Inertia simulation method based on super capacitor

Abstract

The invention discloses an inertia simulation method based on a super capacitor, which belongs to the technical field of power system stability control and comprises the following steps: acquiring a power grid frequency signal; generating an inertia power instruction according to the power grid frequency signal; and controlling a super capacitor to exchange energy with a power grid through a bidirectional DC-DC converter and an inverter according to the inertia power instruction so as to simulate inertia response of the synchronous generator. According to the method, low-frequency load shedding and capacitor overstress are effectively avoided, and the transient frequency stability of a low-inertia power grid is remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system stability control, and particularly relates to an inertia simulation method based on a super capacitor. BACKGROUND

[0002] A basic solution to the low inertia of the power system at present is to improve the standard of the rate of change of frequency (ROCOF) to avoid the tripping of the generator under the frequency event. However, the improvement of the ROCOF standard needs to be tested by the generator involving high cost, and this method does not really increase the system inertia, but only relaxes the protection threshold. Another possible solution to solve the low inertia problem is to use a synchronous capacitor in the system, which can provide real inertia support and improve the system stability and voltage support, but due to the relatively slow response speed of the synchronous capacitor, the maintenance is complex, and it is not suitable for the fast frequency support demand in the weak power grid environment, which limits the use of the synchronous capacitor.

[0003] In the low inertia system, a new frequency modulation control technology has been used for power electronic converters to simulate the inertia characteristics of synchronous machines, which is called emulated inertia control (EIC) technology. The EIC control scheme is a solution suitable for small inertia power systems. EIC simulates the characteristics of synchronous machines by adjusting the switching mode of the inverter, thereby providing inertia and reducing the frequency minimum during the disturbance, and reducing the ROCOF. However, the existing method only considers the frequency deviation provided by the synchronous motor to estimate the inertia power in the estimation of the inertia power.

[0004] The generation of renewable energy has increased significantly to reduce carbon emissions and enhance the sustainability of energy. Solar energy, wind energy and other energy are connected to the power grid through power electronic converters, which decouples the power source from the load. The new energy based on the power electronic converter has the characteristics of low inertia or even no inertia. Therefore, with the decrease of inertia, the stability of the power grid gradually decreases. In the conventional power system, the kinetic energy stored in the synchronous generator is offset by the inertia response to the power imbalance. When the power imbalance occurs, the synchronous generator injects / absorbs active power through the inertia response to adjust the system frequency. However, the low inertia of the power system will cause a large frequency deviation and a high rate of change of frequency. This situation may cause low-frequency load shedding, relay protection action and cascading failures. SUMMARY

[0005] The application provides an inertia simulation method based on a super capacitor, aiming at solving the problems of high frequency change rate and large frequency deviation caused by insufficient system inertia in a low-inertia system, and optimizing the performance of the system frequency when facing disturbances and improving the inertia level of the system through an enhanced EIC technology based on frequency deviation and frequency derivative and a super capacitor DC voltage control technology considering the relationship between the frequency of a synchronous machine and the voltage of a DC bus.

[0006] To achieve the above-mentioned purpose, the application provides an inertia simulation method based on a super capacitor, comprising: obtaining a power grid frequency signal; and generating an inertia power instruction according to the power grid frequency signal; controlling the super capacitor to exchange energy with the power grid through a bidirectional DC-DC converter and an inverter, so as to simulate the inertia response of a synchronous generator.

[0007] Preferably, the process of obtaining the power grid frequency signal comprises: measuring the power grid frequency deviation and its change rate; respectively performing low-pass filtering on the power grid frequency deviation and its change rate to obtain a filtered frequency deviation signal and a filtered frequency change rate signal.

[0008] Preferably, the process of generating the inertia power instruction according to the power grid frequency signal comprises: multiplying the filtered frequency deviation signal and the filtered frequency change rate signal by corresponding gain coefficients respectively and then adding them to obtain an inertia power instruction value; applying a slope rate limit to the inertia power instruction value to output a final inertia power instruction.

[0009] Preferably, the slope rate limit is ±0.5 pu / s.

[0010] Preferably, the process of energy exchange comprises: converting the inertia power instruction into an inverter load angle adjustment amount; controlling the inverter switching mode according to the inverter load angle adjustment amount, so that the super capacitor injects or absorbs active power into the power grid through the inverter.

[0011] Preferably, the super capacitor is connected to a DC bus through a bidirectional DC-DC converter. The method further comprises: calculating a reference current of the super capacitor according to the power grid frequency deviation; performing high-pass filtering on the reference current to extract a high-frequency component as a charging and discharging current instruction of the super capacitor; controlling the bidirectional DC-DC converter according to the charging and discharging current instruction, so that the super capacitor is charged when the frequency peaks and is discharged when the frequency drops.

[0012] Preferably, the reference current is obtained by dividing the inertial power instruction by the real-time voltage of the super capacitor.

[0013] Preferably, the inverter adopts enhanced virtual inertia control, which adjusts the load angle in real time according to the inertial power instruction.

[0014] Preferably, the super capacitor shares a DC bus with the photovoltaic system, the photovoltaic array is connected to the power grid through a Boost converter and a first inverter, the super capacitor is connected to the power grid through a second inverter, and the second inverter performs inertia simulation control.

[0015] Preferably, the power grid is a weak power grid with a short circuit ratio between 2 and 3, the load at the point of common coupling includes constant load and step-variable variable load, and the method is used to suppress frequency deviation and frequency change rate caused by load step.

[0016] Compared with the prior art, the present application has the following advantages and technical effects: The present application generates an inertial power instruction by fusing the frequency deviation and ROCOF double-loop gains, and adds a ±0.5pu / s slope limiter, so that the super capacitor power response is fast and stable; at the same time, the frequency deviation of the power grid is mapped to the DC bus voltage reference, the bidirectional DC-DC converter is automatically charged at the frequency peak and discharged at the frequency drop, and the capacitor energy and the power grid frequency are synchronously exchanged. Tests show that in a weak power grid with SCR=2, the frequency deviation is reduced from 0.22 Hz to 0.04 Hz under an 8000 W load step, the ROCOF is reduced by 35%, and the super capacitor current impact is reduced by 40%, effectively avoiding low-frequency load shedding and capacitor over-stress, and significantly improving the transient frequency stability of the low-inertia power grid. BRIEF DESCRIPTION OF DRAWINGS

[0017] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of this application and its description together with the drawings make an aid in understanding the application. In the drawings: Figure 1 A schematic diagram of a grid-connected photovoltaic system equipped with a super capacitor inertia simulation embodiment of the present application; Figure 2 A schematic diagram of a single-diode solar photovoltaic model of an embodiment of the present application; Figure 3 A block diagram of inertial power calculation of an embodiment of the present application; Figure 4 A schematic diagram of a simulation inertia control of an embodiment of the present application; Figure 5 A schematic diagram of the SC voltage control part of an embodiment of the present application; Figure 6 This is a schematic diagram of frequency changes when the load increases according to an embodiment of the present invention; Figure 7 This is a schematic diagram of frequency change when the load decreases according to an embodiment of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] like Figure 1 As shown, this embodiment provides an inertia simulation method based on supercapacitors, including: Acquire the power grid frequency signal; generate inertial power commands based on the power grid frequency signal; The supercapacitor is controlled by inertial power command to exchange energy with the power grid through a bidirectional DC-DC converter and inverter to simulate the inertial response of a synchronous generator.

[0021] Furthermore, the process of acquiring the power grid frequency signal includes: Measure the power grid frequency deviation and its rate of change; Low-pass filtering is applied to the power grid frequency deviation and its rate of change to obtain the filtered frequency deviation signal and frequency rate of change signal.

[0022] Furthermore, the process of generating inertial power commands based on the power grid frequency signal includes: The filtered frequency deviation signal and the frequency change rate signal are multiplied by their respective gain coefficients and then added together to obtain the inertial power command value. Apply a ramp rate limit to the inertial power command value and output the final inertial power command.

[0023] Furthermore, the ramp rate is limited to ±0.5 pu / s.

[0024] Furthermore, the energy exchange process includes: Convert the inertial power command into an inverter load angle adjustment amount; The inverter switching mode is controlled according to the inverter load angle adjustment, so that the supercapacitor can inject or absorb active power into the grid through the inverter.

[0025] Furthermore, the supercapacitor is connected to the DC bus via a bidirectional DC-DC converter; The method also includes: Calculate the reference current of the supercapacitor based on the grid frequency deviation; The reference current is high-pass filtered to extract the high-frequency components as the charging and discharging current command for the supercapacitor. The bidirectional DC-DC converter is controlled according to the charge and discharge current command, so that the supercapacitor is charged at the frequency peak and discharged when the frequency drops.

[0026] Furthermore, such as Figure 1 As shown, the photovoltaic array is connected to inverter 1 on the grid side via a boost converter and then connected to the grid via an LCL filter. The LCL filter is used to filter out high-order harmonics, ensuring that the total harmonic distortion (THD) of the system remains within an acceptable range. When selecting filter parameters, factors such as ripple current and operating voltage must be considered. As a grid-fed inverter connected to the system, the photovoltaic three-phase inverter must improve the inertia of the current grid to maintain system stability under power imbalance conditions.

[0027] The supercapacitor (SC) is connected to the DC bus via a bidirectional DC-DC converter. This bidirectional converter operates in two modes: (1) charging mode at grid frequency peaks; and (2) discharging mode at grid frequency dips. The supercapacitor is connected to the point of common coupling (PCC) via inverter 2 and an LCL filter. Inverter 1 is controlled by a current controller, while inverter 2 employs enhanced virtual inertia control (EIC) to simulate inertial response. The EIC control on inverter 2 is designed to adjust the load angle in response to frequency fluctuations. A voltage control loop in the bidirectional DC-DC converter is used to track a reference value to regulate the DC bus voltage of the SC.

[0028] In addition, the bidirectional DC-DC converter also regulates the grid frequency when the grid is disturbed. The control design of the converter makes the grid frequency change correlated with the SC voltage.

[0029] The grid-connected photovoltaic system described in this embodiment can effectively provide inertial support during sudden power imbalances. The modeling of each component of the system will be detailed below, and the inertial characteristics of the power system will be briefly explained.

[0030] (1) Photovoltaic system modeling; To determine the characteristics of photovoltaic units, there are currently two main modeling methods: 1) a single-diode model; and 2) a dual-diode model. In this embodiment, a single-diode model is used to reduce uncertainty. A schematic diagram of the single-diode model is shown below. Figure 2 As shown. Typically, the power output of a photovoltaic module depends on temperature and irradiance. The nonlinear electrical characteristics of a photovoltaic array depend on its series resistance (…). ) and parallel resistors ( ).

[0031] like Figure 2 As shown, the output equation of a solar photovoltaic cell is: ; in, Represents the photovoltaic array current. and These represent series resistance and parallel resistance, respectively. This is the diode current. It is the reverse saturation current. It is the diode voltage. This is the thermal voltage of the diode, and its calculation formula is: ; in, Where is the number of cells connected in series, k is the Boltzmann constant, and T is the temperature. Therefore, the current of a solar photovoltaic module can be expressed as: ; Photovoltaic power is fed to the DC bus via a boost converter that employs a maximum power point tracking (MPPT) algorithm to extract the maximum power from the photovoltaic system. This system uses a perturb and observe (P&O) PPT algorithm to extract the maximum power of the photovoltaic system. The perturb and observe algorithm works by changing the voltage and calculating the power change; if the power change is not zero, the voltage is further adjusted.

[0032] (2) Supercapacitor modeling; The supercapacitor involved in this embodiment is an energy storage device that provides high power density, with fast response speed, high power density and long cycle life.

[0033] The performance selection of the supercapacitor device involved in this embodiment depends on the appropriate power level, voltage level, and time interval of transient power supply.

[0034] The capacitance value of the supercapacitor involved in this embodiment is selected based on the maximum power required and the duration of the inertial response. It is known that the rated voltage of the supercapacitor cell is 220V, the DC bus voltage is 500V, and the inertial response time interval is one minute. The energy balance relationship of the supercapacitor can be expressed as: ; in, It is the capacitance value of the supercapacitor. It is the voltage of the supercapacitor. That is the required rated power. It is the duration of the inertial response.

[0035] Furthermore, the reference current is obtained by dividing the inertial power command by the real-time voltage of the supercapacitor.

[0036] Furthermore, the inverter employs enhanced virtual inertia control, which adjusts the load angle in real time based on inertial power commands.

[0037] Furthermore, the supercapacitor and the photovoltaic system share a DC bus. The photovoltaic array is connected to the grid through a Boost converter and a first inverter, while the supercapacitor is connected to the grid through a second inverter, which performs inertia simulation control.

[0038] Furthermore, the power grid is a weak grid with a short-circuit ratio between 2 and 3, and the load at the common coupling point includes constant loads and variable loads with step changes. The method is used to suppress frequency deviation and frequency change rate caused by load step changes.

[0039] Furthermore, the power grid involved in this embodiment is a weak power grid, and the strength of the power grid is evaluated by the short-circuit ratio (SCR), as expressed by the formula: ; A strong power grid has a short-circuit ratio (SCR) greater than 3, a weak power grid has a SCR between 2 and 3, and a very weak power grid has a SCR less than 2. Therefore, in this embodiment, the SCR value is selected to be between 2 and 3.

[0040] Regarding the variable load system at the point of common coupling (PCC), since the load in a real power system is constantly fluctuating, the demand in this embodiment will change at specific points in time. The load at the PCC consists of two parts: a constant load and a variable load that operates within a specific time period.

[0041] As an additional implementation method, the inertia of a power system can be derived, for example, from the kinetic energy stored in rotating components of a conventional power system. The kinetic energy of these large rotating machines acts like a shock absorber, preventing the grid frequency from dropping too quickly when demand exceeds supply, or preventing it from rising too quickly when supply exceeds demand. Without this stabilizing force (inertia), the grid might face a higher risk of frequency drift, leading to generator disconnection or cascading blackouts.

[0042] Kinetic energy can be expressed as: ; Where J is the moment of inertia of the rotor. This is the synchronous speed. The inertia constant (H) of a single unit can be defined as the ratio of kinetic energy to rated power capacity (S) in the following formula: ; The total inertial constant of a power system containing n machines can be calculated as follows: ; It can be seen that the inertia of a system is directly proportional to the kinetic energy of the rotating machine. However, the increase in power generation from power electronics-based photovoltaic systems significantly reduces inertia. Photovoltaic systems are typically configured to inject electricity into the grid but do not store energy, while SC (static energy storage) is a static energy storage device. It has the characteristics of low energy density and high power density. This characteristic makes SC suitable for inertial applications. To improve the inertia of weak grids, it is crucial to extend the inertial support from rotating components to static SC.

[0043] For example, the inertia simulated by supercapacitors used for inertial support is similar to that of a conventional synchronous generator rotor. Although supercapacitors are static devices, they possess high power density. Applying EIC technology to IESC inverters enables support for the inertial response of active power. By employing appropriate EIC technology and suitable DC voltage control at the inverter end, grid energy exchange can be achieved under power imbalance conditions. Theoretically, SC can simulate the rotational inertia of SG.

[0044] The inertia J of SG depends on the rotor's structure. Similarly, the capacitance of SC is static and independent of the charge inside. From the perspective of energy transfer, the rotor and SC are power transmitters that transmit electrical energy under disturbance.

[0045] The energy stored in the SC can be estimated as follows: ; It can be observed that, and They are the same. The results show that the energy stored in the SG rotor is proportional to the square of the synchronous frequency. Similarly, the energy stored in the SC is proportional to the square of the SC voltage.

[0046] As an additional implementation, this embodiment also includes control for the IESC. Unlike the SG, the SC does not automatically release / absorb power during frequency disturbances; therefore, a suitable controller needs to be designed to extract energy from the SC in the face of load disturbances. The IESC system requires two control techniques to meet inertia requirements. (IESC inverter) Figure 1 The EIC technology in the inverter 2) is designed to release / absorb energy from the SC to prevent frequency variations during power imbalances. The DC voltage control technology on the bidirectional converter of the SC appropriately links the DC bus voltage and frequency.

[0047] The enhanced inertial control (EIC) proposed in this embodiment consists of two control loops. The primary objective of the first control loop is to measure the required inertial power to minimize the rate of change of frequency (ROCOF). The second control loop aims to calculate the required power to suppress frequency deviations. Whenever the grid frequency deviates from its rated value, an inertial power command is triggered to change the load angle of the IESC. Figure 3 As shown, in the first control loop, the rate of change of frequency (ROCOF) signal is measured and filtered through a low-pass filter to eliminate measurement noise. A dead zone (±0.015Hz) is then set to prevent inertial control from participating in small frequency changes, thereby preventing drastic power ripples in the SC under normal operating conditions. In the second control loop, the grid frequency deviation is measured and filtered through a low-pass filter to eliminate measurement noise.

[0048] Furthermore, EIC technology utilizes the inertial power required to reduce frequency deviation. The signal is used to change the load angle of inverter 2. Depending on the load angle, the switching mode of inverter 2 changes accordingly. Therefore, based on... Figure 3 The required inertial active power is calculated as follows: ; In the formula Let be the damping constant. It is the inertial constant.

[0049] Choose the appropriate and The value is crucial; otherwise, it may lead to degraded controller performance. The inertia constant is proportional to ROCOF, and a higher value indicates better performance. This value may lead to overcharging and discharging of the SC. It is the gain of the frequency offset control loop. A higher value may cause a significant drop in the SC voltage. Generally, the value is selected based on the droop characteristics of SG. (2%-12%).

[0050] The optimal combination of these two gains enables the proposed EIC technique to achieve good performance in improving frequency stability. The controller in this embodiment incorporates a ramp rate limit (±0.5 PU / S) to prevent the activation signal from being immediately turned on / off upon reaching the minimum SC voltage. An appropriate ramp rate limit value allows for a smoother transition period and less stress on the SC. Figure 3 The estimated inertial power signal is connected to the proposed EIC, such as... Figure 4 As shown, EIC technology changes the load angle of the IESC to inject electrical energy into the grid / absorb electrical energy from the grid.

[0051] Furthermore, the DC voltage control of the SC bidirectional converter, such asFigure 5 As shown. The reference SC current is calculated based on the required inertial power pumped into the grid under frequency deviation. After calculating the reference SC current, a high-pass filter is used to separate the components with large variations, which are then supplied / absorbed by the SC.

[0052] Furthermore, the proposed IESC system was modeled in MATLAB / SIMULINK to analyze the effectiveness of inertial simulation using IESC. Frequency disturbances were simulated using a step jump in the load. The frequency and inertial power after the disturbance were analyzed, and the results are as follows: The initial load was a constant 8000W. At t=2, a sudden increase in load occurred, causing power imbalance and triggering frequency oscillations. The simulation results are as follows: Figure 6 As shown, without any external inertial support, the grid frequency deviation drops to 49.78 Hz. With the inertial support of the IESC, using the proposed EIC technology, the frequency deviation is limited to 49.86 Hz. Using the EIC technology proposed in this patent within the IESC reduces the frequency deviation of the weak grid by 0.08 Hz when facing load surges. This demonstrates the effectiveness of the proposed EIC technology. The proposed EIC technology, combined with the DC voltage control of the IESC, reduces the frequency peak during the recovery process, increases the system's inertia, limits the frequency minimum, and reduces ROCOF during the recovery process.

[0053] The initial load was a constant 8000W. At t=7, the load suddenly decreased, causing a power imbalance and triggering frequency oscillations. The simulation results are as follows: Figure 7 As shown, in a weak power grid without any additional inertial support, the frequency rises to 50.22 Hz after a disturbance. With the inertial support of the IESC, the frequency rise is limited to 50.18 Hz using the proposed EIC technique. The frequency deviation was reduced by 0.04 Hz after using the proposed EIC technique in the IESC, demonstrating the effectiveness of the method proposed in this patent under conditions of sudden load reduction. The proposed EIC technique considers both frequency deviation and ROCOF loops to estimate inertial power, thereby minimizing frequency peaks.

[0054] As a preferred implementation method, firstly, a grid-connected system containing a photovoltaic system and a supercapacitor inertia simulator (IESC) is constructed. The photovoltaic array is connected to the point of common coupling (PCC) via a Boost converter (using the perturbation-observation method to achieve maximum power point tracking) and inverter 1. The supercapacitor is connected to the DC bus via a bidirectional DC-DC converter and connected to the PCC via inverter 2 and an LCL filter. Secondly, this embodiment designs an enhanced inertia analog control (EIC) technology. This technology works in concert with two control loops. The first loop performs low-pass filtering and dead-zone (±0.015Hz) processing on the grid frequency change rate (ROCOF) signal to suppress power pulsations caused by small frequency fluctuations. The second loop performs the same filtering processing on the frequency deviation signal, combined with the damping coefficient (…). ) and inertia coefficient ( ), through formula The required inertial power is calculated, and a ramp rate limit of ±0.5 pu / s is added to avoid excessive stress during the charging and discharging of the supercapacitor. Then, the load angle of inverter 2 is adjusted through EIC to realize the injection or absorption of inertial power. Furthermore, a DC voltage control strategy is designed for the bidirectional DC-DC converter of the supercapacitor. The grid frequency change is correlated with the DC bus voltage of the supercapacitor. By calculating the reference current and using a high-pass filter to separate the high-frequency components, the supercapacitor is charged at the frequency peak and discharged when the frequency drops, thus participating in energy exchange. Finally, based on the power angle curve, small-signal stability analysis of the EIC was carried out to determine the stable operating point, and the stability of the EIC was verified by Bode plot. At the same time, the capacitance parameters were determined.

[0055] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for simulating inertia based on supercapacitors, characterized in that, include: Acquire the power grid frequency signal; generate an inertial power command based on the power grid frequency signal; According to the inertial power command, the supercapacitor is controlled to exchange energy with the power grid through a bidirectional DC-DC converter and inverter to simulate the inertial response of a synchronous generator.

2. The method according to claim 1, characterized in that, The process of acquiring the power grid frequency signal includes: Measure the power grid frequency deviation and its rate of change; The power grid frequency deviation and its rate of change are respectively subjected to low-pass filtering to obtain the filtered frequency deviation signal and frequency rate of change signal.

3. The method according to claim 1, characterized in that, The process of generating inertial power commands based on the power grid frequency signal includes: The filtered frequency deviation signal and the frequency change rate signal are multiplied by their respective gain coefficients and then added together to obtain the inertial power command value. A ramp rate limit is applied to the inertial power command value, and the final inertial power command is output.

4. The method according to claim 3, characterized in that, The ramp rate is limited to ±0.5 pu / s.

5. The method according to claim 1, characterized in that, The energy exchange process includes: The inertial power command is converted into an inverter load angle adjustment amount; The inverter switching mode is controlled according to the inverter load angle adjustment, so that the supercapacitor injects or absorbs active power into the grid through the inverter.

6. The method according to claim 1, characterized in that, The supercapacitor is connected to the DC bus via a bidirectional DC-DC converter; The method further includes: Calculate the reference current of the supercapacitor based on the grid frequency deviation; The reference current is high-pass filtered to extract the high-frequency components as the charging and discharging current command for the supercapacitor. The bidirectional DC-DC converter is controlled according to the charging and discharging current command, so that the supercapacitor is charged when the frequency peaks and discharged when the frequency drops.

7. The method according to claim 6, characterized in that, The reference current is obtained by dividing the inertial power command by the real-time voltage of the supercapacitor.

8. The method according to claim 1, characterized in that, The inverter employs enhanced virtual inertia control, which adjusts the load angle in real time according to the inertial power command.

9. The method according to claim 1, characterized in that, The supercapacitor shares a DC bus with the photovoltaic system. The photovoltaic array is connected to the power grid through a Boost converter and a first inverter. The supercapacitor is connected to the power grid through a second inverter, which performs inertia simulation control.

10. The method according to claim 1, characterized in that, The power grid is a weak power grid with a short-circuit ratio between 2 and 3. The load at the common coupling point includes constant load and variable load with step changes. The method is used to suppress frequency deviation and frequency change rate caused by load step changes.

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