# Offshore Power Plants Integrating a Wind Farm: Design Optimisation and Techno-Economic Assessment Based on Surrogate Modelling

^{*}

## Abstract

**:**

_{2}) emissions in comparison to all the other concepts evaluated. The economic analysis showed the difficulty to repay the additional investment for a wind farm and the necessity of favourable conditions, in terms of gas and carbon dioxide (CO

_{2}) prices.

## 1. Introduction

_{2}emissions could potentially be achieved in comparison to local power generation solutions [11]. The extent of these cuts was strongly dependent on the method to account for the emissions associated with power from shore [3]. Further, it was shown that the economic competitiveness of electrification could be disputable and would need strong support in terms of energy policies [12]. The uncertainties with offshore electrification were the drivers for investigating alternatives. The utilisation of offshore wind power does not require the laying of long subsea cable to ensure the connection to the onshore grid and the wind power can be accounted for as emission free (or close to emissions free from a life cycle assessment standpoint).

_{2}emissions reduction of 53.8 kt (approximately 40%) compared to the reference case based on the utilisation of two gas turbines. This included an operating strategy where one of the gas turbines was allowed to shut-down according to specified criteria. Further, no considerations were made with regard to the process heat to be supplied to the plant. The dynamic simulations were used to establish the maximum amount of wind power integration, which resulted to be between 20 MW and 25 MW [13]. An additional step towards efficient offshore energy supply involved the combination of combined cycles and wind farms. This concept has been investigated in Reference [16], where a wind farm of 10 MW was integrated to three combined cycle units constituted of a gas turbine (rated for 16.5 MW) and a 4.5 MW organic Rankine cycle (ORC) module. The performance of the combined cycle units was compared to that of simple cycle gas turbine units. Even though a couple of co-generative solutions were discussed, the necessity to supply heat in parallel to power was not simulated in detail. In a follow-up paper [17], an economic analysis was proposed, comparing the economic performance of the wind farm coupled with three combined cycles to that of the wind farm coupled with three gas turbines. The results showed that the first concept (wind power and combined cycle) becomes more convenient when fuel cost increases or when the CO

_{2}tax increase. A comparison between the integration of wind power and an independent combined cycle was not provided. The papers referenced in the literature review investigated the coupling of arbitrary wind power capacities into local power generation units. No assessments have been performed to establish the optimal wind capacity to be installed. Small installed wind capacities could limit the environmental benefits associated with the exploitation of wind power. On the other hand, large installed wind capacities, apart endangering the grid stability and the economic feasibility, could result in dissipation of large fractions of wind power in periods of low power demand. To add up to the complexity, large wind farms could lead to operation of the combined cycle at very low part-loads with low efficiency. Moreover, the power plant needs to be able, at all operating conditions, to supply heat to the process, an issue which is often neglected in the literature.

_{2}emissions; (ii) the total cost to supply energy to the plant; and (iii) the weight of the onsite power cycle. Another key characteristic of the optimisation procedure is that it measures the performance in all the significant operating conditions at which the power plant is expected to operate. The importance of considering several relevant operating conditions in the definition of a design was demonstrated in a previous paper [18], in which the novel design succeeded in decreasing the lifetime CO

_{2}emissions by 17.4 kt with respect to a standard design. Because of the complexity of such an optimisation process, requiring a very large number of simulations of the system, the model needs to be simple enough for reasonable computational time. On the other hand, a good level of accuracy has to be guaranteed in order to obtain reliable results. The necessity of finding a balance between these contrasting requirements is typical for such optimisation problems [19]. Surrogate modelling techniques could serve the purpose to accomplish this [20] and were applied to the current analysis. The optimisation procedure described was applied to a case study and a Pareto front of optimal solutions was obtained. The results were analysed and a specific design pinpointed to be further investigated. A techno-economic assessment was performed with the objective to provide a comprehensive evaluation on the effectiveness of the wind power integration in comparison to more standard concepts. The assessment covered the long time span of expected lifetime of an offshore installation and thus future scenarios on the development of economic parameters and energy policies needed to be considered.

## 2. Methods

#### 2.1. Process Modelling of the Offshore Power Plant

_{x}and CO emissions).

#### 2.2. Surrogate Model Based on Kriging and Off-Design Correlation

#### 2.3. Design Optimisation Procedure Considering Off-Design Performance

_{PW}is the wind power capacity installed. In this study, the wind integration is assumed as always possible, regardless the size of the wind farm. A design i is defined by the Kriging model after assigning a value to each of the decision variables. The performance of the specific design is then evaluated at n off-design operating conditions. The set of operating conditions is selected to represent the relevant modes of plant operation during its lifetime. The off-design performances are obtained starting from the information provided by the Kriging model and applying the off-design correlations. The values of selected objective functions are calculated, so to define the array $\overline{z}$ of objective functions to minimize:

_{2}emissions, (ii) the total cost to supply energy to the plant and (iii) the weight of the onsite power cycle. The first two objectives are typical indicators of the sustainability of a project. The third objective considered was believed of significance for offshore applications as the very limited deployment of offshore combined cycles is likely due to issues with their sizes and weights.

_{2}emissions ($C{O}_{2}^{\ast}$). It is calculated as the summation of the annual CO

_{2}emissions (m

_{CO2,y}) over the plant’s lifetime. Every year is described by a power demand that is to be covered by a combination of wind power and combined cycle power. Given the irregularity of the wind power contribution, the year will be further characterized by several off-design conditions at which the combined cycle has to be operated to meet the power demand. A specific design will perform differently at those various off-design conditions, resulting in a correspondent number of mass flow rates of emitted CO

_{2}(ṁ

_{CO2,i}). The annual CO

_{2}emission is then the summation of those emissions (ṁ

_{CO2,i}) weighed over the equivalent number of hours (h

_{eq}) at which an off-design condition is expected to apply to one year:

_{y}). The TCR is assumed to be made before the installation starts operation. The total investment for the power cycle (TCR

_{cc}) is calculated in accordance with [30], as the summation of direct and indirect costs, estimated by a factor method. Table 1 shows a breakdown of the TCR

_{cc}together with the factors used. The purchased-equipment cost (PEC) is an output of the surrogate model. The factors are selected based on the indications provided by Bejan et al. [30], applying a rather high contingency factor (25% of the total cost) and are in line with another paper that performed an estimation of the TCR to install an offshore combined cycle [9]. With regard to the wind farm, the estimation of the TCR

_{wind}(4503 $/kW), including direct and indirect costs, is based on the information retrieved from the European Commission’s report ETRI 2014 [31].

_{y}is calculated as:

^{gas}) and with the CO

_{2}taxation (CF

^{CO2}) are calculated as weighed summation over the off-design conditions characterising a specific year:

_{gas}is the mass flow rate of natural gas used as fuel, LHV

_{gas}is the lower heating value of the natural gas, c

_{gas}is the gas price, ṁ

_{CO2}is the mass flow rate of the emitted CO

_{2}, c

_{CO2}is the CO

_{2}price and h

_{eq}are the equivalent operating hours per year. An estimation of the gas price and of the CO

_{2}price is needed for each year of plant’s operation. Hence, a scenario for the future developments of those economic parameters has to be used. For the gas price, the new policies scenario developed by the International Energy Agency (IEA) is considered and the related annual gas price used [32]. The new policies scenario reflects the way the governments see their energy sectors developing in the coming decades. For the CO

_{2}price, the Norwegian situation is evaluated. The petroleum sector in Norway is subjected to a rather high CO

_{2}tax (0.12 $/Sm

^{3}in 2016 [33]), while contemporary takes part to the European Union Emissions Trading System (EU ETS). In the recent years, the trend had been to adjust the CO

_{2}taxation in order to make up for the increase in the costs associated with the ETS so to keep the overall CO

_{2}price approximately constant. Assuming that the same strategy will apply in the years to come, the level of CO

_{2}price is kept constant and equal to 46 $/t.

_{component}), provided by the Kriging model.

## 3. Case Study

#### 3.1. Offshore Installations

- Early life—29.7 MW (year 2016)
- Middle life—35.5 MW (years 2017 to 2018 and years 2021 to 2023)
- Peak—39.9 MW (years 2019 and 2020)
- Tail years—33.0 MW (years 2024 to 2034)

#### 3.2. Combined Cycle

_{steam}) was constrained by the GT outlet temperature and, in fact, some differences can be noted when a different GT is used. The lower bound was set to ensure a reasonably high steam quality at the steam turbine outlet. The steam evaporation pressure (p

_{steam}) and the condenser pressure (p

_{cond}) were varied within a range which was sufficiently large to not exclude optimal solutions while guaranteeing feasible ones. The lower bound of p

_{cond}was also selected in accordance with typical limitations of the vacuum and sealing systems. The upper load of the GTs was set at 0.95 in order to maintain a safety margin in case of sudden increase of plant load. The lower bound was limited to ensure the capability of the cycle to meet the process heat demand in any instance. The bounds to the pinch point differences (ΔT

_{OTSG}and ΔT

_{cw}) were defined in accordance with the practical limitation discussed by Nord et al. [8].

#### 3.3. Wind Power

_{PW})—the remaining decision variable of the optimisation problem—was let range between 0 and 30 MW, with 5 MW step intervals. The annual contribution of wind power was then fully defined, further influencing the working conditions at which the combined cycle has to be operated to provide back-up power. Given the discretization of the lifetime power demand (4 instances as shown in Figure 3) and of the annual contribution of the wind power (5 instances as shown in Figure 5), for a selected wind farm size, a set of 20 off-design conditions at which the combined cycle has to operate was automatically defined. An example is given in Table 3, considering a wind power capacity installed of 10 MW.

## 4. Results

^{−3}) over a number of stall generations (5). The Pareto fronts obtained can be observed in Figure 6, where the decision map showing trade-offs between total cost and CO

_{2}emissions is represented. The third objective functions (i.e., the weight of the bottoming cycle) is shown through shades of colours: the darker the colour, the heavier the design. The two Pareto fronts refer to the cycles based on the GT A (blue) and on the GT B (green).

_{PW}) was considered in the design optimisation. wind

_{PW}was allowed to take values multiple of 5 MW, within the bounds assigned (i.e., 0 and 30 MW). The steps in the Pareto fronts correspond to the various levels of wind

_{PW}and highlight the strong influence that the size of the wind farm had on the environmental and economic performance. Within each of these “Pareto steps” the heavier designs are generally those with the lower CO

_{2}emissions but higher costs. This makes sense as the heavier combined cycles are likely the most efficient ones but the related increased complexity translates in higher investment costs. By looking at the general trend, it can be noted that increasing wind

_{PW}meant worse economics compared to a lower value of wind

_{PW}. Accordingly, the designs returning the best economic performance were those not integrating any wind capacity. In other words, the reduced operating expenses coming along with the exploitation of wind power were not sufficient to balance out the increased initial investment. On the other hand, increasing wind

_{PW}always led to a reduction of CO

_{2}emissions. Adding capacity to the wind farm increased the environmental performance of the plant more than what a refined—thus more expensive and bulkier—design of the combined cycle could possibly do. These considerations are confirmed by observing Figure 7 where the Pareto solutions with no wind integration and with maximum wind integration are highlighted. Those solutions showed to be those returning optimal economic and environmental performance, respectively.

## 5. Discussion and Analysis of the Results

_{2}emissions and the maximum weight of the bottoming cycle. A weight threshold was set at 120 t, while the maximum allowable amount of CO

_{2}emissions was ranged between 2.0 Mt and 2.6 Mt. Among the designs fulfilling the criteria indicated, the optimal one was then selected as that returning the best economic performance. Figure 8 gives a visual representation of the screening mechanism applied to the Pareto solutions with the GT A, for a maximum CO

_{2}emissions level of 2.3 Mt (and maximum weight of 120 t). The optimal design identified was termed Design A (CC+W). The same screening mechanism was applied to the Pareto solutions of GT B and the optimal design Design B (CC+W) was pinpointed. Table 4 and Table 5 report the characteristics of these optimal designs that were further used for the following techno-economic analyses.

_{2}emissions constraint between 2.0 Mt and 2.6 Mt are shown in Figure 9. For each optimal design identified the lifetime economic performance and the wind farm size are reported. The set of results helped to make some considerations on the optimal wind power integration. A trade-off emerged between the extent of the environmental and economic aspects. The outcome confirmed what already hinted by the stepwise trend of the Pareto fronts. On one hand, the installation of offshore wind is economically challenging and, in fact, the total cost is consistently increasing with increasing wind power capacity installed. On the other hand, cutting the expected CO

_{2}emissions is challenging as well and the most effective way (also under an economical point of view) to meet more severe emissions limitations is to increase the size of the wind farm. Summing up, it can be argued that the optimal size of the wind farm should be selected by carefully defining and weighing the performance requirements (environmental and economic) that are to be achieved by the plant.

#### 5.1. Comparison between the Cycles Based on the Two Gas Turbines

#### 5.2. Performance Analysis of Offshore Power Plant

- Combined cycles with wind power—Design A (CC+W)
- Combined cycles—Design A (CC)
- Simple GT cycles with wind power—Design B (GT+W)
- Simple GT cycles—Design B (GT)

_{2}emissions for each option simulated that ultimately add up to give the overall CO

_{2}footprint. Figure 11 shows the evolution of the total cost to supply energy to the plant (cost*) during the years of plant operation that ultimately constitute the economic performance of the various concepts. The cost* is always negative as only costs were considered in the analysis. The advanced offshore power plant proposed—Design A (CC+W)—reached the best environmental performance. The cuts of CO

_{2}emissions ranged between 272 kt (a 11.9% reduction) in comparison to Design A (CC) and 557 kt (a 24.4% reduction) in comparison to Design B (GT). Whilst advantageous in terms of environmental impact, the integration of wind power implied worse economics. Design B (GT) returned the lowest cost for the offshore energy supply, followed by Design A (CC). In comparison to their counterparts without wind power, Design A (CC+W) and Design B (GT+W) entailed an additional cost of 19 M$ and 21 M$, respectively. The operational costs were minimized with Design A (CC+W) but the savings achieved were not sufficient to repay the additional investment for the wind farm. Conversely, Design B (GT) showed the highest operational costs but the smaller initial investment guaranteed an overall better economic performance.

#### 5.3. Sensitivity Analysis on Economic Parameters

**Wind farm total capital requirement (TCR**. The economic performances of Design A (CC+W) would have matched that of Design A (CC) if the specific value of the TCR

_{wind})_{wind}had dropped to 2611 $/kW from the reference value of 4503 $/kW. Albeit that number is in line with the most optimistic future scenarios, it is much lower than the current situation [31]. When the comparison was made with respect to Design B (GT+W) and Design B (GT), the TCR of the wind farm had to decrease down to, respectively, 3416 $/kW and 1353 $/kW before returning a better economic performance.

**Combined cycle total capital requirement (TCR**. The calculation of TCR

_{cc})_{cc}was believed to be subjected to a large degree of uncertainty. The costs to install the necessary components offshore are significantly higher compared to typical onshore applications and difficult to estimate as very site specific. The numbers proposed, even though calculated taking into account a large contingency, could be under-estimated. In the comparative analysis between the various concepts, the impact of the high uncertainty level was limited by the fact that the options integrating wind power included the same power generation unit of the equivalent options without wind power. Larger differences could potentially arise between the concepts based on a combined cycle and those based on a simple GT cycle. In order to assess that, the TCR

_{cc}was increased by a factor 2 and 5 (cases TCR2 and TCR5, respectively). Figure 12 shows the resulting cost* trends. The concepts based on a GT simple cycle became more and more attractive since the gap of capital investment with respect to concepts based on a combined cycle increased. If in the base case Design A (CC) and Design B (GT+W) had similar performances, already at TCR2 Design B (GT+W) returned a better economic performance by about 29 M$. Ultimately, the increase of the cost to install the power generation unit on the platform benefitted more conservative solutions (e.g., Design B (GT)) over more advanced ones (e.g., Design A (CC+W)).

**Discount rate (r).**The effect of a lower (5%) and higher (9%) discount rate was evaluated. Figure 13 shows the related profile of the cost* throughout the plant’s lifetime. At lower discount rates, it becomes more important to minimise the operational costs as they will weigh more on the final economic performance. Accordingly, the concepts entailing lower operational costs—for instance, Design A (CC+W)—are favoured by lower values of the discount rate. Conversely, the concepts with lower investment costs but higher operational costs—for instance, Design B (GT)—are favoured by higher values of the discount rate. Ultimately, even though the economic gap between the various concepts changed with the different discount rates applied, the relative economic performance remained the same.

**CO**Figure 14 shows the relative effect of different CO

_{2}price (c_{CO2})._{2}prices on the economic performance. Keeping Design A (CC+W) as the reference for comparison, the Δcost* obtained at the end of the lifetime is reported in the figure for the other concepts. A positive value indicates a better economic performance with respect to Design A (CC+W). Conversely, a negative value indicates a worse economic performance. The analysis showed that the CO

_{2}price had to exceed 174.1 $/t for Design A (CC+W) to entail an economic advantage over Design A (CC). Economic competitiveness could be achieved with relatively smaller levels of CO

_{2}price (i.e., 121.0 $/t and 158.8 $/t) with respect to Design B (GT+W) and Design B (GT). Such high levels of CO

_{2}price are foreseen in the future from some specific scenarios involving a strong international commitment on environmental issues (e.g., the 450 scenario by IEA displayed a CO

_{2}price of 140 $/t in 2040 [32]). However, they appear unlikely in the short term.

**Gas price (c**Figure 15 shows the effect of both higher (+25%) and lower (−25%) gas prices, alongside a variable c

_{gas})._{CO2}. When the gas prices were increased, the situation became more favourable to the integration of wind power. Though, rather high levels of CO

_{2}prices (between 124.7 and 141.3 $/t) would still be needed to even the economic performance. The low levels of gas price seemed to rule out the possibility to achieve economic competitiveness for offshore wind power integration, as CO

_{2}prices around 200 $/t would be needed.

## 6. Conclusions

_{2}emissions of 272 kt (−11.9%) and of 557 kt (−24.4%) with respect to the same combined cycle and to a simple GT cycle not integrating a wind farm. The economic performance was questionable. A wind farm meant an increased initial investment. Even though lower operational costs were obtained, paying back such additional investment proved to be challenging. With the current levels of gas and CO

_{2}prices, the final cost for the offshore energy supply was about 19 M$ and 32 M$ higher compared to the two concepts without wind power. The sensitivity analysis showed that very favourable price conditions would be needed to even out the difference. Conservative concepts, displaying a lower initial investment, demonstrated to be advantageous under an economic point of view. The results presented are case specific and cannot be generalized. For instance, in larger offshore projects with a longer lifetime, the reduced operational costs would result in a better economic outlook. In addition, it should be pointed out that the offshore power plant integrating a wind farm achieved a substantial cut in CO

_{2}emissions that affected the economic analysis only through a reduced cost for the CO

_{2}emitted. In an energy system including emission caps and penalties for the plants failing to fulfil such requirements, the better environmental performance could contribute to close the economic gap and, possibly, make offshore wind power integration economically feasible.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | Heat transfer area, m^{2} |

c_{CO2} | CO_{2} price, $/t |

c_{gas} | Gas price, $/MWh |

CF | Cash flow |

CF^{CO2} | Cash flows associated with the CO_{2} emissions, M$ |

CF^{gas} | Cash flows associated with the onsite gas consumption, M$ |

$C{O}_{2}^{\ast}$ | Total CO_{2} emissions, Mt |

cost* | Total cost to supply energy to the plant, M$ |

C_{S} | Constant flow coefficient |

DCF | Discounted cash flow, M$ |

F_{CU} | Factor accounting for copper losses |

GT load | Gas turbine load |

h_{eq} | Equivalent hours per year, h |

k_{ε} | Correction factor |

LHV_{gas} | Lower heating value of the natural gas, kJ/kg |

load | Mechanical load |

ṁ_{steam} | Steam mass flow rate, kg/s |

m_{CO2} | CO_{2} emissions, Mt |

ṁ | Mass flow rate, kg/s |

ṁ_{CO2} | Mass flow rate of emitted CO_{2}, kg/s |

ṁ_{cw} | Mass flow rate of cooling water, kg/s |

ṁ_{gas} | Mass flow rate of natural gas, kg/s |

ṁ_{WHRU} | Mass flow rate in the WHRU, kg/s |

p_{cond} | Condenser pressure, bar |

p_{in} | Turbine inlet pressure, bar |

p_{out} | Turbine outlet pressure, bar |

p_{steam} | Steam evaporation pressure, bar |

P_{CC} | Combined cycle power requirement, MW |

P_{net} | Net cycle power output, MW |

P_{ST} | Steam power output, MW |

P_{O} | Offshore power demand, MW |

P_{W} | Wind power contribution, MW |

PEC | Purchased-equipment cost, M$ |

r | Discount rate |

T_{cond,in} | Temperature at the condenser inlet, °C |

T_{in} | Turbine inlet temperature, °C |

T_{steam} | Superheated steam temperature, °C |

TCR | Total capital requirement, M$ |

TCR_{CC} | Total capital requirement for the combined cycle, M$ |

TCR_{wind} | Total capital requirement for the wind farm, M$ |

U | Overall heat transfer coefficient, kW/K/m^{2} |

UA_{ECO1} | UA coefficient of the 1st economizer, kW/K |

UA_{ECO2} | UA coefficient of the 2nd economizer, kW/K |

UA_{OTB} | UA coefficient of the evaporator, kW/K |

UA_{SH} | UA coefficient of the superheater, kW/K |

UA_{WHRU} | UA coefficient of the waste heat recovery unit, kW/K |

$\dot{V}$ | Volumetric flow rate, m^{3}/s |

wind_{PW} | Wind power capacity installed, MW |

W_{component} | Weight of the specific component of the power cycle, t |

W* | Total weight of the bottoming cycle, t |

W_{OTSG} | Weight of the OTSG, t |

W_{ST} | Weight of the steam turbine, t |

W_{GEN} | Weight of the generator, t |

W_{COND} | Weight of the condenser (wet), t |

$\overline{x}$ | Array of decision variables |

$\overline{z}$ | Array of objective functions |

Greek Letters | |

γ | Exponent of the Reynolds number in the heat transfer correlation |

Γ | Marginal likelihood |

Δh_{T,is} | Isentropic enthalpy difference, kJ/kg |

Δp | Pressure drop, bar |

Δp_{ECO1} | Pressure drop in the 1st economizer, bar |

Δp_{ECO2} | Pressure drop in the 2nd economizer, bar |

Δp_{OTB} | Pressure drop in the evaporator, bar |

Δp_{OTSG} | Overall pressure drop in the OTSG, bar |

Δp_{SH} | Pressure drop in the superheater, bar |

ΔT_{cw} | Cooling water temperature difference, °C |

ΔT_{OTSG} | Pinch point difference in the OTSG, °C |

η_{cycle} | Net cycle efficiency |

η_{gen} | Generator efficiency |

η_{pump} | Pump isentropic efficiency |

η_{T} | Isentropic steam turbine efficiency |

ϑ_{k} | Hyperparameter |

σ^{2} | Process variance |

ψ | Correlation function |

Ψ | Correlation matrix |

Acronyms | |

DC | Direct costs |

GA | Genetic algorithm |

GT | Gas turbine |

IC | Indirect costs |

MAE | Mean average error |

NOC | Number of off-design conditions |

NPV | Net present value |

OTSG | Once-through steam generator |

TIT | Turbine inlet temperature |

WHRU | Waste heat recovery unit |

## Appendix A. Kriging Surrogate Modelling Technique

^{2}and a correlation matrix Ψ. Z(x) takes into account localized variations and ensures the interpolation of the training data. The correlation function ψ is parametrized by a set of hyperparameters ϑ

_{k}, determined using the maximum likelihood estimation. The correlation function used is the following:

^{2}is the process variance and Ψ is the n X n correlation matrix. While the first term represents the quality of the fit, the second term can be interpreted as a complexity penalty. The combination of the two allows balancing between flexibility and accuracy.

## Appendix B. Correlations for the Off-Design Performance Predictions

_{ε}is a correction factor. It was noted that the error in the estimation of the heat transfer coefficients increased with the decrease of the plant load and became relevant at very low loads (of importance in the scenarios including wind power integration). The off-design model of the heat transfer coefficient was tuned in order to address this effect. The correction factor k

_{ε}is defined as a function of the deviation of the flow rate from the design value. It is applied to all the heat exchange sections but the superheater of the OTSG, where it is not necessary.

_{S}is the constant flow coefficient, ṁ is the mass flow rate, T

_{in}is the turbine inlet temperature, p

_{in}is the turbine inlet pressure and p

_{out}is the turbine outlet pressure.

_{T}is the isentropic efficiency of the turbine at off-design and Δh

_{T,is}is the isentropic enthalpy difference due to the expansion in the turbine.

_{gen}is the generator efficiency, load is the mechanical load and F

_{CU}is a term representing the copper losses (produced in the winding of the stator). The term F

_{CU}is set equal to 0.43 [28].

_{pump}is the isentropic efficiency of the pump and $\dot{V}$ is the volumetric flow rate.

## Appendix C. Validation of the Kriging Model

_{COND}). The related MAE were 3.18% and 2.30% and substantial prediction errors were highlighted by the parity plot in Figure A4. However, it was also noted that the W

_{COND}contributed marginally (between 4% and 10%) to the total weight of the bottoming cycle, whose estimation resulted to be rather good with MAE of 0.37% and 0.34%. Therefore, a slightly worse accuracy in the prediction of W

_{COND}was considered acceptable. Another term with MAE larger than 1% was the UA coefficient of the superheater (UA

_{SH}). However, it was noted that UA

_{SH}had a limited impact on the overall heat transfer process occurring in the OTSG, due to the limited degree of superheating implemented in the various designs. Overall, the accuracy demonstrated by the Kriging model was within reasonable levels and the model was, thus, considered validated.

Output Parameters | GT A | GT B | |
---|---|---|---|

Description | Symbol | MAE | MAE |

Net cycle efficiency | η_{cycle} | 0.03% | 0.07% |

Net power output | P_{net} | 0.05% | 0.05% |

Mass flow rate in the WHRU | ṁ_{WHRU} | 0.01% | 0.04% |

UA coefficient of the WHRU | UA_{WHRU} | 0.00% | 0.02% |

UA coefficient of the first economizer | UA_{ECO1} | 0.58% | 0.78% |

UA coefficient of the second economizer | UA_{ECO2} | 0.52% | 0.68% |

UA coefficient of the evaporator | UA_{OTB} | 0.30% | 0.44% |

UA coefficient of the superheater | UA_{SH} | 1.35% | 1.28% |

Pressure drop in the first economizer | Δp_{ECO1} | 0.00% | 0.00% |

Pressure drop in the second economizer | Δp_{ECO2} | 0.03% | 0.04% |

Pressure drop in the evaporator | Δp_{OTB} | 1.02% | 0.99% |

Pressure drop in the superheater | Δp_{SH} | 0.00% | 0.00% |

Steam mass flow rate | ṁ_{steam} | 0.23% | 0.29% |

Isentropic steam turbine efficiency | η_{T} | 0.39% | 0.43% |

Temperature at the condenser inlet | T_{cond,in} | 0.00% | 0.00% |

Mass flow rate of cooling water | ṁ_{cw} | 0.54% | 0.56% |

Weight of the OTSG | W_{OTSG} | 0.42% | 0.56% |

Weight of steam turbine | W_{ST} | 0.48% | 0.41% |

Weight of generator | W_{GEN} | 0.19% | 0.27% |

Weight of the condenser (wet) | W_{COND} | 3.18% | 2.30% |

Purchased-equipment cost | PEC | 0.23% | 0.27% |

## Appendix D. Validation of the Off-Design Correlations

GT A | GT B | |||||
---|---|---|---|---|---|---|

Design #1 | Design #2 | Design #3 | Design #1 | Design #2 | Design #3 | |

GT load | 0.90 | 0.82 | 0.93 | 0.90 | 0.69 | 0.82 |

p_{steam} | 20 | 32 | 27 | 30 | 18 | 35 |

T_{steam} | 328 | 390 | 360 | 350 | 320 | 290 |

ΔT_{OTSG} | 25 | 20 | 15 | 25 | 12 | 18 |

p_{cond} | 0.07 | 0.05 | 0.04 | 0.07 | 0.04 | 0.09 |

ΔT_{cw} | 8 | 5 | 6 | 8 | 5 | 4 |

Design #1 | Design #2 | Design #3 | Overall | |
---|---|---|---|---|

MAE | MAE | MAE | MAE | |

GT A | ||||

η_{cycle} | 0.20% | 0.26% | 0.27% | 0.24% |

P_{net} | 0.20% | 0.26% | 0.27% | 0.24% |

ṁ_{CO2} | 0.00% | 0.00% | 0.00% | 0.00% |

P_{ST} | 0.87% | 1.18% | 1.21% | 1.08% |

p_{steam} | 0.79% | 1.13% | 1.26% | 1.06% |

T_{steam} | 0.45% | 0.21% | 0.29% | 0.32% |

ṁ_{steam} | 0.66% | 0.79% | 1.06% | 0.84% |

GT B | ||||

η_{cycle} | 0.12% | 0.17% | 0.05% | 0.11% |

P_{net} | 0.12% | 0.17% | 0.05% | 0.12% |

ṁ_{CO2} | 0.00% | 0.00% | 0.01% | 0.01% |

P_{ST} | 0.57% | 1.00% | 0.42% | 0.66% |

p_{steam} | 0.80% | 1.19% | 0.50% | 0.83% |

T_{steam} | 0.41% | 0.12% | 0.63% | 0.39% |

ṁ_{steam} | 0.67% | 0.69% | 0.52% | 0.63% |

_{cycle}) and the CO

_{2}emissions (ṁ

_{CO2}), were predicted with good accuracy even at low part-loads (see Figure A5 with the parity plot of η

_{cycle}). The simulation of the steam cycle demonstrated to be somewhat challenging, especially the heat transfer process in the OTSG. At low part-loads the accuracy of the correlation for the heat transfer coefficients started to diminish, resulting in less precise values of the steam parameters (see for example Figure A7) and consequently in a larger error in the steam power output (P

_{ST}) calculated. This was particularly evident by looking at the parity plot of P

_{ST}in Figure A6, where the region of low part-loads (i.e., the bottom left corner of the parity plot) is characterised by a larger scattering of the results. However, a proper tuning of the correlations allowed to contain the maximum error within few percentage points and the MAE close to 1%. Considering that the contribution of the ST to the total power output is rather small, the performance predictions at off-designs were deemed as adequate to be used in an optimisation procedure.

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**Figure 1.**Layout of the offshore energy system integrating a wind farm and a combined cycle to supply energy to the processing block of a platform.

**Figure 3.**Lifetime power demand of the installation. The dashed line represents an approximation of the power demand profile.

**Figure 5.**Duration curve for the wind power. The dashed line represents an approximation of the wind power available throughout one year.

**Figure 6.**Decision map of the Pareto front showing trade-offs between total cost and CO

_{2}emissions. The shades of colour represent different levels of weights of the optimal designs: the darker the colour, the heavier the design.

**Figure 7.**Decision map of the Pareto front showing trade-offs between total cost and CO

_{2}emissions for the designs based on GT A (

**a**) and GT B (

**b**). The results referring to no wind integration (0 MW) and maximum wind integration (30 MW) are highlighted.

**Figure 8.**Visual representation of the screening mechanism of the Pareto designs. The grey empty diamonds are the designs screened out, the blue empty diamonds are the designs complying with the two criteria and the red full circle is the design selected.

**Figure 9.**Characteristics of the designs identified through the selection process at the different maximum levels of CO

_{2}emissions. The bars represent the optimal wind capacity to be installed. The empty dots represent the total plant cost.

**Figure 10.**Annual CO

_{2}emissions for the concepts analysed: Design A (CC+W), Design A (CC), Design B (GT+W) and Design B (GT).

**Figure 11.**Evolution of the total plant cost throughout plant’s lifetime for the concepts analysed: Design A (CC+W), Design A (CC), Design B (GT+W) and Design B (GT).

**Figure 12.**Evolution of the total plant cost throughout plant’s lifetime when the total capital requirement of the onsite power generation unit is increased by (

**a**) a factor 2 (TCR2) or (

**b**) 5 (TCR5).

**Figure 13.**Evolution of the total plant cost throughout plant’s lifetime when the discount rate is set to (

**a**) 5% or (

**b**) 9%.

**Figure 14.**Variation of the total plant cost of Design A (CC), Design B (GT+W) and Design B (GT) relative to Design A (CC+W), as a function of the CO

_{2}price.

**Figure 15.**Variation of the total plant cost of Design A (CC), Design B (GT+W) and Design B (GT) relative to Design A (CC+W), as a function of the CO

_{2}price, when the gas price is increased by (

**a**) +25% or decreased by (

**b**) 25%.

**Table 1.**Breakdown of the costs included in the total capital requirement [9] (Reprinted with permission from Pierobon, L; et al., Multi-objective optimization of organic Rankine cycles for waste heat recovery: Application in an offshore platform, published by Elsevier, 2013).

Direct Cost (DC) | Range from [30] | Factor Selected |
---|---|---|

Onsite cost | ||

Purchased-equipment costs (PEC) | ||

Purchased-equipment installation | 20–90% of PEC | 45% |

Piping | 10–70% of PEC | 35% |

Instrumentation and controls | 6–40% of PEC | 20% |

Electrical equipment and materials | 10–15% of PEC | 11% |

Offsite cost | ||

Civil, structural and architectural work | 15–90% of PEC | 30% |

Service facilities | 30–100% of PEC | 65% |

Indirect Cost (IC) | ||

Engineering and supervision | 6–15% of DC | 8% |

Construction costs and constructors profit | 15% of DC | 15% |

Contingencies | 8–25% of total cost | 25% |

**Table 2.**List of the independent variables of the Kriging model, with the lower and upper bounds considered. The same bounds apply for the optimisation problem (OTSG: once-through heat recovery steam generator; GT: gas turbines).

Input Parameters | GT A | GT B | |||
---|---|---|---|---|---|

Description | Symbol | Lower Bound | Upper Bound | Lower Bound | Upper Bound |

Gas turbine load | GT load | 0.80 | 0.95 | 0.60 | 0.95 |

Steam evaporation pressure (bar) | p_{steam} | 15 | 40 | 15 | 40 |

Superheated steam temperature (°C) | T_{steam} | 300 | 410 | 280 | 370 |

Pinch point temperature difference in the OTSG (°C) | ΔT_{OTSG} | 10 | 30 | 10 | 30 |

Condenser pressure (bar) | p_{cond} | 0.03 | 0.10 | 0.03 | 0.12 |

Condenser cooling water temperature difference (°C) | ΔT_{cw} | 3 | 10 | 3 | 10 |

**Table 3.**Off-design conditions to be tested by the optimisation procedure given a wind power capacity installed of 10 MW.

Power Demand Offshore | Wind Power | Combined Cycle Power |
---|---|---|

P_{O} | P_{W} | P_{CC} = P_{O} − P_{W} |

MW | MW | MW |

29.7 (year 2016) | 10.0 | 19.7 |

7.5 | 22.2 | |

5.0 | 24.7 | |

2.5 | 27.2 | |

0.0 | 29.7 | |

35.5 (years 2017 to 2018 and years 2021 to 2023) | 10.0 | 25.5 |

7.5 | 28.0 | |

5.0 | 30.5 | |

2.5 | 33.0 | |

0.0 | 35.5 | |

39.9 (years 2019 and 2020) | 10.0 | 29.9 |

7.5 | 32.4 | |

5.0 | 34.9 | |

2.5 | 37.4 | |

0.0 | 39.9 | |

33.0 (years 2024 and 2034) | 10.0 | 23.0 |

7.5 | 25.5 | |

5.0 | 28.0 | |

2.5 | 30.5 | |

0.0 | 33.0 |

GT A | ||||
---|---|---|---|---|

Design A (CC+W) | Design A (CC) | Design A (GT+W) | Design A (GT) | |

Decision variables | ||||

GT load | 0.86 | 0.86 | - | - |

p_{steam} (bar) | 17.7 | 17.7 | - | - |

T_{steam} (°C) | 355.8 | 355.8 | - | - |

ΔT_{OTSG} (°C) | 18.3 | 18.3 | - | - |

p_{cond} (bar) | 0.09 | 0.09 | - | - |

ΔT_{cw} (°C) | 6.1 | 6.1 | - | - |

wind_{PW} (MW) | 10 | - | 10 | - |

Objective functions | ||||

$C{O}_{2}^{\ast}$ (Mt) | 2.3 | 2.6 | 2.8 | 3.3 |

W* (t) | 102 | 102 | - | - |

cost* (M$) | 387 | 369 | 396 | 399 |

GT B | ||||
---|---|---|---|---|

Design B (CC+W) | Design B (CC) | Design B (GT+W) | Design B (GT) | |

Decision variables | ||||

GT load | 0.62 | 0.62 | - | - |

p_{steam} (bar) | 16.7 | 16.7 | - | - |

T_{steam} (°C) | 323.3 | 323.3 | - | - |

ΔT_{OTSG} (°C) | 24.7 | 24.7 | - | - |

p_{cond} (bar) | 0.09 | 0.09 | - | - |

ΔT_{cw} (°C) | 5.8 | 5.8 | - | - |

wind_{PW} (MW) | 15 | - | 10 | - |

Objective functions | ||||

$C{O}_{2}^{\ast}$ (Mt) | 2.3 | 2.6 | 2.6 | 2.8 |

W* (t) | 104 | 104 | - | - |

cost* (M$) | 407 | 369 | 377 | 356 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Riboldi, L.; Nord, L.O.
Offshore Power Plants Integrating a Wind Farm: Design Optimisation and Techno-Economic Assessment Based on Surrogate Modelling. *Processes* **2018**, *6*, 249.
https://doi.org/10.3390/pr6120249

**AMA Style**

Riboldi L, Nord LO.
Offshore Power Plants Integrating a Wind Farm: Design Optimisation and Techno-Economic Assessment Based on Surrogate Modelling. *Processes*. 2018; 6(12):249.
https://doi.org/10.3390/pr6120249

**Chicago/Turabian Style**

Riboldi, Luca, and Lars O. Nord.
2018. "Offshore Power Plants Integrating a Wind Farm: Design Optimisation and Techno-Economic Assessment Based on Surrogate Modelling" *Processes* 6, no. 12: 249.
https://doi.org/10.3390/pr6120249