# Model-Based Assessment of Energy Efficiency in Industrial Pump Systems: A Case Study Approach
## 1 Introduction
### The Need for Credible Energy-Savings Assessments  
Accurately estimating the potential energy savings from upgrading pump drives is particularly difficult with VSDs compared to mains-fed motors. It is important to evaluate the energy consumption of the current system over a period of time and compare it to the projected efficiencies of the upgraded system. This approach ensures an accurate estimate of the energy consumption of the upgraded system. General assessments based on flat-rate assumptions can lead to incorrect estimates and counterproductive results [7]. On the other hand, more accurate modelling of pump characteristics for variable-speed operation using affinity laws and the assumption that efficiency is maintained based on this does not lead to credible results either.  
Although many authors have recently focused on the energy efficiency of pump drives, a systematic approach to modelling the entire VSDP with detailed consideration of all its components is still difficult to find. Most research focuses on a specific component of the VSDP, e.g., the design of the impeller blades [14], the shape of the inlet pipe [15], or the selection of the optimal motor type [16; 17; 19; 29]. Many of these studies also consider only limited operating points and not the entire operating range, where efficiency can vary significantly [16; 17]. This fragmented approach often fails to capture the complex interactions within the entire system. Some recent studies have investigated the efficiency of the converter, motor, pump, and the entire system at different water flows [26], or compared energy consumption between IM and SRM motor types at different speeds and loads [18; 19; 29]. However, these studies do not comprehensively cover several pump types simultaneously and do not provide a complete map of operating efficiency. The present work aims to fill these gaps by systematically modelling the complete VSDP system, evaluating all key components under a wide range of operating conditions, and providing detailed efficiency comparisons for different motor and pump configurations.  
To address this challenge, we have developed a sophisticated method for modelling the efficiency characteristics of VSDs. This method takes into account different motor efficiency classes and modern pump specifications from current catalogues. The main problem is that VSDP characteristics cannot be easily modelled due to the lack of data for variable-speed operation. In addition to the rated efficiencies, manufacturers of electric motors generally specify discrete efficiency values in their catalogues at some partial-load points (e.g., 0.5\(\cdot\)\(T_{r}\), 0.75\(\cdot\)\(T_{r}\)) for operation at mains frequency in accordance with IEC 60034-2-1 [35; 36; 37]. It is quite difficult to find a manufacturer that provides a motor efficiency curve for the entire load range for operation at mains frequency [38]. It is even more difficult to find manufacturer data on losses if the motor is used in variable-speed drive for the seven operating points required by Regulation (EU) 019/1781 [39]. Similarly, pump manufacturers generally only specify efficiency values at a few discrete points on the \(Q\)-\(H\) performance curves, namely at the speeds at which mains-fed IMs rotate at the rated load [33; 40]. The efficiency curve of a pump can practically be called up via the \(Q\)-\(H\) and shaft power curves. In this way, it is only possible to determine the efficiencies at the speeds at which mains-fed IMs with different numbers of pole pairs rotate and for which the pump manufacturers specify the characteristic data. Of course, determining the efficiency of a VSDP system also requires the most accurate possible data on efficiency at medium speeds and loads, both for the motor and for the pump. Fortunately, one manufacturer has recently updated its drive composer database to include more detailed data for high-efficiency motors, allowing us to model the speed and load characteristics of motors more accurately.