Transient stability control methods, systems, equipment, and media for grid-type energy storage based on dynamic phase angle evolution.
By using a dynamic phase angle evolution control method, the continuous phase angle space of the energy storage system is reconstructed, additional damping commands are generated, and phase advance compensation is performed. This solves the transient stability problem of grid-type energy storage systems under high-proportion renewable energy transmission conditions and improves the stability of the power grid.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ELECTRIC POWER RES INST OF EAST INNER MONGOLIA ELECTRIC POWER
- Filing Date
- 2026-06-17
- Publication Date
- 2026-07-17
AI Technical Summary
Existing grid-based energy storage systems face the challenges of transient energy retention and active power surplus under conditions of high proportion of renewable energy transmission. These issues include phase angle model inaccuracy, reference benchmark fragmentation, and negative damping risks caused by hardware delays, leading to grid transient instability.
A control method based on dynamic phase angle evolution is adopted. Through a transient phase-locked loop module, an absolute dynamic phase angle reconstruction module, an EEAC command synthesis module, and a lead-limiting drive module, the continuous dynamic phase angle space is reconstructed, additional damping commands are generated, and phase lead compensation is performed to ensure the continuity and damping stability of the control system in the global coordinate system.
It effectively solves the secondary impact caused by phase angle model inaccuracy and reference benchmark separation in traditional control strategies, reshapes the transient stability boundary of the power grid with a high proportion of new energy transmission, eliminates the negative damping risk caused by hardware delay, and improves the transient stability of the power grid.
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Figure CN122418890A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power system transient stability control technology, specifically relating to a method, system, equipment, and medium for transient stability control of grid-type energy storage based on dynamic phase angle evolution. Background Technology
[0002] Currently, under the macro-background of the construction of a new power system, ultra-high voltage direct current (UHVDC) transmission, as a core channel for achieving optimal allocation of resources across regions, undertakes an important mission of energy transmission. Taking a typical large-scale DC transmission project as an example, the continuous expansion of the scale of new energy integration into the sending-end power grid has led to a significant decrease in the system's equivalent short-circuit ratio (SCR), which in turn causes the power grid operation to exhibit new characteristics such as strong power electronics, strong randomness, and strong coupling.
[0003] Under the aforementioned high-proportion renewable energy transmission conditions, when a severe short-circuit fault occurs in the receiving-end AC system or DC bipolar blocking occurs, the DC power transmission will experience a sharp drop. At this time, because the mechanical power or generating power of the sending-end conventional units and renewable energy plants cannot change abruptly due to inertia, a severe problem of "transient energy retention and active power surplus" will instantly arise within the system. For example, patent application CN116054284A discloses a transient active power control method applicable to flexible DC transmission systems, which also addresses the issue of surplus active power.
[0004] In recent years, grid-formed energy storage has been widely introduced into power grids to improve transient stability due to its active voltage construction and inertia support capabilities. Its core control is usually based on the Virtual Synchronous Generator (VSG) model. However, when faced with the aforementioned problems of "transient energy retention and active power surplus," the excess energy will cause the virtual rotor of the grid-formed converter to accelerate sharply, which will cause the phase angle of the converter's internal potential to increase rapidly. This can easily induce transient power angle instability or even collapse of the entire sending-end system.
[0005] Currently, existing technologies have the following significant shortcomings in both theoretical modeling and engineering implementation when designing transient stability control strategies for grid-based energy storage: First, the static phase angle assumption, which is theoretically simplified, fails. Traditional control systems, in order to simplify calculations when performing transient mathematical modeling for large disturbances, typically assume that the internal potential phase angle of the converter remains constant for tens of milliseconds after a short-circuit fault. However, in actual physical processes, once the rotor accelerates, the phase angle inevitably becomes a dynamic variable with high-frequency, drastic changes. If it is forcibly treated as a constant, the model will completely ignore the enormous kinetic energy accumulated by the rotor during the fault, causing the calculated power command to deviate from the actual requirements based on the Extended Equal Area Criterion (EEAC), and thus failing to provide accurate transient damping.
[0006] Second, the fragmentation of control references across stages triggers secondary shocks. Existing control strategies often employ segmented, independent control logic and reference coordinate systems when handling the period during which a fault persists and the post-fault recovery period after fault clearance. Due to the lack of a global absolute phase reference reference throughout the entire process, a severe physical break occurs in the voltage fitting trajectory at the moment of fault clearance, causing drastic mathematical jumps in control commands, which in turn cause severe "secondary electrical shocks" to the already fragile power grid.
[0007] Third, ignoring the risk of negative damping caused by underlying hardware delays. In actual engineering, the sampling of electrical quantities, digital signal processing (DSP), and pulse width modulation (PWM) of energy storage converters all have millisecond-level pure time delays. When dealing with transient high-frequency power angle fluctuations, this inherent delay will cause severe phase lag in the control signal, which can easily distort the positive damping that the system should output into a "negative damping" that exacerbates the problem, thereby accelerating the grid's loss of synchronization and collapse.
[0008] In summary, there is an urgent need for a transient stability control method for grid-type energy storage that can adapt to large disturbances in physical processes, has an absolute reference for phase angle continuity, and can effectively resist engineering delays. Summary of the Invention
[0009] To address the problems in related technologies, this invention proposes a transient stability control method, system, device, and medium for grid-type energy storage based on dynamic phase angle evolution, thereby overcoming the technical issues existing in current technologies. Starting from the underlying virtual rotor motion mechanism, this invention restores the phase angle to a continuous dynamic high-order variable, using the initial fault reference angle as the globally unique benchmark. Combined with the equal area rule and phase lead compensation technology, it reshapes the transient damping boundary of the high-proportion renewable energy power grid, solving technical problems in traditional control strategies such as inaccurate phase angle models, reference benchmark fragmentation, and negative damping caused by engineering delays.
[0010] The technical solution of the present invention is implemented as follows: a transient stability control system for grid-type energy storage based on dynamic phase angle evolution, wherein the control system is connected to the control port of the grid-type energy storage converter; The control system includes a transient phase-locked module, an absolute dynamic phase angle reconstruction module, an EEAC command integration module, and an advance limiting drive module connected in sequence. The transient phase-locked loop module is used to collect electrical quantities at the grid-connected point of the grid-type energy storage system in real time, and to extract the voltage amplitude at the grid-connected point. Deviation from real-time virtual angular frequency It is also used to forcibly latch the current internal algorithm phase angle at the instant when a transient large disturbance drop occurs in the control system, and set it as the globally unique initial fault reference angle for the entire transient process. ; The absolute dynamic phase angle reconstruction module is used to abandon the simplified assumption of a constant phase angle during short circuits and to use the initial fault reference angle. As the absolute coordinate zero point, the deviation of the real-time virtual angular frequency High-precision numerical integration is performed to solve and reconstruct a strictly continuous and differentiable absolute dynamic phase angle space sequence; The EEAC instruction synthesis module is used to receive the absolute dynamic phase angle space sequence, substitute the absolute dynamic phase angle space sequence into different transfer functions, and calculate the active power additional damping instruction with dynamic phase angle over-limit penalty characteristics and the reactive power additional damping instruction with very early voltage differential feedforward characteristics, so as to reduce the acceleration area and expand the deceleration area. The advance limiting drive module is used to perform phase advance correction on the generated active and reactive additional damping commands in the complex frequency domain, filter out the risk of negative damping divergence caused by delay, and perform flexible limiting allocation within the safety boundary of the maximum apparent capacity of the grid-type energy storage converter, and finally generate control waveforms for driving power switching devices.
[0011] Furthermore, the transient phase-locked loop module includes a high-speed electrical quantity acquisition unit, a high-frequency analog-to-digital converter, a DSP computing unit, a hardware-level interrupt and latch unit, and a register connected in sequence; The high-speed electrical quantity acquisition unit is used to acquire the electrical quantities; the electrical quantities include three-phase instantaneous voltage. and three-phase instantaneous current ; The high-frequency analog-to-digital converter is used to convert analog signals of electrical quantities into digital signals; The DSP computing unit includes a continuous sliding window counter; the DSP computing unit uses a coordinate transformation algorithm on the digital signal and calculates the voltage amplitude at the grid connection point. Deviation from real-time virtual angular frequency The continuous sliding window counter is used to monitor the voltage amplitude at the grid connection point. Perform continuous sliding window monitoring; The hardware-level interrupt and latch unit is used to latch the current internal algorithm phase angle as the initial fault reference angle. And save it to the register.
[0012] Furthermore, the absolute dynamic phase angle reconstruction module includes a continuous trajectory fitting unit, and a high-precision numerical integration unit and a zero-point reference clamping unit respectively connected to the continuous trajectory fitting unit; The high-precision numerical integration unit employs a discrete numerical integration algorithm to measure the real-time virtual angular frequency deviation. Perform real-time high-precision integration and solve for the dynamic phase angle relative deviation. ; The zero-point reference clamping unit is used to forcibly disconnect the original conventional phase-following branch and latch the initial fault reference angle stored in the register. The zero point of the clamp is used as the sole absolute coordinate zero point for reference clamping, thus obtaining the zero point reference of the clamp; The continuous trajectory fitting unit is used to measure the relative deviation of the dynamic phase angle. Adding the zero-point reference of the clamping to reconstruct a strictly continuous and differentiable absolute dynamic phase angle space sequence; Furthermore, the zero-point reference clamping unit is connected to the register; the high-precision numerical integration unit is connected to the DSP computing unit. Furthermore, the high-precision numerical integration unit includes a digital discrete integrator; the digital discrete integrator is used to perform continuous accumulation and iteration calculations to solve for the dynamic phase angle relative deviation in real time. .
[0013] Furthermore, the EEAC instruction synthesis module includes a phase angle safety dead zone comparator, a penalty function calculator, a voltage differential calculator, a conventional closed-loop control unit, and a summation unit; The absolute dynamic phase angle reconstruction module is connected in sequence to the phase angle safe dead zone comparator and the penalty function calculator; The summation unit is connected to the advance limiting drive module, the voltage differential calculator, and the conventional closed-loop control unit, respectively. The phase angle safety dead zone comparator is used to substitute the received absolute dynamic phase angle spatial sequence into the transfer function, and when the received dynamic phase angle relative deviation is... When the absolute value exceeds the preset limit margin, the penalty function in the penalty function calculator will be activated immediately; The penalty function calculator is used to amplify the over-limit difference and superimpose it with the conventional transient inertia and damping components to calculate the active additional damping command with dynamic phase angle over-limit penalty characteristics. The voltage differential calculator and the conventional closed-loop control unit, after being summed by the summing unit, output a reactive additional damping command with very early voltage differential feedforward characteristics to the advanced limiting drive module. Furthermore, the continuous trajectory fitting unit is connected to the phase angle safe dead zone comparator; the DSP calculation unit is connected to the voltage differential calculator and the conventional closed-loop control unit, respectively.
[0014] Furthermore, the advanced amplitude limiting drive module includes a digital filtering compensation unit, a dynamic safety boundary adaptive amplitude limiting unit, and a wave generation execution unit connected in sequence; The digital filtering compensation unit is used to perform phase lead correction on the active and reactive additional damping commands in the complex frequency domain. The dynamic safety boundary adaptive limiting unit is used to receive the corrected active and reactive additional damping commands, monitor the operating status of the grid-type energy storage converter in real time and dynamically update the allowable transient maximum apparent power, and strictly perform flexible limiting allocation within the safety boundary of the maximum apparent capacity of the grid-type energy storage converter according to the flexible allocation logic of "protecting reactive power and squeezing active power", and output controlled commands. The waveform generation unit generates a high-frequency pulse signal corresponding to the control waveform according to the controlled instruction, and sends it to the power switching device. Furthermore, the digital filtering compensation unit is connected to the penalty function calculator and the summation unit, respectively; Furthermore, the digital filtering compensation unit uses discretization transformation to convert the first-order phase lead compensator in the continuous domain into a digital filter, and performs phase lead correction on the generated active and reactive additional damping commands in the complex frequency domain, actively providing a positive lead phase angle to accurately cancel the pure time delay caused by sampling, calculation and wave generation.
[0015] A transient stability control method for grid-type energy storage based on dynamic phase angle evolution is applied to a grid-type energy storage transient stability control system as described above. The method includes the following steps: Step S1: High-frequency sensing of transient disturbances in the control system and absolute anchoring of the initial fault angle; using a transient phase-locked loop module to collect electrical quantities at the grid-connected point of the grid-type energy storage in real time at high frequency, and extracting the voltage amplitude at the grid-connected point. Deviation from real-time virtual angular frequency Then, preset the voltage drop dead zone threshold. By judgment To latch the initial fault reference angle Then, the real-time virtual angular frequency deviation is... and initial fault reference angle Transmitted to the absolute dynamic phase angle reconstruction module, grid connection point voltage amplitude Transmitted to the EEAC instruction synthesis module; Step S2: Construct a strictly continuous absolute dynamic phase angle evolution equation across stages; build a dynamic phase angle evolution model through the absolute dynamic phase angle reconstruction module, and calculate the relative deviation of the dynamic phase angle in real time. Then through the formula To construct the absolute dynamic phase angle at the current moment Then it is transmitted to the EEAC instruction integration module; Furthermore, the absolute dynamic phase angle space sequence includes absolute dynamic phase angles. ; Step S3: The transient damping command based on the equal area rule (EEAC) is comprehensively reshaped; that is, based on the equal area rule (EEAC), the active power additional damping command and the reactive power additional damping command are generated through the EEAC command synthesis module, and the two additional damping commands are transmitted to the advance limiting drive module. Step S4: Complex frequency domain phase lead compensation and adaptive limiting execution to counteract inherent system delay; After receiving active and reactive power additional damping commands, phase lead compensation is introduced through the lead limiting drive module to offset the inherent pure time delay. Impact; After the lead cancellation hysteresis, the dynamic limiting allocation command is used to finally generate a control waveform to drive the power switching device to generate a waveform.
[0016] Further, in step S1, when detected When a transient large disturbance is detected in the receiving-end power grid, the control system enters a transient emergency support state. The instant the disturbance is triggered is recorded as follows: At that moment, and in The current internal algorithm phase angle is constantly latched and set as the initial fault reference angle. At the same time, it serves as the absolute reference zero point for subsequent phase angle deduction; The internal algorithm phase angle specifically refers to the absolute phase angle generated by the internal algorithm integration; It should be emphasized that step S1 aims to rapidly identify transient active power surplus impacts through local electrical quantities without relying on global wide-area communication, and to establish an absolute physical coordinate system for the entire subsequent process. Furthermore, step S1 specifically includes the following steps S11 to S13: Step S11: Real-time high-frequency sampling of the three-phase instantaneous voltage and three-phase instantaneous current at the grid connection point (PCC) of the grid-connected energy storage converter, and obtaining the grid connection point voltage amplitude through Park transformation. and the actual electromagnetic active power output by the converter Simultaneously, the real-time virtual angular frequency deviation output from the virtual synchronous generator (VSG) model inside the grid-type energy storage converter is extracted. ; Step S12: Set the voltage sag dead zone threshold that reflects the transient intensity of the power grid. ; By continuously monitoring with sliding windows, when a detection is made When it is determined that a short circuit or DC blockage has occurred in the receiving-end power grid, the control system enters the transient emergency support state. Step S13: At the moment when the system is determined to have experienced a transient large disturbance (precisely recorded as...) (At a certain moment), a low-level hardware interrupt is forcibly triggered, and the data is read and deeply latched. The absolute phase angle data generated by the internal algorithm of the grid-type energy storage converter; the specific instantaneous phase angle of this latch is defined as the initial fault reference angle. It serves as the absolute reference zero point for subsequent phase angle space deduction within the transient full-time domain.
[0017] Furthermore, step S2 aims to break the reduced-order assumption in traditional control that "the phase angle remains constant within a very short time during a large disturbance," reconstruct a continuously differentiable phase evolution trajectory, and eliminate the secondary impact caused by reference frame switching; step S2 further includes: Step S21: Restore the internal potential phase angle of the grid-type energy storage converter to a continuous dynamic variable driven by transient active power imbalance; when a large transient disturbance occurs, due to the virtual mechanical power Inertia prevents abrupt changes, while electromagnetic power... The sudden drop causes an imbalance in acceleration power, resulting in angular acceleration in the virtual rotor. At this point, the derivative of the internal phase angle... ; Step S22: During both the short-circuit fault persistence phase and the post-fault recovery phase after fault clearance, the initial fault reference angle latched in step S13 is forcibly and uniquely adopted. As a globally unified phase reference standard; Step S23: Under a unified phase reference, the virtual angular frequency deviation is calculated using a discrete numerical integration algorithm. Perform real-time high-precision integration to solve for the relative deviation of the dynamic phase angle throughout the transient process. The calculation formula is as follows: (1); in, The range of values is ; The timestamp at the moment the disturbance was triggered; This represents the real-time virtual angular frequency deviation. Step S24: Superimpose the obtained dynamic phase angle relative deviation onto the absolute reference zero point to obtain the absolute dynamic phase angle used for bottom layer wave generation at the current moment. Its expression is: (2); By constructing this equation (2), the seamless connection of the voltage fitting trajectory at the moment of fault clearing is ensured, and the phase angle is continuously differentiable on the entire time axis.
[0018] Further, step S3, based on the continuous dynamic phase angle variable output in step S2, generates additional damping commands from both active and reactive power dimensions to reduce the acceleration area and expand the deceleration area of the system; step S3 further includes: Step S31: Generate an active power additional damping command with a dynamic phase angle over-limit penalty term. This instruction is superimposed on the steady-state active power instruction to forcibly consume the transient active power surplus. The active power additional damping instruction... The transfer function formula is: (3); Where s is the Laplace operator, a complex frequency variable; For transient inertial terms, the frequency differential characteristic is used to simulate the real rotor inertia to resist abrupt changes; For the proportional damping term, a conventional damping torque proportional to the speed deviation is provided; This is a unique dynamic phase angle exceeding limit penalty term in this invention; This is the preset phase angle safety and stability limit margin; when the actual dynamic phase angle deviates from the absolute value of the initial fault angle... When the dynamic phase angle exceeding the limit penalty term is zero, the output of the term is zero. When the dynamic phase angle exceedance penalty term is activated, it will be activated immediately (i.e., the penalty function in the penalty function calculator will be activated), and the output will increase sharply as the phase angle deviation increases. The dynamic phase angle exceedance penalty term is physically equivalent to applying a nonlinear rigid pull-back torque to the virtual rotor, directly forcibly cutting the acceleration area in the EEAC coordinate system to suppress step loss (i.e., forcibly cutting the acceleration area by generating a negative power command). Step S32: Generate reactive power additional damping command with voltage differential feedforward. This instruction is used to rapidly increase the bus voltage in the initial stage of a fault to expand the deceleration area; the reactive power additional damping instruction... The transfer function formula is: (4); in, The target voltage threshold for expected recovery; For proportional gain; For integral gain; The voltage differential feedforward term is used to excite the energy storage converter to output capacitive reactive current to raise the voltage valley value at the moment of a step drop in the grid connection point voltage. In the very early stage of a transient fault, when the grid connection point voltage experiences a step drop, the voltage differential feedforward term generates a transient impulse response, instantly exciting the energy storage converter to output the ultimate overload capacitive reactive current, raising the grid connection point voltage valley value as quickly as possible, shifting the electromagnetic power characteristic curve upward as a whole, and ensuring the effective expansion of the deceleration area.
[0019] Furthermore, step S4 aims to eliminate the potential transient "negative damping" caused by hardware sampling and modulation delays, and step S4 further includes: S41. First, obtain the inherent pure time delay of the control system caused by signal sampling, algorithm calculation, and pulse width modulation (PWM) of the insulated gate bipolar transistor (IGBT). The delay In the complex frequency domain, it is equivalent to At the transient dominant power angle oscillation frequency The location will cause a size of Severe phase lag; S42, in the active power additional damping command and reactive power additional damping command A first-order phase lead compensator is embedded in series in the transmission channel of the inner loop controller of the grid-type energy storage converter; the first-order phase lead compensator The expression is: (5); in, It is the leading factor, and ; The time constant is used; this invention achieves precise tuning. and This allows the first-order phase lead compensator to operate at the oscillation frequency. The positive leading phase angle generated at the location Approximately equal to the hysteresis angle This actively counteracts the phase loss caused by pure lag, ensuring that the energy storage device outputs stable positive damping energy.
[0020] S43. For transient additional commands after phase lead compensation, combined with the transient maximum overload apparent power limit of the grid-type energy storage converter. Dynamic boundary limiting is performed, and the flexible safety principle of "reactive voltage support is given absolute priority, and the remaining capacity is allocated to active damping" is followed (that is, after phase advance compensation, reactive output is given priority, and the remaining apparent capacity is allocated to active damping command for boundary limiting), and the final controlled active and reactive drive commands are output to the wave generation execution unit.
[0021] A computer device includes a memory, a network interface, an input / output device, and a processor, all connected to a system bus. The memory stores a computer program, and when the processor executes the computer program, it implements the above-described method for transient stability control of grid-type energy storage based on dynamic phase angle evolution.
[0022] A non-transitory computer-readable storage medium includes a stored computer program that, when executed by a processor, implements the above-described transient stability control method for grid-type energy storage based on dynamic phase angle evolution.
[0023] The beneficial effects of this invention are: (1) The present invention eliminates the secondary electrical shock caused by cross-stage state separation from the underlying algorithm; the present invention proposes the "initial fault angle absolute anchoring" mechanism for the first time, so that the control equations of the fault period and the post-fault recovery period are unified under a single coordinate system, eliminating the power jump caused by the sudden change of the reference system at the moment of circuit breaker operation in traditional segmented control.
[0024] (2) This invention reshapes the transient stability boundary of a high-proportion new energy weak grid; and breaks through the simplified assumption of constant phase angle in traditional analysis, and proposes a "dynamic phase angle limit penalty term", which can generate huge pull-back damping torque like a nonlinear rigid spring when the rotor approaches the step loss limit; combined with the impulse reactive power support generated by voltage differential feedforward, it achieves a precise balance between acceleration energy and deceleration energy at the EEAC physical level.
[0025] (3) Without increasing any additional hardware and communication costs, this invention utilizes a complex frequency domain phase lead compensator to eliminate the dead zone and calculation delay of the control link, fundamentally resolving the serious crisis of positive damping distortion becoming "negative damping" under high frequency disturbances, which meets the safety requirements of the complex power grid at the UHVDC sending end for control equipment. Attached Figure Description
[0026] Figure 1 This is a schematic diagram of the structure of the grid-type energy storage transient stability control system based on dynamic phase angle evolution in Example 1; Figure 2 This is a schematic diagram of the connection between the transient phase-locked module and the grid-type energy storage converter in Example 1; Figure 3This is a schematic diagram showing the connection of each module in the grid-type energy storage transient stability control system based on dynamic phase angle evolution in Example 1. Figure 4 This is a schematic diagram of the steps of the transient stability control method for grid-type energy storage based on dynamic phase angle evolution in Example 2; Figure 5 This is a flowchart illustrating steps S2 to S4 in Example 2; Figure 6 This is a schematic diagram of the structure of a computer device in Example 3. Detailed Implementation
[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0028] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.
[0029] Example 1 like Figure 1-3 As shown, this embodiment provides a transient stability control system for grid-type energy storage based on dynamic phase angle evolution, wherein the control system is connected to the control port of the grid-type energy storage converter; The control system includes a transient phase-locked module, an absolute dynamic phase angle reconstruction module, an EEAC command integration module, and an advance limiting drive module connected in sequence. It should be noted that the control system described in this embodiment can be physically mounted on a digital signal processor (DSP), a field-programmable gate array (FPGA), or a main control board of their collaborative architecture. Logically, it is divided into four deeply coupled parallel functional modules (i.e., transient phase-locked loop module, absolute dynamic phase angle reconstruction module, EEAC instruction synthesis module, and advance limiting drive module).
[0030] Specifically, in the control system, The transient phase-locked loop module is used to collect electrical quantities at the grid-connected point of the grid-type energy storage system in real time, and to extract the voltage amplitude at the grid-connected point. Deviation from real-time virtual angular frequency It is also used to forcibly latch the current internal algorithm phase angle at the instant when a transient large disturbance drop occurs in the control system, and set it as the globally unique initial fault reference angle for the entire transient process. ; The absolute dynamic phase angle reconstruction module is used to abandon the simplified assumption of a constant phase angle during short circuits and to use the initial fault reference angle. As the absolute coordinate zero point, the deviation of the real-time virtual angular frequency High-precision numerical integration is performed to solve and reconstruct a strictly continuous and differentiable absolute dynamic phase angle space sequence; The EEAC instruction synthesis module is used to receive the absolute dynamic phase angle space sequence, substitute the absolute dynamic phase angle space sequence into different transfer functions, and calculate the active power additional damping instruction containing the dynamic phase angle over-limit penalty feature and the reactive power additional damping instruction containing the very early voltage differential feedforward feature, so as to reduce the acceleration area and expand the deceleration area. The advance limiting drive module is used to perform phase advance correction on the generated active and reactive additional damping commands in the complex frequency domain, filter out the risk of negative damping divergence caused by delay, and perform flexible limiting allocation within the safety boundary of the maximum apparent capacity of the grid-type energy storage converter, and finally generate control waveforms for driving power switching devices.
[0031] like Figure 2-3 As shown, the transient phase-locked loop module is equipped with a high-speed electrical quantity acquisition unit, and captures the instantaneous three-phase voltage at the grid connection point in real time at a set high-frequency sampling rate through a high-frequency analog-to-digital converter. With three-phase instantaneous current The coordinate transformation algorithm built into the DSP computing unit is used to convert it into components in a synchronous rotating coordinate system, and the voltage amplitude at the grid connection point is calculated in real time. and deviation from real-time virtual angular frequency ; To prevent minor voltage fluctuations caused by conventional grid load switching from triggering malfunctions, the DSP computing unit is also equipped with a continuous sliding window counter (with a sliding window data array) to compare the voltage amplitude at the grid connection point in real time. Compared with the preset drop dead zone threshold ; A transient large disturbance drop is determined to have occurred and a valid transient large disturbance signal is output only when voltage over-limit is detected for multiple consecutive cycles within the sliding window. Upon receiving the valid transient large disturbance signal, the underlying hardware-level interrupt and latch unit of the transient phase-locked loop module is immediately triggered, forcibly retrieving the absolute phase angle variable from the current virtual synchronous generator core algorithm and deeply writing it into a write-protected non-volatile register, thereby establishing it as the globally unique initial fault reference angle for the entire transient process. .
[0032] like Figure 3 As shown, the absolute dynamic phase angle reconstruction module breaks the inherent simplification assumption of a constant phase angle during a short circuit in the traditional reduced-order model, providing an absolutely continuous physical coordinate space for subsequent transient damping calculations. During the entire large disturbance cycle of the control system's transient drop and subsequent fault recovery, the zero-point reference clamping unit of the absolute dynamic phase angle reconstruction module forcibly cuts off the original conventional phase-following branch, latching the initial fault reference angle stored in the register. Use it as the sole absolute coordinate zero point for reference clamping; Subsequently, the built-in high-precision numerical integration unit receives the real-time virtual angular frequency deviation. By using a digital discrete integrator to perform continuous iterative calculations, the dynamic phase angle relative deviation can be solved in real time. ; Finally, the continuous trajectory fitting unit will calculate the relative deviation of the dynamic phase angle. Adding the zero-point reference of the clamping to reconstruct a strictly continuous and differentiable absolute dynamic phase angle space sequence; The absolute dynamic phase angle reconstruction module ensures, from the underlying algorithm structure, that the voltage fitting trajectory of the AC / DC hybrid system has strict continuity before and after topological changes, eliminating the secondary impact caused by reference frame switching.
[0033] like Figure 3 As shown, the EEAC command integration module generates control commands through two independent digital channels, active and reactive, to reduce the acceleration area and expand the deceleration area. Regarding the active power channel, the EEAC instruction synthesis module incorporates a phase angle safety dead zone comparator and a penalty function calculator. It substitutes the received absolute dynamic phase angle spatial sequence into the transfer function. When the received absolute value of the dynamic phase angle deviation exceeds a preset limit margin (i.e., ... When this occurs, the penalty function is immediately activated, amplifying the over-limit difference and superimposing it with the conventional transient inertia and damping components to calculate the active power additional damping command that includes the dynamic phase angle over-limit penalty characteristics. This command forcibly extracts the rotor's kinetic energy and directly cuts the transient acceleration area in the EEAC theory; Regarding the reactive power channel, the EEAC command integration module has a built-in voltage differential calculator. In the very early stages of a fault, it generates a transient impulse signal based on the voltage drop rate at the grid connection point, and calculates an additional reactive power damping command that includes the very early voltage differential feedforward characteristics by combining the output of a conventional closed-loop control unit. The instruction aims to instantly inject extreme capacitive reactive power into the power grid, rapidly boost the voltage trough at the grid connection point, and shift the electromagnetic power characteristic curve upward as a whole, thereby significantly expanding the deceleration area of the system.
[0034] like Figure 3 As shown, the advanced limiting drive module filters out the risk of negative damping divergence caused by the inherent delay of the control system and ensures the safe operation of the converter hardware. The digital filter compensation unit inside the advance limiting drive module uses discretization transformation to convert the first-order phase advance compensator in the continuous domain into a digital filter. In the complex frequency domain, it performs phase advance correction on the generated active and reactive additional damping commands and actively provides a positive advance phase angle to accurately cancel the pure lag delay caused by sampling, calculation and wave generation. After compensation, the instruction then enters the dynamic safety boundary adaptive limiting unit. This unit monitors the converter's operating status in real time and dynamically updates the maximum allowable transient apparent power. Following the flexible allocation logic of "protecting reactive power and squeezing out active power," it strictly performs flexible limiting allocation within the safety boundary of the converter's maximum apparent capacity. Finally, the controlled command is sent to the waveform generation unit, converted into a high-frequency pulse signal, and ultimately generates a control waveform for driving the power switching device.
[0035] Example 2 like Figure 4-5 As shown, this embodiment also provides a transient stability control method for grid-type energy storage based on dynamic phase angle evolution, which is applied to a transient stability control system for grid-type energy storage based on dynamic phase angle evolution as described above; features not explained in this embodiment can be explained using the explanation in Embodiment 1, and will not be repeated here.
[0036] It should be noted that this embodiment takes a typical high-proportion new energy UHVDC sending-end power grid as the application scenario, and explores in depth the underlying discretization execution process of the grid-type energy storage transient stability control method based on dynamic phase angle evolution provided in this embodiment in the actual digital signal processor (DSP) and field programmable gate array (FPGA) collaborative architecture.
[0037] Combination Figure 4-5 The method described in this embodiment operates in each sampling and control cycle of the controller (e.g., the switching frequency is 10kHz, and the sampling cycle is...). The difference between this embodiment and Embodiment 1 is that the method described in this embodiment is executed according to extremely strict timing logic (i.e., steps S1 to S4).
[0038] Step S1: High-frequency sensing of system transient disturbance state and absolute anchoring of initial fault angle; In actual power grid operation, due to the highly random timing of large disturbances, the control system must have microsecond-level state recognition capability to ensure accurate capture of transient characteristics. Step S1 specifically includes steps S11 to S13.
[0039] In step S11, the sampling circuit in the high-speed electrical quantity sampling unit senses the three-phase instantaneous AC voltage at the grid connection point (PCC) of the grid-connected energy storage converter in real time through Hall voltage / current sensors. and three-phase instantaneous alternating current The analog signal is sampled by a high-frequency analog-to-digital converter (ADC) and then sent to the DSP computing unit. Inside the DSP computing unit, a second-order generalized integrator (SOGI) or a notch filter is first used to filter out negative sequence components and high-frequency harmonic interference that may be caused by asymmetric faults. Subsequently, the DSP computing unit uses Clark and Park transformations to decouple the AC quantities in the three-phase stationary coordinate system to two-phase rotating coordinates. In the coordinate system, calculate the per-unit amplitude of the positive-sequence fundamental wave of the current grid voltage. and the instantaneous electromagnetic active power actually injected into the grid by the converter With reactive power ; Simultaneously, the DSP computing unit extracts the virtual angular frequency deviation output from the eigenvalue equations of the virtual synchronous generator (VSG) within the current control cycle and iteratively calculates it. .
[0040] In step S12, to prevent minor voltage fluctuations caused by the switching of conventional grid loads from triggering transient control malfunctions, the system pre-sets a strict voltage sag dead zone threshold in the non-volatile memory. (In this embodiment, the rated voltage is preferred.) pu); The algorithm configures a continuous sliding window counter in the DSP computing unit if and only if there are 3 consecutive sampling periods (i.e., All (internal) were detected Only when the state machine formally determines that the receiving-end power grid has experienced a serious "transient disturbance" such as a commutator phase fault, DC bipolar blocking, or three-phase short circuit in the AC line, will the control system smoothly switch from the "steady-state power grid following / support mode" to the "transient emergency boundary reshaping mode".
[0041] Step S13 is the core operation in this embodiment to eliminate subsequent reference frame fragmentation; In step S13, at the moment of physical triggering the state machine transition and determining the occurrence of a large disturbance (precisely recorded as a microsecond-level timestamp)... At this moment, the DSP computing unit will immediately trigger a highest-priority software interrupt; in this interrupt service routine, the absolute phase angle value output from the VSG integrator at this moment will be forcibly read and deeply latched into a protected register; this specific instantaneous phase angle is strictly defined as the initial fault reference angle. ; During all subsequent transient and recovery cycles, the value of this register is absolutely frozen and serves as the sole origin of the coordinate system for phase space derivation.
[0042] Step S2: Construct a strictly continuous absolute dynamic phase angle evolution equation across stages; Many existing reduced-order transient models, when faced with short-circuit faults on the order of hundreds of milliseconds, artificially assume that the phase angle of the internal potential of the converter is frozen in order to simplify the solution of ordinary differential equations; step S2 abandons this assumption that violates the laws of rotor kinematics; step S2 further includes: Step S21: The energy storage VSG control algorithm imparts a virtual moment of inertia to the converter. In electromagnetic power Sudden drop and virtual mechanical power In the instant of a fault that cannot be abruptly changed, the enormous unbalanced acceleration power will inevitably cause the virtual rotor to generate angular acceleration, thus causing the derivative of the internal phase angle to... It becomes a high-frequency dynamic variable that cannot be ignored; Step S22: Regardless of whether the system is in the survival stage of a short-circuit fault depth drop or in the post-fault dynamic recovery stage after the circuit breaker trips and the fault is cleared, the DSP's phase angle deduction algorithm forcibly and uniquely addresses and calls the latched value in step S13. As a globally unified phase reference standard; Step S23: In the discrete-time domain of the digital discrete integrator, a high-precision trapezoidal integration algorithm (replacing the Euler method, which is prone to truncation errors) is used to... Perform real-time solution: (6); In equation (6), For the current sampling cycle, This is the previous sampling cycle; the numerical integration process is strictly executed in each interrupt cycle to solve for the relative deviation. ; Step S24: Superimpose the obtained dynamic phase angle relative deviation onto the absolute reference zero point to obtain the absolute dynamic phase angle used for bottom layer wave generation at the current moment. The formula is: (2); By constructing formula (2), the seamless connection of the voltage fitting trajectory at the moment of fault clearing is ensured, and the secondary impact caused by the switching of reference frame is eliminated.
[0043] Step S3: Digital discretization and reconstructing of transient damping commands based on the equal area rule (EEAC); Step S3 is the core of the control in this embodiment; the DSP calculation unit calculates the continuous phase angle variable as described above, in... In the instruction generation module for the rotating coordinate system, the physical energy boundary is reshaped from two independent channels: active and reactive power; step S3 further includes: Step S31: In the active channel (used for forced cutting to accelerate the area), the transfer function calculation formula is as follows: (3); Formula (3) needs to be converted into a discrete difference equation in the DSP computing unit; For transient inertial terms To prevent high-frequency noise from being amplified by the pure differentiating element, a first-order low-pass filter is usually connected in series in practical engineering (the cutoff frequency is configured as follows). Its discretization expression is to use backward difference to calculate the mutation rate of virtual frequency to simulate real inertia resistance; The key point of step S31 is the dynamic phase angle over-limit penalty term. The DSP calculation unit determines whether the current cumulative absolute value of the phase angle offset has exceeded the preset safe dead zone. (For example, the corresponding actual work angle) (Margin); once the limit is exceeded, the penalty term is immediately applied and a negative power command is output; since grid-connected energy storage is essentially a voltage source operating in four quadrants, this negative command will forcibly drive the energy storage to instantly reverse from "sending power to the grid" to "absorbing huge amounts of active power from the grid," which is in EEAC's On the power angle curve, it is equivalent to directly hollowing out the excess fault injection energy (i.e., cutting acceleration area) during the acceleration phase. Step S32: In the reactive power channel (used for rapid expansion of the deceleration area), the transfer function calculation formula is as follows: (4); The conventional PI control in formula (4) The response is slow when dealing with sudden voltage drops; the voltage differential feedforward term introduced in this embodiment is used. Specializing in the very early transient phase; Before the failure occurred Inside, This will generate extremely high numerical impulses; when the DSP computing unit performs discretization calculations, that is... (7); This huge capacitive reactive power command, after being superimposed, will instantly drive the energy storage grid-connected inverter to output almost... to Short-time reactive power at twice the rated current; In physics, injecting a large amount of reactive current into a weak power grid will rapidly increase the voltage at the PCC point, thereby exceeding the electromagnetic power transfer limit of the entire system. Significantly improved; the overall upward shift of the electromagnetic power curve directly widens the deceleration area used by the control system to restrain the rotor after fault clearance.
[0044] Step S4: Complex frequency domain phase lead compensation and adaptive amplitude limiting to resist inherent system delay; Step S41: Through rigorous control loop delay identification, the delay chain of the grid-type energy storage includes: ADC conversion delay approximately... DSP algorithm execution delay PWM zero-order hold delay Total delay ; In such The low-frequency oscillation band, This will result in a hysteresis angle of approximately tens of degrees. This is sufficient to worsen positive damping into negative damping that causes system instability; Step S42, as Figure 5 As shown, a first-order phase lead compensator is embedded in series in the transmission channel of the converter's underlying inner loop controller when the additional damping command is issued. : (5); By precisely tuning the lead coefficient and time constant This causes the positive leading phase angle generated at the oscillation frequency to be actively canceled out. The resulting phase loss is mitigated to counteract the potential for negative damping. In the C programming implementation, it is discretized into an IIR digital filter using the bilinear transform (Tustin) method: (8); In equation (8), For the input uncompensated command, The output is the compensated instruction; through tuning Provide a leading phase angle to cancel out the hysteresis angle. ; Step S43: The compensated command must be subject to strict thermal and electromagnetic safety boundary limits; the inner loop controller reads the IGBT junction temperature and DC bus voltage in real time, and dynamically calculates the maximum allowable transient apparent capacity of the grid-type energy storage converter. And execute the "voltage protection" limiting allocation logic: prioritize satisfying Reactive power output, remaining capacity Then allocate all of them to the active power damping command. The limited instruction is converted into six independent duty cycle signals by the space vector pulse width modulation (SVPWM) module, which drive the underlying inverter bridge to generate waves.
[0045] Example 3 like Figure 6 As shown, this embodiment also provides a computer device. Features not explained in this embodiment can be explained using the methods described in Embodiment 2, and will not be repeated here. The difference between this embodiment and Embodiment 2 is as follows: The computer device includes a memory, a network interface, an input / output device, and a processor, all connected to a system bus. The memory stores a computer program. When the processor executes the computer program, it implements the above-described method for transient stability control of grid-type energy storage based on dynamic phase angle evolution.
[0046] Example 4 This embodiment also provides a non-transitory computer-readable storage medium. Features not explained in this embodiment can be explained using the methods in Embodiment 2, and will not be repeated here. The difference between this embodiment and Embodiment 2 is as follows: The storage medium includes a stored computer program, which, when executed by a processor, implements the above-described transient stability control method for grid-type energy storage based on dynamic phase angle evolution.
[0047] Based on the disclosure and teachings of the foregoing specification, those skilled in the art can make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments disclosed and described above, and some modifications and changes to the present invention should also fall within the protection scope of the claims of the present invention. Furthermore, although some specific terms are used in this specification, these terms are only for convenience of explanation and do not constitute any limitation on the present invention.
Claims
1. A transient stability control system for grid-type energy storage based on dynamic phase angle evolution, connected to the control port of a grid-type energy storage converter, characterized in that, It includes a transient phase-locked loop module, an absolute dynamic phase angle reconstruction module, an EEAC instruction synthesis module, and an advance limiting drive module connected in sequence; The transient phase-locked module is used to collect electrical quantities at the grid-connected point of the grid-type energy storage system in real time, and to extract the voltage amplitude at the grid-connected point. Deviation from real-time virtual angular frequency It is also used to forcibly latch the current internal algorithm phase angle at the instant when a transient large disturbance drop occurs in the control system, and set it as the initial fault reference angle for the entire transient process. ; The absolute dynamic phase angle reconstruction module is used to reconstruct the initial fault reference angle. As the absolute coordinate zero point, the deviation of the real-time virtual angular frequency Perform high-precision numerical integration to solve and reconstruct a continuous and differentiable absolute dynamic phase angle space sequence; The EEAC instruction synthesis module is used to receive the absolute dynamic phase angle space sequence and calculate the active power additional damping instruction with dynamic phase angle over-limit penalty characteristics and the reactive power additional damping instruction with voltage differential feedforward characteristics. The advanced limiting drive module is used to perform phase advance correction on the generated active and reactive additional damping commands in the complex frequency domain, and to perform flexible limiting allocation within the safety boundary of the maximum apparent capacity of the grid-type energy storage converter, and finally generate control waveforms for driving power switching devices.
2. The grid-type energy storage transient stability control system based on dynamic phase angle evolution according to claim 1, characterized in that, The transient phase-locked loop module includes a high-speed electrical quantity acquisition unit, a high-frequency analog-to-digital converter, a DSP computing unit, a hardware-level interrupt and latch unit, and a register connected in sequence. The high-speed electrical quantity acquisition unit is used to acquire the electrical quantities; the electrical quantities include three-phase instantaneous voltage. and three-phase instantaneous current ; The high-frequency analog-to-digital converter is used to convert analog signals of electrical quantities into digital signals; The DSP computing unit includes a continuous sliding window counter; the DSP computing unit uses a coordinate transformation algorithm on the digital signal and calculates the voltage amplitude at the grid connection point. Deviation from real-time virtual angular frequency ; The continuous sliding window counter is used to monitor the voltage amplitude at the grid connection point. Perform continuous sliding window monitoring; The hardware-level interrupt and latch unit is used to latch the current internal algorithm phase angle as the initial fault reference angle. And save it to the register.
3. The grid-type energy storage transient stability control system based on dynamic phase angle evolution according to claim 1, characterized in that, The absolute dynamic phase angle reconstruction module includes a continuous trajectory fitting unit, and a high-precision numerical integration unit and a zero-point reference clamping unit respectively connected to the continuous trajectory fitting unit; The high-precision numerical integration unit employs a discrete numerical integration algorithm to measure the real-time virtual angular frequency deviation. Perform real-time high-precision integration and solve for the dynamic phase angle relative deviation. ; The zero-point reference clamping unit is used to set the initial fault reference angle. The zero point of the absolute coordinates is used as the reference clamping point to obtain the zero point reference of the clamping. The continuous trajectory fitting unit is used to measure the relative deviation of the dynamic phase angle. By adding the zero-point reference of the clamp, a continuously differentiable absolute dynamic phase angle space sequence is reconstructed.
4. The grid-type energy storage transient stability control system based on dynamic phase angle evolution according to claim 1, characterized in that, The EEAC instruction integration module includes a phase angle safety dead zone comparator, a penalty function calculator, a voltage differential calculator, a conventional closed-loop control unit, and a summation unit; The absolute dynamic phase angle reconstruction module is connected in sequence to the phase angle safe dead zone comparator and the penalty function calculator; The summation unit is connected to the advance limiting drive module, the voltage differential calculator, and the conventional closed-loop control unit, respectively. The phase angle safety dead zone comparator is used to substitute the received absolute dynamic phase angle spatial sequence into the transfer function, and when the received dynamic phase angle relative deviation is... When the absolute value exceeds the preset limit margin, the penalty function in the penalty function calculator will be activated immediately; The penalty function calculator is used to calculate the active power additional damping command with dynamic phase angle over-limit penalty characteristics; The voltage differential calculator and the conventional closed-loop control unit, after being summed by the summing unit, output a reactive power additional damping command with voltage differential feedforward characteristics to the advanced limiting drive module.
5. The grid-type energy storage transient stability control system based on dynamic phase angle evolution according to claim 1, characterized in that, The advanced amplitude limiting drive module includes a digital filtering compensation unit, a dynamic safety boundary adaptive amplitude limiting unit, and a wave generation execution unit connected in sequence. The digital filtering compensation unit is used to perform phase lead correction on the active and reactive additional damping commands in the complex frequency domain. The dynamic safety boundary adaptive limiting unit is used to receive the corrected active and reactive additional damping commands, and according to the flexible allocation logic, to perform flexible limiting allocation within the safety boundary of the maximum apparent capacity of the grid-type energy storage converter, and output controlled commands. The waveform generation unit generates a high-frequency pulse signal corresponding to the control waveform according to the controlled instruction, and sends it to the power switching device.
6. A transient stability control method for grid-type energy storage based on dynamic phase angle evolution, characterized in that, The method is applied to a grid-type energy storage transient stability control system based on dynamic phase angle evolution as described in any one of claims 1 to 5; the method includes the following steps: Step S1: Use a transient phase-locked loop module to collect electrical quantities at the grid-connected point of the grid-type energy storage system in real time, and extract the voltage amplitude at the grid-connected point. Deviation from real-time virtual angular frequency Then, preset the voltage drop dead zone threshold. By judgment To latch the initial fault reference angle Then, the real-time virtual angular frequency deviation is... and initial fault reference angle Transmitted to the absolute dynamic phase angle reconstruction module, grid connection point voltage amplitude Transmitted to the EEAC instruction synthesis module; Step S2: Construct a dynamic phase angle evolution model through the absolute dynamic phase angle reconstruction module, and calculate the relative deviation of the dynamic phase angle in real time. Then through the formula To construct the absolute dynamic phase angle at the current moment Then it is transmitted to the EEAC instruction integration module; Step S3: Based on the equal area rule, generate active power additional damping command and reactive power additional damping command through the EEAC command integration module, and transmit the two additional damping commands to the advance limiting drive module. Step S4: After receiving the active and reactive power additional damping commands, phase advance compensation is introduced through the advance limiting drive module to offset the inherent pure time delay. Impact; After the lead cancels the hysteresis, the dynamic limiting allocation command is used to finally generate a control waveform to drive the power switching device to generate a waveform.
7. The transient stability control method for grid-type energy storage based on dynamic phase angle evolution according to claim 6, characterized in that, In step S1, when detected When a transient large disturbance is detected in the receiving-end power grid, the control system enters a transient emergency support state. The instant the disturbance is triggered is recorded as follows: At that moment, and in The current internal algorithm phase angle is constantly latched and set as the initial fault reference angle. ; In step S2, the dynamic phase angle relative deviation amount The calculation formula is: ; in, The range of values is ; The timestamp of the moment the disturbance was triggered; This represents the real-time virtual angular frequency deviation.
8. The transient stability control method for grid-type energy storage based on dynamic phase angle evolution according to claim 6, characterized in that, In step S3, the active power additional damping command The transfer function formula is: ; Where s is the Laplace operator, a complex frequency variable; This is the transient inertial term; This is the proportional damping term; This is a penalty for exceeding the dynamic phase angle limit. This is the preset limit margin; The reactive power additional damping command The transfer function formula is: ; in, The target voltage threshold for expected recovery; For proportional gain; This is the integral gain; This is the voltage differential feedforward term; In step S4, a first-order phase lead compensator is implanted in series in the transmission channel where the additional damping command is issued; the first-order phase lead compensator The expression is: ; in, It is the leading factor, and ; is the time constant.
9. A computer device, comprising a memory, a network interface, input / output devices, and a processor respectively connected to a system bus, characterized in that, The memory stores a computer program, and when the processor executes the computer program, it implements a transient stability control method for grid-type energy storage based on dynamic phase angle evolution as described in any one of claims 6-8.
10. A non-transitory computer-readable storage medium comprising a stored computer program, characterized in that, When the computer program is executed by the processor, it implements a transient stability control method for grid-type energy storage based on dynamic phase angle evolution as described in any one of claims 6-8.