Abstract: The constant pressure variable frequency negative pressure-free water supply system is the most widely used new generation of energy-saving water supply system in residential communities in my country. This paper analyzes and calculates the performance of the constant pressure variable frequency negative pressure-free water supply system from the perspective of systems thinking and using the principle of similarity. It finds that it is not energy-saving. This is caused by the structure of the system. This paper proposes three water supply systems with structural energy-saving attributes. Keywords: Variable frequency water supply system, similarity principle, systems thinking, energy saving 1 Introduction The constant pressure variable frequency negative pressure-free water supply system is an energy-saving water supply system promoted by the Ministry of Construction in 2003. The main working principle of this device is to transform the open water tank of the community water supply system into a closed water tank with a smaller volume, and install a vacuum eliminator VE on the water tank to eliminate the negative pressure in the tank during peak load, thereby creating a direct suction effect on the municipal tap water network to meet the requirements of safe operation of the tap water network, as shown in Figure 1. The vacuum eliminator is actually a pressure window device that keeps the pressure P0 in the tank following the changes in the tap water network supply pressure, that is, changing between 0 and the normal pressure of the municipal tap water network. When the pressure inside the tank is below the lower limit, the vacuum eliminator opens, allowing air to enter the tank; when the pressure inside the tank is above the upper limit, the vacuum eliminator opens, releasing some air from the tank. That is, the vacuum valve only opens when the pressure inside the tank is below the lower limit or above the upper limit, allowing for air intake or exhaust. If the pressure inside the tank is between the lower and upper limits, the vacuum valve is closed. Since the head P0 of approximately 20 mH2O from the municipal water supply network is not lost during water intake in the community, the variable frequency pump P1 of the community water supply system can reduce its head by approximately 20 mH2O during community water supply, thus achieving energy-saving water supply. The performance of this system is analyzed below from a systems thinking perspective. [align=center] Figure 1 Flowchart of the Community Constant Pressure Variable Frequency No-Negative Pressure Water Supply System[/align] 2 Performance Analysis of the Constant Pressure Variable Frequency Water Supply System under Partial Load The flowchart of the constant pressure variable frequency no-negative pressure water supply system is shown in Figure 1. It belongs to an open direct-flow water system, where building n is the highest and furthest point in the community, and is the most unfavorable water point in the community. In the design of water supply systems, the most unfavorable water usage point is required to have a water supply head of 3-5 mH2O. Therefore, the head ΔPp0 of the water pump in the design operating condition is determined by formula (1), the effective power consumption Wpe0 of the water pump in the design operating condition is determined by formula (2), the total power consumption Wpt0 of the water pump in the design operating condition is determined by formula (3), and the total power consumption saved by the water pump in the design operating condition Wpset0 is determined by formula (4): Where: ΔPp0—head of the water pump in the design operating condition, Pa; S0—comprehensive resistance coefficient of the water supply pipeline in the design operating condition from the water pump outlet, Pa×s2/m6; H0—natural height of the most unfavorable water usage point relative to the water pump inlet, also called natural head, mH2O; P0—water supply head of the municipal tap water network in the design operating condition, Pa; Wpe0—effective power consumption of the water pump in the design operating condition, W; Wpt0—total power consumption of the water pump in the design operating condition, W; ηps0 — Shaft efficiency of the pump under design conditions, %; ηm0 — Shaft efficiency of the pump motor under design conditions, %; ηinv0 — Efficiency of the pump inverter under design conditions, %. Wpset0 — Total power consumption saved by the pump under design conditions, W. The design condition is the condition under which the water supply system operates at its maximum water consumption. During different water usage periods, the water supply head P0 of the municipal water supply network fluctuates, being lower during peak periods and higher during off-peak periods. This causes the operating point of the pump in the community's constant pressure variable frequency water supply system to drift with the fluctuations in the network's water supply head. According to the water company's requirement to ensure the safe operation of the municipal water supply network, the community's water supply system must not affect or interfere with changes in the water supply pressure P0. This adds considerable difficulty to utilizing the pressure energy of the fluctuating water supply head P0 and ensuring that the variable frequency pump operates at its highest efficiency point at all times to achieve significant energy savings. However, to achieve this goal, a deep understanding of the system's structure and performance is essential. The following analysis examines the characteristics of the constant pressure variable frequency water supply system without negative pressure when tracking changes in water consumption in the community, especially its energy-saving characteristics, to deepen the understanding of the system. According to the principle of hydroelectric analogy, when the static pressure of the water supply network increases from P0 to P1 at the rated flow rate L0, the calculation formulas of the Gilchoff water pressure law for the most unfavorable water point of the system are (5) and (6): In the formula, the subscript "0" represents the design state parameter, and the subscript "1" represents the state parameter when the static pressure of the network is P1. ΔPp—Pump head, Pa; Sst—Total comprehensive resistance coefficient of the pipeline system from the pump outlet, Pa×s²/m⁶; Ss0—Equivalent total comprehensive resistance coefficient of the (n-1) resistance elements with unchanged geometric parameters before the most unfavorable water supply point from the pump outlet, Pa×s²/m⁶; L—Pump flow rate, m³/s; Si—Comprehensive resistance coefficient of the i-th resistance element in the water supply path at the most unfavorable water supply point, Pa×s²/m⁶; Li—Flow rate through the i-th resistance element in the water supply path at the most unfavorable water supply point, m³/s; Sn—Comprehensive resistance coefficient of the end tap in the water supply path at the most unfavorable water supply point, Pa×s²/m⁶; Ln—Flow rate through the end tap at the most unfavorable water supply point, m³/s. In formulas (5) and (6), we specifically highlight the water supply head of the faucet at the most unfavorable water point because the combined resistance coefficient Si[i=1～(n-1)] of the (n-1) resistance elements before the faucet at the end of the water circuit at the most unfavorable water point remains constant. Only the combined resistance coefficient Sn of the faucet at the most unfavorable water point changes with the faucet opening. Under design conditions, the pipeline characteristics formed by the (n-1) resistance elements with constant combined resistance coefficients before the faucet at the end of the water circuit at the most unfavorable water point are shown as the R00 curve in Figure 2. After adding the water supply head of the faucet at the most unfavorable water point under design conditions, the resistance characteristic curve of the water supply system becomes R0. The design point is A0, the design flow rate is L0, and the intersection of the R00 curve and the constant flow curve L0 is B. Then, the pressure difference between point A0 and point B is the water supply head of the faucet at the most unfavorable water point under design conditions, as shown in Figure 2. [align=center] Figure 2 Performance curve of constant pressure variable frequency water supply pump without negative pressure[/align] According to the principle of centrifugal pump, there is a relationship between the pump head ΔPp and the outer circle linear velocity u2 of the pump impeller as shown in formula (8): Where: kp — a constant related to the pump's geometric parameters and flow rate; ρ — the mass density of water, kg/m3; u2 — the outer circle linear velocity of the pump impeller, m/s. When the static pressure of the water supply network is P0 and P1, the pump speed and flow rate remain unchanged. Therefore, from formula (8), we can derive that (5) = (6). From this relationship, we can derive formula (9): As can be seen from formula (9), the static pressure increment (P1-P0) of the water supply network is added to the taps at all water points in the water system. In order to obtain the same flow rate when the tap is turned on as usual, each tap must be turned on slightly. The expression in formula (9) is () > 0. That is to say, the tap must be turned on slightly to increase the throttling loss in order to consume the pressure head added to the tap. If the water supply head on the tap is too high, it is easy to cause water hammer effect and noise in the water supply system, which will reduce the water supply quality and the safety of the system. From the perspective of energy saving, the constant pressure variable frequency water supply system only transfers the static pressure of the water supply network to the tap for throttling loss. This is not substantially different from the ordinary constant pressure variable frequency water supply system which throttles the static pressure of the water supply network in the inlet pool. It does not achieve the original intention of using the static pressure of the water supply network for energy saving. In addition, the constant pressure variable frequency water supply system only seals the inlet tank and changes the structure of the vacuum eliminator during construction. The operation of the parallel water pumps in its core part still adopts the common method of constant pressure variable frequency water supply system - one variable and multiple fixed. The author analyzed two major disadvantages of constant pressure variable frequency water supply system in the literature [1]: First, the variable frequency water pump does not run at the same point when the working condition changes, resulting in low efficiency; second, when the working condition changes, most of the static pressure head is added to the faucet and is lost due to throttling, resulting in large water supply loss and also reducing the water supply quality and safety of the water supply system. The constant pressure variable frequency water supply system does not fundamentally change the non-energy-saving attribute of the constant pressure variable frequency water supply system in its design. Instead, it introduces the static pressure of the water supply network into the water supply system and adds it to the faucet of the system, which amplifies the inherent disadvantages of the constant pressure variable frequency water supply system and still maintains the non-energy-saving attribute of the structure. In order to overcome the inherent disadvantages of the constant pressure variable frequency water supply system, it is necessary to start by changing the structure of the water supply system. 3. Structural Modifications of Constant Pressure Variable Frequency Water Supply Systems To gain a clearer understanding of the characteristics of constant pressure variable frequency water supply systems and to clarify the essence of achieving the safety and energy-saving goals of water supply systems, we further analyze the performance of constant pressure variable frequency water supply systems using the principle of hydroelectric analogy. Both water and electrical systems operate according to the law of conservation of energy and fundamental physical principles, and are essentially the same; hence the principle of hydroelectric analogy. According to the principle of hydroelectric analogy, water pressure is equivalent to voltage, water potential is equivalent to electric potential; water resistance is equivalent to electrical resistance, water resistance elements with unchanged geometric dimensions are equivalent to fixed resistors, and regulating valves with changing geometric dimensions are equivalent to variable resistors; water flow is equivalent to current. Thus, we can use familiar circuit principles, such as Ohm's law, Gilchrist's loop voltage theorem, and Gilchrist's contact current theorem, to calculate the water circuit. Although the principle of hydroelectric analogy provides us with a very powerful tool for analyzing water circuit performance, we must also be clearly aware that water circuits and electrical circuits are significantly different. The most significant difference is that the fixed water resistance in a water circuit is not its resistance value but a constant comprehensive resistance coefficient, while the resistance value of a fixed water resistance is variable. This is something we must pay special attention to when applying the principle of hydroelectric analogy. [align=center] Figure 3 Hydroelectric analogy diagram of constant pressure variable frequency negative pressure water supply system[/align] Using the principle of hydroelectric analogy, the constant pressure variable frequency negative pressure water supply system in Figure 1 is equivalent to the electrical circuit system in Figure 3. As can be seen from Figure 3, the transformer source E1, which is equivalent to the static pressure P0 of the pipeline network, and the constant pressure converter source E1, which is equivalent to the head ΔPp0 of the constant pressure variable frequency water pump, are connected in series and superimposed to act on the circuit system. The equivalent circuit of the water circuit at the most unfavorable water point under different operating conditions is given by the Gilchoff voltage law formula (10) and (11): From formula (12), it can be seen that the voltage fluctuation of the equivalent transformer source is added to the equivalent variable resistor Rn at the end. In order to keep the current at the most unfavorable end constant at In0, the resistance value Rn1 should be increased to eliminate the voltage increase. This conclusion is exactly the same as the conclusion of the analysis results of the water circuit system. In the design of modern water supply systems, the requirements for water supply systems are high water quality, high safety, and energy saving. The specific manifestation of this requirement in the water system is that, regardless of any time or operating condition, the water supply head at the pressure transmitter Ps3 at the most unfavorable water point (as shown in Figure 1 and Figure 3) is constant at (3~5) mH2O. If this condition is met, the requirements for the water supply system can be satisfied. However, current designers of constant pressure variable frequency negative pressure water supply systems inappropriately extend concepts applicable only to water pumps to the entire water supply system. They are unclear about or completely unaware of the system science principles that require a fundamental change in the performance of the water pump after it is integrated into the system. This results in uncoordinated operation between subsystems of the water supply system, leading to a structurally flawed system. Consequently, at the overall level, the water supply system naturally lacks the structural attributes of high water quality, safety, and energy efficiency. In a constant pressure variable frequency negative pressure water supply system, the static pressure of the pipeline network, acting as a pressure source, and the pressure drop and flow rate at the most unfavorable water tap are all randomly changing. The constant pressure variable frequency water pump, in its equivalent circuit, is a constant pressure variable current source. It can only track the system's fluctuating flow rate at a constant pressure, but cannot track the randomly changing water supply pressure Ps3 at the most unfavorable water tap. The random variation of Ps3 is caused by the random changes in the static pressure P0 of the pipeline network connected in series with the water system and acting on the entire system, as well as the pressure drop and flow rate at the most unfavorable water tap. The system's practice of tracking flow rate changes without tracking pressure changes results in an energy-inefficient structure and poor water quality and safety in the water supply system. Having identified the root causes of these issues in the constant pressure variable frequency water supply system, we can address them by modifying the system structure to achieve energy efficiency, high water quality, and high safety. There are three types of variable frequency water supply system structures with high energy saving, high water quality and safety: (1) The pressure signal is collected from the pressure transmitter Ps3 set in front of the tap at the most unfavorable water point in the water supply system, so that the variable frequency water pump tracks the change of Ps3 in the range of (3~5) mH2O. The system can automatically follow the change of Ps3 caused by random factors. The core of the system, the variable frequency water pump, operates in the state of variable pressure and variable flow, basically in the highest efficiency condition. Since Ps3 changes in the range of (3~5) mH2O, according to the principle of communicating vessels, the water supply pressure of all taps in the water supply system is basically in the design state at any time, without large fluctuations. At the same time, the static pressure P0 of the pipeline network can be fully utilized, so that the system can truly achieve the requirements of energy saving, high water quality and safety. However, this requires the system structure to be fully variable frequency, the control system to be wirelessly networked, and the system has the disadvantage of high cost; (2) Using software to control Ps3 to be basically constant, but the mathematical model relied on is a mathematical model that is comprehensively and statistically fitted from the historical data of the measurement parameters, and the control accuracy is relatively poor. Therefore, compared with scheme (1), it is inferior in terms of energy saving, water supply quality and safety, but the structure of the control system is greatly simplified and it is also convenient for the transformation of the old system. This system structure scheme also requires the water pump to be fully variable frequency. (3) Using a high-level water tank, the interference of drastic changes in the water volume of the water system and the efficient water supply operation of the water pump are isolated. In order to make full use of the static pressure P0 of the pipeline, the water pump of the water supply system must also be fully variable frequency. The three structural schemes of the water supply system that make full use of the water supply head of the tap water supply pipeline to achieve a significant energy saving effect of the water supply system are all feasible. However, the water pumps in the system of schemes (1) and (2) need to undertake the task of tracking the drastic random changes in flow rate, the operating conditions are large, and the overall efficiency is relatively low compared with scheme (3). In the system constructed by scheme (3), the water pump does not undertake the task of tracking the drastic random changes in the flow rate of the system. The variable frequency pump only deals with the random changes in the static pressure P0 of the pipeline network. It is relatively simple and the water pump can maintain high efficiency operation. It is the scheme with the best energy saving effect among the three schemes. 4 Conclusion (1) Theoretical proof shows that the constant pressure variable frequency water supply system has the attributes of poor energy saving, poor water supply quality and safety in terms of structure; (2) The article proposes three water supply systems with good energy saving, good water supply quality and safety, and easy engineering implementation.