Numerical modelling of a hydro-pneumatic energy storage system for smoothing power fluctuations from offshore wind

Energy storage systems are imperative in tackling the regulation of electricity supply and demand mismatch to avoid curtailment of wind energy. Co-locating energy storage in the same operating region as the offshore wind farms allows for an unobtrusive environment while also steering away from rising land prices. The presented work involves an offshore Hydro-Pneumatic Energy Storage (HPES) system made up of a subsea accumulator pre-charged with compressed air. The Energy Conversion Unit (ECU) of the system consists of a megawatt-scale hydraulic pump and a turbine. This paper discusses a novel numerical model developed in Python™ for simulating the operation of the ECU pump and turbine of the offshore HPES system by using a simple moving average, based on a time window of wind data, whilst also introducing a one-step-ahead forecasting model. The results of the research are split into two parts; Firstly, the analysis and validation of the Seasonal Auto Regressive Integrated Moving Average (SARIMA) forecasting model is performed. Secondly, results on the pump and turbine performance based on the smoothened power are shown. The research found that despite the centrifugal pump limitations due to variable head operation, a smoothened power output is efficiently (> 90 %) attained in retaining the intermittent power generated.


Introduction
According to DNV GL's Energy Transition Outlook published in 2022 [1], virtually 50 per cent of Europe's primary energy supply will be coming from wind energy, and 6 per cent of this amount will be specifically floating offshore, by 2050.Lew et al. [2] reported that increasing wind energy output leads to challenges in merging renewable energy sources (RES) to the grid due to wind energy intermittency.Katsaprakakis [3] explained that introducing energy storage systems (ESSs) to tackle intermittency is required to reap economically-viable operation of power systems by regulating the electricity supply and demand mismatch.Introducing energy storage to smoothen this mismatch will minimise the need for spinning reserves which are still operated using conventional fuels, thereby contributing to reductions in carbon dioxide emissions [4].In recent years, the co-location of ESSs with RES generation offshore has progressively become a more feasible option.Leporini et al. [5] created a tool which aids decision-making by studying the various technicalities in decommissioning or converting existing offshore platforms into useful sites for renewable energy (RE) generation.Hazim et al. [6] found that repurposing ageing offshore pipeline setups into an ESS based on an offshore hydro-pneumatic energy storage (HPES) system competed economically in comparison with decommissioning the existing structure.Kaldellis and Kapsali [7] summarised that the reasons for pushing offshore wind energy generation were due to the higher wind speeds experienced, overpopulation near coastal regions and the absence of obstacles and feasible onshore sites.Furthermore, Slocum [8] described an offshore environment as unobtrusive and safe, with offshore energy storage taking advantage of the surrounding sea water by making use of the large hydrostatic pressures.
Previous research has shown that power smoothing can aid in reducing storage capacity and operational costs [9]- [11].Sharma et al. [12] specified that forecasting is useful for ESS operation since it aids in storage management and flexibility over the storage system's operational lifecycle.Wurth et al. [13] emphasised the importance of minute-scale forecasting to balance out the power grid, as well as for the validation of forecasting models.The most classic forecasting methods in relation to wind speed and wind power are statistical models, such as the Auto Regressive Moving Average (ARMA), due to their time-series-based modelling.Such forecasting methods are typically used for 10-minute-ahead forecasts, with Wurth et al. [13] highlighting that an existing knowledge gap is understanding how statistical forecasting methods would perform at smaller future timesteps.Johnson et al. [14] applied a simple moving average (SMA) method paired with battery energy storage to reduce power fluctuations from photovoltaic (PV) power.Alam et al. [15] explained that the averaging window is the controlling factor on the charging or discharging of the storage system.A long averaging window causes large power differentials to be handled by the storage system as well as time delays, and a window too short can potentially still lead to an intermittent power output.
This paper presents a novel numerical model for simulating the operation of megawattscale hydraulic machines (centrifugal pump and Pelton Turbine wheel) to obtain a smoothened power output based on an input theoretical SMA of intermittent power from a 10 MW wind turbine.The hydraulic machines make up the energy conversion unit (ECU) of an offshore hydro-pneumatic energy storage (HPES) system [16].The system is upscalable and is able to support gigawatt-scale offshore wind projects.Sant et al. [17] carried out a preliminary evaluation on the costs for an HPES system.The numerical model also applies a one-step-ahead time-series forecasting model to predict the power diverted to the ECU and identifies which hydraulic machine will be required to feed a smoothened power output to the grid.

Methodology
The numerical model, which was developed in Python TM (version 3.9.13),consists of two parts; (i) The dataset was inputted and the prediction model was selected and tested on the said dataset.(ii) The time-series simulation was commenced, modelling a seven hour simulation of ECU performance of the offshore HPES system.
The wind power data used throughout this paper is based on time-series wind speed measurements during the month of January 2016 obtained for the Maltese Islands, located in the Central Mediterranean, and applied to a 10 MW NREL wind turbine [18].Figure 1 shows a snippet of the time-series of power output data from the NREL turbine.The trace plotted indicates intermittent data, with periods of high power as well as periods of no power, depending on the wind speed experienced.The data required further analysis to help converge towards selecting the correct model for forecasting.The following subsection discusses how the prediction model was selected and tested.Figure 2 shows a flowchart of the prediction modelling and validation method adopted.Once the wind turbine power output data were plotted, a moving average (MA) based on the previous 24 hours of data was applied (P smt ).Simultaneously, a seasonal decomposition was performed to observe trend and seasonality of the data, which are plotted in Figure 3.While no obvious trend was identified, a seasonality was clear, meaning the data's behaviour repeated itself periodically.Stationarity signifies that the probability distribution of a stochastic process is independent of time [19].The Augmented Dickey-Fuller (ADF) test checks for data stationarity by analysing if the Auto Regressive (AR) model has a unit root [21].Equation 1shows the ADF equation which tests whether γ = 0, with the null hypothesis stating that the data is non-stationary.

Prediction Model and Validation Procedure
where y t is the data input, α is a constant value and β reflects a time trend coefficient.Once the data were checked, the dataset could be split into a train-test ratio by using 80 % of the data for training and the remaining 20 % for testing.Due to the seasonality in the data, as observed in Figure 3, the Seasonal Auto Regressive Integrated Moving Average (SARIMA) forecasting tool in-built in Python TM was found to be best suited [20].The SARIMA model in Python TM is represented as (p, d, q) × (P, D, Q) s , where p and q are the AR and MA order terms respectively, with d being an integer to represent differencing (only necessary if data is non-stationary).Meanwhile, P , D and Q represent the seasonal component and s is the seasonal period (24 hours in this case).Equation 2shows the SARIMA model equation.
where ϕ p and φp represent the AR and seasonal AR orders respectively, θ q and θq are the MA and seasonal MA orders, ∆ d and ∆ D s are the differencing and seasonal differencing orders (if required), y t is the time-series data and L, A(t) and ζ t are the lag operator, the trend component and white noise respectively.The selection of the best SARIMA model involved computing the Akaike Information Criterion (AIC), where the lowest AIC from the different SARIMA orders tested was deemed the most accurate forecasting model [20] [21].The forecasting model was then run, and the power difference between the actual values and forecasted values could be calculated, with the Root Mean Square Error (RMSE) being computed as a forecasting accuracy metric.

The ECU Simulator
Figure 4 shows the working principle of the offshore HPES system operating in tandem with the wind turbine.The system considered is described thoroughly in previous work by Buhagiar et al. [16], where the Pressure Containment System (PCS) is located subsea to make use of the surrounding seawater as an excellent heat source and heat sink.When the intermittent power (P raw ) is greater than the SMA (P smt ), the excess power is defined as the ECU power input (P ECU,I ).Meanwhile, when the intermittent power (P raw ) is less than the SMA (P smt ), the power is represented as P smt,W T , depicted in Figure 4, and is equal to the intermittent power (P raw ) where the input to the ECU (P ECU,I ) is equal to zero.During such situations, the ECU is to output power (P ECU,O ) which should be adequate to meet the smoothened power (P smt ) required.As a result, the smoothened power output (P smt,O ) calculation is dependent on whether the system is charging or discharging and is shown in Equations 3 and 4 hereunder.Figure 5 summarises the full process of the ECU simulator.The simulator's operation starts off by forecasting the one-step-ahead intermittent power (P f orecasted ) and calculating whether this power was greater or less than the SMA (P smt ).When positive, the multi-stage centrifugal pump was to be operated during the following minute based on that power value, while the Pelton Wheel was to be operated when the power difference was negative.The centrifugal pump was operated at variable speed, where modelling was performed based on the polynomial equations of the pump's characteristic curves.Interpolation between curves was used to adjust the pump's speed, which in turn updated the pump flowrate, its overall efficiency and power output.The Pelton Wheel consisted of two requirements, whereby the optimal bucket-to-speed ratio of 0.48 was to be maintained, and the spear valve position was adjusted per timestep to attain the power desired post Pelton turbine efficiency [22].As the flowchart depicts, the power difference was updated every minute based on the new forecasted power and SMA.Depending on whether the pump or turbine were in operation, the PCS's state of charge was also updated.The hydraulic machinery and PCS parameters are shown in Tables 1 and 2 respectively.Once the simulation was finalised, the overall efficiency comparing the intermittent power and the resulting output power fed into the grid could be computed.Equation 5shows the equation used to calculate the overall efficiency.
Overall System Ef f iciency = where ∆HP ES is the net power out or into the HPES system.

Results and Discussion
This section presents the results obtained showing the reliability of the forecasting model and the ECU response to producing a smoothened power output.Figure 6 highlights the part of the intermittent data selected for simulation.This part was particularly selected due to the high levels of fluctuations above and below the power values of the SMA, as well as the power difference being reasonably manageable by a single ECU model with the pump and turbine power capacities outlined in Table 1.
Figure 6.The data section considered for the ECU simulation example.
Table 3 summarises the results required to confirm if the dataset being used was stationary or not, based on Equation 1 previously shown in Section 2.1.Since the P-value was less than 0.05, the null hypothesis could be rejected, confirming the data as stationary.A double check was performed by comparing the test statistic to the stationarity check at different intervals, with a more negative number increasing the confidence that our data was stationary [21].Since the test statistic is in fact smaller compared to the different confidence interval checks, the data was confirmed stationary.The one-step-ahead forecasting model resulted in an average RMSE of 117.2 kW across the seven-hour simulation, calculated by taking the mean value of the difference between the forecasted (P f orecasted ) and actual values (P raw ), shown in Equation 6.
Figure 7 shows the different power curves superimposed.The theoretical SMA (P smt,I ) is the ideal moving average which is desired to be followed.As may be observed, the smoothened output (P smt,O ) is identical to the theoretical SMA (P smt,I ) during Pelton wheel operation since this machinery offers excellent control variability due to its variable speed and spear valve control, as described in Section 2.2.During pump operation, the smoothened power output (P smt,O ) has portions of intermittency, indicated in Figure 7, where the intermittent power (P raw ) is superimposed by the smoothened power output (P smt,O ).This occurrence is due to the required power being too low (according to the pump characteristic curves) to reach the high pressures within the PCS at lower powers (typically < 1.3 MW).The reason for the 1.3 MW value is based on the pump characteristic curves (depicted by the grey line in Figure 7), where the centrifugal pump produces a pressure of 80 bar at a power of 1.3 MW.As a result, whenever powers were less than this value, the pump's centrifugal effect could not utilise the low power input while simultaneously reaching the required pressure based on the PCS.As a result of the pump's variable head operation, another case of intermittency at a higher power than 1.3 MW is seen after approximately 30 minutes of operation, where a power of 1.8 MW at a pressure of 110 bar was not enough power for the pump to reach the said pressure requirement.Figure 8 shows the pressure variation within the PCS, showing a net decrease in system pressure in order to reduce intermittency across the simulation duration.While the Pelton Wheel's overall efficiency throughout the simulation was consistently maintained between 88 to 89 %, the centrifugal pump's efficiency fluctuated based on the PCS pressure (shown in Figure 8) and the power input into the ECU (P ECU,I ).Consequently, a histogram, shown in Figure 9, was used to demonstrate the different pump efficiencies experienced across the simulation duration.The pump's efficiency averaged at 68.1 % during operation.Despite the pump's average efficiency value, the overall system efficiency calculated using Equation 5 in Section 2.2 was 92.6 %.The reason for this high efficiency is that only a portion of the wind turbine's intermittent power passes through the ECU.Furthermore, the standard deviation of the smoothened power output (P smt,O ) was reduced by approximately three times in comparison to the intermittent signal (P raw ).This result is expected to reduce the requirements for spinning reserves substantially, which are presently used to balance intermittent loads from large offshore wind farms.Table 4 summarises the results based on the scenario simulation performed.

Conclusions
This study has utilised a novel numerical simulation to address the knowledge gap of understanding how megawatt-scale hydraulic machinery making up the ECU of an offshore HPES system would perform in smoothing intermittent power from a 10 MW wind turbine.A one-stepahead SARIMA forecasting model was implemented and this performed well in predicting the power to be fed into the ECU, having an average RMSE of 117.2 kW throughout the simulation.
Results have shown that the Pelton Turbine wheel offers a high degree of flexibility in meeting the necessary smoothened power efficiently due to its variable speed and spear valve.Meanwhile, a single centrifugal pump is limited in its ability to meet the smoothing requirements of the wind turbine when operating under the HPES system's variable head constrains, even when operated at variable speeds.This is due to the inherent performance characteristics of the centrifugal pump, making it impossible to operate at low power inputs while also meeting the high pressure requirements (80 to 200 bar) of the HPES system.As a result, further work by analysing the system using a multitude of smaller pumps instead of a large, singular one is required.The overall system efficiency in delivering a smoothened power output is still exceptionally high, resulting in a 92.6 % efficiency over the seven hour simulation example.Further work will evaluate the cost feasibility of the proposed system.

Figure 1 .
Figure 1.Time-series wind power output data based on measured LiDAR data.

Figure 2 .
Figure 2. A flowchart showing the prediction modelling and validation procedure.

Figure 3 .
Figure 3.The trend and seasonal time-series plots.

F
or Charging : P smt,O = P smt,W T where P ECU,O = 0 (3) F or Discharging : P smt,O = P smt,W T + P ECU,O

Figure 4 .
Figure 4.The working principle of the overall system.

Figure 5 .
Figure 5.A flowchart showing the ECU simulation process.

Figure 7 .
Figure 7.The various power curves over the 7-hour simulation (SMA of 24 hours).

Figure 9 .
Figure 9.A histogram of the pump efficiencies over the 7-hour simulation.

Table 1 .
The ECU main parameters.

Table 2 .
The PCS main parameters.

Table 3 .
The ADF test results.

Table 4 .
Summary of the simulation results.