Generation of input spectrum for electrolysis stack degradation test applied to wind power PEM hydrogen production

0 Introduction

Under the guidance of the “30-60”double-carbon goal,the source side of the power system is transitioning from a power supply structure dominated by thermal power units to high-proportion new energy grids.The natural uncertainty,randomness,and intermittency of renewable energy sources,such as wind and solar power,significantly impact the power supply reliability of power systems [1-3].Therefore,the source side of the power system should be equipped with more energy storage methods and controllable power generation to ensure safe and stable operation.

As a type of green and pollution-free clean energy storage,hydrogen energy is an important carrier for realizing green and low-carbon emissions from power grids,offering broader application prospects than traditional energy storage methods [4,5].Hydrogen production by proton exchange membranes (PEM) has strong fluctuation adaptability and a wider operation range,making it better suited to fluctuating power sources such as wind power.This gives it broader application prospects in power systems with a high proportion and volatility of renewable energy output on the source side [6,7].However,a significant problem with PEM hydrogen production is the high cost of electrolysis stack materials,which results in a lack of engineering demonstrations and commercial verification [8].

The rapid development of the renewable energy hydrogen production industry has increased the requirements for large-scale,low-cost,and long-life PEM hydrogen production equipment.Currently,the research hotspots for PEM electrolyzers are large-scale production and cost reduction.A three-phase interleaved buck rectifier topology based on a thyristor was proposed to improve the power quality of large PEM systems [9].The authors of [10] developed a large-scale finite element method PEM fuel cell model and studied the factors affecting its performance,providing meaningful guidance for PEM fuel cell stack assemblies.Studies have shown that mixed metal oxides can help reduce the cost of PEM electrocatalysts[11].In [12],a techno-economic feasibility study of a highpressure PEM water electrolyzer and its future projections was comprehensively discussed.A learning curve to predict the future decline in the capital cost of the electrolytic cell was generated by considering whether the operational performance of the electrolyzer had improved [13].This research promotes the development of renewable-energy PEM hydrogen production to a certain extent.

Few studies currently investigate the performance changes of electrolysis stacks under dynamic power input conditions.The authors of [14,15] analyzed the dynamic response,hydrogen production performance,and overall system performance of a hydrogen energy utilization system under varying wind and photovoltaic power conditions.The authors of [16] proved that the performance degradation of the PEM electrolysis stack occurs under significant photovoltaic power fluctuations and frequent starts and stops,leading to a decrease in hydrogen production efficiency.The negative effects of dynamic behavior on the electrolyzer were demonstrated by manually changing the electrolytic current density and observing the changes in the electrolyzer parameters under simulated transient fluctuation behavior [17].Considering the dynamic power range of the electrolysis stack,the optimal hydrogen production efficiency under power fluctuations was calculated,and an optimization model was constructed to maximize the economy of the hydrogen production system [18].Existing research lacks a systematic analysis of the influence of fluctuation input on the source side of the electrolysis stack and has limited guiding significance for performance degradation tests of electrolysis stacks.

The typical operating conditions of the electrolysis stack refer to the working mode of the simulated test electrolysis stack under typical application scenarios.Corresponding studies have been currently conducted on the typical operating conditions of equipment such as energy storage batteries and electric vehicles [19-21].However,no relevant standard exists for studying the typical operating conditions of PEM electrolysis stacks in wind-power hydrogen production scenarios,and related studies are limited [22].Constructing typical operating conditions of PEM electrolysis stacks in wind power hydrogen production scenarios can decompose the fluctuation characteristics and performance degradation factors with significant differences.This approach provides test input conditions for the fluctuation adaptability analysis of electrolysis stacks and the exploration of material life performance degradation under laboratory conditions.It also aids in constructing a fluctuation adaptability evaluation system,which helps standardize relevant industry standards and accelerates the development of renewable energy hydrogen production.

Based on the above discussion,this paper proposes a method for generating the cycle condition spectrum of a PEM electrolysis stack degradation test in a wind-powered hydrogen production system,as shown in Fig.1.First,the fluctuation characteristics of multiple wind farm stations in the region were analyzed,and the wind farm output power sample set with the largest fluctuations was extracted.Next,the output characteristic quantities that have a key influence on the degradation life of the electrolyzer were defined,and principal component analysis (PCA) was used to reduce the dimensions of the output characteristic quantity matrix.Furthermore,the data were classified using an improved Gaussian mixture model (GMM) clustering method,and the optimal clustering results were selected to construct the condition spectrum set applied to the degradation test of the PEM electrolysis stack,combined with the scenario probability.Finally,a simulation test of the electrolysis stack model was conducted to verify the feasibility of the construction method under the specified operating conditions.

Fig.1 Cycle spectrum generation method for degradation test conditions of electrolysis stack

1 Application scenarios of wind power electrolysis hydrogen production

Coupled hydrogen production from wind power is divided into grid-connected and off-grid types [23].In gridconnected wind power systems,the grid realizes voltage and frequency control through an energy-management system to ensure that the electrolyzer produces hydrogen at a relatively stable voltage.The primary grid-connected methods include synchronous and asynchronous grid-connected wind power systems [24].There are two main application scenarios for grid-connected wind power coupled with hydrogen production: one involves using surplus wind power to produce hydrogen,serving as a means of peak shaving for the power grid;the other involves utilizing hydrogen energy and power generation through technologies like fuel cells to fill the valley of the power grid [25].In short,this type uses a grid power supply to solve the intermittency problem of wind power and enhances the stability and reliability of the hydrogen production system.A grid-connected wind power hydrogen production scenario is shown in Fig.2.In the figure,the black solid line represents the power flow,and the blue arrow represents the hydrogen energy flow.

Fig.2 Grid-connected wind power hydrogen production scenario

Compared to the grid-connected mode,off-grid wind power eliminates the need for grid-connected auxiliary equipment,avoids problems caused by grid connection,and reduces the cost of hydrogen production.Off-grid power generation can effectively solve the issue of power transmission for offshore wind power.In addition,oil and natural gas transmission infrastructure can be used as a transmission channel for offshore wind power hydrogen production,significantly reducing the investment cost of the corresponding pipeline.Generally,off-grid wind power coupled with hydrogen production has two main application scenarios: the obtained hydrogen is output through a gas pipeline or a hydrogen carrier.A microgrid system is constructed using wind power,converters,electrolyzers,hydrogen storage equipment,and fuel cells.A scenario for hydrogen production from off-grid wind power is shown in Fig.3.

Fig.3 Off-grid wind power hydrogen production scenario

Based on the above analysis,to reflect the influence of wind power fluctuation output on the operating conditions and degradation performance of the electrolysis stack,this study examined the typical operating conditions of the corresponding electrolysis stack under different types of wind power in the hydrogen production scenario of wind farms in a remote area.

The hydrogen production scenario in this remote area is assumed to be as follows:

1) In remote areas,the cost of grid extension is high;therefore,the mode of wind off-gird hydrogen production is adopted,meaning all the energy required for hydrogen production comes from wind farms.

2) Considering the small load capacity in this area,the primary utilization of hydrogen energy is to supply other hydrogen loads,with the remainder stored in a hydrogen storage tank for electrohydrogen conversion.

3) The design of the wind power direct-coupling electrolysis stack was adopted,ignoring the power error of the converter;that is,assuming all the wind power is converted into the input power of the electrolysis stack.

2 Operation condition generation of PEM electrolysis stack

2.1 Quantitative indexes of wind farm fluctuation characteristics

(1) The change rate of wind power was measured using the first-order difference component of the per-unit value of wind power output on time scales of 1 min,15 min,and 1 h.

(2) The hourly average peak-valley difference of the wind power output is defined as the difference between the hourly peak mean and the hourly valley mean of the wind power output.The peak mean avg (Pimax) of wind power output refers to the hourly average output with the largest intraday amplitude,whereas the valley mean avg (Pimin)is the hourly average output with the smallest intraday amplitude.The difference between the two measures the intraday fluctuation amplitude of wind power.The expression for the intraday time-averaged peak-valley difference is shown in (1).

2.2 PEM electrolysis stack degradation model

2.2.1 Electrolysis stack voltage mode

The total voltage at both ends of the PEM cell,Ucell,is mainly composed of the open-circuit voltage E,activation overpotential Uact,diffusion overpotential Udiff,and ohmic overpotential Uohm [26].

where Eo represents the standard electromotive force;T represents the electrolysis stack temperature;R is the gas constant;F is Faraday constant;represents the water activity between the electrode and electrolyte;αa and αc denote the anode and cathode charge transfer coefficients,respectively;j represents the current density;j0,a and j0,c denote the anode and cathode exchange current densities,respectively;denote the concentrations of oxygen and hydrogen at the interface between the membrane and the porous electrode,respectively;anddenote the standard reference values of oxygen and hydrogen concentrations at the interface between the membrane and the porous electrode,respectively;tm represents the proton exchange membrane thickness;and σm represents the resistivity of PEM.

2.2.2 Influence of fluctuation conditions on the degradation of PEM electrolyzer

It has been pointed out in [27,28] that continuous operation at high current densities leads to cation poisoning,increased ion resistance,and charge transfer resistance,as well as a decrease in exchange current density.Operating the stack at high temperature causes a linear increase in ohmic resistance and charge-transfer resistance over time.At low current densities,stack performance degradation is primarily distributed to a decrease in anode exchange current density,while also facing hydrogen and oxygen mixing safety concerns.Under variable load conditions,cyclic operation between high and low current densities reduces degradation compared to short cycles of intermittent operation.

2.3 Definition of operation condition indexes

Considering that the maximum operating limit of the PEM electrolysis hydrogen production system is 150% of the rated power,the capacity configuration of the system was determined.Key characteristic quantities of wind power output,critical for the degradation life of the electrolyzer,were identified,and a matrix of these annual wind power output characteristics was generated.Current research on electrolyzers degradation life primarily focus on constant current,fluctuations,and start-stop conditions [29].

Based on the accelerated oxidation of the proton membrane and dissociation of the catalyst due to continuous overload of the PEM electrolyzer,as well as the detrimental effects of low-load states increasing hydrogen peroxide concentration and damaging the membrane structure,rapid current fluctuations under variable load conditions can further accelerate the loss of ionic polymers from the catalyst layer.In addition,repeated start-stop cycles contribute to damage to both the catalyst and membrane structure [21,28,30,31].These operating conditions significantly impact the lifespan of electrolyzer.Given this context and in conjunction with aforementioned method for constructing working conditions,the following clustering key feature indices for clustering are defined:

1) Low load time: time when the hydrogen production system operates at 5% to 30% of rated power;

2) Normal operation time: time when the hydrogen production system operates at 30% to 100% of rated power;

3) Overload time: time when the hydrogen production system operates at more than 100% of rated power;

4) Shutdown time: time when the hydrogen production system operates at less than 5% of rated power;

5) Average ramp rate of output: average rate of output increase/min by the hydrogen production system;

6) Average drop rate of output: average rate of output decrease/min by the hydrogen production system;

7) Start-stop times: number of transitions between low-load and shutdown states in the hydrogen production system.To reduce the influence of frequent electrolysis stack shutdowns on clustering results due to high-frequency output power fluctuations,a shutdown duration exceeding 10 min was defined as single shutdown event.

2.4 PCA and dimension reduction of operating condition indexes

PCA transforms a set of high-dimensional variables,potentially correlated,into linearly independent lowdimensional variables.This transformation is crucial for reducing the number of wind power output scenarios,by forming high-dimensional feature vectors that characterize clustering features in wind power output.PCA effectively identifies key feature factors impacting clustering,reduces data complexity,and facilitates visualization of highdimensional data.The basic steps are as follows.

1) Data standardization.Standardize the wind power output characteristic matrix using mean variance to obtain the standardized matrix X.

2) Calculate covariance matrix.Compute the covariance matrix R from the standardized sample matrix.

3) Compute eigenvalues and eigenvectors.Determine eigenvalues from λ1 to λp,and corresponding eigenvectors from k1 to kp of the covariance matrix R.

4) Calculate variance and cumulative variance contribution rates.The variance contribution rate represents the ability of a principal component to describe the original data.The greater the cumulative variance contribution rate of the first i principal components,the smaller is the information loss when using the first i principal components to replace the original matrix for analysis.The cumulative variance contribution rate of the ith principal component was calculated using Eq.(6).

2.5 Scenario reduction based on the improved GMM clustering

2.5.1 GMM clustering

GMM is a clustering method based on a probabilitydistribution model.By determining the probability that the input sample belongs to a certain class to determine its final attribute grouping,the correlation and dependence between data attributes can be better captured [32].The model is expressed as follows:

where N(x | μ k,σk)is the Gaussian probability density function;ωk,μk,and σk denote the weight,mean,and covariance matrix of the first component in the mixed N(x | μ k,σk)model,respectively;and p(x)is the probability density function of the GMM.

Usually,the expectation-maximum (EM) algorithm[33] is used to iteratively estimate parameters for GMM.The fundamental principle of EM is to maximize the likelihood estimation of model parameters by introducing latent variables.This involves iteratively updating formulas for latent variable expectations and model parameter reestimations until convergence of the likelihood function value.The procedure unfolds in two main steps:

1) The probability of data points being generated by the GMM (likelihood function) is calculated.Due to its computational complexity,the logarithm of the likelihood function is often employed,as shown in Eq.(8)

2) The EM algorithm iteratively estimates model parameters by updating formulas to maximize the likelihood function,thereby greatly reducing the computational complexity of maximum likelihood estimation.This algorithm proceeds through two primary steps: the expectation step (E-Step) and the maximization step(M-Step).

The probability that data xi is generated by the kth component,obtained during the E-Step,is expressed as

The GMM parameters estimated during the M-Step are expressed as:

2.5.2 DPC algorithm

Density peak clustering [34-36] characterizes the local density ρi of each data point xi and its relative distances δi to other points to identify clustering centers and determine the number of clusters based on density peaks γi.The local density ρi is typically calculated using a cutoff kernel:

where χ(d ij-dc) is the logical judgment value between data points;χ(x) is a logical judgment function;i and j are the ith and jth data points,respectively;dij denotes the Euclidean distance between data points xi and xj;and dc denotes the cutoff distance.

2.5.3 DPC-KL-EM-GMM clustering

The EM algorithm is known to be sensitive to initial input values.Traditional random initialization often leads to local optima,resulting in poor algorithm robustness.Moreover,iterative parameter estimation does not guarantee optimal parameter values upon termination.Although DPC addresses the challenges of estimating cluster numbers and initial centers,its clustering accuracy suffers when class samples overlap.

Therefore,this study used DPC to initialize the EM algorithm,thereby mitigating the EM algorithm’s sensitivity to initial values.Moreover,the Kullback (KL) divergence serve as the termination criterion for EM algorithm iterations,optimizing parameter estimation values in the GMM algorithm.The KL divergence quantifies the similarity between two probability distributions,reflecting the similarity between fuzzy and reference distributions.

where N is the number of samples,pi is the size of the probability distribution function P at the sample xi,and p0i is the size of the probability distribution function P0 at the sample xi.

For the fixed distance dKL,which represents the similarity between the reference distribution function P0 and the probability distribution function P,a larger value indicates greater model robustness and a more conservative optimization strategy.The following expression was used to determine the number of samples with a KL divergence less than the specified threshold dKL.

where,i=1,2,…,Nis the number of samples;j=1,2,…,T is the number of iterations of EM algorithm.

The total number of samples with a KL divergence less than the threshold dKL in a particular iteration can be calculated using Eq.(16).The iteration termination condition of the EM algorithm can be obtained using Eq.(17),where termination occurs when the number of such samples is minimal compared to the adjacent two iterations.At termination,the parameter values from that iteration are taken as the estimated output of the EM algorithm.

2.5.4 Determination of optimal clustering number

To determine the optimal number of clusters,GMM often uses the Bayesian information criterion (BIC) [37],expressed as follows:

where L is the maximum likelihood function of the GMM model and k is the number of model parameters.

However,when determining the optimal cluster set,relying solely on the BIC may lead to a monotonically decreasing phenomenon.Therefore,the rate of change of BIC is proposed to determine the optimal cluster set,which reflects the sensitivity of BIC to an increase in the number of clusters to some extent [38,39].This rate is obtained as follows:

When increasing the number of clusters from k to k+1,a large change rate of BIC illustrates that the current number of clusters k is insufficient to accurately describe the original data set,suggesting an increase to k+1.On the contrary,a small change rate suggests minimal improvement in data description accuracy between the k and k+1 cluster sets.Considering computational costs,k can be considered the optimal cluster set when the corresponding BIC change rate reaches a minimum.

2.6 Cluster validity assessment

It is typically used to evaluate the effectiveness of clustering algorithms and select the optimal number of clusters based on the degree of separation between clusters and the cohesion within clusters.Commonly used clustering evaluation indexes,such as the Calinski-Harabasz index (CHI),Davies-Bouldin index (DBI),and silhouette coefficient (SC) [40,41],are calculated as follows:

where,tr(B) and tr(W) denote the trace of the distance covariance matrix between clusters and in the cluster,respectively;K is the number of clusters;d avg(Ci)and d avg(Cj)denote the average distance from intracluster sample to the cluster center for clusters i and j,respectively;d cen (C i,Cj)denotes the inter-cluster distance of clusters i and j;a represents the average distance from the sample point to other sample points in the cluster,and b represents the average distance from the sample point to other cluster points.The larger the value of CHI,the smaller the value of DBI,and the closer the value of SC to 1,the better the clustering effect.

2.7 Typical operation condition generation strategy of wind power hydrogen production system

Based on the seven characteristic indexes defined in Section 2.3,four operating conditions—low load,normal operation,overload,and shutdown—were defined to correspond to all levels on the operating condition curve.The degradation test condition spectrum for the PEM electrolysis stack was constructed according to the characteristic clustering centers of each scenario.The construction method for the operating conditions is as follows.

1) Owing to the low sensitivity level and minimum response characteristics of the PEM electrolysis stack,the transition time of the electrolysis stack operating power from 0% to 5% during shutdown can be ignored.Therefore,in this study,the degradation test conditions set the output power at shutdown condition to 5%.

2) Normal operation and slight overload power under each operating condition are taken as the average output of the respective operational scenario.

3) To apply these in the degradation test of the electrolysis stack,a constant variable load rate was adopted between each type of output condition,based on the daily maximum variable load rate average in each clustering scenario,all represented as per-unit values.

4) The test condition curve for the electrolysis stack starts from low-load operation,proceeds through start-stop,load increase,and load reduction phases,and ultimately returns to the low-load operation condition,completing the cycle of the operating condition spectrum in this scenario.

3 Case study

Based on the output samples collected from five wind farm stations within a wind farm group in Northwest China,with a sampling interval of 1 min per year,the degradation test conditions of the PEM electrolysis stack were studied using the operational condition spectrum generation method proposed in this paper.

3.1 Comparative analysis of wind farms fluctuation characteristics

The quantitative indexes describing the fluctuation characteristics,as defined in Section 2.1 of this paper,were selected to characterize the fluctuations of each wind farm and wind power cluster in the region.All data from all the wind farm stations were normalized.

(1) Wind-power change rate

The distribution of fluctuating power change rates for each wind farm and wind power cluster,at a 95%confidence level across different time-sampling intervals,is shown in Fig.4.Wind Farm 5 exhibits the highest power fluctuation rate in the area at a 1-min sampling interval,suggesting it could have the greatest impact on the PEM electrolysis hydrogen production system.Additionally,the fluctuation rates of Wind Farms 1 and 2 remain high at 15 min and 1h sampling intervals.

Fig.4 Graph of wind power rate of change at 95%confidence level

(2) The intraday average peak-valley difference in wind power output.

The cumulative distribution function (CDF) of the intraday time-averaged peak-valley difference for each wind farm and wind power cluster is shown in Fig.5.The results reveal that the maximum daily peak-to-valley difference for each wind farm reached approximately 80% of their rated capacity,highlighting significant demands on the power operational range for the wind power PEM hydrogen production system.

Fig.5 CDF graph of intraday hourly average peak-to-valley difference

Combining Figs.4 and 5 shows that for the configuration of PEM electrolytic hydrogen storage in regional wind farms,prioritizing wind farms with significant output volatility (such as Wind Farm 5 in the example)is crucial.This prioritization ensures thorough study of the electrolyzer’s typical operating conditions within the wind power hydrogen production system under maximum fluctuation in this area.

3.2 PCA results of output characteristic matrix

Based on the characteristic indices defined in Section 2.3 of this paper,the daily output characteristic matrix of Wind Farm 5 throughout the year,consisting of sevendimensional characteristic quantities,was extracted.PCA was used to reduce the dimensions of the high-dimensional feature matrix.The cumulative variance contribution rate of each principal component after PCA dimension reduction is presented in Table 1.

Table 1 Cumulative variance contribution of each principal component

As shown in Table 1,the cumulative variance contribution rates of the first three principal components exceeded 85%.Therefore,these first three principal components can be used to represent the main information of the high-dimensional feature matrix of the wind power output for the cluster reduction analysis.

3.3 Determination of cluster number and result analysis

The three principal components were used as input data after dimensionality reduction,and the improved EM algorithm was used for GMM clustering.The iterative threshold was 0.01,the maximum number of iterations was 10,000,and the maximum number of cluster sets was nine.The BIC and its rate of change for different cluster sets are shown in Fig.6.When the cluster set was five,the BIC change rate reached a minimum value of 3.76%,indicating that the fitting result was optimal at this point.Considering both fitting accuracy and computational cost,the optimal number of clusters was determined to be five.

Fig.6 BIC and BIC change rate under different cluster numbers

K-means clustering,fuzzy C-means (FCM) clustering,hierarchical agglomerative clustering (HAC),GMM clustering,and improved GMM clustering were used to cluster the typical scenarios.The clustering results were evaluated and compared using the three clustering validity evaluation indices listed in Table 2.

Table 2 Comparison of the effect of different clustering methods

The method proposed in this study is evidently superior to the other four clustering methods based on the calculation results of the three evaluation indices.Among these indices,the CHI and SC index values were the highest,indicating that the clustering results were more similar within their categories,different from other categories,and overall demonstrated better clustering performance.The DBI value was the lowest,indicating that the clustering result had a large inter-class distance and a small intra-class distance,reflecting a better clustering effect.These results demonstrate the superiority of the method used in this study.

A heat map of the clustering center of each scenario feature after clustering reduction is presented in Fig.A1.To characterize each cluster more intuitively,z-score normalization was performed for each feature.All types of clusters from Scenarios 1 to 4 were seen to have obvious clustering characteristics,and each cluster has good discrimination.

To further verify the effectiveness of the optimal clustering results,the clustering validity of the original output characteristic quantity matrix for each cluster was analyzed.A box plot was used to represent the discreteness between the sample eigenvalues and clustering centers in each cluster.Scenarios 1 (34.0%) and 5 (30.4%),which had the highest proportion of output scenarios,were selected for analysis.A box plot of each scenario’s eigenvalues is shown in Fig.A2.The ordinate in the figure represents the relative value of the distance between each feature and the cluster center.Scenarios 1 and 5,which account for the largest proportion of the reduced scenario,have a better clustering effect on most feature quantities.Among these,the outliers of Scenario 1 are mostly distributed in Feature 7,accounting for 14% of the scenario samples,whereas Scenario 5 outliers are mostly distributed in Feature 4,accounting for 12% of the scenario samples.In addition,the proportions of outlier samples in the total number of clusters in the other three scenarios were 13%,12%,and 14%,all of which were less than 15%.Thus,the clustering results were effective.

3.4 Generation of degradation test conditions spectrum of electrolysis stack

The feature matrix clustering reduction results were used as the basis for dividing the different scenarios.The minimum timescale was set at 1 min.A comparison of the proportion of each clustering scenario and the clustering center values is presented in Table B1.

Combined with Table B1,the input power curves of the PEM electrolysis stack under the corresponding operating conditions for each scenario are shown in Fig.B1.

Considering the degradation test conditions of the PEM electrolyzer in Scenario 5 in Fig.B1 (e) as an example,and combined with the simplified cluster center values in Table B1,the average input powers of the PEM electrolysis stack under low overload and normal operation were calculated to be 0.17,0.57 and 1.07 times the rated power,respectively.Additionally,the average maximum load increase and decrease rates were calculated to be 9.6%/min and 8.2%/min,respectively.This scenario consisted of three startstop conditions: including two low-load-stop-low-load condition cycles.Based on the low-load time and the number of low-load operations in the daily test conditions,the duration of each low-load condition was calculated,and a complete start-stop condition spectrum was constructed.Subsequently,using the maximum climbing rate,the load was adjusted to normal operating and overload conditions.Finally,using the maximum load reduction rate,the low-load condition was restored,completing the PEM electrolysis stack degradation test condition spectrum cycle for the scenario.The construction method for the operational condition spectrum for the other scenarios followed the same approach.When the overload duration is close to the variable load time,as in Scenarios 3 and 4,the system does not enter variable load condition operation.

Under the degradation test conditions of each reduced scenario,the normal operation time of Scenario 1 was the longest at 1295 min,accounting for approximately 91% of the entire scenario cycle condition spectrum,with a maximum climbing rate of 11%/min.The overload time in Scenario 2 was the longest,reaching 358 min and accounting for 25%of the total,with a maximum load-shedding rate of 13%/min.Scenario 3 had the longest underload time,also reaching 358 min (accounting for 25 %),and the highest start-stop count,reaching 11.The downtime in Scenario 4 was 1222 min,accounting for 85% of the time.The operating conditions were combined according to the proportion of reduced scenarios.Based on the calculation of the proportion of each scenario in Table B1,the operating condition spectrum of the PEM electrolytic stack degradation test can be formed from Scenarios 1 to 5 according to the operating condition cycle of 4a-1b-2c-1d-4e,as shown in Fig.7.Each operating condition fragment was observed to contain the features of the characteristic quantities that significantly impact the decay life of the PEM electrolysis stack in this scenario.This reflects the different operating conditions of the PEM electrolysis stack in the wind power hydrogen production system corresponding to the typical scenarios of the annual fluctuation output of wind farms,providing a test condition spectrum reference for the actual electrolysis stack degradation test.

Fig.7 Cycle of degradation test condition spectrum for PEM electrolytic stack

3.5 Effectiveness test of typical operating condition

In this study,a simulated voltage model of the electrolysis stack was constructed with reference to the semi-empirical voltage model of the electrolysis stack in [26],which was built using MATLAB/Simulink.The electrolysis process was set up with a water temperature control system,and the electrolysis environment temperature was maintained at 75°C.To measure the degree of performance degradation,the voltage degradation rate (μV/h) [42] was used.The smaller the value,the lower the performance degradation of the electrolysis stack.Typical operating condition curves before and after simplification were input into the electrolysis stack simulation model for verification.The simulation results,listed in Table 3,demonstrate that the simplified operating conditions proposed in this study are very similar to the original curve in terms of the performance degradation of the electrolysis stack,with the relative error of the calculated voltage degradation rate being less than 10%.

Table 3 Comparison of the simulation test result

4 Conclusions

Based on the case study of hydrogen production from wind power in remote areas,this study extracted a sample set from a wind farm in Northwest China exhibiting the largest fluctuations over a short time scale.The data was analyzed for volatility and dimensionality reduction techniques were applied.Improved GMM clustering was then used to identify typical scenarios.Based on these results,distinctive operating curves were derived.The following conclusions are drawn from the case study:

(1) The rate of change of wind power output and the average peak-valley difference in this area show great volatility.

(2) Indices that affect the life of the electrolyzer,such as low load time,shutdown time,and average ramp rate of the output,were extracted as clustering features.PCA was used to reduce the number of feature parameters from seven to three.

(3) DPC algorithm was used to initialize EM algorithm,and KL divergence was used as the iterative termination condition of EM algorithm,which realizes the optimal selection of the parameter estimation values of the GMM.The optimal number of clusters was obtained by using BIC and BIC change rate,which improves the rationality of GMM clustering.Compared with K-means,FCM,HAC and GMM methods,the CHI and SC index calculation results of the improved GMM clustering are the largest in the five clustering methods,which are 357.2 and 0.583,respectively,and the DBI result of IGMM is the smallest,which is 0.694,indicating that the proposed method has better scenario discrimination.

(4) The degradation test cycle spectrum of the PEM electrolysis stack was constructed,and the operating conditions were divided into five categories,that is,low load,normal operation,overload,start-stop and variable load.The normal operation time accounts for 55.3% of the cycle time of the whole working condition spectrum,and the low load,overload and shutdown time accounts for 24.1%,3.3% and 17.3%,respectively.The maximum climbing rate of the electrolysis stack operation scenario reaches 9.6%/min,and the maximum load reduction rate reaches 8.2%/min.Through simulation,the relative error of the voltage degradation rate obtained by the operating condition and the original data is less than 10%,which reflects the effectiveness of the typical operating condition extracted in this paper in the performance test experiment of the electrolysis stack.

The typical operation condition spectrum of electrolysis stack obtained in this paper provides the basic test data for the performance degradation of the electrolysis stack in the subsequent wind power electrolysis water hydrogen production scenario,which is of great significance to the exploration of the performance degradation law of the electrolysis stack.

Appendix A

Fig.A1 Clustering center heat map of scenario reduction features

Fig.A2 Box graph of characteristic values distribution for cluster samples

Appendix B

Fig.B1 Construction of PEM electrolytic stack degradation test conditions for each scenario

Table B1 Comparison of clustering scenario share and clustering center

continue

Acknowledgements

This work was supported by the National Key Research and Development Program of China (Materials and Process Basis of Electrolytic Hydrogen Production from Fluctuating Power Sources such as Photovoltaic/Wind Power,No.2021YFB4000100).

Declaration of Competing Interest

We declare that we have no conflict of interest.