Energy storage system fundamental wave phasor modeling method considering dynamic loss and anti-saturation integration

Abstract

The invention provides an energy storage system fundamental wave phasor modeling method considering dynamic loss and anti-saturation integration. According to the technical scheme, the energy storage system fundamental wave phasor modeling method comprises the steps that an equivalent circuit model of a rechargeable chemical battery is established; establishing an inverter fundamental wave phasor model considering the dynamic loss of an alternating current side filtering link, and connecting a direct current side and an alternating current side through a power conservation relation; establishing a network construction type system control link model including virtual synchronous machine control and droop control; fine modeling is carried out on a control loop, specifically, a PI controller with an anti-saturation strategy is adopted to construct a voltage outer loop, and a PI controller containing cross decoupling and overmodulation amplitude limiting is adopted to construct a current inner loop. Compared with the prior art, the method has the advantages that the accuracy of the fundamental wave phasor model of the energy storage system can be remarkably improved, and a simulation result can be better matched with the dynamic response of an actual system.

Description

Technical Field

[0001] This invention relates to the field of power system simulation technology, and in particular to a fundamental phasor modeling method for energy storage systems that considers dynamic losses and anti-saturation integrals. Background Technology

[0002] With the rapid increase in the proportion of new energy power generation in the power system, the proportion of traditional synchronous generators has decreased accordingly, leading to problems such as insufficient rotational inertia and poor frequency stability in the power system. Grid-based energy storage systems, by simulating the external characteristics of synchronous generators in converter control, can actively participate in the frequency and voltage regulation of the system when disturbances occur in the grid, thereby effectively improving the stability of the power system.

[0003] When studying new power systems, the high cost and significant risks of conducting large-scale physical experiments on actual systems necessitate the use of modeling and simulation to analyze their operational characteristics. Fundamental phasor simulation, with its millisecond-scale simulation steps, achieves a good balance between computational efficiency and model accuracy, making it a crucial tool for studying power system stability. Therefore, accurate fundamental phasor modeling of grid-connected energy storage systems has significant research value and engineering implications.

[0004] However, existing fundamental phasor models for grid-connected energy storage systems have the following shortcomings: First, when dealing with the losses of the inverter and its filtering stages, they are typically treated as a fixed power transfer efficiency coefficient, simply relating the electrical quantities on the AC and DC sides. This approach ignores the actual fluctuations in the DC-side voltage of the energy storage system and the changes in losses in the filtering stages during dynamic processes. When the grid voltage also fluctuates, this static loss model cannot accurately reflect the true dynamic behavior of the system.

[0005] Secondly, simplified proportional-integral (PI) controller mathematical models are often used when modeling the control loop of energy storage systems. These models typically assume that system fluctuations are small, thus ignoring or simply handling the integral saturation (integral anti-saturation) phenomenon commonly found in the integral element. However, in practical engineering applications, anti-integral saturation controllers are a mature and widely used technology. If the anti-saturation element is not considered in the simulation model, when the system experiences large disturbances, the integrator output may continuously accumulate errors, leading to significant differences between the simulation results and the actual operating conditions. In some cases, the actual system may remain stable while the simulation results show divergence and instability. Summary of the Invention

[0006] The purpose of this invention is to provide a fundamental phasor modeling method for energy storage systems that considers dynamic losses and anti-saturation integrals, in order to solve the problems existing in the prior art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A fundamental phasor modeling method for energy storage systems considering dynamic losses and anti-saturation integrals is characterized by the following steps:

[0009] A mathematical model for a rechargeable chemical battery is established, wherein the model establishes the relationship between port current and port voltage;

[0010] A fundamental phasor model of the inverter stage under PWM control is established. The inverter stage model includes: a DC-side capacitor stage model, which calculates the DC bus voltage based on basic circuit principles and uses the calculated DC bus voltage as the input to the inverter body model; an inverter body model, which uses a controlled voltage source modeling method to generate an AC-side voltage based on the voltage modulation signal output from the current inner loop control stage and the DC bus voltage output from the DC capacitor stage, and uses this voltage as the input to the AC-side filter stage model; and an AC-side filter stage model, which calculates the AC-side branch current based on the AC voltage output from the inverter body model. The filter stage can accurately reflect the dynamic losses of the filter stage during power transmission.

[0011] For the measured data of electrical quantities in the control loop, convert them to per-unit values ​​in the synchronous rotating coordinate system;

[0012] A control loop model for a grid-connected system is established. The actual injected active and reactive power of the grid-connected nodes, as well as the control reference values ​​of active and reactive power, are taken as inputs. The voltage phase angle reference signal is generated by the virtual synchronous machine control loop, and the voltage amplitude reference signal is generated by the droop control loop. The above signals are used as inputs to the voltage outer loop control loop.

[0013] A voltage outer loop control model is established. The voltage amplitude, phase angle reference value and actual measured voltage result output by the control loop of the network system are used as inputs. A current reference value is generated by a PI control with anti-saturation integral and a d-axis priority limiting loop, and then transmitted to the current inner loop control loop. The PI control loop with anti-saturation integral can control the integral result to the limiting value in real time when the integrator reaches the limiting value.

[0014] A current inner loop control model is established, with the current reference value output by the voltage outer loop and the actual measured current as inputs. PI control is adopted, and feedforward control cross-decoupling terms are considered to generate a voltage modulation signal and output it to the inverter body model.

[0015] Specifically, the mathematical model for establishing a rechargeable chemical battery is equivalent to a circuit model of a voltage source and a resistor connected in series, and its mathematical relationship is as follows:

[0016] in, This is the per-unit value of the DC-side capacitor voltage, in pu, with the reference value being the rated voltage of the DC-side bus of the inverter. All parameters were obtained by fitting the battery discharge curve. , The unit is V. The unit is 1 / (A·h); Polarization voltage, in volts (V). This refers to battery capacity, measured in Ah. This is the rated voltage of the DC bus of the inverter, and also the rated DC voltage of the chemical cell, in V. The state of charge of a battery is a dimensionless number between 0 and 1. This is the per-unit value of the battery port current, in pu, with the reference value being the rated current of the DC side branch of the inverter. This is the per-unit value of the voltage source output voltage in the equivalent circuit, in pu, with the reference value being the rated voltage of the DC bus of the inverter. It is the per-unit value of the resistance in the equivalent circuit, with the unit being pu. The base value is the ratio of the rated voltage of the DC bus of the inverter to the rated current of the DC branch of the inverter. This refers to the rated capacity of the DC-side bus of the inverter, in VA. The initial state of charge of the battery is a dimensionless number between 0 and 1. This is the rated current of the DC-side branch of the inverter, expressed in amperes (A).

[0017] In the above model, set Lower limit protection, when When the value is less than or equal to a given non-zero positive threshold, the battery enters a cutoff state and stops discharging. The per-unit value of the battery port voltage is fixed at the lower limit. This avoids model calculation divergence.

[0018] Furthermore, the establishment of the fundamental phasor model of the PWM-controlled inverter stage includes: the DC-side capacitor stage model is modeled based on basic circuit principles, reflecting the impact of input and output power fluctuations on DC voltage; the inverter body model ignores the losses on the inverter bridge arms and the transient processes during device switching, unlike the full-wave model which uses detailed switching models to simulate the switching actions of each power electronic device. The inverter body model adopts the average value modeling concept suitable for fundamental phasor simulation, treating the inverter as a controlled voltage source that can instantaneously output its average voltage within its switching cycle, thereby eliminating the influence of high-frequency switching actions, preserving the fundamental dynamic characteristics of the system, and ensuring that its port output power is completely equal to its input power; the AC-side filter stage model is modeled based on basic circuit principles, considering the resistance loss of the filter branch and the impact of inductor current fluctuations in the filter branch on its transmitted active power.

[0019] Furthermore, the capacitor circuit model establishes the relationship between the DC side and the AC side through the active power conservation relationship, and the mathematical relationship is as follows:

[0020] in, This is the per-unit value of the DC-side port voltage, in pu, with the reference value being the rated voltage of the DC-side bus of the inverter. This is the per-unit value of the DC-side capacitor, in p1. These are the control circuit outputs to the inverter modulation voltage port. The per-unit value of the shaft voltage, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. AC side of the inverter The per-unit value of the shaft current, in pu, with the reference value being the rated line current of the AC side branch of the inverter. This is the per-unit value of the active power input from the chemical battery to the capacitor circuit, measured in pu. The base value is the rated capacity of the AC bus of the inverter. This is the per-unit value of the active power output to the AC side of the inverter, measured in pu, with the base value being the rated capacity of the inverter's AC bus. In the above model, This is used to characterize the impact of DC-side voltage fluctuations on the amplitude of the AC-side voltage output by the inverter after PWM modulation. Changes in the AC-side voltage amplitude further affect the active power at the inverter output port. .

[0021] Furthermore, the relationship between the power at the inverter output port and the power at the system grid connection point is determined by the characteristics of the filter circuit, and its mathematical relationship is as follows:

[0022] in, This is the per-unit value of the port voltage of the chemical cell, i.e., the DC side port voltage, in pu. The reference value is the rated voltage of the DC side bus of the inverter. These are the control loop inputs to the inverter modulation voltage port. The per-unit value of the shaft voltage, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. AC side of the inverter Shaft current value, in pu, with the reference value being the rated line current of the AC side branch of the inverter; These are the system grid connection points. Shaft voltage value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter; These are the per-unit values ​​of the filter inductor's inductance, reactance at power frequency, and equivalent resistance, respectively, in units of pu.

[0023] Furthermore, the filtering circuit model takes into account the dynamic characteristics of the filter inductor, which can accurately characterize the dynamic loss of the filter branch.

[0024] The dynamic loss of the filter branch includes the loss caused by the change in the energy stored in the filter branch inductance due to current fluctuations, and the resistance loss of the filter branch.

[0025] The resistance loss of the filter branch is calculated as follows:

[0026] in, This represents the active power of the resistive losses in the filter branch.

[0027] The loss caused by the change in energy stored in the filter branch inductor due to current fluctuations is calculated as follows:

[0028] in, This is the per-unit value of the loss caused by the change in energy stored in the filter branch inductor due to current fluctuations, in pu. The base value is the rated capacity of the AC bus of the inverter. This is the per-unit value of the filter inductance, in pu; These are the AC side branches of the inverter. The per-unit value of the shaft current, in pu, is the reference value, which is the rated line current of the AC side branch of the inverter.

[0029] Furthermore, in the step of establishing the voltage outer loop control link and the current inner loop control link model, the modeling approach of the control link is based on a commonly used two-level control structure: the voltage outer loop control link is responsible for monitoring and adjusting the system's output voltage, obtaining a voltage error signal by comparing the actual output voltage with a reference voltage signal, and outputting a current reference value after processing by a PI controller to guide the operation of the current inner loop control link; the current inner loop control link is responsible for quickly responding to and tracking the current reference value generated by the voltage outer loop, obtaining a current error signal by comparing the measured current value with the current reference value, and generating an input signal for the inverter's modulation voltage port after processing by a PI controller, thereby adjusting the magnitude and direction of the current by controlling the inverter's output voltage. Those skilled in the art can repeat this control method based on the disclosed content.

[0030] Furthermore, the voltage outer loop control model is established. The input to the voltage outer loop control is a voltage reference value, which outputs d-axis and q-axis current reference values ​​via a PI controller. The PI controller employs an anti-saturation integral strategy. The mathematical relationships of the voltage outer loop control model are as follows:

[0031] in, , For the proportional and integral coefficients of the d-axis; , For the proportional and integral coefficients of the q-axis; , These are the per-unit values ​​of the d-axis and q-axis voltage reference values ​​input to the outer voltage loop control, in units of pu. The reference value is the rated line voltage of the AC bus of the inverter. , These are the per-unit values ​​of the d-axis and q-axis voltages at the inverter output ports, in pu. The reference value is the rated line voltage of the inverter's AC bus. The unlimited output of the PI stage The per-unit value of the shaft current reference value, in pu, is based on the rated line current of the AC side branch of the inverter.

[0032] Furthermore, the integral stage in the PI circuit employs an anti-saturation strategy: During integrator operation, an external control sets a limit value for the output value. When the integrator reaches the limit value during calculation, the integrator input is set to zero, and the integral value is maintained at the limit value to prevent it from exceeding the limit. If the integrator's limiting range narrows due to external factors during normal operation, and the current output value has already exceeded the limit value, the integrator output value is forcibly set to the limit value. In the voltage outer loop control stage of the fundamental phasor model, the integrator's limit value comes from... The axis-priority current limiting circuit provides... The shaft reference current limit value, and the input signal of the integrator is the voltage deviation signal, the expression of which is as follows:

[0033] in, , They are respectively axis, The per-unit value of the shaft voltage deviation signal, in pu, with the reference value being the rated line voltage of the AC bus of the inverter; , They are respectively axis, The input quantity of the shaft integrator is in pu, and the reference value is the rated line voltage of the AC bus of the inverter. , They are respectively axis, The output of the shaft integrator is in pu, and the reference value is the rated line current of the AC side branch of the inverter. , AC side of the inverter axis, Maximum shaft current, in pu, with the reference value being the rated line current of the AC side branch of the inverter.

[0034] Furthermore, the limiting step adopts... The axis-first approach, mathematically expressed as:

[0035] in, These are the outputs to the inner loop control of the current. The per-unit value of the shaft current reference value, in pu, is based on the rated line current of the AC side branch of the inverter.

[0036] Furthermore, the mathematical model for establishing the current inner loop control loop is as follows:

[0037] in , For the proportional and integral coefficients of the d-axis current control loop; , For the proportional and integral coefficients of the q-axis current control loop; , These are the limited d-axis and q-axis current reference values ​​output by the voltage outer loop control loop, in units of pu. The base value is the rated line current of the AC side branch of the converter. , These are the per-unit values ​​of the d-axis and q-axis currents of the AC output branch of the inverter, in pu. The base value is the rated line current of the AC branch of the converter. The unlimited output of the PI stage The per-unit value of the shaft voltage reference value, in pu, is based on the rated line voltage of the AC bus of the inverter.

[0038] For output signal After applying PI limiting, we get:

[0039] in, , This is the per-unit value of the voltage reference after PI limiting, in pu. The reference value is the rated line voltage of the AC bus of the inverter. These are the minimum and maximum per-unit values ​​of the d-axis voltage reference value, respectively, in pu. The reference value is the rated line voltage of the AC bus of the inverter. These are the per-unit values ​​of the minimum and maximum values ​​of the q-axis voltage reference, respectively, in pu. The reference value is the rated line voltage of the AC bus of the inverter.

[0040] Introducing a cross-decoupling term in the current inner loop control , and compensation items , Its mathematical expression is:

[0041] in, These are the unmodulated amplitudes obtained after introducing cross-decoupling and compensation terms, respectively. The per-unit value of the shaft voltage reference value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. These are respectively after the PI stage and its limiting stage. The per-unit value of the shaft voltage reference value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. These are the AC side of the inverter. The per-unit value of shaft voltage, in pu, with the reference value being the rated line voltage of the AC bus of the inverter; This is the per-unit value of the reactance of the filter inductor at power frequency, in pu. The base value is the ratio of the rated line voltage of the AC bus of the inverter to the rated line current of the AC branch of the inverter. AC side of the inverter The per-unit value of the shaft current, in pu, with the reference value being the rated line current of the AC side branch of the inverter.

[0042] Furthermore, the overmodulation limiting circuit for the voltage reference value input to the inverter modulation voltage port employs an amplitude scaling method. When the amplitude of the voltage reference value exceeds a set upper or lower limit, it respectively... The axis voltage reference value is scaled, and its mathematical expression is as follows:

[0043] in, These are the outputs to the inverter modulation voltage port. The per-unit value of the shaft voltage reference value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. The voltage reference value is the per-unit value of the unmodulated voltage reference value, in pu. The reference value is the rated line voltage of the AC bus of the inverter. They are respectively unmodulated and unlimited The shaft voltage reference value is a per-unit value, and the base value is the rated line voltage of the AC bus of the inverter. These are the per-unit values ​​of the minimum and maximum amplitudes of the limiting voltage reference value, respectively, in pu, with the reference value being the rated line voltage of the inverter's AC bus.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1) This invention establishes a filter circuit model that considers the dynamic characteristics of the filter inductor, which accurately characterizes the power loss of the inverter stage in the dynamic process, overcomes the error caused by the use of a fixed efficiency coefficient in the traditional model, and enables the model to more realistically reflect the dynamic response of the energy storage system under grid disturbances.

[0046] 2) This invention introduces a PI controller model with anti-saturation strategy into the voltage outer loop control. This model can effectively handle the saturation problem of the integral element under large system disturbances, prevent the simulation results from becoming unstable due to integral oversaturation, and ensure a high degree of consistency between the simulation results and the actual engineering situation, thereby significantly improving the reliability and practical value of the simulation model. Attached Figure Description

[0047] To more clearly illustrate the technical solution of the present invention, the accompanying drawings are briefly described below:

[0048] Figure 1 This is a flowchart of an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of the overall structure of the model obtained by using the fundamental phasor modeling method for energy storage systems that considers dynamic losses and anti-saturation integrals provided in the embodiments of the present invention.

[0050] Figure 3This is a schematic diagram of the equivalent circuit model of a rechargeable chemical battery in an embodiment of the present invention;

[0051] Figure 4 The diagram shows a comparison of active power in simulations between the fundamental phasor model obtained by the fundamental phasor modeling method for energy storage systems that considers dynamic losses and anti-saturation integrals provided in this embodiment of the invention, the traditional fundamental phasor model, and the full-wave model. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, not all embodiments. 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.

[0053] Example 1

[0054] refer to Figure 1This embodiment provides a fundamental phasor modeling method for energy storage systems that considers dynamic losses and anti-saturation integrals. The method includes: establishing a mathematical model of a rechargeable chemical battery, where the model establishes the relationship between port current and port voltage; establishing a fundamental phasor model of the inverter stage under PWM control, whereby the inverter stage model includes: 1) a DC-side capacitor stage model, calculating the DC bus voltage based on basic circuit principles and using the calculated DC bus voltage as input to the inverter body model; 2) an inverter body model, based on the average value modeling concept suitable for fundamental phasor simulation, using a controlled voltage source modeling method, generating an AC-side voltage based on the voltage modulation signal output from the current inner loop control stage and the DC bus voltage output from the DC capacitor stage, which serves as input to the AC-side filter stage model; 3) an AC-side filter stage model, calculating the AC-side branch current based on the AC voltage output from the inverter body model, where the filter stage accurately reflects the dynamic losses of the filter stage during power transmission; converting the measured data of electrical quantities in the control loop to per-unit values ​​in a synchronous rotating coordinate system; and establishing... A grid-type system control loop model is established, taking the actual injected active and reactive power of the grid-connected nodes and the control reference values ​​of active and reactive power as inputs. A voltage phase angle reference signal is generated by a virtual synchronous machine control loop, and a voltage amplitude reference signal is generated by a droop control loop. These signals are used as inputs to the voltage outer loop control loop. A voltage outer loop control loop model is established, taking the voltage amplitude and phase angle reference values ​​output by the grid-type system control loop and the actual measured voltage results as inputs. A PI control with anti-saturation integral and a d-axis priority limiting loop are used to generate a current reference value, which is then transmitted to the current inner loop control loop. The PI control with anti-saturation integral can control the integral result to the limiting value in real time when the integrator reaches the limiting value. A current inner loop control loop model is established, taking the current reference value output by the voltage outer loop and the actual measured current as inputs. PI control is used, and feedforward control cross-decoupling terms are considered to generate a voltage modulation signal, which is then output to the inverter body model.

[0055] Reference Figure 2The energy storage system control strategy provided in this embodiment can be divided into the following key stages. First, there is the Virtual Synchronous Machine (VSG) control stage, which collects AC-side power data to calculate the grid angle and active voltage reference values. Then, through the outer-loop PI stage containing an anti-integral windup, the output current reference value is determined using a d-axis priority current limiting method (CurrentLimit stage). Finally, through the inner-loop PI stage, the output voltage reference value is limited using an amplitude scaling modulation limiting method (Module Limit stage), while introducing cross-coupling terms during calculation to output a voltage reference value that meets the requirements to control the inverter's primary circuit. Furthermore, the modeling method for the system's primary circuit in this embodiment considers the dynamic processes of the DC-side capacitor and AC-side reactor, and strictly distinguishes between the inverter output port voltage and the AC bus grid-connected voltage.

[0056] 1.1 Rechargeable Chemical Battery Model

[0057] Reference Figure 3 A rechargeable chemical battery model is equivalent to a circuit consisting of an ideal voltage source connected in series with an internal resistance. This model can describe the relationship between the battery's port voltage, current, and state of charge. Its mathematical model is as follows:

[0058] in, This is the per-unit value of the DC-side capacitor voltage, in pu, with the reference value being the rated voltage of the DC-side bus of the inverter. All parameters were obtained by fitting the battery discharge curve. , The unit is V. The unit is 1 / (A·h); Polarization voltage, in volts (V). This refers to battery capacity, measured in Ah. This is the rated voltage of the DC bus of the inverter, and also the rated DC voltage of the chemical cell, in V. The state of charge of a battery is a dimensionless number between 0 and 1. This is the per-unit value of the battery port current, in pu, with the reference value being the rated current of the DC side branch of the inverter. This is the per-unit value of the voltage source output voltage in the equivalent circuit, in pu, with the reference value being the rated voltage of the DC bus of the inverter. It is the per-unit value of the resistance in the equivalent circuit, with the unit being pu. The base value is the ratio of the rated voltage of the DC bus of the inverter to the rated current of the DC branch of the inverter. This refers to the rated capacity of the DC-side bus of the inverter, in VA. The initial state of charge of the battery is a dimensionless number between 0 and 1. This is the rated current of the DC-side branch of the inverter, expressed in amperes (A).

[0059] In the above model, set Lower limit protection, when When the value is less than or equal to a given non-zero positive threshold, the battery enters a cutoff state and stops discharging. The per-unit value of the battery port voltage is fixed at the lower limit. To avoid model calculation divergence, this embodiment will... The lower limit is set to 0.2.

[0060] 1.2 DC-side capacitor and inverter model

[0061] The fundamental phasor model of the inverter stage mainly establishes the connection between the DC and AC sides through the power conservation relationship on the DC-side capacitor. The mathematical relationship is as follows:

[0062] in, This is the per-unit value of the DC-side port voltage, in pu, with the reference value being the rated voltage of the DC-side bus of the inverter. This is the per-unit value of the DC-side capacitor, in p1. These are the control circuit outputs to the inverter modulation voltage port. The per-unit value of the shaft voltage, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. AC side of the inverter The per-unit value of the shaft current, in pu, with the reference value being the rated line current of the AC side branch of the inverter. This is the per-unit value of the active power input from the chemical battery to the capacitor circuit, measured in pu. The base value is the rated capacity of the AC bus of the inverter. This is the per-unit value of the active power output to the AC side of the inverter, measured in pu, with the base value being the rated capacity of the AC bus of the inverter.

[0063] In the above model, This is used to characterize the impact of DC-side voltage fluctuations on the amplitude of the AC-side voltage output by the inverter after PWM modulation. Changes in the AC-side voltage amplitude further affect the active power at the inverter output port. .

[0064] 1.3 AC Side Filtering Stage Model

[0065] One of the core aspects of this model is its accurate description of the dynamic process of the AC side filter stage of the inverter, taking into account dynamic losses. The model primarily considers the dynamic characteristics of the filter inductor and the power loss caused by the circuit's equivalent resistance. The relationship between the power at the inverter output port and the power at the system grid connection point is determined by the characteristics of the filter circuit, and its mathematical relationship is as follows:

[0066] in, This is the per-unit value of the port voltage of the chemical cell, i.e., the DC side port voltage, in pu. The reference value is the rated voltage of the DC side bus of the inverter. These are the control loop inputs to the inverter modulation voltage port. The per-unit value of the shaft voltage, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. AC side of the inverter Shaft current value, in pu, with the reference value being the rated line current of the AC side branch of the inverter; These are the system grid connection points. Shaft voltage value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter; These are the per-unit values ​​of the filter inductor's inductance, reactance at power frequency, and equivalent resistance, respectively, in units of pu.

[0067] Compared to the model equations considered in the filtering stage of traditional fundamental phasor simulation systems, the filter circuit model equations described above consider the differential term of current with respect to time. and Expressing the differential calculations in the equation using the operator s, we get:

[0068] Where s represents the differential operator, i.e. In the equations of this filtering stage model, the effect of current fluctuations on voltage is similar to that on resistance. The power transmission change caused by the differential term of the current is considered as part of the dynamic loss of the filtering stage during the dynamic process. The dynamic loss of the filtering branch includes the loss caused by the change in the energy stored in the inductance of the filtering branch due to current fluctuations, as well as the resistance loss of the filtering branch.

[0069] The resistance loss of the filter branch is calculated as follows:

[0070] in, This represents the active power of the resistive losses in the filter branch.

[0071] The loss caused by the change in energy stored in the filter branch inductor due to current fluctuations is calculated as follows:

[0072] in, This is the per-unit value of the loss caused by the change in energy stored in the filter branch inductor due to current fluctuations, in pu. The base value is the rated capacity of the AC bus of the inverter. This is the per-unit value of the filter inductance, in pu; These are the AC side branches of the inverter. The per-unit value of the shaft current, in pu, with the reference value being the rated line current of the AC side branch of the inverter.

[0073] Per-unit value of d-axis voltage at grid connection point q-axis voltage per unit value The voltage amplitude and phase angle at the system grid connection point, as well as the phase angle signal output by the virtual synchronous machine control loop, are all factors influencing the system's operation. The calculation is as follows:

[0074] in, This is the per-unit value of the inverter's AC side grid-connected bus voltage amplitude, in pu. The base value is the rated voltage of the inverter's AC side bus. The phase angle of the inverter's AC side grid-connected bus voltage, in rad; Output phase angle signal for the virtual synchronous machine control loop.

[0075] 2. Control System Modeling

[0076] 2.1 Control components of a grid-type system (active power - frequency, reactive power - voltage)

[0077] In the control stage of the grid-type system, active power is controlled using a virtual synchronous generator (VSG) to simulate the inertial response of a synchronous generator, while reactive power is controlled using droop control. The mathematical model is as follows:

[0078] in, This represents the inertial time constant corresponding to the virtual moment of inertia, expressed in seconds (s). This is the per-unit value of the system angular frequency, in pJ units, with a reference value of [missing value]. , , The system's rated frequency; and These are the per-unit values ​​of the active power reference value and the per-unit values ​​of the actual measured active power value, respectively. The damping coefficient; The internal phase angle of the network control is the output phase angle signal of the virtual synchronous machine control loop, measured in rad. This is the per-unit value of the d-axis voltage reference value input to the voltage outer loop control; This is the constant reference voltage value in droop control, in pu; and These are the per-unit values ​​of the reference value and the per-unit value of the actual measured value of reactive power, respectively. This represents the reactive power droop factor. Actual power value. and The calculation method is as follows:

[0079] in, and These are the per-unit values ​​of the measured d-axis and q-axis voltages, in pu, with the reference value being the rated line voltage of the inverter's AC side bus.

[0080] 2.2 Voltage outer loop control (including anti-saturation PI)

[0081] The voltage outer loop control uses a PI controller with anti-saturation integral. This is another core element of this model, used to solve the integral saturation problem in traditional models.

[0082] In this invention, the input of the voltage outer loop PI controller is the bus voltage error, that is, the difference between the d-axis and q-axis voltage reference values ​​and the actual measured values, and the output of the PI controller is the d-axis and q-axis current reference values.

[0083] The modeling approach for establishing the voltage outer loop control and current inner loop control is based on a commonly used two-level control structure: the voltage outer loop control is responsible for monitoring and adjusting the system's output voltage. It obtains a voltage error signal by comparing the actual output voltage with a reference voltage signal. This voltage error signal is processed by a PI controller and outputs a current reference value to guide the operation of the current inner loop control. The current inner loop control is responsible for quickly responding to and tracking the current reference value generated by the voltage outer loop. It obtains a current error signal by measuring the current value and comparing it with the current reference value. This current error signal is processed by a PI controller and generates an input signal for the inverter's modulation voltage port, thereby controlling the inverter's output voltage to adjust the magnitude and direction of the current. Those skilled in the art can repeat this control method based on the disclosed content.

[0084] The mathematical relationship of the voltage outer loop control model is as follows:

[0085] in, , For the proportional and integral coefficients of the d-axis; , For the proportional and integral coefficients of the q-axis; , These are the per-unit values ​​of the d-axis and q-axis voltage reference values ​​input to the outer voltage loop control, in units of pu. The reference value is the rated line voltage of the AC bus of the inverter. , These are the per-unit values ​​of the d-axis and q-axis voltages at the inverter output ports, in pu. The reference value is the rated line voltage of the inverter's AC bus. The unlimited output of the PI stage The per-unit value of the shaft current reference value, in pu, is based on the rated line current of the AC side branch of the inverter.

[0086] The integral stage in the PI circuit employs an anti-saturation strategy: when the integrator is working, the output value limit is set by external control. When the integrator reaches the limit during the calculation process, the input of the integrator is set to zero, and the integral value of the integrator is kept at the limit value to ensure that it does not continue to exceed the limit. When the integrator's limit range is reduced due to external reasons during normal operation, if the current output value has exceeded the limit value, the integrator output value is forcibly set to the limit value.

[0087] In the voltage outer loop control loop of the fundamental phasor model, the integrator's limiting value comes from... The axis-priority current limiting circuit provides... The shaft reference current limit value, and the input signal of the integrator is the voltage deviation signal, the expression of which is as follows: ,

[0088] in, , They are respectively axis, The per-unit value of the shaft voltage deviation signal, in pu, with the reference value being the rated line voltage of the AC bus of the inverter; , They are respectively axis, The input quantity of the shaft integrator is in pu, and the reference value is the rated line voltage of the AC bus of the inverter. , They are respectively axis, The output of the shaft integrator is in pu, and the reference value is the rated line current of the AC side branch of the inverter. , AC side of the inverter axis, Maximum shaft current, in pu, with the reference value being the rated line current of the AC side branch of the inverter.

[0089] Integrator limit value The mathematical relationship of the current limiting circuit originating from the d-axis priority is as follows:

[0090] in, These are the outputs to the inner loop control of the current. The per-unit value of the shaft current reference value, in pu, is based on the rated line current of the AC side branch of the inverter.

[0091] 2.3 Current inner loop control (including cross-decoupling and overmodulation limiting)

[0092] The inner current control loop employs PI control and includes a cross-coupling feedforward term for decoupling. Its output voltage reference value is overmodulated and limited by a scaling factor. Its mathematical model is as follows:

[0093] in , For the proportional and integral coefficients of the d-axis current control loop; , For the proportional and integral coefficients of the q-axis current control loop; , These are the limited d-axis and q-axis current reference values ​​output by the voltage outer loop control loop, in units of pu. The base value is the rated line current of the AC side branch of the converter. , These are the per-unit values ​​of the d-axis and q-axis currents of the AC output branch of the inverter, in pu. The base value is the rated line current of the AC branch of the converter. The unlimited output of the PI stage The per-unit value of the shaft voltage reference value, in pu, is based on the rated line voltage of the AC bus of the inverter.

[0094] For output signal After applying PI limiting, we get:

[0095] in, , This is the per-unit value of the voltage reference after PI limiting, in pu. The reference value is the rated line voltage of the AC bus of the inverter. These are the minimum and maximum per-unit values ​​of the d-axis voltage reference value, respectively, in pu. The reference value is the rated line voltage of the AC bus of the inverter. These are the per-unit values ​​of the minimum and maximum values ​​of the q-axis voltage reference, respectively, in pu. The reference value is the rated line voltage of the AC bus of the inverter.

[0096] Introducing a cross-decoupling term in the current inner loop control , and compensation items , Its mathematical expression is:

[0097] in, These are the unmodulated amplitudes obtained after introducing cross-decoupling and compensation terms, respectively. The per-unit value of the shaft voltage reference value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. These are respectively after the PI stage and its limiting stage. The per-unit value of the shaft voltage reference value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. These are the AC side of the inverter. The per-unit value of shaft voltage, in pu, with the reference value being the rated line voltage of the AC bus of the inverter; This is the per-unit value of the reactance of the filter inductor at power frequency, in pu. The base value is the ratio of the rated line voltage of the AC bus of the inverter to the rated line current of the AC branch of the inverter. AC side of the inverter The per-unit value of the shaft current, in pu, with the reference value being the rated line current of the AC side branch of the inverter.

[0098] The final voltage reference value input to the inverter control terminal and From the reference signal This is achieved through an over-modulation limiting stage. This stage uses an amplitude scaling method, where the amplitude of the voltage reference value is... When the set limit is exceeded, the d-axis and q-axis components are scaled proportionally. The mathematical expression is as follows:

[0099] in, These are the outputs to the inverter modulation voltage port. The per-unit value of the shaft voltage reference value, in pu, with the reference value being the rated line voltage of the AC bus of the inverter. The voltage reference value is the per-unit value of the unmodulated voltage reference value, in pu. The reference value is the rated line voltage of the AC bus of the inverter. They are respectively unmodulated and unlimited The shaft voltage reference value is a per-unit value, and the base value is the rated line voltage of the AC bus of the inverter. These are the per-unit values ​​of the minimum and maximum amplitudes of the limiting voltage reference value, respectively, in pu, with the reference value being the rated line voltage of the inverter's AC bus.

[0100] 3. Model Validation

[0101] To verify the advantages of the fundamental phasor modeling method for energy storage systems considering dynamic losses and anti-saturation integrals provided by this invention, a corresponding energy storage system model (denoted as the model proposed in this invention) was established using the modeling method provided by this invention. Fundamental phasor modeling and simulation of an energy storage system were performed on a computer. The simulation results were compared with those of a traditional fundamental phasor model of an energy storage system that does not consider the voltage outer loop anti-saturation PI integral and the dynamic losses of the filter branch (denoted as the traditional fundamental phasor model) and a universally recognized high-precision full-wave model (built in PSCAD / EMTDC software, denoted as the full-wave model). The difference between the model equations of the traditional fundamental phasor model of the energy storage system and the model proposed in this invention is that the traditional fundamental phasor model does not consider the differential terms in the model equations of the filter element, i.e., the differential terms... and The value is fixed at 0; the PI control loop in the voltage outer loop control loop model does not consider the anti-saturation integral loop described in this invention; apart from the above differences, the remaining loops of the traditional fundamental phasor model are consistent with the model proposed in this invention.

[0102] Reference Figure 4 The figure shows the dynamic response curves of the active power output of the grid-connected node of the energy storage system obtained by three models under the same disturbance. As can be seen from the figure, compared with the traditional fundamental phasor model, the simulation results obtained using the model proposed in this invention have a higher degree of overlap with the simulation results of the full-wave model, indicating that the model proposed in this invention has higher simulation accuracy. Furthermore, the energy storage system modeling method provided by this invention ignores high-frequency switching dynamics. Compared with the full-wave model that analyzes the detailed switching process, the complexity of the model proposed in this invention is significantly reduced. The simulation time of the three models is shown in Table 1. The table data shows that the model proposed in this invention has higher computational efficiency when applied to simulations compared to the full-wave model.

[0103] Table 1. Statistics on simulation time for various models

[0104]

[0105] This fully demonstrates that by using the fundamental wave phasor modeling method for energy storage systems that considers dynamic losses and anti-saturation integrals provided by this invention, the resulting model achieves significantly improved simulation efficiency while maintaining accuracy comparable to the full-wave model, demonstrating extremely high practicality and accuracy.

[0106] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fundamental phasor modeling method of energy storage system considering dynamic loss and anti-windup, characterized in that, The method comprises the following steps: establishing a mathematical model of a rechargeable chemical battery, the model establishing a relationship between a port current and a port voltage; A fundamental phasor model of a PWM-controlled inverter link is established, the inverter link model comprising: a DC side capacitor link model, a DC bus voltage being calculated based on a basic circuit principle and being taken as an input of an inverter body model; The inverter body model adopts a modeling method of a controlled voltage source, generates an AC side voltage according to a voltage modulation signal output by a current inner loop control link and a DC bus voltage output by the DC capacitor link, and takes the AC side voltage as an input of an AC side filter link model; the AC side filter link model calculates an AC side branch current based on the AC voltage output by the inverter body model; Measurement data of electrical quantities in a control loop are converted to a unit value in a synchronous rotating coordinate system; A grid-forming system control link model is established, taking actual injected active power and reactive power of a grid-connected node and control reference values of the active power and the reactive power as inputs, generating a voltage phase angle reference signal through a virtual synchronous machine control link and a voltage amplitude reference signal through a droop control link, and taking the signals as inputs of a voltage outer loop control link; A voltage outer loop control link model is established, taking voltage amplitude and phase angle reference values output by the grid-forming system control link and actual measurement voltage results as inputs, generating a current reference value through PI control with anti-saturation integration and d-axis priority amplitude limiting, and transmitting the current reference value to a current inner loop control link; A current inner loop control link model is established, taking the current reference value output by the voltage outer loop and actual measurement current as inputs, generating a voltage modulation signal through PI control and considering a feedforward control cross-decoupling term, and outputting the voltage modulation signal to the inverter body model.

2. The modeling method of claim 1, wherein, The mathematical model of the rechargeable chemical battery is equivalent to a circuit model of a voltage source and a resistor in series, and the mathematical relationship is: ； wherein, is the rated value of the DC side capacitor voltage, with unit of p.u., and the reference value is the inverter DC side bus rated voltage; are parameters obtained by fitting the battery discharge curve, , with unit of V, with unit of 1 / (A·h); is the polarization voltage, with unit of V; is the battery capacity, with unit of A·h; is the inverter DC side bus rated voltage, which is also the DC rated voltage of the chemical battery, with unit of V; is the state of charge of the battery, which is a dimensionless number between 0 and 1; is the battery port current per unit, with unit of p.u., and the reference value is the inverter DC side branch rated current; is the voltage source output voltage per unit in the equivalent circuit, with unit of p.u., and the reference value is the inverter DC side bus rated voltage; is the resistance per unit in the equivalent circuit, with unit of p.u., and the reference value is the ratio of the inverter DC side bus rated voltage to the inverter DC side branch rated current; is the inverter DC side bus rated capacity, with unit of VA; is the initial state of charge of the battery, which is a dimensionless number between 0 and 1; is the inverter DC side branch rated current, with unit of A; In the above model set Lower limit protection, when When less than or equal to a given non-zero positive threshold value, the battery enters a cutoff state and no longer continues to discharge, at which time Fixed as the lower limit value, the unit of the battery port voltage , to avoid model divergence.

3. The modeling method of claim 1, wherein, The fundamental phasor model of the PWM-controlled inverter link comprises: The DC side capacitor link model is modeled based on a basic circuit principle, reflecting the influence of input and output power fluctuations on the DC voltage; The inverter body model ignores the losses on the inverter bridge arms and the transient process when the devices are turned on and off, and is different from the method of simulating the switching action of each power electronic device in the full-wave model, the inverter body model adopts an average value modeling concept suitable for fundamental phasor simulation, equivalent to a controlled voltage source that can instantaneously output the average voltage in its switching period, to eliminate the influence of switching high-frequency action and retain the fundamental dynamic characteristics of the system, and the port output power is completely equal to the input power; The AC side filter link model is modeled based on a basic circuit principle, considering the resistance loss of the filter branch and the influence of the inductance current fluctuation of the filter branch on the transmission of active power.

4. The modeling method of claim 3, wherein, The capacitor link model establishes a relationship between the DC side and the AC side through the active power conservation relationship, and the mathematical relationship is as follows: ； wherein, is the DC side port voltage per unit, with the reference value being the inverter DC side bus rated voltage; is the DC side capacitor per unit, with the reference value being the inverter DC side bus rated voltage; respectively are the control loop output to the inverter modulation voltage port is the axis voltage per unit, with the reference value being the inverter AC side bus rated line voltage; respectively are the inverter AC side is the axis current per unit, with the reference value being the inverter AC side branch rated line current; is the active power per unit from the chemical battery input to the capacitor link, with the reference value being the inverter AC side bus rated capacity; is the active power per unit output to the inverter AC side, with the reference value being the inverter AC side bus rated capacity; In the above model, For characterizing the influence of the DC side voltage fluctuation on the AC side voltage amplitude of the PWM modulated inverter output, the change of the AC side voltage amplitude will further affect the active power of the inverter output port .

5. The modeling method of claim 3, wherein, The power relationship between the inverter output port and the system grid-connected node is determined by the characteristics of the filter circuit, and the mathematical relationship is as follows: ； wherein, is the port voltage of the chemical battery, i.e. the DC side port voltage, in per unit (p.u.) with the rated voltage of the DC bus of the inverter as the reference value; are the control loop input to the modulation voltage port of the inverter, respectively, is the per unit value of the shaft voltage, in p.u. with the rated line voltage of the AC bus of the inverter as the reference value; are the AC side of the inverter, respectively, is the per unit value of the shaft current, in p.u. with the rated line current of the branch of the AC bus of the inverter as the reference value; are the system grid point, respectively, is the per unit value of the shaft voltage, in p.u. with the rated line voltage of the AC bus of the inverter as the reference value; are the per unit value of the inductance of the filter inductor, the per unit value of the reactance at the power frequency, and the per unit value of the equivalent resistance, respectively, in p.u.

6. The modeling method of claim 3, wherein, The filter link model considers the dynamic characteristics of the filter inductance, The dynamic loss of the filter branch includes a loss caused by a change in energy stored in the filter branch inductance due to current fluctuation, and a resistance loss of the filter branch; The resistance loss of the filter branch is calculated as follows: ； wherein, Ploss,ref is the normalized active power of the resistance losses in the filter branch, in p.u. The loss caused by the change in energy stored in the filter branch inductance due to current fluctuation is calculated as follows: ； wherein, is the normalized value of the loss caused by the change of the energy stored in the filter branch inductance due to the current fluctuation, with the unit of p.u. and the reference value being the rated capacity of the AC bus of the inverter; is the normalized value of the filter inductance, with the unit of p.u; are the normalized values of the line current and the neutral current of the AC side of the inverter, respectively, with the unit of p.u. and the reference value being the rated line current of the AC side of the inverter; is the normalized value of the shaft current, with the unit of p.u. and the reference value being the rated line current of the AC side of the inverter.

7. The modeling method of claim 1, wherein, In the step of establishing the voltage outer loop control link and the current inner loop control link model, the modeling idea of the control link is based on a two-stage control structure: the voltage outer loop control link is responsible for monitoring and adjusting the output voltage of the system, and a voltage error signal is obtained by comparing the actual output voltage with the reference voltage signal; the voltage error signal is processed by a PI controller to output a current reference value, which guides the work of the current inner loop control link; the current inner loop control link is responsible for quickly responding and tracking the current reference value generated by the voltage outer loop, and a current error signal is obtained by comparing the measured current value with the current reference value; the current error signal is processed by a PI controller to generate an input signal of the inverter modulation voltage port, so as to control the output voltage of the inverter to adjust the size and direction of the current.

8. The modeling method of claim 1, wherein, The input of the voltage outer loop control link is a voltage reference value, and the d-axis and q-axis current reference values are output after a PI link, wherein the PI link adopts an anti-saturation integral strategy, and the mathematical relationship of the voltage outer loop control link model is as follows: ； wherein, , is a proportional link coefficient, an integral link coefficient of the d-axis; , is a proportional link coefficient, an integral link coefficient of the q-axis; , is a unit value of the d-axis, q-axis voltage reference value input to the voltage outer loop control, in p.u., with a reference value being a rated line voltage of an inverter AC side bus; , is a unit value of the d-axis, q-axis voltage of the inverter output port, in p.u., with a reference value being a rated line voltage of an inverter AC side bus; are respectively the unclipped axis current reference values of the PI link outputs, in p.u., with a reference value being a rated line current of an inverter AC side branch.

9. The modeling method of claim 8, wherein, The integral link in the PI link adopts an anti-saturation strategy: when the integrator is working, the limit value of the output value is set by external control, and when the integrator reaches the limit value in the calculation process, the input of the integrator is set to zero, and the integral value of the integrator is maintained as the limit value, so as to ensure that it does not continue to exceed the limit; when the integrator is in the normal working process, if the current output value has exceeded the limit value due to external reasons, the integrator output value is forced to be set as the limit value; In the voltage outer loop control link in the fundamental phasor model, the amplitude limiting value of the integrator comes from The amplitude limiting value of the axis priority current limiting link is given by The axis reference current limiting value, the input signal of the integrator is the voltage deviation signal, and its expression is as follows: ； ； wherein, , are respectively axis, axis voltage deviation signal, unit is p.u., reference value is the rated line voltage of the inverter AC side bus; , are respectively axis, axis integrator input quantity, unit is p.u., reference value is the rated line voltage of the inverter AC side bus; , are respectively axis, axis integrator output quantity, unit is p.u., reference value is the rated line current of the inverter AC side branch; , is the inverter AC side axis, axis current maximum value, unit is p.u., reference value is the rated line current of the inverter AC side branch.

10. The modeling method of claim 9, wherein, The limiting link adopts The axis-priority method is mathematically expressed as: ； wherein, are the output to the current inner loop control the unit of the axis current reference value, the reference value is the rated line current of the inverter AC side branch.

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