Site Suitability Assessment and Grid-Forming Battery Energy Storage System Configuration for Hybrid Offshore Wind-Wave Energy Systems

Abstract

Hybrid offshore wind-wave systems play an important role in renewable energy transition. To maximize energy utilization efficiency, a comprehensive assessment to select optimal locations is urgently needed. The hydraulic power characteristics of these systems cause power fluctuations that reduce grid frequency stability. Thus, a site suitability assessment and a grid-forming battery energy storage system (BESS) configuration method are proposed. Considering energy efficiency, dynamic complementary characteristics, and output stability, a framework integrating three indices of Composite Energy Output Index (CEOI), Time-Shifted Cross-Covariance Index (TS-CCI), and Energy Penetration Balance Index (EPBI) is constructed to assess site suitability. To ensure secure and stable operation of microgrid, the frequency response characteristics of the hybrid system are analyzed, and the corresponding frequency constraint is given. A BESS configuration method considering frequency constraint is developed to minimize life cycle costs and maintain grid stability. Applied to a case study along China’s southeast coast, the assessment method successfully identified the optimal offshore station, confirming its practical applicability. The BESS configuration method is validated on a modified IEEE 30-bus system, with a 6.35% decrease in life cycle cost and complete renewable utilization. This research provides a technical and cost-effective solution for integrating hybrid wind-wave energy into island microgrids.

1. Introduction

Wind energy, as a renewable resource with vast potential in marine exploitation, plays a critical role in substituting fossil fuels and facilitating energy transition. Compared with onshore wind farms, offshore wind farms benefit from more stable and robust wind resources [1]. China’s technically exploitable offshore wind power capacity within 200 km of its coastline reaches 2780 GW. Less than 1.1% of the power capacity has been developed to date, indicating significant expansion potential. Similarly, Australia has planned large-scale offshore wind projects near its major load centers, such as Sydney and Melbourne. These projects hold a combined total capacity that exceeds 25 GW. From a global perspective, the capacity of offshore wind energy is projected to reach a significant milestone of 240 GW by the year of 2030 [2].

Wave energy, as another marine renewable resource with significant potential, offers superior predictability in power generation compared to wind energy [3]. In recent years, global research on wave energy converters (WECs) has been intensified, with extensive adaptability tests conducted across diverse marine environments [4]. The development of wave energy projects requires critical site selection assessments, which have been extensively studied [5]. Meanwhile, accurate resource assessment—a prerequisite for project deployment—has been systematically conducted at global, regional, and local scales, utilizing buoy measurements, wave models, and reanalysis data [6,7].

Hybrid offshore wind-wave energy systems have received widespread attention due to their synergistic benefits. These systems enable efficient resource integration through co-platform or co-site deployment [8]. The advantages include reduced construction and operation costs from shared infrastructure [9,10], complementary temporal and spatial distribution between wind and wave energy to dampen power fluctuations [11], and improved platform stability with increased power generation [12]. Studies show that hybrid systems can significantly reduce intermittency. An 87% downtime reduction and a 6% power fluctuation decrease are achieved in German and Danish waters [13]. The feasibility is also confirmed in the Mediterranean [14]. However, wind and wave energy resources are often assessed independently [15,16], lacking a comprehensive analytical framework. Systematic assessment is required for site selection factors, including wave system characterization, energy availability, wind-wave correlation, temporal lag patterns, energy fluctuations, and device compatibility.

Hybrid offshore wind-wave energy systems offer advantages, yet power fluctuation issues occur [17]. Wave energy output shows a special step-type impact [18], while offshore wind power output is random due to meteorological influences [19]. It makes the grid integration more complicated. Island microgrids, with relatively fragile structures, struggle to withstand periodic power impacts [20]. Unlike traditional large-scale power grids, microgrids lack sufficient spinning reserves and inertial support. As the “double-high” features—high proportion of renewable energy and high proportion of power electronic devices—become increasingly prominent, system inertia and damping levels are further reduced. It severely impairs frequency and voltage regulation capabilities. In scenarios where conventional power sources are insufficient and new energy support capabilities are limited, system may trigger protective actions due to frequency out-of-limit, threatening the safe and stable operation of the power grid. Battery energy storage system (BESS) offers an effective solution to address the issues. BESS holds flexible and rapid power adjustment capability. It can participate in inertial response and primary frequency regulation, significantly enhancing system frequency stability [21]. Grid-forming energy storage can provide voltage support and active inertial characteristics, suppress short-term power fluctuations through Fast Frequency Response (FFR), and improve renewable energy absorption capacity. Reference [22] proposed a BESS capacity configuration method based on system inertia constants and governor characteristics to enhance the frequency response of systems with high wind power penetration. Additionally, References [23,24] established energy storage planning models considering primary frequency regulation reserves from the perspectives of market profit optimization and frequency regulation service optimization, respectively.

To address the challenges in site selection and grid integration for hybrid offshore wind-wave energy systems, an integrated methodology for the efficient and secure utilization of hybrid wind-wave energy is proposed. The methodology combines a comprehensive site suitability assessment method with a grid-forming BESS configuration approach. The assessment framework uses three critical indices. The Composite Energy Output Index (CEOI) quantifies energy output potential. The Time-Shifted Cross-Covariance Index (TS-CCI) assesses the temporal complementarity between wind and wave resources. The Energy Penetration Balance Index (EPBI) evaluates grid integration capacity. The site suitability can be judged by the assessment method. To support the safe grid integration of hybrid wind-wave systems, the frequency response characteristics of WEC, BESS, and gas turbine generators are analyzed. The corresponding frequency constraints are derived. Based on the frequency constraints, a BESS configuration method is proposed. Both the life cycle cost and the frequency stability are considered. The proposed method is validated through MATLAB R2022b simulations.

2. Power Calculation of Wind and Wave

Accurate power calculation is crucial for determining potential energy output and system performance during marine site suitability assessment. A DC-connected hybrid offshore wind-wave energy system is adopted for techno-economic analysis. The system configuration contents one Gamesa G128-5MW wind turbine and four Wavestar C6 600 kW WECs arranged symmetrically around the turbine axis [25]. The Gamesa G128-5MW wind turbine is manufactured by Siemens Gamesa Renewable Energy, headquartered in Pamplona, Spain. The Wavestar C6 600 kW WECs are manufactured by Wave Star AS, headquartered in Brøndby, Denmark.

2.1. Wind Power Calculation

Wind power calculation is closely related to wind speed and air density. Typically, wind speed is measured at a height of 10 m, while the hub height of wind turbines usually exceeds 100 m. Therefore, it is necessary to convert the measured wind speed to the hub height through height adjustment and friction coefficient correction. The correction formula is expressed as follows:

$$u_{\omega }=U_{10}\cdot {\left({\displaystyle \frac{z}{z_{10}}}\right)}^a$$

(1)

where $u_{\omega }$ is the wind speed at hub height, $U_{10}$ is the wind speed at 10 m height, $z$ represents the hub height, $z_{10}$ denotes the measurement height, and a is the friction coefficient, a terrain-dependent function with a value of 0.1 for open water terrain.

Air density ${\rho }_a$ varies with height and can be calculated using the ideal gas law

$${\rho }_a={\displaystyle \frac{353.1}{K}}\cdot \exp ({\displaystyle \frac{-0.0342\cdot z}{K}})$$

(2)

where K is absolute temperature in Kelvin.

The formula for calculating wind power density $p_{\mathrm{wind}}$ is expressed as follows:

$$p_{\mathrm{wind}}={\displaystyle \frac{1}{2}}{\rho }_a{u}_{\omega }^3$$

(3)

Wind power output prediction errors typically follow a normal distribution. Current prediction technologies can maintain the errors within a ±10% range [26]. Therefore, this study incorporates a ±10% prediction error margin into the modeling analysis.

In the specific calculation process, the power characteristic curve of commercial wind turbines is used to determine the wind power generation. This power curve takes the real-time wind speed at the hub height as the input variable and directly outputs the corresponding power generation value through a functional relationship. The power curve of the Gamesa G128 5 MW wind turbine is shown in Figure 1 [27].

2.2. Wave Energy Power Calculation

WECs capture the wave energy and convert it into electricity through sequential energy conversions. As illustrated in Figure 2, the Wavestar 600 kW WEC shows three energy conversion stages. Firstly, wave-induced vertical motion of floating bodies $E_{\mathrm{wave}}$ is captured into mechanical energy $E_{\mathrm{float}}$. Then, a hydraulic system converts mechanical energy to pressurized hydraulic energy $E_{\mathrm{h}}$. Finally, a hydraulic motor and a conventional generator ultimately produce electricity $E_{\mathrm{e}}$. The efficiencies of the three stages are ${\eta }_{\mathrm{capture}}$, ${\eta }_{\mathrm{mech-hyd}}$, and ${\eta }_{\mathrm{PTO}}$, orderly.

Based on linear wave theory, wave power density is related to significant wave height $H_{\mathrm{S}}$ and spectral peak period $T_{\mathrm{P}}$. It can be known from [28] that in the prototype test, when $H_{\mathrm{S}}$ > 2.0 m, due to the low water depth at the location, the waves are steep and breaking, the measured maximum power generation to be 15% lower than the model-predicted value. This deviation indicates that water depth directly affects the capturable energy by changing wave dynamics. The formula for wave energy mechanical power density $p_{\mathrm{wave}}$ is expressed as follows:

$$p_{\mathrm{wave}}={\eta }_{\mathrm{deep}}{\displaystyle \frac{{\rho }_{\omega }{g}^2}{64\pi }}{H}_{\mathrm{S}}^2{T}_{\mathrm{e}}$$

(4)

where ${\eta }_{\mathrm{deep}}$ is the depth coefficient, ${\rho }_{\omega }$ represents the seawater density, $g$ denotes the gravitational acceleration, and $T_{\mathrm{e}}$ is the wave energy period, $T_{\mathrm{e}}=0.857T_{\mathrm{p}}$.

During this process, energy undergoes successive reductions through capture efficiency ${\eta }_{\mathrm{capture}}$, mechanical-to-hydraulic efficiency ${\eta }_{\mathrm{mech-hyd}}$, and power take-off efficiency ${\eta }_{\mathrm{PTO}}$. Within a single power generation cycle, the generator of the hydraulic power system requires a certain period of energy storage, resulting in the intermittent power generation characteristic of wave energy hydraulic systems. The wave height curve and power diagram of the hydraulic energy storage WEC are schematically shown in Figure 3.

The wave energy output power within each cycle can be expressed as follows:

$$P_t^{\mathrm{Wave}}=\left\{\begin{array}{c}{\displaystyle \frac{P_t^{\mathrm{close}}-P_t^{\mathrm{open}}}{T_{\mathrm{W}}^t}}t+P_t^{\mathrm{open}},0\le t\le T_t^{\mathrm{W}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em},T_t^{\mathrm{W}}\le t\le T\end{array}\right.$$

(5)

where $P_t^{\mathrm{Wave}}$ is the output power of the hydraulic energy storage wave power generation device within time period t; $P_t^{\mathrm{open}}$ and $P_t^{\mathrm{close}}$ are the valve-opening power and valve-closing power within time period t, respectively; $T_t^{\mathrm{W}}$ is the duration of wave energy generation; and T represents the power generation cycle.

The formula for the average power over the entire generation cycle is expressed as follows:

$${\overline{P}}_t={\displaystyle \frac{E_{\mathrm{e}}}{T}}$$

(6)

${\overline{P}}_t$, $H_{\mathrm{S}}$, and $T_{\mathrm{e}}$ are compiled into a table called the power matrix [29], which lists the average power output of wave energy converters under different combinations of $H_{\mathrm{S}}$ and $T_{\mathrm{e}}$. The power matrix for the Wavestar C6 600 kW is shown in Figure 4 [25]. In practical calculations, the power output of WECs ($P_{\mathrm{wave} }$) is determined by looking up this matrix.

Test data from the second-phase trials of the Wavestar prototype in the Roshage sea area, Netherlands, demonstrates superior operational performance with an availability rate of 99.4%. The grid-connected ratio during operation is 82.3%. The effective grid-connected time, calculated by multiplying availability rate and grid-connected ratio, reaches 81.8%. The residual time is the energy storage periods when the system actively captures wave energy but does not reach the open-valve power [27]. These findings confirm that the WEC system achieves high grid-connection efficiency in suitable water depth conditions. Based on these operational characteristics, the parameters for this study have been established as follows. Given the system’s high grid-connection ratio, the average power output over a complete generation cycle represents an intermediate value between the power levels during valve opening and closing phases of the hydraulic energy storage WECs, $P_t^{\mathrm{open}}=1.2{\overline{P}}_t$, and $P_t^{\mathrm{close}}=0.8{\overline{P}}_t$. The time scale of wave energy generation is mostly on the order of tens of minutes. In this paper, it is set as $T_t^{\mathrm{W}}=20\min$.

Significant wave height, peak period, and water depth are key parameters affecting wave energy generation, while the vertical distribution characteristics of wind speed dominate the output performance of wind power. During the operation of the hybrid offshore wind-wave energy systems, the inherent intermittent generation characteristics of wave energy, combined with wind power prediction errors, will jointly cause serious power impacts. Two extreme modes need to be focused on. One is the instantaneous power surge when WECs complete energy storage; the other is the stepwise power drop caused by valve-closing actions at the end of the generation cycle. When the two modes superimpose with wind power prediction errors, composite power impacts impose more complex regulatory requirements on grid frequency stability.

3. Marine Site Suitability Assessment

For seasonal analysis, January, April, July, and November are selected as representative months. Hourly data on $H_{\mathrm{S}}$, $T_{\mathrm{P}}$, $h$, and $u_{\omega }$ from the original dataset are chosen as key assessment parameters to construct a four-dimensional feature vector $X=[H_{\mathrm{S}},T_{\mathrm{P}},h,u_{\omega }]$. Through cluster analysis using the K-means algorithm [30], four typical days are identified after convergence. Each typical day contains typical feature vector information of wind and wave conditions, representing distinct seasonal characteristic patterns. Furthermore, based on the mapping relationships shown in Figure 1 and Figure 4, the power output of the hybrid offshore wind-wave energy systems is calculated. Finally, integrating the data analysis results, a comprehensive assessment system for marine site suitability is proposed, covering power generation efficiency, wind-wave complementary characteristics, and permeability balance.

3.1. Comprehensive Energy Output Index

The CEOI quantifies the operational efficiency of the hybrid offshore wind-wave energy systems under typical operating conditions, defined as the ratio of the system’s average power output to its rated capacity. The closer this index is to 1, the closer the energy capture efficiency of the system under specific marine environmental conditions is to the design limit, reflecting an optimal matching state between power generation equipment and site resources.

$${\overline{P}}_i^{\mathrm{wind}}={\displaystyle \frac{1}{24}}{\displaystyle \sum _{t=1}^{24}{P}_{i,t}^{\mathrm{wind}}}$$

(7)

$${\overline{P}}_i^{\mathrm{wave}}={\displaystyle \frac{1}{24}}{\displaystyle \sum _{t=1}^{24}{P}_{i,t}^{\mathrm{wave}}}$$

(8)

$$f_1={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^4({\overline{P}}_i^{\mathrm{wind}}+{\overline{P}}_i^{\mathrm{wave}})}}{4\cdot P_{\max }}}$$

(9)

where ${\overline{P}}_i^{\mathrm{wind}}$ and ${\overline{P}}_i^{\mathrm{wave}}$ are the daily average wind power output and wave energy output corresponding to the typical day i, respectively. $P_{\max }$ is the rated power of the hybrid offshore wind-wave energy systems.

3.2. Time-Shifted Cross-Covariance Index

The TS-CCI quantifies the dynamic complementary characteristics between wind energy and wave energy generation power by calculating their covariance under different time shifts. This index not only considers the matching of fluctuation amplitudes, but also captures the potential for time-offset complementarity between wind and wave power generation. It provides basis for the charging and discharging strategies of BESS. The value range of ${\mathrm{TS-CCI}}^{\mathrm{day}}$ is [−1, 1]. A value closer to 1 indicates stronger complementarity. Index $f_2$ is obtained by normalizing ${\mathrm{TS-CCI}}^{\mathrm{day}}$.

$${\sigma }_i^{\mathrm{wind}}=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{t=1}^{24}(P_{i,t}^{\mathrm{wind}}-}{\overline{P}}_i^{\mathrm{wind}}{)}^2}{24}}}$$

(10)

$${\sigma }_i^{\mathrm{wave}}=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{t=1}^{24}(P_{i,t}^{\mathrm{wave}}-}{\overline{P}}_i^{\mathrm{wave}}{)}^2}{24}}}$$

(11)

$${\mathrm{TS-CCI}}_i^{\mathrm{h}}=\underset{\tau \in [-6h,+6h]}{\min }[{\displaystyle \frac{{\displaystyle {\sum }_{t=1}^{24}(P_{i,t}^{\mathrm{wind}}-{\overline{P}}_i^{\mathrm{wind}})(P_{i,t+\tau }^{\mathrm{wave}}-{\overline{P}}_i^{\mathrm{wave}})}}{24\cdot {\sigma }_i^{\mathrm{wind}}{\sigma }_i^{\mathrm{wave}}}}]$$

(12)

$${\mathrm{TS-CCI}}^{\mathrm{day}}={\displaystyle \frac{1}{4}}{\displaystyle \sum _{i=1}^4{\mathrm{TS-CCI}}_i^{\mathrm{h}}}$$

(13)

$$f_2={\displaystyle \frac{1-{\mathrm{TS-CCI}}^{\mathrm{day}}}{2}}$$

(14)

where ${\sigma }_i^{\mathrm{wind}}$ is the standard deviation of wind power generation on typical day I, ${\sigma }_i^{\mathrm{wave}}$ is the standard deviation of wave energy generation on typical day i, ${\mathrm{TS-CCI}}_i^{\mathrm{h}}$ is the time-shifted cross-covariance index for typical day i, and ${\mathrm{TS-CCI}}^{\mathrm{day}}$ represents the average time-shifted cross-covariance index.

3.3. Energy Penetration Balance Index

The EPBI measures the balance of variations in energy penetration rates between wind and wave energy across seasons, reflecting the output stability of the hybrid offshore wind-wave energy systems. The index quantifies the relative fluctuation of energy penetration rates by calculating the ratio of their standard deviation to average value. The EPBI ranges from 0 to positive infinity. A smaller value indicates slighter seasonal fluctuations in energy penetration, more stable system output, and stronger grid compatibility. The EPBI is defined as the coefficient of variation (CV). It equals the ratio of the standard deviation of energy penetration rates on each typical day to their average value. Index $f_3$ is derived by normalizing CV

$$R_{i,t}={\displaystyle \frac{P_{i,t}^{\mathrm{wind}}+P_{i,t}^{\mathrm{wave}}}{P_t^{\mathrm{L}}}}\times 100\%$$

(15)

$$CV={\displaystyle \frac{{\sigma }_{\mathrm{R}}}{\overline{R}}}={\displaystyle \frac{\sqrt{\frac{1}{24}{\displaystyle \sum _{t=1}^{24}(R_{i,t}-}{\overline{R}}_i{)}^2}}{\overline{R}}}$$

(16)

$$f_3={\displaystyle \frac{1}{1+CV}}$$

(17)

where ${\overline{R}}_i$ is the average energy penetration rate on typical day i, $\overline{R}$ represents the average energy penetration rate across all typical days, and ${\sigma }_{\mathrm{R}}$ denotes the standard deviation of energy penetration rates.

3.4. Comprehensive Assessment

The CPI considers the system’s power generation efficiency, coordination of seasonal fluctuations, and balance of energy penetration rates, aiming to provide a comprehensive assessment result. Based on the value ranges, the final assessment index $F_1$ is obtained after normalizing the targets

$$F_1=\alpha f_1+\beta f_2+\chi f_3$$

(18)

$$\alpha +\beta +\chi =1$$

(19)

where $\alpha$, $\beta$, and $\chi$ are weight coefficients, with values set as $\alpha$ = 0.5, $\beta$ = 0.3, and $\chi$ = 0.2 in this study.

As a maximization index, the CPI is used for the comparison of the comprehensive performance of different candidate stations. A higher CPI value indicates better overall performance of the site in the three dimensions of CEOI, TS-CCI, and EPBI, making it more suitable for constructing a hybrid offshore wind-wave energy system. Therefore, the goal in site selection should be to maximize the CPI value.

4. Frequency Dynamic Characteristics of Power Systems with Grid-Forming BESS Participation

4.1. Frequency Response Process of Power Systems with Grid-Forming BESS Participation

In hybrid offshore wind-wave energy systems, short-term deviations between hourly power predictions and actual operation can lead to power surpluses or deficits. Since the valve-opening power of WECs is higher than the valve-closing power, the maximum disturbance power borne by the grid is the sum of 10% wind power surplus and the maximum valve-opening power of WECs. Once the active power balance is disrupted, the system frequency undergoes three stages of change. First, the inertial response of synchronous generators—releasing rotational kinetic energy—slows down the frequency drop within the initial few seconds (Δt₁). After the governor deadband elapses, generators with regulation margins initiate primary frequency response (PFR) through governor actions, stabilizing the frequency to a quasi-steady state within 5–25 s (Δt₂). Secondary frequency response (SFR), which further restores frequency over a longer time scale (30 s to 5 min, Δt₃) via automatic generation control, is beyond the scope of this study.

The dashed lines in Figure 5 illustrate the typical frequency response process Δf(t) without BESS support. The full lines indicate the typical frequency response process with BESS support. The green line reflects the frequency change, where the power jumps from zero to the sum of valve-opening power and excess wind power, showing significant fluctuations. The red line corresponds to the power drop, characterized by a progressive decay resulting from the sum of valve-closing power and wind power deficit, with relatively mild fluctuations.

The frequency deviation Δf(t) exhibits typical dynamic behavior. The changing rate of frequency deviation (dΔf(t)/dt) initially reaches extreme value and then progressively diminishes through oscillatory decay due to virtual inertia effects and system primary frequency response. It continues until the system stabilizes at a quasi-steady state. Considering that the time scale of wave energy generation is mostly on the order of tens of minutes [31], it can be assumed that after the first disturbance, frequency is restored to its initial value through frequency regulation measures such as secondary frequency modulation. Therefore, when configuring grid-forming BESS to improve frequency stability, only frequency safety under power surplus needs to be considered.

The FFR provided by grid-forming BESS enables fast power injection within 1 s of power imbalance occurrence. This paper treats PFR and FFR as approximately linear functions, which is a perspective validated in [32]. The response process is schematically illustrated in Figure 6, with the formulas given in (20)–(22)

$$FR(t)=PFR(t)+FFR(t)+WFR(t)$$

(20)

$$PFR(t)=\left\{\begin{array}{cc}{\displaystyle \sum _{g\in \mathrm{G}}}{R}_g^{\mathrm{P}}\cdot {\displaystyle \frac{t}{{\mathrm{T}}_{\mathrm{PFR}}}}& \hspace{1em}\mathrm{if} t\le {\mathrm{T}}_{\mathrm{PFR}}\\ {\displaystyle \sum _{g\in \mathrm{G}}}{R}_g^{\mathrm{P}}& \hspace{1em}\mathrm{if} t>{\mathrm{T}}_{\mathrm{PFR}}\end{array}\right.$$

(21)

$$FFR(t)=\left\{\begin{array}{cc}{\displaystyle \sum _{e\in \mathrm{E}}}{R}_{\mathrm{e}}^{\mathrm{F}}\cdot {\displaystyle \frac{t}{{\mathrm{T}}_{\mathrm{FFR}}}}& \hspace{1em}\mathrm{if} t\le {\mathrm{T}}_{\mathrm{FFR}}\\ {\displaystyle \sum _{e\in \mathrm{E}}}{R}_{\mathrm{e}}^{\mathrm{F}}& \hspace{1em}\mathrm{if} t>{\mathrm{T}}_{\mathrm{FFR}}\end{array}\right.$$

(22)

where $FR(t)$ is the total frequency response capacity of the system, comprising the PFR capacity $PFR(t)$ from synchronous generators, the FFR capacity $FFR(t)$ provided by grid-forming BESS, and the inherent primary frequency response $WFR\left(t\right)$ of WECs. $R_g^{\mathrm{P}}$ is the PFR power of unit g. $R_e^{\mathrm{F}}$ denotes the FFR power of the grid-forming BESS numbered e. E is the number of grid-forming BESS units. ${\mathrm{T}}_{\mathrm{PFR}}$ and ${\mathrm{T}}_{\mathrm{FFR}}$ are the full response times of PFR and FFR, respectively, with $R_G={\displaystyle \sum _{g\in G}}{R}_g^{\mathrm{P}}$ and $R_E={\displaystyle \sum _{e\in E}}{R}_e^{\mathrm{F}}$ defined as such.

The gradual power output reduction following valve opening in WECs exhibits inherent frequency regulation characteristics, autonomously mitigating active power imbalances. The difference between open-valve power and the actual power output shown in Figure 3 corresponds to the WECs frequency response (WFR). This behavior, analogous to conventional primary frequency response, is quantified through the derived parameter $WFR\left(t\right)$ in (23), with the corresponding dynamic response profile depicted by the red trajectory in Figure 6.

$$WFR(t)=\left\{\begin{array}{cc}{\displaystyle \frac{P_t^{\mathrm{open}}-P_t^{\mathrm{close}}}{{\mathrm{T}}_{\mathrm{W}}^t}}t& \hspace{1em}\mathrm{if} t\le {\mathrm{T}}_{\mathrm{w}}^t\\ 0& \hspace{1em}\mathrm{if} t>{\mathrm{T}}_{\mathrm{w}}^t\end{array}\right.$$

(23)

4.2. System Frequency Security Constraints with Grid-Forming BESS

When a power disturbance occurs in the power system, the dynamic process of frequency variation can be mathematically described by the classic swing equation. A simplified first-order model, as shown in Equation (24), is adopted for rapid assessment in the power system planning phase. In the analysis of system frequency characteristics, the load-damping effect was intentionally omitted. This simplification is justified because the influence of load damping on frequency variations during transient periods is relatively minor [33]

$${\displaystyle \frac{2H}{f_0}}\cdot {\displaystyle \frac{d\Delta f(t)}{dt}}=FR(t)-\Delta P_{\mathrm{e}}$$

(24)

where $d\Delta f(t)$ is the frequency deviation at time t, H represents the total inertia of the system, $f_0$ is the system’s standard frequency, and $\Delta P_{\mathrm{e}}$ denotes the system’s unbalanced power.

To ensure the frequency security of the power system, three indicators—RoCoF, quasi-steady-state frequency, and frequency zenith—must satisfy the corresponding constraints, which are specified as follows.

(1)

RoCoF constraint

The maximum RoCoF occurs at t = 0, where the system’s unbalanced power reaches its peak and the frequency response power remains within the deadband. Frequency security requires that the maximum $f_{\mathrm{RoCoF},t=0}$ be limited to a value below the system’s safety threshold $f_{\mathrm{RoCoF}}^{\max }$. The RoCoF constraint is expressed as follows:

$$\left|f_{\mathrm{RoCoF},t=0}\right|={\displaystyle \frac{\Delta P_{\mathrm{e}}\cdot f_0}{2H}}\le f_{\mathrm{RoCoF}}^{\max }$$

(25)

where in the total system inertia H is provided by the inertia of synchronous generators and the virtual inertia of grid-forming BESS.

$$H={\displaystyle \sum _{g\in G}{H}_g}{P}_{g,\max }^{\mathrm{Gen}}{I}_{g,t}+{\displaystyle \sum _e{H}_e}{P}_{e,\max }^{\mathrm{GFM}}$$

(26)

where H is the inertia constant of generator unit g.

(2)

Quasi-steady-state constraint

Before SFR kicks in, the system frequency stabilizes at quasi-steady state (Q-S-S). Assuming RoCoF is 0 under quasi-steady conditions—the FFR of grid-forming BESS and PFR of synchronous units have fully responded by then—the total FR must be at least equal to the power deficit $R_G+R_E\ge \Delta P_{\mathrm{e}}$. The Q-S-S constraint is expressed as follows:

$$\left|R_G+R_E+{\displaystyle \frac{P_t^{\mathrm{open}}-P_t^{\mathrm{close}}}{{\mathrm{T}}_{\mathrm{W}}^t}}(\Delta t_1+\Delta t_2)\right|\ge \left|\Delta P_{\mathrm{e}}\right|$$

(27)

(3)

Frequency zenith constraint

As demonstrated in [34], the frequency reaches the peak at $t_{\mathrm{zenith}}$, which falls within the interval of $[{\mathrm{T}}_{\mathrm{FFR}},{\mathrm{T}}_{\mathrm{PFR}}]$. By substituting the corresponding values from the piecewise function of FR(t) into Equation (24) and solving the differential equation, the expression for the frequency variation $\Delta f(t)$ is obtained.

$$\Delta f(t)={\displaystyle \frac{f_0}{2H}}[{\displaystyle \frac{R_{\mathrm{G}}}{2{\mathrm{T}}_{\mathrm{PFR}}}}{t}^2+R_{\mathrm{E}}(t-{\displaystyle \frac{{\mathrm{T}}_{\mathrm{FFR}}}{2}})+{\displaystyle \frac{P^{\mathrm{open}}-P^{\mathrm{close}}}{{\mathrm{T}}_{\mathrm{w}}}}t-\Delta P_{\mathrm{e}}t]$$

(28)

Set $f_{\mathrm{RoCoF}}$ to 0, substitute the FR(t) function of the corresponding time period into Equation (24), and solve for the value of $t_{\mathrm{zenith}}$.

$$t_{\mathrm{zenith}}={\displaystyle \frac{(\Delta P_{\mathrm{e}}-R_{\mathrm{E}}){\mathrm{T}}_{\mathrm{PFR}}{\mathrm{T}}_{\mathrm{w}}}{R_{\mathrm{G}}{\mathrm{T}}_{\mathrm{w}}+(P^{\mathrm{open}}-P^{\mathrm{close}}){\mathrm{T}}_{\mathrm{PFR}}}}$$

(29)

Finally, substituting Equation (29) into Equation (28) yields the frequency zenith constraint, expressed as follows:

$${\displaystyle \frac{f_0}{4H}}({\displaystyle \frac{{(\Delta P_{\mathrm{e}}-R_{\mathrm{E}})}^2{\mathrm{T}}_{\mathrm{PFR}}{\mathrm{T}}_{\mathrm{w}}}{R_{\mathrm{G}}{\mathrm{T}}_{\mathrm{w}}+(P^{\mathrm{open}}-P^{\mathrm{close}}){\mathrm{T}}_{\mathrm{PFR}}}}-R_{\mathrm{E}}{\mathrm{T}}_{\mathrm{FFR}})\le \Delta f_{\max }$$

(30)

The linearization of Equation (30) is provided in Appendix A.

5. Configuration Model for Energy Storage Systems

The grid-forming BESS, generator, and wind-wave hybrid power generation system are first modeled. Subsequently, the objective function of the overall configuration model, as well as the system operation constraints, are introduced.

5.1. Modeling of Grid-Forming BESS

$$\left|P_{e,t}^{\mathrm{c}}\right|\le {\mathrm{u}}_{e,t}^{\mathrm{c}}{P}_{e,\max }^{\mathrm{GFM}},e\in \mathrm{E},t\in \mathrm{T}$$

(31)

$$\left|P_{e,t}^{\mathrm{d}}\right|\le {\mathrm{u}}_{e,t}^{\mathrm{d}}{P}_{e,\max }^{\mathrm{GFM}},e\mathrm{\in }E,t\in \mathrm{T}$$

(32)

$${\mathrm{u}}_{e,t}^{\mathrm{c}}+{\mathrm{u}}_{e,t}^{\mathrm{d}}\le 1,e\in \mathrm{E},t\in \mathrm{T}$$

(33)

$$P_{e,t}^{\mathrm{GFM}}=P_{e,t}^{\mathrm{c}}-P_{e,t}^{\mathrm{d}}$$

(34)

$$-P_{e,\max }^{\mathrm{GFM}}-P_{e,t}^{\mathrm{d}}+P_{e,t}^{\mathrm{c}}\le R_{e,t}^{\mathrm{F}}\le P_{e,\max }^{\mathrm{GFM}}-P_{e,t}^{\mathrm{d}}+P_{e,t}^{\mathrm{c}},e\in \mathrm{E},t\in \mathrm{T}$$

(35)

$$\Delta E_{e,t}={\displaystyle \frac{1}{3600}}{R}_{e,t}^{\mathrm{F}}(\Delta t_1+\Delta t_2+{\displaystyle \frac{1}{2}}\Delta t_3),e\in \mathrm{E},t\in \mathrm{T}$$

(36)

$$E_{e,\min }^{\mathrm{GFM}}\le E_{e,t}^{\mathrm{GFM}}\le E_{e,\max }^{\mathrm{GFM}},e\in \mathrm{E},t\in \mathrm{T}$$

(37)

$$E_{e,\min }^{\mathrm{GFM}}\le E_{e,t}^{\mathrm{GFM}}-\Delta E_{e,t}\le E_{e,\max }^{\mathrm{GFM}},e\in \mathrm{E},t\in \mathrm{T}$$

(38)

$$E_{e,t+1}^{\mathrm{GFM}}=E_{e,t}^{\mathrm{GFM}}+{\eta }_{e,t}{P}_{e,t}^{\mathrm{GFM}},e\in \mathrm{E},t\in \mathrm{T}$$

(39)

$${\eta }_{e,t}=\left\{\begin{array}{c}{\eta }^c,P_{e,t}^{\mathrm{GFM}}\ge 0\\ {\eta }^d,P_{e,t}^{\mathrm{GFM}}<0\end{array}\right.$$

(40)

$$E_{e,\mathrm{T}}^{\mathrm{GFM}}=E_{e,0}^{\mathrm{GFM}},e\in \mathrm{E}$$

(41)

where $\Delta E_{e,t}$ denotes the energy variation of BES when providing FFR, with $\Delta t_1$, $\Delta t_2$, and $\Delta t_3$ being 5 s, 25 s, and 300 s, respectively. $P_{e,t}^{\mathrm{c}}$ and $P_{e,t}^{\mathrm{d}}$ represent the charging power and discharging power of the e-th BESS unit in time period t, respectively. $P_{e,\max }^{\mathrm{GFM}}$ is the maximum charge–discharge power of the e-th BESS unit in time period t. ${\mathrm{u}}_{e,t}^{\mathrm{c}}$ and ${\mathrm{u}}_{e,t}^{\mathrm{d}}$ are 0–1 variables indicating the charging and discharging operating states of BESS, respectively. $P_{e,t}^{\mathrm{GFM}}$ stands for the actual output power of the e-th BESS unit in time period t. $E_{e,\min }^{\mathrm{GFM}}$ and $E_{e,\max }^{\mathrm{GFM}}$ are the minimum and maximum capacity limits of the e-th BESS unit, respectively. $E_{E_{i,t}^{\mathrm{G}\mathrm{F}\mathrm{M}}}^{\mathrm{GFM}}$ is the remaining energy of the e-th BESS node in time period t. ${\eta }_{e,t}$ refers to the charge–discharge efficiency of the e-th BESS unit in time period t. ${\eta }^c$ and ${\eta }^d$ are the charging efficiency and discharging efficiency of BESS, respectively.$E_{e,\mathrm{T}}^{\mathrm{GFM}}$ is the remaining energy at the end of a scheduling cycle.

5.2. Modeling of Gas Turbine Generator

The modeling of gas turbine generator includes the unit output upper and lower limit constraints (42), the unit startup and shutdown time constraints (43) and (44), and the unit ramping constraints (45) and (46) [35].

$$P_g^{\min }{I}_{g,t}\le P_{g,t}^{\mathrm{Gen}}\le P_g^{\min }{I}_{g,t}$$

(42)

$$[X_{\mathrm{on},g,(t-1)}-{\mathrm{T}}_{\mathrm{on},g}]\cdot [I_{g,(t-1)}-I_{g,t}]\ge 0$$

(43)

$$[X_{\mathrm{off},g,(t-1)}-{\mathrm{T}}_{\mathrm{off},g}]\cdot [I_{g,t}-I_{g,(t-1)}]\ge 0$$

(44)

$$P_{g,t}^{\mathrm{Gen}}-P_{g,(t-1)}^{\mathrm{Gen}}\le {\mathrm{UR}}_g\cdot I_{g(t-1)}+P_g^{\min }\cdot (I_{g,(t-1)}-I_{g,t})+P_g^{\max }\cdot (1-I_{g,(t-1)})$$

(45)

$$P_{g,(t-1)}-P_{g,t}^{\mathrm{Gen}}\le {\mathrm{DR}}_g\cdot I_{g,t}+P_g^{\min }\cdot (I_{g,(t-1)}-I_{g,t})+P_g^{\max }\cdot (1-I_{g,(t-1)})$$

(46)

where $I_{g,t}$ is a binary variable indicating the operating status of synchronous generator unit g. $P_g^{\min }$ and $P_g^{\max }$ are the lower and upper limits of the output power of synchronous generator unit g. $X_{\mathrm{on},g,t}$ and $X_{\mathrm{off},g,t}$ are the continuous startup time and continuous shutdown time of unit g during period t. ${\mathrm{T}}_{\mathrm{on},g}$ and ${\mathrm{T}}_{\mathrm{off},g}$ are the minimum startup time and minimum shutdown time constraints, respectively. ${\mathrm{UR}}_g$ and ${\mathrm{DR}}_g$ are the ramping rate limits upward and downward of the unit.

5.3. Modeling of Hybrid Offshore Wind-Wave Energy Systems

The output of the hybrid offshore wind-wave energy systems is affected by real-time meteorological conditions such as wind speed, temperature, and humidity. The maximum output in a certain period is the value from maximum power point tracking (MPPT). To improve the absorption of new energy, the upper and lower limits of wind turbine output are set to satisfy the following conditions:

$$\gamma (P_{i,t}^{\mathrm{wind},\max }+P_{i,t}^{\mathrm{wave},\max })\le P_{i,t}^{\mathrm{wind}}+P_{i,t}^{\mathrm{wave}}\le P_{i,t}^{\mathrm{wind},\max }+P_{i,t}^{\mathrm{wave},\max }$$

(47)

where $P_{i,t}^{\mathrm{wind},\max }$ and $P_{i,t}^{\mathrm{wave},\max }$ are the maximum power point tracking values of the wind turbine and WEC during period t on typical day i, respectively. $\gamma$ is the minimum utilization rate, with a value of 80%.

5.4. Optimization Objectives

The objective of BESS planning is to minimize the average daily cost during the planning period, which includes the average daily investment and construction cost, operation and maintenance cost, fuel cost, synchronous unit startup–shutdown cost, curtailment penalty cost, and carbon emission cost. The objective function can be expressed as follows:

$$F_2=\min (C_{\mathrm{plan}})=\min (C_{\mathrm{inv}}+C_{\mathrm{main}}+C_{\mathrm{G}}+C_{\mathrm{SS}}+C_{\mathrm{W}}+C_{\mathrm{E}})$$

(48)

where $C_{\mathrm{plan}}$, $C_{\mathrm{inv}}$, $C_{\mathrm{main}}$, D, $C_{\mathrm{G}}$, $C_{\mathrm{SS}}$, $C_{\mathrm{W}}$, and $C_{\mathrm{E}}$ are the average daily investment and construction cost, operation and maintenance cost, fuel cost, synchronous unit startup–shutdown cost, curtailment penalty cost, and carbon emission cost, respectively,

$$C_{\mathrm{inv}}={\displaystyle \frac{1}{365}}{\displaystyle \frac{r^{\mathrm{ESS}}{(1+r^{\mathrm{ESS}})}^{y^{\mathrm{ESS}}}}{{(1+r^{\mathrm{ESS}})}^{y^{\mathrm{ESS}}}-1}}[C_{\mathrm{E},\mathrm{inv}}^{\mathrm{GFM}}{E}_{\mathrm{inv}}^{\mathrm{GFM}}+C_{\mathrm{P},\mathrm{inv}}^{\mathrm{GFM}}{P}_{\mathrm{inv}}^{\mathrm{GFM}}]$$

(49)

where $r^{\mathrm{ESS}}$ is the discount rate of BESS. $y^{\mathrm{ESS}}$ is the service life of BESS. $C_{\mathrm{E},\mathrm{inv}}^{\mathrm{GFM}}$ and $C_{\mathrm{P},\mathrm{inv}}^{\mathrm{GFM}}$ are the unit capacity investment cost and unit power investment cost of grid-forming BESS, respectively. $E_{\mathrm{inv}}^{\mathrm{GFM}}$ and $P_{\mathrm{inv}}^{\mathrm{GFM}}$ are the grid-connected storage capacity and power capacity of grid-forming BESS, respectively,

$$C_{\mathrm{main}}=\zeta \cdot C_{\mathrm{inv}}$$

(50)

$$C_{\mathrm{G}}={\displaystyle \sum _{t=1}^{\mathrm{T}}{\displaystyle \sum _{g=1}^G{\mathrm{c}}_{\mathrm{f}}{P}_{g,t}^{\mathrm{Gen}}}}$$

(51)

$$C_{\mathrm{SS}}={\displaystyle \sum _{t=1}^{\mathrm{T}}{\displaystyle \sum _{g=1}^G({\mathrm{c}}_g^{\mathrm{su}}}}{I}_{g,t}+{\mathrm{c}}_g^{\mathrm{sd}}{I}_{g,t})$$

(52)

$$C_{\mathrm{W}}={\displaystyle \sum _{t=1}^{\mathrm{T}}{\displaystyle \sum _{w=1}^{\mathrm{W}}{\mathrm{c}}_{\mathrm{w}}}}(P_{w,t}^{\max }-P_{w,t}^{\mathrm{W}})$$

(53)

$$C_{\mathrm{E}}={\displaystyle \sum _{t=1}^{\mathrm{T}}{\displaystyle \sum _{g=1}^{\mathrm{G}}{\mathrm{c}}_{\mathrm{e}}}}{\mathrm{e}}_{\mathrm{car}}{P}_{g,t}^{\mathrm{Gen}}$$

(54)

where $\zeta$ is the operation and maintenance cost coefficient. ${\mathrm{c}}_{\mathrm{f}}$ is the unit fuel cost of the generator set. ${\mathrm{c}}_g^{\mathrm{su}}$ and ${\mathrm{c}}_g^{\mathrm{sd}}$ are the startup and shutdown cost coefficients of unit g, respectively. ${\mathrm{c}}_{\mathrm{w}}$ and ${\mathrm{c}}_{\mathrm{e}}$ are the curtailment and carbon emission cost coefficients, respectively. ${\mathrm{e}}_{\mathrm{car}}$ is the carbon emission coefficient of the gas turbine generator unit.

5.5. System Operation Safety Constraints

In addition to the three frequency safety constraints (Equations (25), (27) and (30)), the system operation safety constraints also include system power balance constraints and DC power flow constraints.

The power balance constraint for node a is expressed as follows:

$$P_{a,t}^{\mathrm{Gen}}+P_{a,t}^{\mathrm{wave}}+P_{a,t}^{\mathrm{wind}}+P_{a,t}^{\mathrm{GFM}}=P_{a,t}^{\mathrm{Load}}+P_{l,t}^{\mathrm{L}}$$

(55)

where $P_{a,t}^{\mathrm{Gen}}$, $P_{a,t}^{\mathrm{GFM}}$, and $P_{a,t}^{\mathrm{Load}}$ are the total output of gas turbine generator units, grid-forming BESS output, and node load at node a during period t, respectively. $P_{l,t}^{\mathrm{L}}$ is the transmission power of line l during period t.

In this study, the maximum impact load of the microgrid considered refers to the wind power uncertainty within each hour, and the instantaneous power surge at the end of energy storage in the WEC is expressed as follows:

$$\Delta P_{\mathrm{e},t}=10\%\cdot {\displaystyle \sum _{w=1}^{\mathrm{W}}{P}_{w,t}^{\mathrm{Wind}}}+{\displaystyle \sum _{m=1}^{\mathrm{M}}{P}_{m,t}^{\mathrm{open}}}$$

(56)

Since BESS is not involved in SFR, all synchronous units in the offshore oil and gas field must also meet the following spinning reserve conditions to prevent generator tripping accidents.

$${\displaystyle \sum _{g\in G}{I}_{g,t}{P}_{a,t}^{\mathrm{Gen}}-}{\displaystyle \sum _{g\in G}{I}_{g,t}{P}_{\min }^{\mathrm{Gen}}}\ge \Delta P_{\mathrm{e},t}$$

(57)

The DC power flow approximation [36] is employed, omitting reactive power and voltage effects for computational efficiency in the planning stage analysis.

$$P_{l,t}^{\mathrm{L}}=({\theta }_{a,t}-{\theta }_{b,t})/x_l,{\theta }_{\mathrm{ref},t}=0$$

(58)

$$-P_{l,t,\max }^{\mathrm{L}}\le P_{l,t}^{\mathrm{L}}\le P_{l,t,\max }^{\mathrm{L}}$$

(59)

$$-{\theta }_{\max }\le {\theta }_{a,t}\le {\theta }_{\max },a\in \mathrm{N}$$

(60)

where ${\theta }_{a,t}$ and ${\theta }_{b,t}$ are the phase angles of the nodes connected to line l. ${\theta }_{\max }$ is the maximum phase angle of the grid nodes. $P_{l,t,\max }^{\mathrm{L}}$ is the maximum transmission power of line l. $x_l$ is the line reactance of line l.

6. Case Study

6.1. Parameters

Four offshore stations along the southeast coast of China are selected for the case study to assess the optimal location for developing a combined wind and wave energy power station within the region. Assessments are conducted on Xiaochangshan Island (XCS), Zhifudao Island (ZFD), the Yellow Sea coast of Lianyungang (LYG), and Nanji Island (NJI) along China’s coastal areas, aiming to determine the optimal site for constructing a hybrid offshore wind-wave energy systems microgrid. The analysis of development prospects for coastal areas is provided in Appendix B.1. The geographical locations of the offshore stations are shown in Figure 7, and a summary of the geographical information of the stations is presented in

Table 1. Geographical information of offshore stations.

Station	No.	Station Coordinates	Water Depth/m
XCS	A	122.7° E, 39.2° N	31
ZFD	B	121.4° E, 37.6° N	10
LYG	C	119.4° E, 34.8° N	24
NJI	D	121.1° E, 27.5° N	34

.

The data in this study are derived from the National Marine Science Data Center [37], a national science and technology resource sharing service platform in China. This platform provides abundant hourly marine observation data, including information on waves, wind fields, water levels, etc. These data have undergone strict quality control and standardization processing, with high reliability and accuracy.

The simulation utilizes an extended IEEE 30-bus system, as shown in Figure 8. The total load is 18.92 MW. The rated power of hybrid wind-wave generation system is 7.4 MW. The configured energy storage unit is a lithium–iron phosphate battery of 0.1 MW·h/0.05 MW. Both the hybrid system and the energy storage system are connected in bus 5. The maximum quantity of BESS units is 100. The initial SOC of all energy storage units is set at 50%. The parameters for system dynamic characteristics are set as follows. $H_{\mathrm{g}}$ is set as 6 s. $H_{\mathrm{e}}$ is set as 4 s. The reference frequency $f_0$ is 50 Hz. The maximum frequency change rate limit $f_{\mathrm{RoCoF}}^{\max }$ is 1 Hz/s. Complete system specifications are documented in Appendix B.2, including generator parameters (

Table A2. Gas turbine generator data.

Unit	Pmax (MW)	Pmin (MW)	a ($·MW−2)	b ($·MW−1)	c ($)	MUT (h)	MDT (h)	std ($)	spd ($)	bus	Rup	Rdown	H	${\mathbf{E}}_{\mathbf{C}{\mathbf{O}}_2}$
1	15	4	0	100	625	3	1	150	150	22	20	20	6	0.85
2	13	1	0	325	83	2	1	100	100	27	22	22	6	0.76

), nodal network data (

Table A3. Extended IEEE 30-bus system parameters.

Bus	Type	Pd (MW)	Qd (MVar)	Bus	Type	Pd (MW)	Qd (MVar)
1	PV	0	0	16	PQ	0.35	0.18
2	PV	2.17	1.27	17	PQ	0.9	0.58
3	PQ	0.24	0.12	18	PQ	0.32	0.09
4	PQ	0.76	0.16	19	PQ	0.95	0.34
5	PQ	0	0	20	PQ	0.22	0.07
6	PQ	0	0	21	PQ	1.75	1.12
7	PQ	2.28	1.09	22	Slack	0	0
8	PQ	3	0.3	23	PV	0.32	0.16
9	PQ	0	0	24	PQ	0.87	0.67
10	PQ	0.58	0.2	25	PQ	0	0
11	PQ	0	0	26	PQ	0.35	0.23
12	PQ	1.12	0.75	27	PV	0	0
13	PV	0	0	28	PQ	0	0
14	PQ	0.62	0.16	29	PQ	0.24	0.09
15	PQ	0.82	0.25	30	PQ	1.06	0.19

), and storage system characteristics (

Table A4. BESS parameters.

Parameters	Value
Cost of BESS Unit Capacity Investment/($·(MW·h)−1)	300
Cost of BESS Unit Power Investment/($·(MW)−1)	500
Charging and Discharging Efficiency	0.9
Discount Rate/%	8
SOC Minimum Percentage%	10
SOC Maximum Percentage%	90
service life (years)	20
operation and maintenance cost coefficient%	30

) [38].

6.2. Suitability Analysis

Based on the measured data provided by the National Marine Science Data Center, this study conducts a systematic analysis of wind and wave characteristics at four candidate stations along the southeast coast of China in 2023 [37]. The original wind speed data from each monitoring station are statistically analyzed and fitted into a graph (Figure 9), with the fitting process detailed in Appendix B.3.

In addition, the daily average values of significant wave height and wave peak period at each site are calculated through data aggregation, and these data are overlaid as scatter plots on the power matrix diagram of the WaveStar C6 600 kW (Figure 10). The analysis results show that all stations fall within the operating range of the WEC, among which only ZFD and NJI are located in the high-efficiency region. The wind speed distribution of the four stations exhibits distinct regional characteristics, with NJI having an annual average wind speed of 6.8 m/s, significantly higher than that of other stations. The overlay analysis of the scatter distribution of significant wave height-wave peak period at each site and the Wavestar C6 600 kW power matrix indicates that the significant wave height at NJI is concentrated in the range of 1.25–3.25 m, and the wave peak period is mainly distributed between 4.5–8 s, demonstrating excellent synergistic characteristics of wind and wave resources.

As can be seen from the theoretical data of the stations in

Table 2. Theoretical data of stations.

	${\overline{\mathit{U}}}_{10}(\mathit{m}/\mathit{s})$	${\overline{\mathit{H}}}_{\mathit{S}}(\mathit{m})$	${\overline{\mathit{T}}}_{\mathit{e}}(\mathit{s})$	${\mathit{f}}_1$	${\mathit{f}}_2$	${\mathit{f}}_3$	F
A	3.4909	0.7603	4.9097	0.0643	0.6452	0.6567	0.3571
B	4.2395	0.7170	4.2222	0.0855	0.7260	0.6693	0.3944
C	5.3196	0.5326	4.6276	0.1488	0.6783	0.7235	0.4226
D	6.7689	1.6596	6.3458	0.5172	0.6703	0.6369	0.5871

, in the comprehensive assessment of marine suitability and hybrid system performance among the four candidate stations along the southeast coast of China, NJI is recommended as the optimal development site with its significant comprehensive performance index, with a value of 0.5871.

The core competitiveness of Nanji Island is mainly reflected in three aspects. First, Nanji Island has excellent wave energy capture efficiency, with its wave energy efficiency index reaching 0.5172, which is much higher than that of other stations. This is due to the optimal combination of significant wave height and wave peak period in this sea area, enabling the hybrid power generation system to maintain an output of more than 60% of the rated power under more than 60% of the working conditions. Second, the energy penetration stability index of Nanji Island is 0.6369, the smallest among the four stations, indicating that the volatility of its energy penetration rate is the largest. It is urgent to pay attention to the typical day with the highest penetration rate in subsequent optimizations to ensure grid compatibility. Finally, the temporal–spatial complementarity index of Nanji Island is 0.6703, at a medium level among the four stations, which still indicates that there is a good 4- to 6-h peak-shifting effect between wind energy and wave energy output, creating key time margins for the second-level frequency support of the BESS.

The secondary development option is LYG, whose energy penetration stability index is as high as 0.7235, ranking first among the four stations, showing excellent stability of energy penetration rate. In addition, the temporal–spatial complementarity index of Lianyungang is 0.6783, higher than that of Nanji Island, ranking second. However, the main index of Lianyungang is relatively small, and its comprehensive performance is still inferior to that of Nanji Island, so it is slightly lower in development priority.

ZFD is excluded from the priority development sequence due to hard geographical constraints. Its water depth is only 10 m, which is lower than the minimum deployment requirement of WEC, leading to further attenuation of actual wave energy efficiency. Although its energy penetration stability index is 0.6693 and its temporal–spatial complementarity index is the highest among the four stations, its technical infeasibility cannot offset the limitations of its geographical conditions.

6.3. Results and Analysis of Configuration Method

Based on the analysis results in Section 6.2 and the assessment index system proposed in this paper, NJI is identified as the optimal site for the construction of the hybrid power generation system. This site exhibits a high penetration rate of renewable energy, but its energy penetration stability is relatively insufficient. Therefore, it is necessary to configure a grid-forming BESS according to the operating characteristics of its peak penetration day.

Figure 11 shows the typical daily curves of wind power, wave energy, and load on the day with the maximum penetration rate in the Nanji Island area. The effectiveness of the proposed method is verified by analyzing the extreme frequency points during system operation.

To comprehensively assess the comprehensive performance of the grid-forming BESS, this study designs two comparative scenarios for quantitative analysis:

• Case 1 (Baseline case): the original microgrid system without a configured BESS;
• Case 2 (Optimized configuration case): a grid-forming BESS is configured to participate in new energy accommodation and frequency regulation simultaneously.

Table 3. Comparison of BESS configuration schemes for Case 1 and Case 2.

Case	Fuel Cost ($)	Up/Down Cost ($)	Curtail Penalty ($)	Carbon Cost ($)	BESS Construction Cost ($)	BESS Operation Cost ($)	Total Cost ($)	Utilization Rate (%)	BESS Capacity (MW·h)
1	51,672	1050	206	7224	——	——	60,143	96.8	——
2	48,085	350	0	7136	686	205	56,462	100	8.2

lists the optimization results of Cases 1 and 2. The optimized BESS configured in Case 2 has a rated capacity of 8.2 MWh and a rated power of 4.1 MW. Compared with the case without BESS (Case 1), the investment and operating costs in the optimized configuration case (Case 2) can be fully offset by reducing the startup–shutdown costs, fuel costs, carbon emission costs of gas turbines, and curtailment penalties. It yields significant economic benefits.

A comparison between Cases 1 and 2 reveals that in Case 1, frequency disturbances caused by sudden power surges can only be mitigated by the dynamic responses of gas turbines and WECs themselves to meet system frequency security constraints. Since the disturbance power is proportional to the output of the hybrid generation system, satisfying frequency security constraints can only be achieved by reducing disturbances or increasing the reserve capacity of gas turbines. This necessitates operating multiple gas turbines, and due to the minimum power output constraints of these units, generation curtailment occurs even at relatively low penetration rates, lowering the utilization efficiency of renewable energy.

In Case 2, the deployment of grid-forming BESS effectively addresses the issues of insufficient inertia resources and weak renewable energy accommodation capacity in island microgrids. The virtual inertia provided by grid-forming BESS can replace that of gas turbines, significantly enhancing the overall inertia of the power grid. Meanwhile, FFR enables rapid responses to meet frequency constraints during large disturbances, and grid-following BESS optimizes power distribution through peak shaving and valley filling. This configuration achieves the following optimization effects: a 57% reduction in the number of operating gas turbines, full accommodation of renewable energy, and a 6.35% decrease in total system costs. The optimized configuration ensures safe system operation while significantly improving the economy and environmental friendliness of the power grid.

The operation analysis of Case 2 is shown in Figure 12. The hourly output curves of each gas turbine generator are shown in Figure 13. The hybrid generation system, BESS, and gas turbine generator achieve optimized scheduling through coordinated operation. During light-load period from 1:00 to 7:00, hybrid wind-wave generation system and Generator 1 operate to balance load. When net load further decreases, the BESS operates in charging mode to fully utilize renewable energy and satisfy frequency constraints. At 8:00, as load increases and hybrid wind-wave generation decrease, Generator 2 starts operating to meet reserve requirements. Generator 1 operates near its rated power, minimizing startup–shutdown cycles while maintaining sufficient downward regulation capacity to accommodate renewable energy fluctuations. Meanwhile, Generator 2 maintains its minimum generation level to enhance system inertia. When load drops sharply at 24:00, Generator 2 shuts down. The system reverts to single-unit operation with Generator 1, while the BESS discharges to maintain power balance.

Figure 14 and Figure 15 show the output curve and FFR power of the grid-forming BESS, respectively. Analysis indicates that the BESS performs charging operations during net load trough periods such as 8:00, 13:00, 17:00, 22:00, and 23:00. During these periods, due to the limited reserve capacity of generators, the system maintains the reserve level by increasing power output, while the BESS absorbs excess power to ensure power balance. Restricted by the upper limit of charging power, the FFR response power during these periods is relatively reduced.

This operation strategy achieves three optimization effects. First, it significantly reduces the number of startups and shutdowns of generating units. Second, it lowers the BESS capacity requirement. Third, it ensures that the microgrid has sufficient system inertia and rapid response capability. This coordinated operation mode achieves the optimal economic operation goal while ensuring the safe and stable operation of the system.

To verify the effectiveness of the proposed method in cases with lower gas turbine generator capacity, three new cases are simulated. The updated gas turbine generator parameters are detailed in

Table A5. Updated gas turbine generator data.

Unit	Pmax (MW)	Pmin (MW)	a ($·MW−2)	b ($·MW−1)	c ($)	MUT (h)	MDT (h)	std ($)	spd ($)	bus	Rup	Rdown	H	${\mathbf{E}}_{\mathbf{C}{\mathbf{O}}_2}$
1	10	4	0	100	625	3	1	150	150	22	20	20	6	0.85
2	6.5	1	0	325	83	2	1	100	100	27	22	22	6	0.76

. As the capacity of gas turbine generators is reduced, the requirement for BESS is usually bigger. Thus, the maximum number of BESS units is set as 200. The reserve capacity constraint specified in Equation (57) is also relaxed. The comparative study is conducted on three distinct operational scenarios:

• Case 3: Microgrid with updated gas turbine generators, 100% renewable energy utilization rate and without BESS support;
• Case 4: Microgrid with updated gas turbine generators, hybrid wind-wave generation system (without limiting utilization rate as 100%), and without BESS support;
• Case 5: Microgrid with updated gas turbine generators, hybrid wind-wave generation system (without limiting utilization rate as 100%), and a grid-forming BESS.

The simulation results are listed in

Table 4. Comparison of BESS configuration schemes for Case 3, Case 4, and Case 5.

Case	RoCoF Constraint	Q-S-S Constraint	Frequency Zenith Constraint	Total Cost ($)	Utilization Rate (%)	BESS Capacity (MW·h)
3	×	×	×	67,590	100	——
4	√	√	√	69,069	94.4	——
5	√	√	√	66,577	100	18

√ denotes satisfaction of the constraint, and × denotes violation of the constraint.

. Case 3 achieves 100% renewable energy utilization but fails to meet all three frequency security constraints. To satisfy frequency security requirements while enhancing frequency response capability, Case 4 reduces the utilization rate of wind-wave energy to 94.4%. It requires 5.6% spinning reserve capacity to address frequency fluctuations at the cost of resource utilization efficiency. In contrast, Case 5 configures a grid-forming BESS with a rated capacity of 18 MWh and a rated power of 9 MW. It achieves both 100% renewable energy utilization and significant economic benefits. Compared with frequency-unconstrained Case 3, Case 5 achieves an additional 1.5% cost reduction. Meanwhile, it achieves 3.6% cost savings versus frequency-constrained Case 4. It demonstrates that properly configured BESS can simultaneously satisfy frequency security constraints while maintaining a high renewable energy utilization rate and good economic performance.

The simulation verifies the critical role of BESS as a fast-response resource in island microgrid systems with insufficient reserve capacity. The millisecond-level power response capability of BESS effectively compensates for the inertia deficiency caused by reduced gas turbine capacity. The frequency regulation capacity of BESS equivalently replaces traditional synchronous generator spinning reserve requirements, maintaining system stability despite reserve capacity shortages.

7. Conclusions

To improve energy utilization efficiency and operation stability for microgrid integrating with hybrid offshore wind-wave energy systems, a site suitability assessment and a grid-forming BESS configuration method are proposed. Three indices are designed to construct the assessment framework. The Composite Energy Output Index is set for energy output efficiency evaluation. The Time-Shifted Cross-Covariance Index is used for temporal complementarity assessment. The Energy Penetration Balance Index is used for grid integration analysis. By the comprehensive assessment, the most suitable site for hybrid offshore wind-wave energy systems is selected. Due to the unique output characteristics of WEC, the frequency response process of a system simultaneously containing WEC, BESS, and gas turbine generators is analyzed. The corresponding frequency constraints are concluded. To further improve the operation stability of microgrid, a grid-forming BESS configuration method is proposed based on the given frequency constraints. The frequency stability is maintained, and the cost is decreased. The proposed method provides an effective means for the integration of hybrid offshore wind-wave energy systems, which facilitate the utilization of renewable energy and the stable operation of microgrid.