A pump group energy-saving control method based on discrete working condition point clustering search optimization

Abstract

This invention discloses an energy-saving control method for pump sets based on discrete operating point clustering search optimization, belonging to the technical field of pump set scheduling control. It acquires pump set operating data based on sensors, predicts the target flow rate based on historical flow time-series data, and determines the target head. Under the premise of meeting water supply constraints, the frequency of any one or more pumps in the pump set is perturbed, and discrete operating points under different frequency combinations are collected. Clustering search optimization is performed based on the discrete operating points to obtain candidate clusters that meet the target requirements. Within the candidate clusters, a multi-index comprehensive evaluation model is constructed to score the points within the clusters, and the points within the clusters with higher scores are selected as representative points, obtaining a set of representative points. Based on the set of representative points, the representative point that best meets the target requirements and has the lowest adjustment cost is selected as the optimal operating point. This invention directly uses sampled points for optimal solution search, avoiding fitting errors and more closely reflecting actual operating conditions, thus possessing good practicality.

Description

Technical Field

[0001] This invention belongs to the technical field of pump group scheduling and control, specifically relating to a pump group energy-saving control method based on discrete operating point clustering search optimization. Background Technology

[0002] In water supply systems, parallel operation of multiple pumps is a common mode. Traditional energy-saving methods for pump sets rely on fitting pump characteristic curves or multi-pump combination models. However, multi-pump parallel systems are affected by factors such as equipment aging, changes in pipeline resistance, and hydraulic coupling, making model errors difficult to avoid. For example, while existing constant-pressure PID control methods for multi-pump parallel operation can meet basic water supply needs, they have significant shortcomings in energy efficiency optimization. The main reasons are: the head-flow characteristic curves of different pumps cannot be simply superimposed during parallel operation, which is particularly complex in actual operating conditions; and multi-pump parallel operation has coupling characteristics, making it difficult to accurately obtain the performance curves under parallel conditions through theoretical modeling. Summary of the Invention

[0003] The purpose of this invention is to provide a pump group energy-saving control method based on discrete operating point clustering search optimization, which aims to solve the above-mentioned problems.

[0004] This invention is mainly achieved through the following technical solutions:

[0005] An energy-saving control method for pump sets based on discrete operating point clustering search optimization includes the following steps:

[0006] Step S1: First, acquire pump set operating data based on sensors, including total flow rate, outlet head, and effective power of a single pump; based on historical flow time series data, predict the target flow rate using a time series prediction model. and determine the target lift. ;

[0007] Step S2: Under the premise of satisfying the water supply constraints, apply a disturbance to the frequency of any one or more pumps in the pump set, and collect discrete operating points under different frequency combinations. ;

[0008] in: It is the frequency of the m-th pump at the i-th operating point;

[0009] It is the total water supply flow rate of the pump set under the i-th operating condition;

[0010] It is the total head of the pump unit under the i-th operating condition;

[0011] It is the total power of the pump unit under the i-th operating condition;

[0012] Step S3: Perform cluster search optimization based on discrete operating points to obtain candidate clusters that meet the target requirements;

[0013] Step S4: Within the candidate cluster, using power-to-flow ratio, pump efficiency, power consumption per unit head, frequency sensitivity, operational stability, and data confidence as characteristics, a multi-index comprehensive evaluation model is constructed through normalization and adaptive weight calculation. Points within the cluster are scored, and those with higher scores are selected as representative points, thus obtaining the representative point set. ;

[0014] Step S5: Based on the representative point set The optimal operating point is selected as the representative point that best meets the target requirements and has the lowest adjustment cost.

[0015] The optimal search is performed by combining the cost of operating condition changes, and the operating scheme that meets the flow rate and head constraints and has the lowest energy consumption is selected; the cost of operating condition changes includes pump start-up and shutdown differences and frequency offset distance.

[0016] To better realize the present invention, step S3 further includes the following steps:

[0017] Step S31: Clustering and Grouping; Based on the flow-head characteristics, cluster the discrete operating points and divide all discrete operating points into K clusters to obtain a set of clusters. ;

[0018] Step S32: Initial feasibility screening at the cluster level; perform hard screening at the cluster level based on the maximum water supply capacity constraint; use the cluster center / cluster boundary / representative point information within each cluster to screen out clusters that do not meet the target requirements. Clusters that meet the target requirements are formed.

[0019] Step S33: Obtain the priority score by weighted summation of cluster center distance, coverage and sample density; then, perform soft screening based on the priority score to select the top n clusters with the highest priority scores to obtain candidate clusters that meet the target requirements.

[0020] To better implement the present invention, further, in step S31, after clustering and grouping, intra-cluster preprocessing is performed, including the following steps:

[0021] (1) Based on IQR statistics, remove operating conditions where flow rate and power are abnormally biased;

[0022] (2) Eliminate working conditions that are not feasible based on physical constraints;

[0023] (3) Calculate the variance of flow rate and head within the cluster respectively, perform steady-state detection based on threshold, and screen operating points.

[0024] To better realize the present invention, step S32 further includes the following steps:

[0025] Step S321: Calculate any cluster In traffic Yangcheng Extreme values ​​in a dimension;

[0026] (1) First, calculate the cluster In traffic mean in dimensions :

[0027] ;

[0028] (2) Subsequently, the clusters are calculated. Yangcheng mean in dimensions :

[0029] ;

[0030] (3) Determine the cluster center :

[0031] ,

[0032] (4) Through clusters exist , Extreme value representation clusters in dimensions boundary :

[0033] ;

[0034] in: Cluster The number of samples included;

[0035] For clusters Internal Samples exist Values ​​in a dimension;

[0036] Representative cluster Internal Samples exist Values ​​in a dimension;

[0037] , Clusters exist Minimum and maximum values ​​in each dimension;

[0038] , Clusters exist Minimum and maximum values ​​in each dimension;

[0039] Step S322: If or Then remove the cluster. Otherwise, retain the cluster. .

[0040] To better implement the present invention, step S33 further includes the following steps:

[0041] Step S331: Define the standardized Euclidean distance The spatial difference between the cluster center and the target requirement is quantified;

[0042] ;

[0043] in: , These are the scale normalization parameters;

[0044] Step S332: Define intra-cluster coverage, which measures the proportion of samples in a cluster that meet the target requirements;

[0045] ;

[0046] in: For clusters Simultaneously satisfy , The number of samples required for each dimension;

[0047] , The degree to which the cluster covers the target requirements;

[0048] Step S333: Constructing a cluster Priority score ;

[0049] ;

[0050] in: As a cluster density normalization index;

[0051] These are the weighting coefficients;

[0052] The hyperbolic tangent function is used to... Mapped to interval;

[0053] Step S334: Filter to obtain the top n clusters with higher priority scores.

[0054] To better realize the present invention, step S4 further includes the following steps:

[0055] Step S41: Construct an index vector for each operating point based on multiple indicators. And after normalization, we obtain ;

[0056] in: Energy efficiency ratio;

[0057] For the overall efficiency of the pump set;

[0058] Power consumption per unit head;

[0059] Gain per unit frequency;

[0060] For operational stability index;

[0061] Step S42: Determine the weight of each indicator;

[0062] (1) Determining PCA weights based on variance contribution rate ;

[0063] (2) Combined with Shannon entropy weight correction get ;

[0064] ;

[0065] in: Custom parameters;

[0066] The index weights are determined based on Shannon's entropy weight method.

[0067] Step S43: Local nonlinear fitting and stability surface analysis;

[0068] Step S431: Based on the intra-cluster data, firstly, a power surface is constructed as the energy consumption constraint model for the operating condition region, and then an energy efficiency surface is derived from it.

[0069] Step S432: Calculate the energy efficiency residual for each operating point. :

[0070] ;

[0071] in: For based on (Q)i H i The predicted power at the i-th operating point is obtained by fitting the power surface;

[0072] Step S433: Stability analysis based on derived energy efficiency surface;

[0073] Calculate the gradient magnitude at each working condition point. :

[0074] ;

[0075] Where: ∇ is the gradient operator;

[0076] Based on (Q) i H i The energy efficiency at the i-th operating point is obtained by fitting the energy efficiency surface;

[0077] Step S434: Final construction of stability score :

[0078] ;

[0079] in: These are the weighting coefficients;

[0080] Step S44: Determine representative points within the cluster based on multi-model fusion decision;

[0081] Step S441: Construct a multi-indicator comprehensive evaluation model and calculate the comprehensive score:

[0082] ;

[0083] in: This is an empirical coefficient;

[0084] For the j-th index at the i-th working condition point The normalized value;

[0085] Step S442: Based on the formula for comprehensive scoring, calculate the comprehensive score set of the working conditions within the cluster, and remove the working conditions that are 30% lower than the average value of the comprehensive score set;

[0086] Step S443: Sort Score_i from high to low, extract the top 3 cluster points, perform dynamic operating condition consistency re-check, and take the point with the highest consistency score as the representative point.

[0087] To better implement the present invention, step S5 further includes the following steps:

[0088] Step S51: Calculate the distance across dimensions;

[0089] (1) Calculate the distance to the open state Cost of changing the start-up and shutdown of the quantization pump;

[0090] ;

[0091] ;

[0092] ;

[0093] in: This is the pump unit's start-up state vector from the previous moment;

[0094] For the first The start / stop status of the pump at the previous moment;

[0095] For the first The start / stop status of the pump at the previous moment;

[0096] This represents the start-up state vector of the point pump unit;

[0097] As a representative point The start / stop status of the pump;

[0098] As a representative point The start / stop status of the pump;

[0099] m is the number of pumps included in the pump set;

[0100] (2) Calculate the frequency distance Quantify the magnitude of frequency change;

[0101] ;

[0102] ;

[0103] ;

[0104] in: This is the frequency vector of the pump unit at the previous moment;

[0105] For the first The operating frequency of the pump at the previous moment;

[0106] This represents the frequency vector of the point pump group;

[0107] As a representative point Operating frequency of the pump;

[0108] The global standard deviation of the pump set operating frequency;

[0109] Step S52: Calculate the total working distance; introduce weighting coefficients. The total working condition distance is obtained by weighted fusion of distances in each dimension. :

[0110] ;

[0111] Step S53: Based on total working distance Define similarity weights :

[0112] ;

[0113] in, ;

[0114] Step S54: Construct representative points Weighted composite score ;

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] in: As a representative point Requirements for target operating conditions The suitability score ;

[0120] These are the target start-up state vector and the target frequency vector of the pump unit, respectively.

[0121] Enable state matching;

[0122] For frequency adaptation;

[0123] The attenuation coefficient;

[0124] The weighting coefficients for the fit score. ;

[0125] Step S55: Represent the set of points within the cluster In the middle, a weighted comprehensive score is selected. The highest representative point is taken as the optimal operating condition point.

[0126] To better implement the present invention, further, in step S2, a disturbance is applied when any one of the disturbance triggering conditions is met; wherein, the disturbance triggering conditions include:

[0127] (1) Data sparsity: If the number of operating points within a certain flow-head range is less than the threshold If so, perturbation sampling needs to be triggered;

[0128]

[0129] (2) High model uncertainty: If the time series prediction model in step S1 has a prediction standard deviation of a certain operating point, Exceeding the threshold This triggers a disturbance:

[0130]

[0131] (3) Excessive deviation between prediction and actual values: If the difference between the real-time measured flow rate and head and the model prediction exceeds the threshold. If the model fails, new points need to be collected.

[0132]

[0133] in: This represents the actual traffic volume.

[0134] For predicting traffic flow;

[0135] For actual head;

[0136] To predict head.

[0137] To better realize the present invention, further, in step S2, the intensity of the applied disturbance includes:

[0138] (1) Low-intensity disturbance: The amount of disturbance to the single pump frequency based on the current value. Duration ;

[0139] (2) Medium-intensity disturbance: The two pumps are adjusted complementaryly, and the disturbance amount of the single pump frequency based on the current value. Duration ;

[0140] The safety constraints for applying the disturbance include:

[0141] Pump frequency: ;

[0142] Lower limit of export pressure: ;

[0143] If a pressure deviation is detected If there is a sudden change in flow or power, the system will immediately roll back to the previous safe frequency combination.

[0144] in: This indicates the pump set outlet head collected in real time during the disturbance execution process;

[0145] The minimum frequency fixed for the variable frequency pump;

[0146] The maximum frequency fixed for the variable frequency pump;

[0147] This is the lower limit of the export pressure (minimum head).

[0148] The target head set for the dispatching system;

[0149] This is the maximum allowable safety deviation threshold (set empirically).

[0150] The beneficial effects of this invention are as follows:

[0151] (1) This invention introduces frequency disturbances during operation to collect flow rate, head, and power data under different pump frequency combinations, constructing a dataset of operating points. Based on this, it directly searches and optimizes based on discrete points to dynamically select the lowest energy consumption solution that meets water supply demand, thus achieving energy-saving control. Compared with existing pump control methods based on curve fitting, this invention does not rely on a fitting model but directly uses sampling points to search for the optimal solution, avoiding fitting errors and ensuring that the results are closer to actual operating conditions. In practice, this invention can be applied to scenarios requiring multiple pumps to operate in parallel at constant pressure, such as urban water supply pump stations, industrial circulating water pump stations, and HVAC water supply systems. It is particularly suitable for applications with large water load fluctuations and high requirements for energy consumption control and equipment reliability, enabling efficient and energy-saving pump scheduling control.

[0152] (2) This invention can avoid theoretical fitting errors and achieve high-precision energy-saving optimization driven by real operating conditions. This invention does not rely on any theoretical model or fitting curve, but directly collects actual operating data and performs cluster analysis based on discrete operating points. It searches for the optimal combination of operating conditions in the real measurement points, eliminates fitting errors from the source, and makes the energy-saving optimization results consistent with the actual performance of the equipment, thereby significantly improving the accuracy and reliability of energy-saving optimization.

[0153] (3) This invention employs a dual-layer discrimination mechanism of "cluster-level hard screening + soft screening" to improve the accuracy of target operating condition matching. Hard screening directly eliminates all clusters that are insufficient to meet the current water supply demand in terms of maximum flow rate or maximum head capacity; soft screening constructs a priority score based on the standardized distance from the cluster center to the target operating condition, the coverage within the cluster, and the sample density within the cluster, and sorts the clusters that may still meet the demand. Through this dual-layer screening mechanism, this invention can quickly identify a small number of clusters with the most potential, greatly improving search efficiency and target matching accuracy, and avoiding invalid calculations and erroneous scheduling.

[0154] (4) This invention achieves coordinated optimization of energy efficiency and stability by constructing a comprehensive evaluation system for representative points that integrates multiple indicators. Traditional energy-saving strategies often focus only on a single indicator such as power or energy efficiency, which may lead to problems such as poor stability, large pressure fluctuations, or insufficient controllability at the selected operating points. This invention uses a multi-dimensional indicator system within the cluster to comprehensively score representative points, including power ratio per unit flow, pump efficiency, power consumption per unit head, frequency regulation sensitivity, and operational stability. At the same time, it introduces a stability evaluation based on residuals and local gradients, and uses PCA and entropy weight method to adaptively determine weights, ensuring that the selected representative points not only have high energy efficiency, but also stable operating conditions and friendly regulation, thereby achieving unified optimization of energy-saving effect and operational stability.

[0155] (5) This invention introduces a working condition adjustment cost model, balancing energy-saving optimization with equipment lifespan. Directly switching control commands to the theoretical optimum may lead to frequent pump start-stops or significant frequency adjustments, causing mechanical shocks, pressure fluctuations, and even energy consumption rebounds. This invention innovatively introduces working condition adjustment cost weights, including Hamming distance for pump start-stop changes and standardized Euclidean distance for frequency shifts. By using similarity weights, drastic working condition changes are suppressed, making the optimization process smoother and reducing equipment wear and pressure disturbances. This mechanism achieves the dual goals of "energy saving priority" and "reducing mechanical shocks and extending equipment lifespan."

[0156] (6) This invention constructs a disturbance triggering and dynamic data update mechanism, enabling the system to have self-learning capabilities. Due to pump wear, seasonal changes, and changes in pipeline conditions, historical operating data may not reflect the true system state in the long term. This invention constructs three types of triggering conditions: data sparsity detection, system deviation monitoring, and model uncertainty assessment. During low-load periods at night, it automatically performs low-intensity or medium-intensity frequency disturbance sampling to continuously supplement new operating point data. The system updates the clustering structure, representative points within clusters, and comprehensive scores in real time based on the newly added data, enabling the optimization model to have self-learning and adaptive capabilities, maintain energy-saving performance for a long time, and always adapt to changes in the actual operating environment. Attached Figure Description

[0157] Figure 1This is a flowchart of the pump group energy-saving control method based on discrete operating point clustering search optimization according to the present invention. Detailed Implementation

[0158] Example 1:

[0159] An energy-saving control method for pump sets based on discrete operating point clustering search optimization, such as... Figure 1 As shown, it includes the following steps:

[0160] Step 1: Acquire pump unit operating data based on sensors, including total flow rate, outlet head, and effective power of a single pump; predict the target flow rate using a time series prediction model based on historical flow time series data. and determine the target lift. .

[0161] Specifically, a flow meter and pressure sensor are installed at the main outlet of the pumping station to obtain the total flow rate and outlet head. A power meter is installed in the power supply circuit of each pump to collect the effective power of a single pump in real time. Based on the historical flow time-series data collected by the above equipment, a time series prediction model (such as...) is used... , (etc.), predicting traffic demand for the next 24 hours. The traffic is divided into fixed time periods, and the maximum traffic volume in each time period is taken as the traffic scheduling target (target traffic). ).

[0162] Step 2: Under the premise of meeting the water supply constraints, apply a disturbance to the frequency of any one or more pumps in the pump set, and collect discrete operating points under different frequency combinations.

[0163] Step 2.1: Acquisition of operating condition data;

[0164] Under the condition of meeting water supply requirements, the operating frequency of one or more pumps currently controlled by PID is randomly reduced, while the operating frequency of another or more pumps is increased to ensure that the overall head H and flow rate Q meet the user's needs, allowing for a certain range of fluctuations.

[0165] Step 2.2: Construction of the working condition point dataset;

[0166] In the scenario of parallel operation of pump sets, a working point is defined. The overall operating status of the pump unit at a certain moment:

[0167] ;

[0168] in, It is the frequency or switching status of the m-th pump at the i-th operating point; It is the total water supply flow of the pump set under this operating condition; It is the total head of the pump unit under this operating condition; It is the total power of the pump unit under this operating condition.

[0169] The set of operating points was obtained through statistics. ;

[0170] in, This represents the number of discrete operating points collected.

[0171] Under parallel pump operation conditions, the total water supply flow of the pump set is equal to the sum of the actual flow rates of each pump:

[0172] ;

[0173] The total power of the pump set is equal to the sum of the input power of each pump:

[0174] ;

[0175] in, Representing the Table pump at frequency He Yangcheng The actual flow rate; The pump set is at the operating point Total water supply flow rate below;

[0176] Representing the Table pump at frequency and traffic The input power is as follows; The pump set is at the operating point The total input power below.

[0177] Step 3: Perform cluster search optimization based on discrete operating points to obtain candidate clusters that meet the target requirements;

[0178] Step 3.1 Clustering and Grouping: Based on the flow-head characteristics, cluster the discrete operating points and divide all discrete operating points into K clusters to obtain a set of clusters. ;

[0179] Considering the large number of discrete operating points, a direct global search would incur high computational costs. Therefore, a clustering method based on flow rate and head is adopted to obtain the clustering feature vector:

[0180] ;

[0181] use Or density clustering ( The algorithm divides all operating points into K clusters:

[0182] ;

[0183] This ensures that the operating points within the same cluster meet similar water supply needs (similar flow rates and heads), but the pump frequencies and power differ.

[0184] Further, intra-cluster preprocessing is performed;

[0185] The pump station data collected on-site contains a lot of noise, including pressure fluctuations, air entrainment, valve operation, and transients during pump start-up or shutdown. If these are directly mixed into the screening process, it will cause the representative points to be biased towards false operating conditions that are "abnormally good" or "abnormally bad," affecting the overall optimization. Therefore, abnormal operating conditions need to be removed.

[0186] (1) Statistical elimination of operating conditions with abnormally biased flow and power based on IQR;

[0187] ;

[0188] in: The first quartile (25th percentile) means the value located at the 25th percentile after a set of data is sorted from smallest to largest;

[0189] Interquartile range, This indicates the fluctuation range of the middle 50% of the data;

[0190] The third quartile (75th percentile) means the value located at the 75th percentile after sorting.

[0191] (2) Elimination of infeasibility points based on physical constraints, such as sudden drop in head, power spike, and pump frequency jump;

[0192] (3) Statistically analyze the dispersion of flow rate and head at each operating point within the cluster, and calculate the flow rate variance within the cluster. With head variance .

[0193] ;

[0194] ;

[0195] in, , This is the cluster mean. When When this condition is determined, the operating condition cluster is identified as a stable operating condition cluster. The threshold for traffic stability. N represents the head stability threshold. k This represents the total number of operating points within the cluster. Let Variance be the intra-cluster flow rate variance under the i-th operating condition; Let V be the variance of the intra-cluster head under the i-th operating condition.

[0196] Step 3.2: Initial feasibility screening at the cluster level; perform hard screening at the cluster level based on the maximum water supply capacity constraint; use the cluster center / cluster boundary / representative point information within each cluster to screen out clusters that do not meet the target requirements. Clusters that meet the target requirements are formed.

[0197] After completing (Q,H)-based clustering and preprocessing, cluster centers, cluster boundaries, and representative points within each cluster are used to filter out clusters that cannot meet the target requirements. Clusters are formed to create a set of clusters that meet the target requirements, reducing the risk of subsequent computation and intervention.

[0198] Step 3.2.1: Calculate arbitrary clusters In traffic Yangcheng Extreme values ​​in a dimension;

[0199] (1) Given a set of clusters For any cluster First, calculate its position. mean in dimensions The calculation formula is:

[0200] ;

[0201] in, Cluster The number of samples included. For clusters Internal Samples exist Values ​​in a dimension.

[0202] (2) Subsequently, the clusters are calculated. exist mean in dimensions Its expression is:

[0203] ;

[0204] in: Cluster The number of samples included;

[0205] For clusters Internal Samples exist Values ​​in a dimension;

[0206] Representative cluster Internal Samples exist Values ​​in a dimension;

[0207] , Clusters exist Minimum and maximum values ​​in each dimension;

[0208] , Clusters exist Minimum and maximum values ​​in a dimension.

[0209] (3) Based on the calculation results of the above dimensional mean, the cluster can be determined. The center (i.e., the center of mass) Its formal representation is: For clusters boundary (i.e., the extreme value range), can be obtained through this cluster in , The extreme values ​​in a dimension are represented as follows:

[0210] .

[0211] Step 3.2.2: Hard screening;

[0212] A fast and conservative cluster screening strategy is adopted. The core logic is to directly eliminate clusters that do not have the basic ability to meet the requirements by comparing the extreme values ​​of clusters in the target dimension with the requirement threshold.

[0213] (1) Filtering rules;

[0214] If a cluster is in , If the maximum capability in each dimension is lower than the corresponding target requirement threshold, the cluster is determined to be infeasible and is directly removed from the candidate set.

[0215] (2) Mathematical expression;

[0216] For clusters If the following conditions are met: but Clusters deemed infeasible are discarded. Cluster exist The maximum value of a dimension is calculated as follows: , Cluster exist Similarly, the maximum value of the dimension can be obtained as follows: ,in, , Clusters Internal Samples exist , The value of the dimension, For clusters The total number of samples.

[0217] This method directly uses the extreme values ​​of samples within a cluster in the corresponding dimension for screening. It has strict logic and high security, and can ensure that the clusters that are removed do not have the ability to meet the target requirements.

[0218] Step 3.3 Obtain the priority score by weighted summation of cluster center distance, coverage and sample density; then, perform soft screening based on the priority score to select the top n clusters with the highest priority scores to obtain candidate clusters that meet the target requirements.

[0219] (Cluster ranking in scenarios with ambiguous boundaries) After hard screening, the matching relationship between the remaining clusters and the target requirements is usually ambiguous. To further address this, a priority scoring mechanism based on fusion distance, coverage, and density is constructed to rank the remaining clusters, selecting the top clusters for subsequent representative point comparison.

[0220] (1) To quantify the spatial difference between the cluster center and the target requirement, a standardized Euclidean distance is defined. :

[0221] ;

[0222] in, , For clusters exist , Mean of dimension (i.e., cluster center) (the amount of the ingredients); , The scaling normalization parameter can be selected as the standard deviation of the global dataset or samples within a cluster in the corresponding dimension.

[0223] (2) Define intra-cluster coverage This is used to measure the proportion of samples in a cluster that meet the target requirements.

[0224] ;

[0225] in, For clusters Simultaneously satisfy , The number of samples required for each dimension; A larger value indicates a higher degree of coverage of the target requirement by the cluster.

[0226] (3) Based on the above indicators, construct a cluster. Priority score :

[0227] ;

[0228] in, Cluster density normalization index (e.g., "cluster density") "Number of samples / Maximum number of samples in all clusters" is used to encourage clusters with abundant samples; This is the weighting coefficient; the default recommended value is [value]. , , ; Let be the hyperbolic tangent function, Mapped to An interval is used to facilitate weighted calculation.

[0229] Priority score The priority score is negatively correlated with cluster-target distance and positively correlated with intra-cluster coverage and cluster density; that is, the smaller the distance, the higher the coverage, and the richer the density of the cluster, the higher the priority. The top N clusters with the highest priority scores (set to 3) are selected to enter the next round of intra-cluster representative point selection.

[0230] Step 4: Selection of representative points within clusters; Within candidate clusters, a multi-index comprehensive evaluation model is constructed based on characteristics such as power-to-flow ratio, pump efficiency, power consumption per unit head, frequency sensitivity, operational stability, and data confidence. This model is then used for normalization and adaptive weighting calculations to score the points within the clusters. Points with higher scores are selected as representative points, thus obtaining a set of representative points. .

[0231] Step 4.1: Construction of a multi-index energy efficiency system;

[0232] Constructing a five-dimensional comprehensive evaluation index for each cluster The optimal point is selected through internal screening. This forms the index vector for each operating point. All indicators are included in the subsequent comprehensive evaluation;

[0233] ;

[0234] in: Energy efficiency ratio (EER) is the effective flow rate generated per unit power. ;

[0235] The overall efficiency of the pump set is an approximate fit to the "pump efficiency". ;

[0236] Power consumption per unit head is the energy consumption required to maintain the head. ;

[0237] The unit frequency flow gain represents the flow sensitivity caused by frequency variations. ;

[0238] The stability index is the time stability of Q / H.

[0239] In the same cluster Within this process, the minimum value is calculated for each operating point and each indicator dimension. With the maximum value Let the j-th indicator be... To avoid inconsistencies in the dimensions of various indicators, normalization is performed:

[0240] .

[0241] Step 4.2: Weight Adaptive Mechanism; Determine the weights of each indicator based on PCA or Entropy weighting method;

[0242] (1) Determining PCA weights based on variance contribution rate ;

[0243] The normalized index matrix is ​​input into the principal component analysis model, and the covariance matrix is ​​decomposed into eigenvalues ​​to obtain the five principal components and their variance contribution rates. The variance contribution rate of the k-th principal component is defined as the ratio of its eigenvalue to the sum of all eigenvalues, which is used to characterize the explanatory power of the principal component for the original index information.

[0244] Based on the variance contribution rate of each principal component, construct the index weight vector. ,in This indicates the importance of the j-th evaluation indicator in the overall evaluation. For example, PCA yields the contribution rates of the top 5 principal components:

[0245] .

[0246] (2) After further correction using Shannon entropy weights, the final weights are:

[0247] ;

[0248] in: For custom parameters (e.g., 0.7).

[0249] The The index weights, determined based on Shannon's entropy weight method, are calculated as follows:

[0250] First, construct the original evaluation matrix consisting of n operating condition samples and m evaluation indicators:

[0251]

[0252] in, This represents the value of the i-th operating condition under the j-th evaluation index.

[0253] The evaluation matrix is ​​dimensionless to obtain a standardized matrix. :

[0254] ;

[0255] Calculate the information entropy of the j-th indicator based on the standardized matrix. :

[0256] , ;

[0257] in, Characterizes the information uncertainty of the j-th index;

[0258] n represents the number of operating point clusters participating in the evaluation within the current operating condition cluster, and k is used to normalize the information entropy to ensure... In [0, 1].

[0259] Redundancy is calculated based on the information entropy index. :

[0260] ;

[0261] Further, the index weights based on the entropy weight method are obtained. :

[0262] .

[0263] Step 4.3: Local nonlinear fitting and stability surface analysis;

[0264] Since pump sets operate in similar states within the same operating condition cluster, there is a stable mapping relationship between power, flow rate, and head. To avoid interference from instantaneous measurement noise and accidental high-efficiency points in the selection of representative operating conditions, this invention first constructs a power surface as an energy consumption constraint model for the operating condition region, then derives an energy efficiency surface from this model, and further conducts stability analysis.

[0265] (1) Power surface;

[0266] Based on historical sample points within the same working condition cluster Using radial basis function (RBF), Gaussian process regression (GPR), or multinomial regression methods, the power surface is fitted to establish the power... A continuous function of flow rate and head The model:

[0267]

[0268] The power surface is used to describe the actual energy consumption relationship of the pump set in the operating area of ​​the "flow rate-head → power", which constitutes the physical constraint basis for subsequent energy efficiency analysis and stability judgment.

[0269] (2) Energy efficiency surface;

[0270] Under the power response surface constraint, the discrete energy efficiency ratio index is... The expression is:

[0271]

[0272] Substituting into the power surface model, we obtain the continuous energy efficiency mapping relationship:

[0273]

[0274] Thus, an energy efficiency derived surface is constructed on the power surface. The energy efficiency surface no longer depends on discrete power measurement points, but is continuously derived from the power response mother surface. It is used to characterize the overall distribution structure of energy efficiency with flow rate and head within the operating condition cluster, thereby identifying stable and efficient operating areas.

[0275] (3) Energy efficiency residual field construction and power consistency constraints;

[0276] To evaluate the degree of compliance of a single operating point with the power-constrained energy efficiency structure, the energy efficiency residual is defined. for:

[0277] ;

[0278] Among them: Q i P is the actual flow rate at the i-th operating point. i It is the actual power at the i-th operating point, f(Q) i H i ) is the predicted power obtained by fitting the power surface above.

[0279] The energy efficiency residual characterizes the degree of deviation between the actual operating point energy efficiency and the power surface derived energy efficiency, and is used to characterize whether the point belongs to a stable member in the power-constrained energy efficiency structure.

[0280] An energy efficiency residual field is constructed from the residuals of all operating points, serving as an important criterion for excluding accidental high efficiency points and abnormal operating conditions.

[0281] (4) Stability analysis based on derived energy efficiency surfaces;

[0282] The derived energy efficiency surface Calculate the gradient magnitude at each operating point:

[0283]

[0284] This formula is simply the derivative of the energy efficiency surface formula above. The formula represents the energy efficiency at the i-th operating point. This represents the energy efficiency gradient at the i-th operating point.

[0285] It is the gradient operator for bivariate functions. Its gradient is It is a vector representing the direction and rate of the most rapid change of the energy efficiency surface at that point.

[0286] The gradient is used to describe the sensitivity of energy efficiency to operating parameter disturbances under power constraints. The smaller the gradient, the more gradual the energy efficiency distribution in the region, the less sensitive the operating conditions are to parameter fluctuations, and the higher the operating stability.

[0287] (5) Construction of comprehensive stability and energy efficiency evaluation index

[0288] Taking into account the degree of compliance of the power-constrained energy efficiency structure at the operating point and its sensitivity to local changes, a comprehensive stability evaluation index is constructed:

[0289]

[0290] in, , where is the weighting coefficient. The larger the stability evaluation value, the closer the operating point is to the typical high-efficiency structural region under power constraints, and the more gradual the local energy efficiency changes, making it more suitable as a representative operating point for subsequent optimization control.

[0291] Step 4.4: Determine representative points within the cluster based on multi-model fusion decision-making;

[0292] (1) Construct a multi-indicator comprehensive evaluation model and calculate the comprehensive score:

[0293]

[0294] The first term represents the energy efficiency contribution, and the second term represents the stability contribution. This is an empirical coefficient (e.g., 0.3–0.5).

[0295] (2) Based on the comprehensive scoring formula in (1), the comprehensive score set of each working condition point in the cluster is obtained. To reduce the impact of outliers, 30% of operating conditions that are below the average of the comprehensive score set are removed.

[0296] (3) Sort Score_i and take the top three (Top-n candidates, n is usually set to 3);

[0297] .

[0298] (4) Dynamic operating condition consistency re-inspection;

[0299] Check the consistency of the Top-3 clusters at the boundaries of adjacent clusters to avoid being pulled into incorrect clusters;

[0300] (5) The final representative point is the point with the highest consistency score.

[0301] The comprehensive scoring ensures optimal overall performance, rather than the best performance of a single indicator. Low-scoring points are eliminated to reduce the impact of outliers. Top-3 candidates prevent the randomness of single selection. Consistency review can avoid misjudgments caused by clustering errors. The final representative point is more in line with the engineering requirements of stability, reliability and controllability.

[0302] Step 5: Optimal solution search; based on representative point set The optimal operating point is selected by screening out representative points that meet the target requirements and have the lowest adjustment cost. Specifically, an optimal point search is performed in conjunction with the operating condition change cost to select the operating scheme that meets the flow rate and head constraints and has the lowest energy consumption; the operating condition change cost includes pump start-up / shutdown differences and frequency offset distance.

[0303] In the decision-making process for optimizing pump unit operating conditions, representative points within the cluster have already been obtained through preliminary clustering and screening. However, adjustments to pump unit operating conditions (such as pump start-up and shutdown, and changes in operating frequency) are usually accompanied by undesirable impacts such as energy consumption fluctuations and equipment mechanical wear. Therefore, in the final optimization search stage of representative points within the cluster, it is necessary to introduce the pump unit operating condition information from the previous moment and quantify the "cost of operating condition adjustment" through a weighted mechanism. This will achieve synergistic optimization of "meeting target requirements" and "reducing pump unit operating disturbances," ultimately selecting the optimal operating condition point from the representative points within the cluster.

[0304] 5.1 Variable definition;

[0305] Assume the pump set includes For the pump, define the following variables to characterize the operating conditions and the selection criteria:

[0306] The pump unit's operating characteristics at the previous moment are characterized by the start-up state vector and the frequency vector, denoted as: .

[0307] in, for 3D binary vector Indicates the first The start / stop status of the pump at the previous moment (1=on, 0=off); for 3D continuous vector Indicates the first The operating frequency of the pump at the previous moment. Set of representative points within the cluster: Let... For a certain candidate cluster, for The preliminary selection of representative points (such as Top-N fit points); representative point working condition characteristics: any representative point The working condition characteristics are denoted as ,in To enable the state vector, This is a frequency vector, corresponding to the pump unit operating parameters at the point it represents.

[0308] 5.2 Weighted mechanism for operating condition similarity;

[0309] To represent points within the cluster To select the optimal solution that "fits the target requirements and minimizes adjustment costs," it is necessary to first quantify representative points. The degree of fit with the previous time-to-time condition (fit is negatively correlated with adjustment cost). A fusion-based distance index is constructed to address the characteristic differences between "discrete on-state" and "continuous frequency" conditions, and then the similarity weight of the time-to-time condition is defined. This serves as a weighted basis for the selection process.

[0310] (1) Dimensional distance calculation;

[0311] 1) Distance in active state (based on Hamming distance, cost of changing the start / stop of the quantization pump):

[0312] ;

[0313] in, Indicates the first Differences in the start and stop status of the pump (0 = consistent status, 1 = changed status). ; The smaller the value, the higher the degree of consistency between the current point and the previous state, and the lower the cost of starting and stopping adjustments.

[0314] 2) Frequency distance (normalized Euclidean distance, quantifying the frequency change amplitude):

[0315] ;

[0316] in, This is the global standard deviation of the pump unit's operating frequency (used to eliminate the influence of dimensions and achieve scale normalization). ; The smaller the value, the higher the frequency match between the current point and the previous moment, and the lower the cost of frequency adjustment.

[0317] (2) Calculate the total working distance; introduce weighting coefficients. The total working condition distance is obtained by weighted fusion of distances in each dimension. ;

[0318] Considering the cost difference between pump start-up and shutdown adjustments (which involve significant mechanical losses) and frequency adjustments (which are primarily characterized by energy consumption fluctuations), a weighting coefficient is introduced. The total working condition distance is obtained by weighted fusion of distances in each dimension. :

[0319] ;

[0320] in, This can be determined through engineering experience or cross-validation (e.g., taking the side restart stop loss). When focusing on frequency stability, take ).

[0321] (3) Define similarity weights based on total working condition distance (Inverse distance form, negatively correlated with adjustment cost):

[0322] ;

[0323] in, The smaller the difference between the representative point and the operating condition at the previous moment, the better. The closer a value is to 1, the higher its weight in the screening process.

[0324] (4) To balance the adaptability to target needs with low adjustment costs, representative points are constructed. Weighted composite score ;

[0325] To balance "adaptability to target needs" and "low adjustment costs," representative points are constructed. Weighted composite score The similarity weight of the working conditions and the target adaptability score are integrated: in, As a representative point Requirements for target operating conditions Fit score ( The calculation logic is as follows:

[0326] ;

[0327] in, (The lower the value, the higher the matching degree.) (Convert to positive rating) (Frequency adaptability, based on Gaussian function mapping) Positive ratings for the interval, (Attenuation coefficient); Weighting coefficients for fit rating ( ), set according to the focus of the target needs.

[0328] (5) The set of representative points within the cluster In the middle, a weighted comprehensive score is selected. The highest representative point is taken as the optimal operating condition point. This selection result not only ensures adaptability to the target operating condition requirements, but also minimizes the operational disturbances caused by pump set adjustments, thus achieving the goal of collaborative optimization.

[0329] Preferably, in step 2 above, perturbation data expansion and dynamic updates are performed;

[0330] To ensure the long-term adaptability and energy efficiency improvement of the pump set optimization control model, this invention proposes a method based on disturbance sampling and dynamic dataset expansion. This method, while ensuring water supply safety and system stability, continuously enriches the dataset and improves the coverage and accuracy of the optimization model by adding small-amplitude disturbances during operation and collecting new operating point data.

[0331] A1. Set the disturbance trigger conditions;

[0332] A disturbance is triggered when any of the following conditions are met:

[0333] (1) Data sparsity: If the number of operating points within a certain flow-head range is less than the threshold If so, perturbation sampling needs to be triggered.

[0334] ;

[0335] (2) High model uncertainty: If the standard deviation of the optimized model for a certain operating point is high... Exceeding the threshold This triggers a disturbance:

[0336] ;

[0337] (3) Excessive deviation between prediction and actual values: If the difference between the real-time measured flow rate and head and the model prediction exceeds the threshold. If the model fails, new points need to be collected.

[0338] .

[0339] A2. Define the perturbation execution rules; where perturbation types include:

[0340] (1) Low-intensity disturbance: The frequency of a single pump increases or decreases from its current value. Duration

[0341] (2) Medium-intensity disturbance: The two pumps are adjusted in a complementary manner, respectively Duration .

[0342] A3. Safety constraints and rollback mechanisms;

[0343] (1) Pump frequency: ;

[0344] (2) Lower limit of export pressure: ;

[0345] (3) If a pressure deviation is detected If there is a sudden change in flow or power, the system will immediately roll back to the previous safe frequency combination.

[0346] A4. Disturbance scheduling and budgeting;

[0347] To avoid impacting normal water supply, this invention establishes disturbance budget and scheduling rules:

[0348] The disturbance is only executed during low-load periods at night (e.g., 02:00–04:00 daily);

[0349] Moderate-intensity disturbances should not exceed 3 times per week, with each disturbance lasting no more than 5 minutes.

[0350] If the model uncertainty decreases significantly in the near term, the perturbation frequency should be gradually reduced; otherwise, the perturbation frequency should be increased.

[0351] A5. Dataset Update and Labeling;

[0352] After the disturbance sampling is completed, the steady-state observation data will be added to the set of operating points. The clusters and optimal representative points are updated. If a perturbation point is determined to be unstable or infeasible, it is marked as a "high-risk condition" and repeated trials are prohibited.

[0353] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A pump set energy-saving control method based on discrete operating point clustering search optimization, characterized in that, Includes the following steps: Step S1: First, acquire pump set operating data based on sensors, including total flow rate, outlet head, and effective power of a single pump; based on historical flow time series data, predict the target flow rate using a time series prediction model. and determine the target lift. ; Step S2: Under the premise of satisfying the water supply constraints, apply a disturbance to the frequency of any one or more pumps in the pump set, and collect discrete operating points under different frequency combinations. ; in: It is the frequency of the m-th pump at the i-th operating point; It is the total water supply flow rate of the pump set under the i-th operating condition; It is the total head of the pump unit under the i-th operating condition; It is the total power of the pump unit under the i-th operating condition; Step S3: Perform cluster search optimization based on discrete operating points to obtain candidate clusters that meet the target requirements; Step S4: Within the candidate cluster, using power-to-flow ratio, pump efficiency, power consumption per unit head, frequency sensitivity, operational stability, and data confidence as characteristics, a multi-index comprehensive evaluation model is constructed through normalization and adaptive weight calculation. Points within the cluster are scored, and those with higher scores are selected as representative points, thus obtaining the representative point set. ; Step S5: Based on the representative point set The optimal operating point is selected as the representative point that best meets the target requirements and has the lowest adjustment cost. The optimal search is performed by combining the cost of operating condition changes, and the operating scheme that meets the flow rate and head constraints and has the lowest energy consumption is selected; the cost of operating condition changes includes pump start-up and shutdown differences and frequency offset distance.

2. The pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 1, characterized in that, Step S3 includes the following steps: Step S31: Clustering and Grouping; Based on the flow-head characteristics, cluster the discrete operating points and divide all discrete operating points into K clusters to obtain a set of clusters. ; Step S32: Initial feasibility screening at the cluster level; perform hard screening at the cluster level based on the maximum water supply capacity constraint; use the cluster center / cluster boundary / representative point information within each cluster to screen out clusters that do not meet the target requirements. Clusters that meet the target requirements are formed. Step S33: Obtain the priority score by weighted summation of cluster center distance, coverage and sample density; then, perform soft screening based on the priority score to select the top n clusters with the highest priority scores to obtain candidate clusters that meet the target requirements.

3. The pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 2, characterized in that, In step S31, after clustering and grouping, intra-cluster preprocessing is performed, including the following steps: (1) Based on IQR statistics, remove operating conditions where flow rate and power are abnormally biased; (2) Eliminate working conditions that are not feasible based on physical constraints; (3) Calculate the variance of flow rate and head within the cluster respectively, perform steady-state detection based on threshold, and screen operating points.

4. A pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 2 or 3, characterized in that, Step S32 includes the following steps: Step S321: Calculate any cluster In traffic Yangcheng Extreme values ​​in a dimension; (1) First, calculate the cluster In traffic mean in dimensions : ； (2) Subsequently, the clusters are calculated. Yangcheng mean in dimensions : ； (3) Determine the cluster center : ， (4) Through clusters exist , Extreme value representation clusters in dimensions boundary : ; in: Cluster The number of samples included; For clusters Internal Samples exist Values ​​in a dimension; Representative cluster Internal Samples exist Values ​​in a dimension; , Clusters exist Minimum and maximum values ​​in each dimension; , Clusters exist Minimum and maximum values ​​in each dimension; Step S322: If or Then remove the cluster. Otherwise, retain the cluster. .

5. The pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 4, characterized in that, Step S33 includes the following steps: Step S331: Define the standardized Euclidean distance The spatial difference between the cluster center and the target requirement is quantified; ； in: , These are the scale normalization parameters; Step S332: Define intra-cluster coverage, which measures the proportion of samples in a cluster that meet the target requirements; ； in: For clusters Simultaneously satisfy , The number of samples required for each dimension; , The degree to which the cluster covers the target requirements; Step S333: Constructing a cluster Priority score ; ； in: As a cluster density normalization index; These are the weighting coefficients; The hyperbolic tangent function is used to... Mapped to interval; Step S334: Filter to obtain the top n clusters with higher priority scores.

6. The pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 1, characterized in that, Step S4 includes the following steps: Step S41: Construct an index vector for each operating point based on multiple indicators. And perform normalization processing; in: Energy efficiency ratio; For the overall efficiency of the pump set; Power consumption per unit head; Gain per unit frequency; For operational stability index; Step S42: Determine the weight of each indicator; (1) Determining PCA weights based on variance contribution rate ; (2) Combined with Shannon entropy weight correction get ; ； in: For custom parameters; The index weights are determined based on Shannon's entropy weight method. Step S43: Local nonlinear fitting and stability surface analysis; Step S431: Based on the intra-cluster data, firstly, a power surface is constructed as the energy consumption constraint model for the operating condition region, and then an energy efficiency surface is derived from it. Step S432: Calculate the energy efficiency residual for each operating point. : ； in: For based on (Q) i P i The predicted power at the i-th operating point is obtained by fitting the power surface; Step S433: Stability analysis based on derived energy efficiency surface; Calculate the gradient magnitude at each operating point. : ； in: It is a gradient operator; Based on (Q) i P i The energy efficiency at the i-th operating point is obtained by fitting the energy efficiency surface; Step S434: Final construction of stability score : ； in: These are the weighting coefficients; Step S44: Determine representative points within the cluster based on multi-model fusion decision; Step S441: Construct a multi-indicator comprehensive evaluation model and calculate the comprehensive score: ； in: This is an empirical coefficient; For the j-th index at the i-th working condition point The normalized value; Step S442: Based on the formula for comprehensive scoring, calculate the comprehensive score set of the working conditions within the cluster, and remove the working conditions that are 30% lower than the average value of the comprehensive score set; Step S443: Sort Score_i from high to low, extract the top 3 cluster points, perform dynamic operating condition consistency re-check, and take the point with the highest consistency score as the representative point.

7. A pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 1 or 6, characterized in that, Step S5 includes the following steps: Step S51: Calculate the distance across dimensions; (1) Calculate the distance to the open state Cost of changing the start-up and shutdown of the quantization pump; ； ； ； in: This is the pump unit's start-up state vector from the previous moment; For the first The start / stop status of the pump at the previous moment; For the first The start / stop status of the pump at the previous moment; This represents the start-up state vector of the point pump unit; As a representative point The start / stop status of the pump; As a representative point The start / stop status of the pump; m is the number of pumps included in the pump set; (2) Calculate the frequency distance Quantify the magnitude of frequency change; ； ； ； in: This is the frequency vector of the pump unit at the previous moment; For the first The operating frequency of the pump at the previous moment; This represents the frequency vector of the point pump group; As a representative point Operating frequency of the pump; The global standard deviation of the pump set operating frequency; Step S52: Calculate the total working distance; introduce weighting coefficients. The total working condition distance is obtained by weighted fusion of distances in each dimension. : ； Step S53: Based on total working distance Define similarity weights : ； in, ; Step S54: Construct representative points Weighted composite score ; ； ； ； ； in: As a representative point Requirements for target operating conditions The suitability score ; These are the target start-up state vector and the target frequency vector of the pump unit, respectively. Enable state matching; For frequency adaptation; The attenuation coefficient; The weighting coefficients for the fit score. ; Step S55: Represent the set of points within the cluster In the middle, a weighted comprehensive score is selected. The highest representative point is taken as the optimal operating condition point.

8. The pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 1, characterized in that, In step S2, a disturbance is applied when any one of the disturbance triggering conditions is met; wherein the disturbance triggering conditions include: (1) Data sparsity: If the number of operating points within a certain flow-head range is less than the threshold If so, perturbation sampling needs to be triggered; ； (2) High model uncertainty: If the time series prediction model in step S1 has a prediction standard deviation of a certain operating point, Exceeding the threshold This triggers a disturbance: ； (3) Excessive deviation between prediction and actual values: If the difference between the real-time measured flow rate and head and the model prediction exceeds the threshold. If the model fails, new points need to be collected. ； in: This represents the actual traffic volume. For predicting traffic flow; For actual head; To predict head.

9. The pump group energy-saving control method based on discrete operating point clustering search optimization according to claim 8, characterized in that, In step S2, the intensity of the applied disturbance includes: (1) Low-intensity disturbance: The amount of disturbance to the single pump frequency based on the current value. Duration ; (2) Medium-intensity disturbance: The two pumps are adjusted complementaryly, and the disturbance amount of the single pump frequency based on the current value. Duration ; The safety constraints for applying the disturbance include: Pump frequency: ; Lower limit of export pressure: ; If a pressure deviation is detected If there is a sudden change in flow or power, the system will immediately roll back to the previous safe frequency combination. in: This indicates the pump set outlet head collected in real time during the disturbance execution process; The minimum frequency fixed for the variable frequency pump; The maximum frequency fixed for the variable frequency pump; This represents the lower limit of export pressure. The target head set for the dispatching system; This is the maximum permissible safety deviation threshold.

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