A study of the impact of voltage sag on sensitive loads at low-voltage distribution areas

Under the background of the dual carbon goal and the new power system, the power system becomes more complex and diverse, and voltage sag events caused by short-circuit faults, overloads, switching operations, large motor starting, and distributed generation access are more frequent. On the other hand, with the increasing sensitivity of low-voltage distribution network electrical equipment to power quality, especially for precision process control equipment using computers, power electronics, and automation technology, new energy generating units, and electric vehicle charging facilities, voltage sag accidents will cause difficult-to-estimate losses in equipment production and operation, and frequent voltage sag events have become one of the main power quality problems affecting reliable power supply and normal equipment operation. To address this problem, this paper analyzes the impact of voltage sag on low-voltage substation loads from a mechanism perspective, establishes a voltage sag tolerance curve for electronic appliances through experimental research, and simulates and verifies the effectiveness and correctness of the method in this paper using a 3 MW-rated induction generator connected to the distribution network as an example.


Introduction
Strong growth in precision manufacturing, such as semiconductors, has led to an increase in the use of precision equipment in manufacturing.A number of these devices are highly sensitive to voltage sags [1-5]   , and are therefore referred to as voltage sag sensitive devices (hereafter referred to as "sensitive devices"), including AC contactors (ACC), personal computers (PC) [6] , etc.In low-voltage areas, voltage sags are the primary cause of sensitive loads failing to function properly, and numerous investigations have shown that when voltage sags occur in the relevant equipment, the process control system may be disrupted, resulting in interruptions to production lines and significant economic losses to the users [7][8][9] .In this manner, it is possible to ensure that these sensitive devices operate in a normal manner.
A great deal of research has been conducted both theoretically and experimentally by domestic and international scholars in the field of voltage sag withstanding capability for sensitive equipment.For non-linear loads powered by bridge rectifier capacitor filter circuits, including personal computers (PCs), lighting fixtures, liquid crystal displays (LCDs), photocopiers, microwave ovens, etc., the sensitivity of voltage withstand capability has been studied in terms of voltage sag magnitude and duration for PCs from the perspective of simulation, theoretical studies, and tests [10,11] .Based on an energy loss function that measures the impact of voltage sag events on sensitive equipment, Wang et al. [12] considered the voltage sag withstand characteristics of sensitive equipment and calculated the probability of failure.For induction motors, Martin et al. [13] examined the effect of input voltage sags on the variation of the operating point of induction motors under different operating conditions and calculated the limit of the operating speed the motor can withstand during voltage sags.Analytical algorithms were used to study the effects of voltage dips on induction motors [14][15][16] .The analytical algorithms for the critical cut-off times of voltage dips for induction motors and induction generators were presented [14,16] , respectively, but the effects of varying voltage dip amplitudes were not considered.
In this paper, we first introduce and analyze the concepts related to voltage sags as well as their evaluation indicators, analyze the impact of voltage sags on electric and electronic loads, and establish voltage sag tolerance curves for a variety of power-consuming devices.The specific work in this paper is as follows:  In this paper, we analyse the effects of voltage sags on sensitive electronic appliances from a mechanistic point of view.We have conducted extensive tests on different brands of computers, LCD monitors, photocopiers and microwave ovens using experimental research methods.This has allowed us to establish voltage sag tolerance curves for electronic appliances and analyse their tolerance to voltage sags. On the basis of the stable equivalent circuit for the sensor generator, the electromagnetic turning-shift curve of the sensor generator's characteristics is derived.According to the characteristic curve, the impact of the voltage suspension on the sensor motor is analyzed, the duration and critical range of the pressure suspension of the Sensing Generator are demonstrated, and the power of 3 MW is assigned to the sensor generator's access to the power distribution network as an example simulation to verify the effectiveness and correctness of this method.

Low-voltage board load effect of voltage sags
Currently, the types of low-voltage distribution terminal loads identification include at least electronic devices such as air conditioners, photovoltaics, charging piles, computers, communication base stations, and motor-driven loads, such as agricultural irrigation, municipal sewage pumps, etc.

Mechanical analysis of the impact of voltage sags on electronic devices
For electronic devices, there is an internal switch power supply with a bridge rectifier-capacitor filter circuit, mainly composed of a diode bridge rectifier, voltage regulator, and output filter capacitors.The AC power supply is converted into the voltage required for the electronic components to work through the bridge rectifier-capacitor filter circuit, so the quality of the internal power supply of electronic devices directly affects their anti-interference ability to voltage sag.Moreover, the switch power supply structure of these electronic devices is basically the same, all with a bridge rectifier-capacitor filter circuit and the same equivalent circuit as shown in Figure 1.The basic working process of this circuit is that when UAC<UDC, both diodes do not conduct, and capacitor C discharges, providing current to load R and UDC drops.|UAC|<UDC, diodes VD1, VD4, and VD2, VD3 conduct respectively, and load R is powered by the power supply.
Figure 2 shows the changes in the DC side voltage before, during, and after the voltage sag with a magnitude of 30% and no phase angle jump.The dashed line represents the AC voltage waveform, and the solid line represents the DC voltage waveform.When the input voltage sags, the capacitor begins to discharge until the voltage across the capacitor is lower than the sag voltage.Then, the AC power supply starts to recharge the capacitor, and the DC side voltage reaches a new equilibrium again.Although the internal power supply of modern electronic devices can be equivalently represented by a bridge rectifier capacitor filtering structure, their electrical characteristics differ, leading to differences in their tolerance to voltage sags.However, during voltage sags, the main reason for electronic devices' inability to function normally is due to the decrease in the DC side voltage to the minimum voltage threshold required for their normal operation.Therefore, to analyze the impact mechanism of voltage sags on electronic devices, it is necessary to combine the internal power supply and their electrical characteristics.
Taking desktop computers as an example, we will analyze the impact mechanism of voltage sags on them by combining their internal power supply and electrical characteristics.The internal power supply of a desktop computer outputs up to nine different voltages, but the most important two voltages for normal computer operation are the red+5 V and yellow +12 V.The red +5 V mainly provides the working voltage for semiconductor integrated devices such as CPU, PCI, AGP, and ISA and is the main power source in the computer.During voltage sags, due to the decrease in the DC output voltage of the internal power supply, the working status of some semiconductor materials inside the computer will be affected, and the operation of the main hardware inside the computer, such as CPU, memory, and hard disk, will be greatly affected, resulting in data loss, program errors, system crashes, and other situations.When the output voltage of the power supply drops to the minimum threshold allowed for normal operation of the voltage regulator in the computer power supply during voltage sags, the computer power supply will trip and shut down, as shown in the equivalent circuit in Figure 1.
Assuming that the computer can be equivalently represented by a constant impedance load R during voltage sags, and the computer is powered by capacitor discharge during the sag.If the DC side voltage amplitude before the voltage sag is U0, the DC side voltage becomes U t seconds after the sag occurs, and the instantaneous power is P. Then we have Equation (1): During voltage sag, the DC side voltage is: By substituting the expression of the DC side voltage into the equation, we can obtain the following expression: The relationship between voltage and duration can be obtained by transforming Equation (3) as follows: The symbol Um represents the threshold voltage that the computer can tolerate.As can be seen from Equation ( 4), the duration of the voltage sag that a desktop computer can withstand is mainly affected by the amplitude of the initial sag voltage and the threshold voltage of the computer, and is related to the RC parameters.

Analysis of the impact of voltage sags on induction generators
When a voltage sag occurs at the connection point of an induction generator IG, the induction generator will enter a sag process, and its rotor may gradually accelerate to a non-stable operating state, with a significantly increased consumption of reactive power, which can lead to voltage collapse of the power distribution network system.Therefore, studying the impact of voltage sags on induction generators is of great guiding significance for their protection settings.

Critical duration of induction generator.
During normal operation, the rotor of the induction generator is driven to rotate by the prime mover, and its mechanical torque remains constant, making the rotor speed higher than the synchronous rotating magnetic field.Therefore, the slip rate s of the induction generator is less than zero, and the direction of the electromagnetic torque rotation is opposite to that of the rotating magnetic field and the rotor rotation direction, which is a braking torque.When a voltage sag occurs, the electromagnetic torque and slip rate of the induction motor will change.To obtain the electromagnetic torque-slip characteristic curve of the induction generator, it is necessary to establish the steady-state equivalent circuit of the induction generator, as shown in Figure 3 Zm=jXm, and Zs=RS+jXs simplify the circuit to the steady-state simplified equivalent circuit of the induction generator shown in Figure 3(b).From this, the rotor current can be obtained: (b).Steady-state simplified equivalent circuit.Figure 3. Steady-state equivalent circuits of an IG before the fault occurs.
The electromagnetic torque of an induction generator is: The electromagnetic torque-slip characteristic curve of the induction generator can be obtained from Equation ( 7), as shown in Figure 4.In Figure 4, points A and B represent the stable equilibrium point and unstable equilibrium point of the induction motor, respectively, with corresponding slip values of initial slip S0 and critical slip Scrit.The electromagnetic torque of the induction generator is proportional to the square of the voltage magnitude at the stator terminal.When a voltage sag occurs at the induction generator connection point, the electromagnetic torque suddenly decreases, which causes the induction generator to accelerate due to the constant mechanical torque.If the slip of the induction generator is less than the critical slip after the voltage sag disappears, the induction generator can decelerate to a new equilibrium state.However, if the slip exceeds the critical slip, the induction generator will continue to accelerate, leading to voltage collapse in the distribution network.Therefore, the duration from the beginning of the voltage sag to the time when the slip of the induction generator increases to the critical slip can be defined as the critical duration of the induction motor.If the protection device of the generator can trip off the induction generator before the critical duration, the unstable operation of the induction motor can be avoided, and the entire network can be protected.
When the electromagnetic torque Te of the induction generator is not equal to the mechanical torque Tm, the rotor will accelerate.The first-order differential equation of the IG rotor motion can be expressed as: NESP-2023 Journal of Physics: Conference Series 2592 (2023) 012066 The symbol H represents the IG rotor's inertia constant in the equation.S represents the slip rate.The above equation can be written as an integral equation for calculating the critical duration: As shown in Figure 4, when the mechanical torque equals the electromagnetic torque, that is, Te=Tm, the initial slip rate S0 and the critical slip rate Scrit can be obtained: Equation ( 11) is a second-order polynomial equation with S as the variable.Thus, the initial slip S0 and the critical slip Scrit can be obtained by solving the equation as follows: .By substituting Equation ( 12) into ( 9), the critical duration of induction generator can be obtained:  In Figure 5, points A and B represent the stable equilibrium point and unstable equilibrium point of the induction motor, respectively, with corresponding slip values of initial slip S0 and critical slip Scrit.Te is mechanical torque before the voltage sag.Te-sag is mechanical torque after the voltage sag.For an induction generator, not all voltage dips will cause the generator to continue accelerating to an unstable state, and some events with high voltage dip amplitudes will cause the generator speed to accelerate and stabilize at a new speed, as shown in Figure 5.When a voltage dip occurs, the induction generator transitions from operating at point A to point C, where the electromagnetic torque is less than the mechanical torque, causing the generator to accelerate until the electromagnetic torque and mechanical torque balance again at point D. Once the voltage dip is cleared, the generator can return to its original equilibrium state at point A. Therefore, for events with high voltage dip amplitudes, there is no need to calculate the critical clearing time or disconnect the generator.Instead, it is necessary to find the critical amplitude of the voltage dip, above which all voltages are absolutely safe and do not require disconnection of the generator.
In Figure 5, the maximum electromagnetic torque of the induction generator during the voltage dip is Temax-sag, and there is a stable equilibrium point D where the electromagnetic torque during the voltage dip and the mechanical torque is balanced.Since Temax-sag is greater than Tm, the slip rate of the induction generator during the voltage dip will not continue to increase, and it is even less likely to reach the unstable operating point B. Therefore, if the maximum electromagnetic torque during the voltage dip satisfies Equation ( 14), there is no need to disconnect the induction generator.
By substituting Equation ( 7) into (15), the Sm can be obtained: Subsequently, the critical voltage magnitude for the induction generator can be calculated as follows: Finally, by substituting Equation (17) into Equation ( 5), the critical voltage magnitude at the stator terminal of the induction generator, US-in, can be calculated.This paper presents a voltage sag tolerance curve testing study for four types of electronic appliances: computers, LCD monitors, copiers, and microwave ovens.The curves shown in Figure 6 represent the voltage sag tolerance results of typical brand models for each appliance type.The sensitivity curves of other brand models of electronic appliances are similar to those shown in the figure .From the figure, it can be observed that the envelope curves of the tested objects, computers, LCD and copiers, are mostly within the envelope curve of the microwave oven, indicating that the microwave oven is the most sensitive appliance and has the lowest voltage sag tolerance.Furthermore, the tolerance curves of these typical devices, including the microwave oven, are all within the ITIC curve, indicating that they meet the tolerance standards of the ITIC curve.

Induction generators case study
To verify the effectiveness and correctness of the proposed method, this paper takes a 3 MW induction generator (IG) connected to a distribution network as an example and establishes a model for electromagnetic transient simulation analysis in PSCAD/EMTDC.The detailed parameters of the IG are shown in Table 1.
Taking the rated value of the IG itself as the reference value, the short-circuit impedance at the connection point of the induction generator is Rext+jXext=(0.0125+j0.125)pu, and the voltage level of the generator connected to the distribution network is 0.69 kV.The equivalent reactance of the system, Xth, is 1/100 times the rated impedance of the generator, with Xth/Rth=10.The network connection of the single-machine distribution network calculation example is shown in Figure 7.During the voltage sag, the mechanical torque of the induction generator remains constant (Tm=-1), and the slip rate before the voltage sag when the IG is operating normally is s=-0.0052.The mathematical model of the IG can be found in Kundur and Sybille et al.'s works [17,18] .
During the simulation of the testing system, after the induction motor started and reached a steady state, the voltage sag amplitude was gradually adjusted from 100% of the rated value to 0%, while maintaining balanced three-phase voltages.The calculation and simulation results for the critical amplitude of voltage sag for the induction generator are shown in Table 2.The relative error between the calculation and simulation results presented in Table 2 is less than 1%, indicating the effectiveness and accuracy of the proposed method in this study.

Conclusion
Building on research on voltage sag from both domestic and international sources, this paper investigates the impact of voltage sag on low-voltage distribution loads and induction generators.The paper provides a mechanistic analysis of the impact of voltage sag on sensitive equipment such as AC contactors, electronic appliances, and lighting fixtures, and develops voltage sag tolerance curves for such sensitive equipment.
The sensitivity of voltage sag is determined by the characteristics of the equipment and the voltage sag characteristic.The paper tests different types of sensitive equipment, such as AC contactors, electronic appliances, and lighting fixtures, and finds that their voltage sag tolerance curves vary widely due to differences in their electrical characteristics and materials.The paper also compares different brand models of the same equipment and finds that differences in electrical parameters and manufacturing processes also lead to differences in their voltage sag tolerance.Using the steady-state equivalent circuit of an induction generator, the paper derives the electromagnetic torque-slip characteristic curve of the induction generator, analyzes the impact of voltage sag on induction motors, and deduces the critical duration and amplitude of voltage sag for induction generators, and establishes corresponding load models.

Figure 1 .
Figure 1.Equivalent circuit of switch power supply.

Figure 2 .
Figure 2. Voltage waveform of DC side of switch power supply.
(a).RS, Rr and XS, Xr are the resistance and reactance of the stator and rotor, respectively, and Xm is the excitation reactance.IS and Ir are the stator and rotor currents.The voltage phasor at the connection point of the induction generator is US, and the open-circuit voltage and impedance of the Thevenin equivalent circuit of the external network when the rotor is open-circuited are:

Figure 4 .
Figure 4.The electromagnetic torque-slip characteristic curve of induction generator.

2
Critical amplitude of voltage sag for induction generators.

Figure 5 .
Figure 5.The electromagnetic torque-slip characteristic curve of induction generator Ⅱ.
calculate the maximum electromagnetic torque Temax-sag during the sag period, it is necessary to first calculate the slip Sm corresponding to Temax-sag:

Figure 7 .
Figure 7. Single-line diagram of an IG system.

Table 1 .
Parameters of the 3MW IG Rated voltage, Vn Rated power, Pn

Table 2 .
Critical amplitude calculation and simulation results of voltage sag for induction generators.Rotor equivalent terminal voltage, Ue-in /pu Stator terminal voltage US-in /pu