyses were conducted on an hourly basis throughout the entire year. DE 2040 profiles were assumed for load and RES onshore generation, while a more specific producibility analysis was executed for the OW generation. For each OWF, the hourly generation profile was extracted from [44] using latitude and longitude coordinates, considering a 7 MW wind turbine with a 100 m hub height and utilizing wind speed data from the year 2022 available from the MERRA-2 database [45].

Storage systems can vary their absorbed/delivered power within their P_min ÷ P_max range according to the system balance needs.

The RES generation scenario is depicted in Figure 4, while Figure 5 illustrates the load and RES production distribution implemented in the optimization model for all the three bidding zones of the Italian power system considered in this study. A more intense color in the load orange color bar indicates higher consumption concentrations in the Center-South regions. Onshore RES production (green color bar) is more pronounced in the southern regions, although it is relatively uniform within the analysis perimeter. Finally, the blue color bar representing offshore wind production is heavily weighted towards the southern regions.

A representative grid portion incorporating the considered offshore wind generation is illustrated in the single-line diagram of Figure 6.

4. Discussion of Results

4.1. Sizing of the Offshore Network

To size the offshore network, the optimization problem described by (5)–(18) is solved using the CPLEX commercial solver, interfaced with MATLAB through the YALMIP [46] open-source software. To define a best/worst case interval, simulations of the whole year-long generation and load profiles have been conducted considering either winter or summer overhead line ratings. Cable lines, including offshore connections, are assigned a single year-long rating.

The new offshore network retains all existing OWF collection platforms and their export cables. As a first step in defining the new topology, nearby collection platforms are grouped into clusters with a capacity of approximately 2.5 GW. Each cluster is then centered on a new offshore bus, as summarized in

Table 5. OWF clustering.

Bus	Number of OWFs	Capacity (MW)
1	5	1300
2	4	1330
3	1	250
4	4	2570
5	1	840
6	2	1300
7	3	1980
8	2	1350

. These barycentric nodes are then connected by the new offshore lines.

In its current implementation, the algorithm permits connections only between offshore clusters, with exceptions for the terminal (i.e., northernmost and southernmost) nodes of the new offshore array, which can also be connected to the shore. Figure 7 illustrates this, where red lines represent OWF export connections and shaded blue lines depict possible offshore network paths between clusters nodes (black dots).

Considering the hour of maximum offshore generation (P_max = 10750 MW) as the optimization time-stamp T_dim, the resulting optimal network (i.e., the network that minimizes overall OWF generation curtailment) comprises the following branches, shown in blue lines in Figure 8:

• 2 branches between Bus 2 and Bus 4;
• 2 branches between Bus 4 and Bus 1;
• 1 branch between Bus 7 and Bus 1;
• 2 branches between Bus 8 and Bus 5;
• 2 branches between Bus 6 and Bus 3;
• 3 branches between Bus 3 and the onshore network.

Each branch consists of three 400 kV, 2000 mm² single-core copper cables.

Since the time-stamp T_dim corresponds to a winter hour, the optimization is conducted using the winter rating for the onshore network, assuming N − 1 conditions. Subsequently, the OWF power generation/curtailment achievable with the proposed topology for the t = T_dim generation and load profile has been evaluated for both winter and summer overhead line ratings, in both N and N − 1 operating conditions. The results are summarized in

Table 6. Total OWF generation and percent curtailment.

Operating Condition		Pgen (MW)	Curtailment (%)
Winter scenario	N security	8300	22.7
	N − 1 security	8300	22.7
Summer scenario	N security	7700	28.3
	N − 1 security	7460	30.6

.

In winter conditions, maximum offshore power generation is sustainable in all N − 1 scenarios, indicating that single onshore network component outages do not impose further limitations on OWF output. However, in summer conditions, N − 1 scenarios exhibit higher curtailment levels compared to the base case.

Table 7. Offshore cluster node curtailment (in % of the T_dim generating capacity).

Operating Condition		Bus 1	Bus 2	Bus 3	Bus 4	Bus 5	Bus 6	Bus 7	Bus 8
Winter scenario	N security	0	26.8	0	7.3	100	15.9	0	66.4
	N − 1 security	0	26.8	0	7.3	100	15.9	0	66.4
Summer scenario	N security	0	23.4	77.4	0	0	44.9	47.6	79.9
	N − 1 security	0	23.7	100	0	11.6	33.8	46	100

provides a detailed breakdown of curtailment percentages for individual OWF cluster nodes at t = T_dim, as a percentage of the local aggregate generation capacity.

It should be pointed out that the above results are quite sensitive to the presence of storage systems in nearby onshore nodes: up to 3.9 GW are foreseen in the South bidding zone.

Table 8. Total OWF generation and percent curtailment, without storage systems.

Operating Condition		Pgen (MW)	Curtailment (%)
Winter scenario	N security	4930	54.1
	N − 1 security	4890	54.5
Summer scenario	N security	4000	62.3
	N − 1 security	3560	66.8

and

Table 9. Offshore cluster node curtailment (in % of the T_dim generating capacity), without storage systems.

Operating Condition		Bus 1	Bus 2	Bus 3	Bus 4	Bus 5	Bus 6	Bus 7	Bus 8
Winter scenario	N security	11.0	0	100	100	100	88.2	0	71.1
	N − 1 security	47.8	0	100	100	100	26.1	0	100
Summer scenario	N security	37.9	0	100	100	100	100	0	100
	N − 1 security	100	0	100	20.0	100	83.6	100	100

present results obtained in the absence of these storage systems, revealing significantly higher curtailments in all simulated scenarios. By way of comparison, the presence of storage systems reduces the overall (N − 1) winter curtailments by more than half, passing from 54.5% to 22.7% of peak generation, as shown in Table 6 and Table 8. A comparison of Table 7 and Table 9 highlights the substantially higher local curtailments at the nodal (i.e., OWF) level when storage is absent, with several OWFs practically idling in the worst-case scenario.

4.2. Sizing and Optimization of the Reactive Compensation

As outlined in Section 2.3, all offshore cable lines were individually compensated by means of shunt reactors installed at the line terminals. A 95% shunt compensation degree was applied, resulting in a total compensation power of 20.4 GVAr. Of this, 14.3 GVAr is connected to offshore nodes, while 6.1 GVAr is connected to onshore nodes.

Optimization yielded an initial solution with a cost of EUR 424 million to achieve a short-circuit power of 8000 MVA at 400 kV network nodes. This solution incorporates 18 synchronous condensers, each rated 250 MVAr, with 14 of them installed in pairs. Due to the constraint limiting the number of synchronous condensers per node to a maximum of two, the algorithm could not enforce the desired current at all nodes. One node, despite having two condensers installed, exhibited a slightly lower short-circuit power of 7130 MVA. Given this minor discrepancy (approximately 10.3 kA below the target of 11.5 kA), the solution was retained. The calculated pre- and post-optimization short-circuit power values at the network nodes are summarized in Figure 9 as color maps; the attendant distribution of the short-circuit power values at the 400 kV nodes is shown in Figure 10, with the 8000 MVA threshold emphasized.

Duration curves of the reactive power and node voltage at the installation points of synchronous condensers are used to summarize the main results. These curves are shown in Figure 11 for 250 MVAr plants and in Figure 12 for 500 MVAr plants.

The results indicate that synchronous condensers operate almost exclusively in overexcitation throughout the year, as expected given the disappearance of conventional synchronous generators from the grid; the only exception is one unit which operates in slight underexcitation for about 3000 h per year. Regarding the voltages of the SCs, they remain within the range of 0.99 p.u. to 1.03 p.u. for 95% of the hours. Figure 11 and Figure 12 also evidence that practically all foreseen synchronous condensers retain a substantial reactive power reserve, as expected given the stringent nodal constraint on the minimum short-circuit power level at all EHV buses.

5. Conclusions

This paper introduces a novel optimization model, based on the DC security constraints optimal power flow approximation of the network, to determine the optimal meshed offshore AC grid topology that minimizes the overall OWPP generation curtailment.

A representative case study for the Italian power system within a very long-term scenario was modeled using the PTDF matrix. The resulting mixed integer linear programming problem was solved with hourly resolution over an entire year. The model incorporates accurate (both onshore and offshore) RES producibility and load profiles. These profiles are based on historical site-specific time series, appropriately adjusted to account for expected technological advancements and evolutions. Furthermore, the foreseen additional storage capacity, network developments, and connection reinforcements related to the planned OWPPs are included to set up a highly realistic case study.

The analysis investigates the optimal offshore AC network configuration in normal and N − 1 conditions, considering the different seasonal thermal ratings of onshore transmission lines. The procedure yields a meshed topology with offshore branches connecting different OWPPs clusters.

The results obtained for the relevant snapshot of maximum offshore generation demonstrate that the optimal meshed topology limits curtailment to approximately 23% in the winter scenario, increasing to 30% in the summer scenario.

Building upon the results obtained from the DC-SCOPF procedure, the reactive power compensation requirements of the entire onshore and offshore meshed AC grid are assessed through a bi-objective optimization able to define the SCs’ needs and costs to ensure a minimum level of short circuit power at each 400 kV network node.

In the face of challenging EU climate and energy targets, the proposed methodology provides a framework that systematically integrates rigorous and practice-oriented aspects. In addition to significant novel contributions, this study presents a wealth of practical material, as the proposed approach has been applied to the real-world case of the Italian transmission system within a very-long-term energy planning scenario, making it suitable for practical applications.

The findings of this study provide a foundation for the evolution of this approach, integrating the optimal AC offshore network topology with appropriate HVDC links to facilitate the efficient routing of OWPP generation to load areas located far from offshore installations. Future work will address this topic, including technological, operation, and economic aspects.