Wastewater treatment plants (WWTPs) are important and energy-intensive municipal infrastructures. High energy consumption and relatively low operating performance are major challenges from the perspective of carbon neutrality. However, water-energy nexus analysis and models for WWTPs have rarely been reported to date. In this study, a cloud-model-based energy consumption analysis (CMECA) of a WWTP was conducted to explore the relationship between influent and energy consumption by clustering its influent’s parameters. The principal component analysis (PCA) and K-means clustering were applied to classify the influent condition using water quality and volume data. The energy consumption of the WWTP is divided into five standard evaluation levels, and its cloud digital characteristics (CDCs) were extracted according to bilateral constraints and golden ratio methods. Our results showed that the energy consumption distribution gradually dispersed and deviated from the Gaussian distribution with decreased water concentration and quantity. The days with high energy efficiency were extracted via the clustering method from the influent category of excessive energy consumption, represented by a compact-type energy consumption distribution curve to identify the influent conditions that affect the steady distribution of energy consumption. The local WWTP has high energy consumption with 0.3613 kW·h·m−3 despite low influent concentration and volumes, across four consumption levels from low (I) to relatively high (IV), showing an unsatisfactory operation and management level. The average oxygenation capacity, internal reflux ratio, and external reflux ratio during high energy efficiency days recognized by further clustering were obtained (0.2924-0.3703 kg O2·m−3, 1.9576-2.4787, and 0.6603-0.8361, respectively), which could be used as a guide for the days with low energy efficiency. Consequently, this study offers a water-energy nexus analysis method to identify influent conditions with operational management anomalies and can be used as an empirical reference for the optimized operation of WWTPs.
Traditional wastewater treatment is essentially a process of energy consumption and pollution transfer. The process uses electrical energy, chemical agents, and other energy sources to destroy the chemical energy stored in the organic pollutants in wastewater while at the same time transferring the pollution to sludge biomass and the air [1], [2]. As essential municipal infrastructures, wastewater treatment plants (WWTPs) have incredibly high energy consumption and relatively low operating performance, which have become problems that cannot be ignored in the water industry [3], [4], [5]. However, in the past few decades, the design, operation, and management of WWTPs have been oriented toward meeting effluent water standards, and emphasis on the energy aspect has been very low [6]. According to previous research, wastewater treatment consumes approximately 7% of the world's electricity [7]. In the United States, the WWTPs and the wastewater distribution networks consume 2%-4% of their total electricity [8]. In Italy, the power consumption of WWTPs is approximately 3250 GW·h·a−1, equivalent to approximately 500 million EUR per year [9]. Undeniably, while focusing on the treatment depth in the near future, more attention should be paid to the control of energy consumption in the process because of the economic cost and the indirect carbon emission effect it brings [10].
For those developing countries such as China, the wastewater treatment industry started relatively late, with a relatively low level of energy-saving management [11]. The electrical energy consumption of WWTPs in China accounts for approximately 60% of their total operational costs [12]. Furthermore, the average unit treatment capacity consumes 0.3 kW·h·m−3, equivalent to the energy consumption of developed countries in their early stages, indicating a high potential for energy saving [13]. Moreover, increasingly stringent environmental protection requirements and ever-increasing demand for wastewater treatment capacity have put greater pressure on the energy consumption of WWTPs [14], [15]. Suppose the upgrading and transformation of WWTPs continue in the mode of “high energy consumption, high material consumption, low energy efficiency, and low profit.” In that case, the WWTPs cannot keep their sustainable development [16]. Therefore, while establishing the strategies for effective management, attention must be paid to evaluating WWTPs’ energy consumption.
A WWTP is a complex system affected by multiple factors; therefore, many indicators have been proposed to evaluate its energy performance [17], [18], [19]. Among them, influent’s water quality and volume conditions are used as the basis for formulating the operation management control strategy, acting as a significant factor affecting energy consumption [20], [21]. Timely measurement of key water quality parameters can aid in the rapid identification of water quality problems and establish impact load plans. Simultaneously, the rational analysis, evaluation, and simulation of wastewater treatment energy consumption, based on water quality and treatment effect, facilitates operation adjustment strategies to optimize targeted processes and improve wastewater treatment quality and economic benefits. This has far-reaching practical significance for the sustainable development of the wastewater treatment industry.
At present, commonly used methods to measure the system energy consumption include simple analysis methods based on a single indicator, for example, the Unit Energy Consumption (UEC, namely the electrical energy consumed per unit volume of wastewater treatment, kW·h·m−3) [22], and comprehensive evaluation methods with multiple indicators, aspects, and aims, including life cycle assessment (LCA) [23], analytic hierarchy process (AHP) [24], and fuzzy comprehensive evaluation (FCE) [25]. Noteworthy, when evaluating a WWTP’s energy consumption, two types of uncertainties should be considered: ① the randomness encountered during monitoring and analysis of data related to energy consumption; ② the fuzziness reflected in the classification of evaluation standards and levels, and the judgment of the level of energy consumption. Although existing energy consumption analysis methods quantify the multiple factors influencing energy consumption, they still lack careful consideration of the randomness and fuzziness in the energy consumption evaluation process of WWTPs.
Moreover, the energy consumption analysis is mainly based on the annual average value of energy consumption indicators for evaluating and comparing WWTPs. The energy consumption analysis of the WWTP itself is still in the basic statistical stage, and a certain amount of data variation cannot be reasonably used to analyze the energy consumption level accurately [26]. Therefore, for the scientific analysis and evaluation of energy consumption of WWTP, the randomness in the monitoring and analysis of data related to energy consumption, the fuzziness in the classification of evaluation levels, and the judgment of the energy consumption level should be considered simultaneously.
A cloud model is a two-way cognitive model of qualitative and quantitative conversion. Compared with traditional analyses and evaluation methods, it can formally describe the internal relationship between randomness and fuzziness and exhibits obvious theoretical advantages in dealing with uncertainty. Therefore, in recent years, it has been used with increasing frequency in the evaluation and data mining of complex dynamic systems, for example, the ecological environment. Guo et al. [27] proposed a cloud-analytic hierarchy process model. They constructed a wind-erosion-intensity index, and the model was based on seven typical land surface parameters, which could help solve the problem of randomness and uncertainty in determining index weights. It showed good applicability in evaluating wind erosion intensity in the Three-River Source Region of China, with an overall accuracy of 93%. Zhang et al. [28] considered 13 cities in the Beijing-Tianjin-Hebei region of China as research objects, established the corresponding methods to evaluate water-cycle health based on a cloud model and evaluated the water-cycle health from the four dimensions of water ecology, quality, volume, and consumption. Comparative analysis of the evaluation results and those derived from the comprehensive index method proved the reliability. Recently, the cloud model has been maturely applied to evaluation and analyses in many fields. In contrast, traditional methods are still used to evaluate and analyze the energy consumption of wastewater treatment systems. China’s WWTPs currently have low management levels and solidified operation modes under different water influent conditions. This is inseparable from the complex characteristics of WWTPs themselves, with more considerable time variation and delay. Herein, three goals are proposed, as follows: ① to change the empirical regulation mode of municipal WWTPs, ② to improve their operation and management level, and ③ to achieve energy-saving and consumption reduction. It is necessary to measure key water quality parameters on time, rationally analyze the energy consumption, improve the response speed, and formulate process operation and optimization strategies in a targeted manner to achieve these goals.
In this study, we propose a method of energy consumption analysis based on the clustering of influent conditions and a cloud model using a WWTP’s operational data. The novel method can identify those satisfying performance days of a WWTP with outstanding strategies and parameters. The establishment of the method entails the following tasks: ① to classify the influent conditions in order to simplify the identification of operating scenarios based on principal component analysis (PCA) and K-means clustering analysis; ② to establish a standard system as the basis for energy consumption ratings through golden ratio methods and a forward cloud transformation (FCT) algorithm; ③ to explore the energy consumption levels of WWTPs under different influent conditions through a multi-step backward cloud transformation algorithm based on sampling with replacement (MBCT-SR); ④ to evaluate the rationality of the operation and management of the WWTP and perform appropriate problem diagnosis; and ⑤ to indicate the orientation of performance optimization in the WWTP by conducting further K-means clustering. This method can be used as an empirical reference for the regulation and control of a WWTP and as an effective tool for its management, guiding it toward optimized operation.
2. Materials and methods
2.1. Data source
This research collected and analyzed data on operational monitoring of a municipal WWTP spanning 2017. The WWTP is located in Heilongjiang, China, with a designed inflow water volume of 45 000 m3·d−1 and an effluent standard of Grade I-B of the Chinese discharge standard of pollutants for municipal WWTPs [29]. A summary of the data set (Fig. 1) used in this study is as follows. ① The average daily concentration values in the influents and effluents of six water quality parameters, including chemical oxygen demand (COD, mg·L−1), biochemical oxygen demand (BOD5, mg·L−1), suspended solids (SS, mg·L−1), ammonia nitrogen (NH4-N, mg·L−1), total nitrogen (TN, mg·L−1), and total phosphorus (TP, mg·L−1), that analyzed based on the methods stipulated in the Chinese national water environmental protection standard [30]; ② the inflow water volume per day (Q, m3·d−1); ③ the daily energy consumption (E, kW·h·d−1) of the WWTP obtained through smart metering.
Clustering and cloud models were used as the overall process of analyzing the energy-water nexus (Fig. 2). The framework mainly involves three phases: data preparation, clustering of influent conditions, and energy consumption analysis based on the cloud theory. All the calculations were done with MATLAB® R2018a (MathWorks, Inc., USA).
2.2. Data preparation
2.2.1. Data collection
According to the fuzzy correspondence between influent loads and energy consumption in the proposed method, three types of data, including water quality, water flow, and energy consumption data, were selected to explore the operation and energy consumption status of a WWTP under different influent loads. The specific data form is shown in Section 2.1.
2.2.2. Data preprocessing
The accuracy of environmental data are affected by multiple factors, such as on-site sampling, sample preparation, and laboratory analysis. Therefore, the data collected on-site in the WWTP often have certain random and human errors and are not suitable for direct use, requiring preprocessing to avoid interference with subsequent modeling and analysis that reduces the reliability and effectiveness of the model. However, abnormal data are not necessarily erroneous data, that is, abnormal data sometimes contain potentially essential and valuable information and reflect abnormal operating conditions. Therefore, the identification and processing of abnormal data must be combined with real situations; thus, only when necessary can abnormal values be eliminated and regarded as unreasonable data [31]. This study mainly evaluated and processed the abnormal data on influent water quality to investigate the distribution of energy consumption of the WWTP under different influent concentrations and pollutant reduction capabilities and to identify unreasonable operations. Furthermore, to eliminate the dimensional differences among various factors, z-score standardization (Eq. (1)) was performed before multi-dimensional data analysis and modeling to ensure the comparability among variables:
where $\mu_j$ and $σ_j$ are the mean and variance of the $j$th observed attribute of the sample, respectively. The $z$-score standardization makes the distribution of processed sample data approximate to a normal distribution.
2.3. Clustering of influent conditions
2.3.1. Principal component analysis
Given the size and complexity of multivariate water quality data, PCA was used for dimensionality reduction to improve the clustering performance with better centroid points provided [32], [33], simultaneously extracting data characteristics and revealing the implicit relationships among these parameters. PCA is a classic multivariate statistical method. Through dimensionality reduction, it transforms multiple interrelated variables into several comprehensive orthogonal components (i.e., principal components, PCs) [34]. The geometric schematic diagram of PCA is shown in Fig. S1 in Appendix A. The uncorrelated PCs are usually linear combinations of the original variables, which reflect most of the original variables’ information while achieving sound dimensionality reduction and visualization of the data, thus simplifying the research problem [35]. Detailed descriptions of the principle of PCA are presented in Sections S1 in Appendix A. The specific method is as follows:
Assuming that the research object has p observation attributes (x1, x2, …, xj,…, xp), that is, for n groups of observation samples (x1, x2,…, xj,…, xn), the sample data matrix is
where xij is the value for the jth attribute of the ith sample.
It is assumed that the PC equation can be obtained by using the following linear transformation:
Where are all unit vectors satisfying , and $a_{jp}$ is the load coefficient of the pth variable with the jth PC yj, reflecting the importance of the variable to PCs. The goal of PCA is to find the set that maximizes the variance of y1 and the set that maximizes the variance of y2, while y2 is perpendicular to y1, that is, the covariance cov(y1, y2) = 0. Similarly, all p PCs can be obtained, and the first r PCs are selected according to the actual problem to reflect the original data. From a mathematical perspective, the essence of PCA is a diagonalizing covariance matrix. In this study, PCA was used for data preprocessing before clustering, and the complete steps of PCA are given in Section S1.
2.3.2. K-means clustering analysis
Clustering is an important strategy for simplifying a problem. In this study, classification of the dataset (the flow and quality data) based on K-means clustering was adopted to simplify the identification of influent loadings or treatment effect. K-means clustering is a classic unsupervised algorithm widely used in many fields such as pattern recognition and anomaly detection for large-scale datasets and image processing. The specific steps of applying K-means clustering for data analysis are shown in Sections S2 in Appendix A.
This study employed three commonly used internal cluster validity indices (CVIs), the Calinski-Harabasz Index (CHI), Davies-Bouldin index (DBI), and silhouette index (SI) (Eqs. (4), (5), (6)), to help determine the optimal k value by evaluating the clustering results under different cluster numbers within a certain range. The smaller the DBI, the better the clustering effect, and the larger the CHI or SI values, the better the clustering effect. The use of multiple CVIs could ensure good classification to some extent, in particular, when dealing with a more complex dataset.
Where CHI measures the clustering quality by gauging the separation between formed groups based on a ratio of inter-cluster dispersion and intra-cluster dispersion means. BGSS denotes the between-group sum of squares, indicating the sum of squared distances between clusters; WGSS represents the within-group sum of squares, indicating the sum of the squared distances within the cluster; k is the number of clusters, and n denotes the total number of samples.
Where DBI evaluates both inter-cluster and intra-cluster distances to identify the clusters that are compact and far from each other; ci and cj are the centroids of the ith cluster and the jth cluster, respectively; is the average distance of all points to ci in the ith cluster; and is that of all points to cj in the jth cluster; is the distance between centroids ci and cj.
Where SI comprehensively reflects the intra-cluster compactness and inter-cluster separation of clustering structure by checking the similarity of each point with all other points in its cluster and the dissimilarity of the point from the members of the neighboring cluster. In Eq. (6), a(i) is the average value of the distance between the ith sample and the other points in the same cluster; b(i) denotes the minimum value of the average distance between the ith sample and all sample points in different clusters; and s(i) is the silhouette index of the ith sample.
Concerning the selection of the center point of the initial clusters, K-means clustering was conducted multiple times. The initial cluster centroids were randomly generated in each run, and the run with the highest clustering effectiveness was selected as the final result.
2.4. Energy consumption analysis by using cloud model theory
2.4.1. Establishment of evaluation grade criteria system of energy consumption
The cloud model is a novel method that can efficiently address the randomness and uncertainty inherent in a dataset and the evaluation process [36]. The establishment of cloud model is based on cloud generator algorithms shown in Fig. S2 in Appendix A and more information about the cloud model is presented in Sections S3 in Appendix A. In the cloud-model-based energy consumption analysis (CMECA), a cloud is the specific quantitative expression of a qualitative concept, that is, the energy consumption status. Given the widespread use of the indicator in the energy audit [37], the UEC was selected for the energy consumption analysis. According to the original description of the digital characteristics of the cloud model, the physical interpretation of the cloud digital characteristics (CDCs) (Ex, En, He) in the energy consumption evaluation process of the WWTP can be established, as presented in Table 1.Ex is the expected coordinate of all cloud drops (energy consumption values), the most representative energy consumption value under the wastewater treatment effect. En reflects the dispersion of energy consumption value relative to the average energy consumption value and manifests the fluctuation range of the energy consumption value, that is, the uncertainty measure of energy consumption. He indicates the degree of dispersion of entropy. The existence of He distinguishes the Gaussian cloud distribution from the normal distribution. If the WWTP operates independently every day, its energy consumption level can be represented in the Gaussian distribution. However, in the actual operating process, the influent water situation and the regulation strategies on a particular day may affect subsequent operations, so the prerequisites of the central limit theorem are no longer met. In this regard, the Gaussian cloud provides a description method for this case of deviation from the central limit theorem, and He can be used to reflect the situation where the influencing factors are not independent of one another.
In order to establish evaluation criteria, the energy consumption was first divided into N evaluation grades. Then, the golden section method was used to determine the CDCs of each grade when giving the bilateral constraints in the form of [Vmin, Vmax], where Vmin and Vmax are the maximum and minimum UEC values of a WWTP, respectively. According to the golden section method, the ratio between the cloud model parameters of adjacent energy consumption levels was 0.618, which is the most aesthetic proportion to achieve the natural optimal segmentation effect [38], [39]. Finally, an FCT algorithm [40] was employed to generate a set of cloud drops for visualization and simulation.
2.4.2. Energy consumption analysis for different influent conditions
We compared and evaluated energy consumption status under different influent conditions. The MBCT-SR algorithm [41] was employed to calculate the corresponding CDCs based on energy consumption data because of its good stability in a fixed-number sample case, thereby achieving feature extraction. Similarly, the FCT algorithm was then employed to generate a set of cloud drops for visualization and simulation.
Noteworthy, different forms of clouds can be formed based on different probability distributions. Owing to the universality of the normal distribution and the bell-shaped membership function, the typical cloud model has become the most essential and fundamental type of cloud model. It has been proven universal adaptability and has been successfully applied in many fields [42], [43], [44], [45], [46]. Therefore, in this study, energy consumption was evaluated based on the typical cloud model, which satisfies and , while the certainty degree satisfies:
3. Results and discussion
3.1. Principal component analysis of pollutant removal
3.1.1. Correlation analysis
Based on the identification and removal of the abnormal values, 333 effective samples from the dataset were reserved for further analysis. The pollutant reduction concentration was simultaneously selected as the basis for dividing water quality conditions to better analyze the energy efficiency. These parameters are the daily values of removed COD, BOD5, SS, NH4+-N, TN, and TP (marked as COD rem CODrem, BO D5rem, SSrem, NH+4−Nrem, TNrem, and TPrem).Table 2 presents a certain correlation among the six indices, of which NH+4-Nrem and TNrem owned the strongest with a correlation coefficient as high as 0.957. SSrem was also significantly correlated with CODrem, NH+4-Nrem, and TNrem. In general, insoluble COD accounted for most of the total COD composition. When SS in wastewater is removed, most insoluble COD and partially soluble COD are removed simultaneously. Moreover, the influent water of this municipal WWTP was mainly domestic sewage, which exhibited similar quality patterns: An evident consistency could be found between ammonia nitrogen and total nitrogen. The concentration of inorganic suspended matter such as sand and gravel were low, and SS was composed of organic matter. When their concentrations were relatively stable in the effluent water, the correlation between the concentrations of pollutant reduction in these indices was more significant. Correlation analysis showed a certain degree of information overlap in the concentration of pollutant reduction of the above-exhibited indices. It was suitable to use PCA to extract further information on water quality.
3.1.2. Principal component analysis
The data dimensions varied, causing some indices with larger dimensions to be overly stressed in the analysis process; however, the influence of data with smaller values was weakened. Therefore, in this part of the study, z-score standardization was first performed on these data for PCA (Eq. (1)). PCA was used to analyze the concentration of pollutant reduction in the WWTP. The values of the Kaiser-Meyer-Olkin test (0.780) and the Bartlett sphericity test (0.000) further verified the feasibility of the data for PCA. The PC number was selected by combining the cumulative percent variance method [47] and the eigenvalue-0.7 criteria [48]. With this, the first two PCs with eigenvalues greater than 0.7 were selected, explaining an accumulated 78.32% of the total variance. The result is shown in Fig. 3(a). The points in the figure represent samples: Similar samples have similar water quality characteristics, and the sample points far away from other samples may be potential outliers. Furthermore, each sample’s representing water quality maps with influent volume to indicate the relationship between them. The vectors in the figure represent the variables; their arrow directions represent the degree of correlation between the variables and the PCs. Their lengths indicate their degree of contribution to the PCs. The angles between the variables are below 90°, indicating that the corresponding concentration of pollutant reduction values was positively correlated. TPrem and BOD5rem are approximately perpendicular, indicating the weakest correlation between these two attributes. The expressions of PC1 and PC2 are shown in Eqs.
Where xi* is the original variable after standardization.
The expression of the first PC shows that the loadings of PC1 on each variable are very close, suggesting that these variables are equally important. Therefore, the first PC can be considered as the comprehensive component of the concentration of pollutant reduction, representing the overall effect of the WWTP on the removal of influent pollutants. Besides, most samples with a relatively low influent flow pattern exhibit negative loads on PC1, indicating that the wastewater treatment performance was not satisfactory under low treatment quantity. The second PC has a higher positive load on the TPrem, with moderate positive loads on CODrem, moderate negative loads on NH+4 - Nrem, TNrem, and BOD5rem, and a rarely positive load on SSrem. Therefore, in addition to the overall treatment effect, the main differences in the concentration of pollutant reduction are reflected between TPrem, CODrem and NH+4 - Nrem, BOD5rem, among which, SSrem is not considered due to the minor load. The biological nitrogen and phosphorus removal processes are relatively complicated, involving numerous biochemical reactions such as nitrification, denitrification, and phosphorus absorption. The goals and principles of each process are different: The composition of the microbial community, the type of substrate, and the required environmental conditions in each process all vary from each other [49]. Conflicts between various processes inevitably arise when achieving simultaneous denitrification and dephosphorization. The conflicts can happen between carbon source competition, sludge age, nitrate, residual interference of nitrate and dissolved oxygen (DO), phosphorus release, and phosphorus absorption capacity [50]. Some new and efficient simultaneous nitrogen and phosphorus removal processes, such as denitrifying phosphorus removal, may also have these conflicts due to improper bioreactor volume design and poor operation and management. As a result, system dephosphorization and denitrification efficiency in actual projects are low and unstable. The relatively high correlation between BOD5 and NH4+-N, TN indicated that denitrifying bacteria could fully use the carbon source in the anaerobic phase, and nitrogen was removed in a gas form. In the aerobic stage, phosphorus-accumulating bacteria use the remaining carbon source to absorb phosphorus. Then phosphorus is removed with the solid-liquid separation of sludge in the secondary clarifier, and the residual insoluble COD is also removed in the process. The second PC reflects the comparison between the denitrification effect and the phosphorus removal effect. The second PC can be interpreted as the component expressing the comprehensive effect of nitrogen and phosphorous removal in the WWTP. Herein, we reserve both NH4+ - Nrem and TNrem despite the high correlation between them for considering the effect on energy consumption. Furthermore, as shown in Eqs. (8), (9), the loadings of the NH4+-Nrem and TNrem on principal components are 0.458, −0.282 and 0.458, −0.233 respectively, indicating the two variables possess equal importance to overall water quality status, which is reasonable from a modeling perspective.
3.2. K-means clustering of influent water quality and volume
3.2.1. The clustering of pollutant removal
Based on the two-dimensional space of the comprehensive pollutant reduction concentration obtained by the PCA, the K-means clustering method was applied to classify the reduction in the concentration of the influent pollutant over 333 working days. All k values within the value range (n is the number of sample groups, 333) were substituted into the K-means clustering algorithm to determine the optimal number of clusters and evaluate the clustering results. Three cluster validity indicators, namely, CHI, DBI, and SI (Eqs. (4), (5), (6)), were selected to verify the validity of the clustering results. Fig. 3(b) shows the relationship between the values of the three indicators and the number of clusters. The optimal cluster number was 2, and when k = 2, CHI and SI were the largest and DBI was the smallest. Thus, the operating status of the WWTP was divided into two categories according to the overall pollutant removal situation.
After determining the optimal number of clusters, the K-means clustering algorithm was run multiple times, randomly generating different initial cluster centers in each round. According to the silhouette coefficient of each point in the cluster, the result with the best silhouette coefficient distribution was selected as the final clustering result. Fig. 3(c) shows that the silhouette values of the pollutant reduction concentration in the 333 samples were almost all positive, and the average silhouette coefficient was 0.6752, implying that the clustering result was relatively satisfactory [51], [52]. Therefore, the concentration of pollutant reduction on different operating days was categorized into two categories. The distribution of each dataset is shown in Fig. 3(d). The plus sign marks the position of the center point of each cluster, and each origin represents the pollutant reduction concentration of the influent’s water quality indices on a single operating day.
The sample score chart shows that the higher the comprehensive score, the higher the concentration of pollutant reduction. The two clusters of sample points exhibited pronounced stratification on PC1 thus the clustering results were mainly determined by the comprehensive components of the pollutant reduction concentration. Cluster A represented the operating day with a higher concentration of pollutant reduction, 211 samples, and Cluster B represented the operating day with a lower concentration of pollutant reduction, 122 samples. Moreover, the WWTP controlled the effluent concentration following the national discharge standards and was relatively stable, thus the concentration pollutant reduction and influent concentration showed relatively similar trends in their respective variations. If the influent concentration was selected to replace the concentration of pollutant reduction, the same conclusions could be obtained. Clusters A and B can also indicate the number of days when the influent concentrations of water quality indices were high and the days when these concentrations were relatively low, respectively. The distribution of the pollutant reduction concentration and the influent concentration of each sample cluster (Figs. 4(a)-(f)) evidently indicate that the concentration of pollutant reduction and influent concentration were well classified, meaning that the influent pollutant load in the WWTP shows a particular variation on different days.
3.2.2. The clustering of volume
Similarly, the K-means clustering method was used to cluster the influent water volume during the 333 operating days, and the optimal cluster number was determined to be 2. The corresponding influent water volume (Fig. 4(g)) showed that the influent volume in the WWTP fluctuated on different days. Cluster C represented operating days with higher influent water volume, 267 samples, and Cluster D represented operating days with lower influent volume, 66 samples.
Based on the clustering results of the concentration of pollutant reduction and the water volume, the influent condition of the WWTP was divided into four categories. These represented high influent concentration and large water volume (Cluster 1), high influent concentration but small water volume (Cluster 2), low influent concentration and large water volume (Cluster 3), and low influent concentration and small water volume (Cluster 4).
3.3. Energy consumption analysis based on cloud model
3.3.1. The standard cloud model of energy consumption
The standard cloud model of energy consumption is established based on the procedure presented in Section 2.4.1. First, the cloud model was combined with the characteristics of the energy consumption level of the WWTP, and the energy consumption was divided into five evaluation levels: ① grade I, low energy consumption, ② grade II, relatively low energy consumption, ③ grade III, intermediate energy consumption, ④ grade IV, relatively high energy consumption, and ⑤ grade V, high energy consumption. Bilateral constraints [Vmin, Vmax] were used for fuzzy analysis to explain each energy consumption level standard, considering that each energy consumption level requires its upper bound and lower bound to be restricted. In general, Ex is the median of the constraints, En can be derived according to the interval range [53]. He can be reasonably set according to the fuzzy degree of the evaluation itself as an appropriate constant within 0.001-0.100 [54]. Based on the golden section method, the CDCs of each grade was determined with a ratio of 0.618 between the CDCs of adjacent energy consumption levels. Moreover, the closer to the center of the domain, the smaller the value of En and He of the evaluation grade. In this study, the expected values for the first energy consumption level (low energy consumption) and the fifth energy consumption level (high energy consumption) were Ex1 = 0.1741 and Ex5 = 0.7828, respectively. Considering, 0.4785, the central point of energy consumption in the WWTP, as the intermediate evaluation state (medium energy consumption), that is, Ex3 = 0.4785. He was considered as a constant value 0.005 according to a literature study [54]. The parameters of other grades were obtained according to the golden ratio. Eqs. (10), (11), (12) show calculation results of cloud model parameters for each energy consumption level:
In this way, the cloud model parameters of each energy consumption level could be obtained, as presented in Table 3. FCT algorithm was used to realize the cloud processing of the five evaluation levels of energy consumption through the above-stated CDCs. Furthermore, it generates the corresponding cloud chart to visualize standard energy consumption levels, as shown in Fig. 5(a).
3.3.2. Energy consumption analysis based on influent characteristics
Based on PCA and K-means clustering analysis, the influent conditions of the WWTP were divided into four categories. For the energy consumption of these four types of influent conditions, the MBCT-SR was used to calculate digital characteristics that reflect the energy consumption status under the four clusters of influent conditions, as listed in Table 4. Through the three digital characteristics obtained by using the MBCT-SR algorithm, the FCT algorithm generated more cloud drops to simulate the energy consumption value under different influent conditions. Fig. S3 in Appendix A shows the energy consumption of the WWTP operating for 365 days under these four types of influent conditions. For example, point A (0.29, 0.89) indicates that under the condition of low influent concentration and a large water volume, there is a probability of 89% that the unit energy consumption of the WWTP is 0.29 kW·h·m−3.
Fig. 5(b) shows the distribution of energy consumption under various influent conditions. The simulation results clearly show that on the days when the wastewater treatment volume of the WWTP was relatively high, that is, when the influent water volume was relatively high, the average energy consumption of the WWTP was relatively low. It belongs to a lower energy consumption level, whose distribution was relatively concentrated and stable. Under this circumstance, when the influent concentration was higher (Cluster 1) or lower (Cluster 3), the average UEC was 0.2783 or 0.2637 kW·h·m−3, respectively. It implies that the UEC would be higher when treating wastewater with worse water quality. Previous studies showed that the influent load and UEC exhibited a weak positive correlation, indicating that when the water volume of the WWTP was high, its energy consumption followed the general pattern, and its operating strategy was relatively reasonable. In order to explore the energy utilization rate, the specific energy consumption for COD removal (CODsec) was calculated because COD is the most common pollutant whose value is related to the total concentration of organics in the solutions [55]. The average CODsec of Cluster 1 and Cluster 3 was 0.7601 and 1.0064 kW·h·kg−1 COD, implying that the energy efficiency of the Cluster 3 was lower than Cluster 1 despite the better water quality. Further optimizations shall improve the performance of the plant’s aeration system because CODsec largely depends on the energy consumption of the aeration system [56].
On the days when the wastewater treatment volume was low, the average energy consumption of the WWTP was relatively high. The average UEC of the WWTP was the highest under the influent condition of Cluster 4 (low influent concentration and small water volume), that is, 0.3613 kW·h·m−3, which was greater than the energy consumption of 0.3451 kW·h·m−3 for high influent concentration but small water volume (Cluster 2). At the same time, the energy consumption was distributed very discretely on those days, ranging across four levels from low energy consumption to high energy consumption, and seriously deviated from the Gaussian distribution. The energy efficiency of the days with small influent volumes was poor with 1.0440 and 1.3694 kW·h·kg−1 COD of Cluster 2 and Cluster 4, respectively, higher than those with high influent volumes. It shows that the operation and management of the WWTP might have been abnormal when the water inflow was low, and the overall control strategy was not very reasonable, especially in Cluster 4.
The corresponding energy consumption of Cluster 4 can be clustered again to find the dates when the energy consumption is better distributed, along with better control parameters and operating strategies. The results can be used as an empirical reference for the regulation of the WWTP. According to the clustering results (Fig. 6(a)), energy consumption in the case of low influent concentration and small water volume was classified into three categories. According to the clustering analysis, the energy consumption was relatively high on 22 days, with an average UEC of 0.4004 kW·h·m−3. The energy consumption was extremely high on 1 day, with its UEC reaching 0.7828 kW·h·m−3. On the remaining 30 days, the average UEC was 0.3186 kW·h·m−3, between the low and relatively low energy consumption levels, showing a high energy efficiency under this influent condition as well. The corresponding energy consumption cloud model is shown in Fig. 6(b). The average UEC of these 30 days in Cluster 4 was lower than Cluster 2, which is in line with the conclusion that the influent load and the UEC were weakly and positively correlated. Moreover, the corresponding CODsec of the three categories of operating days were 1.5094, 6.2032, and 1.1559 kW·h·kg−1 COD, respectively. Therefore, it is inferred that there were 23 days with abnormal energy consumption or low energy efficiency and 30 days with better energy consumption status or high energy efficiency. The operation of the WWTP on the days with abnormal energy consumption might be faulty with abnormal control strategies. The control strategies for those 23 days should refer to those with better energy consumption, guiding future operations. In typical WWTPs in China, the energy consumption ratio of aeration equipment, external reflux pump, and internal reflux pump is 51.81%, 5.1%, and 1.89%, respectively [57]. Based on the given proportion, the operational circumstances of Cluster 4 can be estimated according to individual energy consumption and theoretical equations of the equipment (Section S4, Eqs. (S4)-(S6) in Appendix A). The calculated operational parameters are listed in Table 5. Under the same influent condition, the average oxygenation capacity per unit flow ranged from 0.2924 to 0.3703 kg O2·m−3 during the high-energy-efficiency days. They were smaller than those with low energy consumption (from 0.3903 to 0.4848 kg O2·m−3). This difference indicated that oxygen supply far outweighed air demand during the low-energy-consumption-efficiency days, leading to energy waste. Similar phenomena were found in the reflux process. In the high-energy-efficiency days, the internal and external reflux ratios ranged 1.9576-2.4787, and 0.6603-0.8361, respectively. However, in days with low energy consumption efficiency, the internal and external reflux ratios were 2.6126-3.2449 and 0.8812-1.0945. The results suggested that the optimal internal and external reflux ratio in the influent condition of Cluster 4 could be set in the range 1.9576-2.4787 and 0.6603-0.8361, respectively. Therefore, the energy consumption can be saved by adjusting the running time of the aeration equipment and the reflux pump to control the aeration volume or reflux flow when a WWTP is in the state of a low influent load.
3.4. The feasibility and applicability analysis of CMECA
Compared with the traditional energy consumption analysis method, energy analysis based on the cloud model can comprehensively consider the uncertainty in the energy consumption evaluation process while simultaneously performing good data mining on the daily energy consumption in combination with the influent condition clustering. It can be used to evaluate the rationality of the WWTP operation and management, obtain reasonable energy consumption distributions and operation strategies under different influent conditions, and guide the WWTP in performing corresponding optimization and regulation.
Data for modeling in the process of CMECA are easily available. For example, a convenient query could access the daily electricity consumption on smart meters. Concurrently, the soft-sensing models realize the timely measurement of indicators that are difficult to measure for the influent water. It plays a crucial role in assisting the daily energy consumption benchmark analysis, helps to diagnose WWTP problems, and fulfills more intelligent adjustments. Consequently, the availability of the data could provide prerequisites for the establishment and extension of the energy analysis method proposed in this research on a smaller time scale in the near future. It is important to note that some of the abnormal points in energy consumption and operation mistakes may also be affected by other boundary conditions. For example, a sudden rainfall incident causes an increase in the influent of the WWTP. However, the water volume is sometimes not recorded correctly owing to some reasons such as monitoring errors. Therefore, in the future modeling process, multiple influencing factors need to be further considered to improve the model's accuracy and enhance the flexibility in regulating the WWTP and its ability to respond to emergencies.
The influent conditions and treatment processes vary for different WWTPs. Applying the proposed energy consumption analysis method may arrive at different evaluation results. However, a relatively reasonable energy consumption distribution can always be found within similar influent conditions. Here, due to the inadequacy of the data obtained, the operational parameters such as the reflux ratio were calculated using the theoretical formula based on the energy consumption ratio of a typical WWTP. The operators can optimize the management according to the specific condition of the equipment from the ledgers or historical data, with the help of the CMECA method, which has a particular guiding role in overcoming the randomness of operation for optimizing the WWTP.
4. Conclusions
This study proposed a cloud-model-based energy consumption analysis method of wastewater treatment systems. A local WWTP in China served as the research object for model verification. We utilized PCA and K-means clustering to classify the influent conditions of the WWTP and established the cloud model based on energy consumption under different influent conditions. Major conclusions are as follows.
(1) The conflict in pollutant removal was mainly between denitrification and phosphorus removal, indicated by the results of dimensionality reduction on water quality data based on PCA. It was related to the relatively low B/N ratio in the actual influent.
(2) The influent conditions of the WWTP were categorized into four clusters. Cluster 4 (low influent concentration and small water volume) showed the highest energy consumption of 0.3613 kW·h·m−3, crossing four energy consumption levels from low (I) to relatively high (IV). It shows more randomness and uncertainty, indicating an unreasonable operation and management in the WWTP.
(3) A better energy consumption distribution of 30 operating days in Cluster 4 representing high energy-utilization rates was found through further clustering. During these specific days, the range of oxygenation capacity per unit flow, internal reflux ratio, and external reflux ratio were 0.2924-0.3703 kg O2·m−3, 1.9576-2.4787, and 0.6603-0.8361, respectively. These data could be used as guidance for the days with low energy efficiency.
As the goal of carbon neutrality fitted into the construction of ecological civilization in China, energy conservation and emission reduction should be key issues considered by WWTPs. This research provides an overall energy-saving and management scheme for WWTPs based on an evaluation and modeling approach. More systematic explorations are still needed. In the future, we need to focus on multiple influencing factors (e.g., boundary factors). Besides, we shall investigate the relationship between the specific operational parameters related to energy consumption and control strategies. Moreover, we need to conduct more refined classification and analysis on smaller time scales to achieve accurate control. Using data from other WWTPs as samples can also be considered to make the model universal.
Acknowledgments
The authors greatly acknowledge the financial support from the National Key Research and Development Program of China (2019YFD1100204); the National Natural Science Foundation of China (52091545); the State Key Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology (2021TS03); The Important Projects in the Scientific Innovation of CECEP (cecep-zdkj-2020-009); and the Open Project of Key Laboratory of Environmental Biotechnology, Chinese Academy of Sciences (kf2018002). We gratefully thank the contribution of the algorithm model and tool support by the Artificial Intelligence department of CECEP Talroad Technology Co., Ltd. We are also thankful to the Heilongjiang Province Touyan Team for their support and guidance.
Compliance with ethical guidelines
Shan-Shan Yang, Xin-Lei Yu, Chen-Hao Cui, Jie Ding, Lei He, Wei Dai, Han-Jun Sun, Shun-Wen Bai, Yu Tao, Ji-Wei Pang, and Nan-Qi Ren declare that they have no conflicts of interest or financial conflicts to disclose.
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