Introduction: Unlike DC motors, asynchronous motors do not use ideal no-load speed and speed drop to express speed. Instead, speed is characterized by synchronous speed n1 and slip S. However, as a type of electric motor, the speed of an asynchronous motor is also composed of ideal no-load speed n0 and speed drop Δn. This is determined by the general laws of electric motor mechanical characteristics and is a common expression of electric motor speed. The synchronous speed of an asynchronous motor is the rate of change of the main magnetic field, not mechanical motion, and cannot be simply considered as the ideal no-load speed. Slip is the relationship between the actual speed and the synchronous speed, and is unrelated to the ideal no-load speed; it cannot be equated with speed drop. Therefore, it is crucial to deeply analyze the ideal no-load speed, speed drop, and their relationship with synchronous speed and slip of the asynchronous motor, and to find the laws governing speed regulation. Perhaps influenced by the above issues, current AC speed regulation theory largely believes that the solution to speed regulation of asynchronous motors lies in changing the synchronous speed, while dismissing speed regulation by changing the slip, arguing that only the former can achieve high-efficiency and high-performance speed regulation. For example, Reference 3 states: "Variable frequency speed control is fundamentally different from variable slip speed control. It can maintain a finite slip rate from high speed to low speed, thus variable frequency speed control has high efficiency, wide range, and high precision speed control performance. It can be considered that variable frequency speed control is a relatively reasonable and ideal speed control method for AC motors." However, in-depth research and practice show that the speed control efficiency and performance of asynchronous motors are not determined by synchronous speed and slip rate. The only characteristic of high-efficiency speed control is changing the ideal no-load speed; synchronous speed is not the only determining factor of the ideal no-load speed. Variable slip speed control schemes also involve changing the ideal no-load speed for high-efficiency speed control. This paper raises discussion points to this issue, hoping to attract the attention of relevant parties. The asynchronous motor speed formula is questioned. A formula is a mathematical expression of objective laws; it can only arise from existing laws and formulas, not from artificial definitions. The classical asynchronous motor speed formula is established as follows. First, define the slip rate as S = (n1-n)/n1 (1) where: n1 is the synchronous speed and n is the motor speed. Obviously, Equation 1 is a definition rather than a formula. From Equation 1, after algebraic transformation, we get ·(1-S) (2). It can be seen that Equation 2 is still a definition, which is just another expression of Equation 1. Also, since (3) is a formula, substituting Equation 3 into definition 2, we get ·(1-S) (4). We notice that Equation 4 is not essentially different from Equation 2. Although Equation 3 is a formula, it only plays the role of parameter transformation and does not change the definition properties of Equations 1 and 2. Therefore, the speed formula 4 we think is just an artificial definition. Before it has been formalized, it cannot be called a formula. The general formula for motor speed and the asynchronous motor speed formula should be derived strictly according to the relevant theorems and formula derivations. As a type of motor, the asynchronous motor speed must follow the general law of motor speed. According to dynamics, the speed of an electric motor can be generally expressed as Ω=PM/M (5) where: Ω is the angular velocity of the electric motor, mechanical power is the electromagnetic torque. According to the conservation of energy conversion in the motor, the power equation of the rotor (or armature) of the electric motor under speed regulation is ΣPem-Σ△P2 (6) where: ΣPem is the net electromagnetic power, Σ△P2 is the net power loss. Therefore, the motor speed is Ω=ΣPem/M-Σ△Ωok-ΔΩ (7) where: Ω=ΣPem/M is called the ideal no-load speed under speed regulation, ΔΩ=Σ△P2/M is called the speed drop. It can be seen that the motor speed can be expressed as the difference between the ideal no-load speed and the speed drop. Among them, the ideal no-load speed is determined by the net electromagnetic power of the rotor (or armature), and the speed drop is determined by the net power loss. There are two methods for speed regulation of the motor: changing the ideal no-load speed and the speed drop. The synchronous speed of the asynchronous machine is not directly and necessarily related to the motor speed. Ideal no-load speed and net electromagnetic power The meaning of ideal no-load speed is: the speed that can be obtained by converting all the electromagnetic power of the motor into mechanical power under the ideal state of no loss. Since this assumption can only be realized under ideal no-load conditions, it is called ideal no-load speed. Under torque balance conditions, ideal no-load speed depends on and is proportional to the net electromagnetic power of the rotor (or armature). Considering the general situation of speed regulation, the net electromagnetic power should be Σ±Pes (8) where Pem is the electromagnetic power transmitted by electromagnetic induction and Pes is the additional power of electromagnetic conduction for rotor speed control. When Pes is fed into the rotor from the outside, the sign is positive, which will increase the net electromagnetic power of the rotor and realize super-synchronous speed regulation. When Pes is fed out from the rotor, the sign is negative, which will decrease the net electromagnetic power of the rotor and the speed regulation is low synchronization. The ideal no-load speed determined by Equation 8 is Ωok=(Pem±Pes)/M (9) Equation 9 shows that the ideal no-load speed of the motor during speed regulation can be changed by controlling Pem and Pes. Equation 9 can be written as Ωok=Pem/M±Ω0 ±Ωk (10) where Ω0 is the ideal no-load speed under the action of Pem alone, and ΩK is the additional ideal no-load speed caused by Pes. If the sign of ΩK is not considered, Ωk=Ω0 – Ω(Ω0 – Ωok)/ Ω0·Ω·Ω0 (11) where (Ω0 – Ωok)/ Ω(n0-n)/n0 (12) is called the slip ratio. Thus, Ωok=(1±SK)Ω and nok=(1±SK)n0 (13) For the ideal no-load speed Ω0 under natural operation, according to the electrical engineering, Ω0 =Pem/M (14) and Φ2 (15) ΦmI2COSΦ2 (16) We can get Ω0=2π converted to speed per minute π·Ω (19) This shows that the ideal no-load speed of the asynchronous machine under natural operation is equal to the synchronous speed. Substituting Equation 18 into Equation 12, the ideal no-load speed of the asynchronous machine is (1±SK)·60f1/p (20). The speed drop and static error rate speed regulation state speed drop is ΔΩ=Ωok-Ω or Δ(nok –n)/nok · (21) where j= (nok –n)/nok is called static error rate. This formula shows that the speed drop is proportional to the static error rate. It can be proved that the net loss power is also proportional to the static error rate, that is, ΣΔP2=jΣPem (22). Therefore, the net loss power is also called static error power. Similarly, it can be proven that (23) the additional electric power is also called electric slip power. Reviewing the slip power in motor science, from (n1-n) we can get that the slip power refers to the difference between electromagnetic power and mechanical power. The expression does not distinguish the components of slip power, thus confusing the different effects of electrical power and loss power on motor speed. Obviously, electrical slip power affects the ideal no-load speed, while static slip power affects the speed drop. The former has high speed regulation efficiency and is energy-saving, while the latter reduces speed regulation efficiency and is energy-consuming. Moreover, the mechanical characteristics of speed regulation are completely different. The former is a family of parallel curves that change the ideal no-load speed point, while the latter is a family of converging curves that keep the ideal no-load speed point unchanged. It can be seen that it is impossible to accurately evaluate speed regulation performance by simply using slip rate and slip power. For example, the rotor series resistance and cascade speed regulation of asynchronous machines both change the slip rate, but the speed regulation efficiency and characteristics are significantly different. Conclusion ① The asynchronous machine speed formula can be expressed by equations 20 and 21 as (1-j)·(1±SK)·(1-j) (24) ② Any high-efficiency speed regulation must change the ideal no-load speed through net electromagnetic power. Whether the synchronous speed changes or not is not necessarily related to the speed regulation efficiency. ③ Slip should be distinguished into electrical slip and static slip. The former affects the ideal no-load speed, while the latter affects speed drop. Speed ​​regulation by changing the electrical slip is highly efficient, while speed regulation by increasing the static slip is inefficient. ④ The essence of motor speed regulation lies in power control. Any speed regulation method must achieve speed regulation by controlling the power of the motor shaft.