A stability judgment method for a full-power pumped storage unit direct-current bus

Abstract

The application provides a kind of full power pumped storage unit DC bus stability determination method, it is related to water power generation technical field.The method comprises: the DC bus capacitor is equivalent to two parallel equivalent capacitors, and with parallel point as limit, pumped storage unit is split into machine side, network side;Respectively, the small signal model of each electrical device of two parts is constructed;Based on each small signal model, the corresponding admittance model is constructed, and then the corresponding impedance model is constructed;Electrical parameters and control parameters are brought into impedance model, and the corresponding Bode diagram is drawn;Under the same working condition, if the phase difference of the amplitude intersection point of two Bode diagrams is less than 90°, under the corresponding working condition, there will be no interaction instability on the DC bus, otherwise interaction instability will occur.The method can effectively reduce the modeling difficulty and model complexity of full power pumped storage unit, accurately reflect the characteristics of pumped storage unit, and can determine the interaction stability of the power system on the DC bus.

Description

Technical Field

[0001] This invention relates to the field of hydropower technology, and in particular to a method for judging the stability of the DC bus of a full-power pumped storage unit. Background Technology

[0002] Currently, new energy power generation technologies, primarily wind and solar power, are developing rapidly and their proportion in the power grid is gradually increasing. However, the volatility, intermittency, and randomness brought to the power grid by new energy power generation result in insufficient regulation capacity of the power system, making it unable to quickly and effectively suppress power fluctuations, leading to wind and solar power curtailment. Compared to doubly-fed pumped storage units, full-power pumped storage units connect to the grid via back-to-back converters, decoupling the motor from the grid frequency, resulting in a wider speed range and a broader power regulation range, making them suitable for large-scale grid power fluctuations. During startup, they can start with water, offering faster startup speed and greater starting torque. Furthermore, because their motors use synchronous motors, they have stronger compatibility with existing older power plants.

[0003] For current small-signal modeling of full-power pumped storage units, the generator cannot directly interact with the grid, requiring back-to-back converters for AC-DC-AC switching. This leads to coupling of various system parameters, resulting in complex system order and parameter relationships for overall modeling, which is detrimental to system stability analysis. Existing small-signal modeling methods mostly ignore the generator-side converters and generators, treating them as equivalent power sources and neglecting the frequency response characteristics of the generator-side components in the low-frequency range. This results in insufficient accuracy of the pumped storage unit model under different operating conditions, failing to reveal the interactive stability issues between the generator side and the grid side of the DC bus in the pumped storage unit. This affects the delineation of power system stability boundaries and is unfavorable for subsequent parameter tuning. Summary of the Invention

[0004] To address the aforementioned technical problems in the existing technology, this invention aims to provide a method that can accurately reflect the characteristics of pumped storage units under different operating conditions, reveal the interactive stability issues between the pumped storage unit's generator side and the grid side, and help improve the accuracy of power system stability boundary delineation and subsequent parameter tuning stability judgment.

[0005] Specifically, the present invention provides a method for judging the stability of the DC bus of a full-power pumped storage unit, the technical solution of which is as follows:

[0006] The DC bus capacitor is equivalent to two parallel equal capacitors, and the pumped storage unit is divided into a machine-side part and a grid-side part with the parallel connection point as the boundary.

[0007] For the turbine side, small-signal models are constructed for the turbine system, synchronous motor, turbine-side converter, turbine-side modulation circuit, and turbine-side control loop, respectively. Based on each small-signal model, a first admittance model is constructed. Based on the first admittance model, a first impedance model is constructed.

[0008] For the grid-side portion, small-signal models are constructed for the grid-side converter, AC-side main circuit, grid-side modulation stage, and grid-side control loop, respectively; based on each small-signal model, a second admittance model is constructed; based on the second admittance model, a second impedance model is constructed.

[0009] Substitute the electrical parameters and control parameters into the first impedance model and the second impedance model respectively to construct the corresponding first impedance frequency domain model and the second impedance frequency domain model.

[0010] Bode plots are drawn according to the first impedance model and the second impedance model in the same coordinate system;

[0011] Adjust the response frequency to determine the amplitude intersection point of the first impedance frequency domain model and the second impedance frequency domain model in the Bode plot;

[0012] Under the same operating conditions, if the phase difference at the intersection point is less than 180°, no interactive instability will occur on the DC bus; otherwise, interactive instability will occur.

[0013] Preferably, for the turbine-side components, small-signal models are constructed for the turbine system, synchronous motor, turbine-side converter, turbine-side modulation circuit, and turbine-side control loop, respectively, specifically as follows:

[0014] (1) Construct a small-signal model of the turbine system, with the following formula:

[0015] ;

[0016] In the formula, Indicates a small semaphore. This refers to the mechanical torque consumed by the turbine system through the main shaft. The time parameter for the water hammer effect in the turbine system. For the Laplace operator, This refers to the proportional coefficient in PID control. The integral coefficient in PID control. The time constant of the blade servo system control delay. This refers to the output power of the synchronous motor;

[0017] (2) Construct the small-signal model of the synchronous motor, the formula is as follows:

[0018] ;

[0019] ;

[0020] ;

[0021] In the formula, Let be the stator voltage of the synchronous motor in the dq coordinate system. Let be the matrix corresponding to the small-signal stator current of the armature reaction of the synchronous motor in the dq coordinate system. Let be the stator current of the synchronous motor in the dq coordinate system. Let be the matrix corresponding to the small signal of the synchronous motor's armature reaction and electrical angular velocity in the dq coordinate system. The electrical angular velocity of the synchronous motor. Let be the d-axis component of the armature inductance in the dq coordinate system. Let be the q-axis component of the armature inductance in the dq coordinate system. Let q be the q-axis component of the stator current of the synchronous motor in the dq coordinate system. Let d be the d-axis component of the stator current of the synchronous motor in the dq coordinate system. Equivalent magnetic flux;

[0022] (3) Construct the small-signal model of the machine-side converter, as shown in the following formula:

[0023] ;

[0024] In the formula, This refers to the DC-side current of the machine-side section. This is the dq component matrix of the modulated wave on the machine side. This is the matrix of the dq components of the stator current on the machine side. This is the equivalent capacitance on the DC side of the machine side. DC side voltage Indicates transpose;

[0025] (4) Construct the small-signal model of the machine-side modulation stage, as shown in the following formula:

[0026] ;

[0027] In the formula, The modulation gain coefficient;

[0028] (5) Construct the small-signal model of the machine-side control loop, as shown in the following formula:

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] In the formula, This represents the transfer function matrix of the inner current loop on the machine side. This is the decoupling matrix for the stator current under small-signal conditions. This is the decoupling matrix for the motor angular velocity under small signal conditions. This is the transfer function matrix for the outer loop of the engine-side rotational speed section. This is the transfer function of the inner loop of the speed PI controller in the machine-side control loop. The transfer function for the outer loop of the PI controller in the engine-side control loop is given. For the armature inductance of the motor, This is the damping coefficient of the synchronous motor.

[0035] Preferably, the formula for the first admittance model is as follows:

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] In the formula, For the machine-side admittance, This refers to the admittance of the DC capacitor on the machine side. For the machine-side AC circuit admittance, For the machine-side control loop admittance, Here is the impedance matrix of the filter circuit. This is the equivalent matrix of the dual closed-loop control branch on the lower side of the small signal. This is the conversion matrix from stator current to electric angular velocity.

[0042] Preferably, for the grid-side portion, small-signal models are constructed for the grid-side converter, AC-side main circuit, grid-side modulation stage, and grid-side control loop, respectively, specifically as follows:

[0043] (1) Construct the small-signal model of the grid-side converter, as shown in the following formula:

[0044] ;

[0045] In the formula, Indicates a small semaphore. This refers to the DC-side current of the grid-side portion. This is the dq component matrix of the modulated wave on the network side. This is the matrix of the dq components of the grid-connected current on the grid side. This is the equivalent capacitance on the DC side of the grid side. This is the DC side voltage;

[0046] (2) Construct the small-signal model of the AC side main circuit, as shown in the following formula:

[0047] ;

[0048] ;

[0049] ;

[0050] In the formula, This represents the d-axis component of the grid-side converter port voltage under the actual phase of the power system. This represents the q-axis component of the grid-side converter port voltage under the actual phase of the power system. The equivalent impedance matrix of the power grid. Here is the impedance matrix of the filter circuit. This represents the d-axis component of the grid-connected current under the actual phase of the power system. This represents the q-axis component of the grid-connected current under the actual phase of the power system. For the Laplace operator, The equivalent inductance of the power grid, This is the equivalent capacitance of the power grid to ground. For filtering inductors, The rotational angular velocity of the grid connection point coordinate transformation obtained by the phase-locked loop;

[0051] (3) Construct the small-signal model of the network-side modulation stage, as shown in the following formula:

[0052] ;

[0053] In the formula, This is the dq component matrix of the grid-side converter port voltage;

[0054] (4) Construct the small-signal model of the grid-side control loop, as shown in the following formula:

[0055]

[0056] ;

[0057] ;

[0058] ;

[0059] In the formula, This represents the dq component matrix of the modulated wave on the network side under actual phase. The modulation gain coefficient of the machine-side converter. This is the transformation matrix for the actual phase transition to the dq component of the voltage at the PCC point under the corresponding controller phase in the phase-locked loop. This is the transformation matrix for the actual phase transition to the modulated wave dq component under the phase-locked loop corresponding controller phase. This is the transformation matrix for the actual phase transition to the current dq component at the PCC point under the corresponding controller phase in the phase-locked loop. This represents the transfer function matrix of the inner loop current on the grid side. This is the decoupling matrix for the grid connection point current under small-signal conditions. The outer loop transfer function matrix of the grid-side voltage section. This is the dq component matrix of the grid-connected voltage on the grid side under the actual phase. This is the matrix of the dq components of the grid-connected current on the grid side under the actual phase. Let be the transfer function of the inner loop of the speed PI controller in the grid-side control loop. This is the transfer function of the outer loop of the DC voltage PI in the grid-side control loop.

[0060] Preferably, the formula for the second admittance model is as follows:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] In the formula, For the network-side admittance, For grid-side DC loop admittance, For grid-side AC loop admittance, For grid-side control loop admittance, This is the matrix of the dq components of the grid-connected current on the grid side. This is the dq component matrix of the modulated wave on the network side. This is the AC / DC coupling matrix for the small-signal network side. The equivalent impedance matrix of the power grid. Here is the impedance matrix of the filter circuit. This is the equivalent matrix of the dual closed-loop control branch on the small-signal network side.

[0068] Compared with existing technologies, the stability judgment method provided by this invention can effectively reduce the modeling difficulty and complexity of full-power pumped storage units through a segmented small-signal modeling method and a DC bus stability judgment method. It can accurately reflect the characteristics of pumped storage units, judge the interactive stability of the power system on the DC bus, and help solve parameter sensitivity analysis and broadband oscillation problem tracing. Attached Figure Description

[0069] Figure 1 This is the overall structure of a full-power pumped storage unit in one embodiment of the present invention.

[0070] Figure 2 This is a structural diagram of the machine-side subsystem of a full-power pumped storage unit in one embodiment of the present invention.

[0071] Figure 3 This is a detailed control block diagram of a water turbine system in one embodiment of the present invention.

[0072] Figure 4 This is a block diagram of the dq axis machine side model in one embodiment of the present invention.

[0073] Figure 5 This is a block diagram of the dq axis machine side model after modification in one embodiment of the present invention.

[0074] Figure 6 This is a structural diagram of the grid-side subsystem of a full-power pumped storage unit in one embodiment of the present invention.

[0075] Figure 7 This is a detailed control block diagram of a phase-locked loop in one embodiment of the present invention.

[0076] Figure 8 This is a block diagram of the dq axis machine side model in one embodiment of the present invention.

[0077] Figure 9 This is a block diagram of the dq axis grid side model after being sorted out in one embodiment of the present invention.

[0078] Figure 10 This is a schematic diagram comparing the frequency sweep results and analysis results of the generator-side and grid-side small systems under power generation conditions in one embodiment of the present invention.

[0079] Figure 11 This is a schematic diagram comparing the frequency sweep results and analysis results of the small system on the pumping side and the network side under the pumping condition in one embodiment of the present invention.

[0080] Figure 12 This is a waveform diagram of DC bus voltage and current under power generation and pumping conditions in one embodiment of the present invention. Detailed Implementation

[0081] The technical solutions provided by the present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0082] Example 1

[0083] Step 1: The overall structure of a full-power pumped storage unit is as follows: Figure 1 As shown, the system includes a turbine system, synchronous motor, excitation system, turbine-side converter, DC bus capacitor, grid-side converter, filter, and power grid. For ease of analysis, the DC bus capacitor is equivalent to two capacitors with identical parameters connected in parallel, each capacitor having half the capacitance of its original capacitor. Based on this equivalence, the pumped storage unit is divided into two main parts: one part is the turbine-side subsystem, i.e., the turbine-side section, which consists of the turbine system, synchronous motor, excitation system, turbine-side converter, and DC capacitor. The other part is the grid-side subsystem, which includes the power grid, filters, grid-side converters, and DC-side equivalent capacitance. This classification method helps simplify the modeling of pumped storage units, improve the modeling accuracy of pumped storage units, and analyze the interaction stability of DC buses. In the figure, Indicates the network-side output terminal Three-phase voltage.

[0084] In step 2: The method for establishing the small-signal model is based on the system being at a steady-state operating point, analyzing the changing trends of the variables of the primary and secondary equipment under small disturbances in a steady-state state. The structure diagram of the full-power pumped storage unit's machine-side subsystem is shown below. Figure 2 As shown. For the smaller systems on the turbine side, it is necessary to separately convert the turbine system, synchronous motor, turbine-side converter, turbine-side modulation circuit, and turbine-side control loop into small signals. (See figure.) This is the pulse trigger signal for the 6th bridge arm of the machine-side converter; , , These are the three-phase components of the machine-side modulation wave; This refers to the three-phase components of the stator current on the machine side. Three-phase components of the stator voltage on the machine side.

[0085] The turbine system is the core of a pumped-storage unit, enabling the conversion of water energy into mechanical energy. Its performance directly determines the unit's operating efficiency and stability. The turbine system consists of a governor, blade servo system, water intake system, and pump-turbine mechanism. A detailed control block diagram of the turbine system is shown below. Figure 3 As shown, its internal control logic is clearly understood. The transfer function of the turbine system is as follows:

[0086] ;

[0087] In the formula, The control electrical signal output by the speed controller. , and These are the proportional coefficient, integral coefficient, and derivative coefficient of the PID control in the speed governor. For the Laplace operator, For the set target power, This refers to the power consumed by the generator motor as a load (the power is negative when it is in generator mode). This represents the actual actuation value of the pump-turbine blades. The time constant of the blade servo system control delay. This refers to the mechanical torque consumed by the turbine system through the main shaft. The parameters represent the time parameters of the water hammer effect in the turbine system. The governor employs PID (Proportional-Integral-Derivative) control for zero steady-state error control.

[0088] As the input terminal of the turbine system, the governor compares the deviation between the setpoint and the actual active power value and outputs a corresponding control electrical signal. This signal is sent to the servo system, which converts it into actual blade movement commands to adjust the guide vane opening through the water intake system and the pump-turbine. When the guide vane opening changes, the water flow through the turbine changes accordingly, ultimately resulting in a change in the turbine's mechanical torque, thus achieving closed-loop regulation of the generator speed and output active power.

[0089] Small-signal processing is performed on the above equation to obtain the small-signal model of the turbine system, as shown in the following formula:

[0090] ;

[0091] In the formula, Indicates a small semaphore. This refers to the output power of the synchronous motor.

[0092] By using small signal processing, various intermediate variables in the turbine system can be effectively eliminated, and the functional relationship between the power change of the pumped storage unit and the mechanical torque change of the turbine system can be obtained intuitively.

[0093] The turbine system and the synchronous motor are connected via a main shaft. The full-power pumped storage unit through the main shaft effectively provides a channel for the power flow between the two. Therefore, there are mechanical equations relating the turbine system and the motor, the expressions of which are as follows:

[0094] ;

[0095] In the formula, The number of rotor pole pairs, The electrical angular velocity of the synchronous motor. This represents the moment of inertia of the synchronous motor. The electromagnetic torque of the synchronous motor. Let be the damping coefficient of the synchronous motor. By performing small-signal processing on the above equation, we can obtain the small-signal model of the mechanical equations of the turbine system and the synchronous motor, as shown in the following formula:

[0096] .

[0097] Under maximum torque control, the electromagnetic torque of a synchronous motor is related to the stator current, as shown in the following formula:

[0098] ;

[0099] In the formula, For equivalent magnetic flux linkage, Let q be the q-axis component of the stator current of the synchronous motor in the dq coordinate system. Let be the d-axis component of the armature inductance in the dq coordinate system. Let be the q-axis component of the armature inductance in the dq coordinate system. Let d be the d-axis component of the stator current of the synchronous motor in the dq coordinate system.

[0100] Considering that the synchronous motor adopts a salient-pole main pole structure, its armature inductance is equally distributed along the dq axis. Therefore, the torque expression for a synchronous motor under small signal conditions is:

[0101] ;

[0102] Combining the above equation with the small-signal model of the turbine system and the mechanical equations of the synchronous motor, the electric angular velocity of the synchronous motor is obtained. The relationship between the current and the stator current is expressed by the following formula:

[0103] ;

[0104] In the formula, This is the conversion matrix from stator current to electric angular velocity. The stator current of the synchronous motor in the dq coordinate system;

[0105] For ease of analysis and calculation, the subscript "dq" in the following formula indicates that it is a 2*1 matrix expression, where one row and one column represent the d-axis component of the parameter, and two rows and one column represent the q-axis component of the parameter.

[0106] The excitation system adopts constant excitation. Considering the strong coupling and nonlinearity of synchronous motors in the three-phase coordinate system, a coordinate transformation operator is used to transform the three-phase stationary abc coordinate system to the two-phase rotating dq coordinate system. The expression is as follows:

[0107] ;

[0108] In the formula, Let q be the q-axis component of the objective variable in a two-phase rotating coordinate system. Let d be the d-axis component of the objective variable in a two-phase rotating coordinate system. Let be the zero-sequence component of the objective variable in a two-phase rotating coordinate system. The angle between the rotor's d-axis and the stator's A-phase axis. Let a be the a-axis component of the target variable in a three-phase stationary coordinate system. Let b be the b-axis component of the target variable in a three-phase stationary coordinate system. Let c be the c-axis component of the objective variable in a three-phase stationary coordinate system.

[0109] Based on the above equation, the electromotive force balance equation of the synchronous motor in the dq coordinate system can be obtained as follows:

[0110] ;

[0111] In the formula, Let be the d-axis component of the stator voltage of the synchronous motor in the dq coordinate system. The winding resistance of the stator of the synchronous motor. The electrical angular velocity of the synchronous motor. Let q be the q-axis component of the stator voltage of the synchronous motor in the dq coordinate system.

[0112] By performing small-signal processing on the above equation, we can obtain the small-signal model of the synchronous motor, as shown in the following formula:

[0113] ;

[0114] ;

[0115] ;

[0116] In the formula, Let be the stator voltage of the synchronous motor in the dq coordinate system. Let be the matrix corresponding to the small-signal stator current of the armature reaction of the synchronous motor in the dq coordinate system. Let be the stator current of the synchronous motor in the dq coordinate system. Let be the matrix corresponding to the small signals of the synchronous motor armature reaction and the synchronous motor electric angular velocity in the dq coordinate system.

[0117] The machine-side converter adopts a dual closed-loop control structure combining an outer speed loop and an inner current loop, as shown in its control block diagram. Figure 2As shown. The outer loop uses motor speed as the control target, and processes the deviation between the actual motor speed and the target speed through a PI (Proportional-Integral Control) regulator, outputting a reference value for the q-axis current. This reference value is then fed into the inner current loop. The inner loop PI controller generates a corresponding output voltage command based on the current deviation to achieve precise torque and speed control. The corresponding control loop expression is as follows:

[0118] ;

[0119] In the formula, Let d be the d-axis component of the modulated wave on the machine side in the dq coordinate system. Let q be the q-axis component of the modulated wave on the machine side in the dq coordinate system. The modulation gain coefficient of the machine-side converter. This is the transfer function of the inner loop of the speed PI controller in the machine-side control loop. The transfer function for the outer loop of the PI controller in the engine-side control loop is given. For the set target power, This represents the actual power.

[0120] By performing small-signal processing on the above equation, we can obtain the small-signal model of the machine-side control loop:

[0121] ;

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] In the formula, Let be the dq component matrix of the modulated wave on the machine side. This represents the transfer function matrix of the inner loop current on the machine side. This is the stator current decoupling matrix under small signal conditions. This is the decoupling matrix for the motor angular velocity under small signal conditions. This is the outer loop transfer function matrix for the engine-side rotational speed portion.

[0127] The machine-side converter uses sinusoidal pulse width modulation (SPWM) to convert the obtained modulated wave into trigger pulses for each bridge arm to control the converter port output voltage. Its small-signal modulation stage expression, i.e., the small-signal model of the machine-side modulation stage, is as follows:

[0128] ;

[0129] In the formula, Let be the stator voltage of the synchronous motor in the dq coordinate system. This is the DC side voltage.

[0130] As shown in the above equation, the output voltage of the generator-side converter is simultaneously controlled by the modulation signal and the DC voltage. This relationship is crucial for achieving energy coupling in AC / DC systems. Structurally, the AC and DC circuits are connected in series via back-to-back converters, meaning power can only be exchanged with the grid through these converters. This series connection dictates that the power on the DC and AC sides must remain balanced, as shown in the following relationship:

[0131] ;

[0132] Combining the above two equations, we can obtain the small-signal model of the machine-side converter:

[0133] ;

[0134] In the formula, This refers to the DC-side current of the machine-side section. This is the matrix of the dq components of the stator current on the machine side. This is the equivalent capacitance on the DC side of the machine side. This indicates transpose.

[0135] In step 3, based on the above formula, the block diagram of the dq axis machine side model can be obtained as follows: Figure 4 As shown, the current is fed into the DC bus of the machine-side converter. For output, two pairs of AC parameters and control parameters are converted, focusing the variables on the change in stator voltage (i.e., small signal quantity). Modulation wave variation Current flowing into the busbar The relationships are organized to obtain the organized machine-side model block diagram as follows: Figure 5 As shown, the AC parameters are then completely converted to DC parameters using the relationships under the above averaging model, thus realizing the construction of the system transfer function from the perspective of the DC bus. Finally, the DC admittance model of the machine side is obtained as follows:

[0136] ;

[0137] ;

[0138] ;

[0139] ;

[0140] ;

[0141] In the formula, For the machine-side admittance, This is the admittance of the DC capacitor on the machine side. For the machine-side AC circuit admittance, For the machine-side control loop admittance, This is the equivalent matrix of the dual closed-loop control branch on the lower side of the small signal.

[0142] In step 4, the block diagram of the small signal state structure on the network side is as follows: Figure 6 As shown, it consists of a grid-side converter, a filter circuit, a power grid, a DC capacitor, and related control loops. When establishing a small-signal model for it, it is also necessary to perform small-signal processing on each of its components.

[0143] The grid-side converter is based on grid-following control and employs a dual closed-loop control strategy combining an outer DC voltage loop and an inner current loop. Its control structure is as follows: Figure 6 As shown. The outer loop uses a stable DC bus voltage as the control objective, and processes the deviation between the actual DC voltage value and the target value through a PI regulator, outputting a reference value for the d-axis current. This reference value is then fed into the inner current loop, and the inner loop PI controller uses it to generate port voltage commands for the grid-side converter, thereby achieving precise control of the DC voltage and grid-connected power. The corresponding control loop expression is as follows:

[0144] ;

[0145] In the formula, The d-axis component of the modulated wave on the grid side under the controller phase. The q-axis component of the modulated wave on the grid side under the controller phase. This represents the transfer function matrix of the inner loop current on the grid side. The outer loop transfer function matrix of the grid-side voltage section. For the set target DC voltage value, Let be the transfer function of the outer loop of the PI control circuit voltage of the grid-side converter. Let be the d-axis component of the grid-connected current in the dq coordinate system. The rotational angular velocity of the grid connection point coordinate transformation obtained from the phase-locked loop (PLL) is... Let be the q-axis component of the grid-connected current in the dq coordinate system. Let d be the d-axis component of the grid-connected voltage in the dq coordinate system. This is the reference value for the q-axis component of the grid-connected current in the dq coordinate system. Let q be the q-axis component of the grid-connected voltage in the dq coordinate system.

[0146] Considering that the phase obtained by the grid-side converter is obtained by a phase-locked loop, which deviates from the actual phase, the upper right corner “s” represents the actual phase of the system and “c” represents the controller phase obtained by the PLL in the grid-side control loop.

[0147] After performing small-signal processing on the above equation, we get:

[0148] ;

[0149] ;

[0150] ;

[0151] ;

[0152] In the formula, The dq component matrix of the network-side modulated wave. Let be the grid connection point voltage in the dq coordinate system. Let be the grid connection point current in the dq coordinate system. This is the decoupling matrix for the grid connection point current under small-signal conditions. Let be the transfer function of the inner loop of the speed PI controller in the grid-side control loop. The transfer function of the outer loop of the DC voltage PI converter in the grid-side control loop. This is a filter inductor.

[0153] Since the grid-side converter control loop is established with the phase provided by the PLL, the impact of the phase-locked loop deviation on the system cannot be ignored. The PLL adopts the widely used single-phase synchronous phase-locked loop technology, with the q-axis component of the voltage at point PCC as the reference. As input, the signal is controlled by a PI controller with zero steady-state error, and then superimposed with the rated angular velocity of the target power grid to achieve rapid tracking. Finally, the controller phase is obtained through double integration. Its structure is as follows: Figure 7 As shown in the figure, Let be the initial angular frequency. After small-signal processing, we can obtain the small-signal model of the controller phase:

[0154] ;

[0155] ;

[0156] In the formula, The phase of the phase-locked loop output phase. For the phase-locked loop PI transfer function. The transfer function of the phase-locked loop under small-signal conditions. is the proportional coefficient of the phase-locked loop PI transfer function. These are the differential coefficients of the phase-locked loop PI transfer function.

[0157] As can be seen from the above equation, under small-signal conditions, the phase of the phase-locked loop (PLL) output is not fixed but is affected by the fluctuation of the q-axis component of the voltage at the point of common coupling (PCC). Therefore, to construct an accurate admittance model, the voltage phase angle deviation introduced by the PLL between the two coordinate systems must be considered. Based on this, it is necessary to... Figure 6 The coordinate transformation operator in the expression is corrected to obtain the corrected expression:

[0158] ;

[0159] ;

[0160] ;

[0161] In the formula, This is the transformation matrix for the actual phase transition to the dq component of the voltage at the PCC point under the corresponding controller phase in the phase-locked loop. This is the transformation matrix for the actual phase transition to the modulated wave dq component under the phase-locked loop corresponding controller phase. This is the transformation matrix for the actual phase transition to the current dq component at the PCC point under the corresponding controller phase in the phase-locked loop. Let d be the d-axis component of the modulated wave in the dq coordinate system of the network side. This represents the q-axis component of the modulated wave in the dq coordinate system of the network side portion.

[0162] Based on the modified equation of the coordinate transformation operator in the above formula, the control equation of the small-signal model of the controller phase can be modified and transformed to the actual phase of the system to obtain the small-signal model of the grid-side control loop, as shown in the following formula:

[0163] ;

[0164] Similar to the modulation stage of the generator-side converter, the grid-side converter also employs SPWM modulation. The small-signal model of the grid-side modulation stage is shown in the following formula:

[0165] ;

[0166] In the formula, This is the dq component matrix of the grid-side converter port voltage. This is the dq component matrix of the modulated wave on the network side.

[0167] The modulation stage enables the control loop to control the converter port voltage. The port voltage is then filtered and transmitted to the PCC point to interact with the grid, thereby changing the grid-side output current and affecting power transmission. Finally, the AC / DC power equations are used to achieve a closed loop, resulting in the small-signal model of the AC-side main circuit, as shown in the following formula:

[0168] ;

[0169] ;

[0170] ;

[0171] In the formula, This represents the d-axis component of the grid-side converter port voltage under the actual phase of the power system. This represents the q-axis component of the grid-side converter port voltage under the actual phase of the power system. The equivalent impedance matrix of the power grid. The equivalent inductance of the power grid, The equivalent capacitance of the power grid to ground;

[0172] The small-signal model of the grid-side converter is constructed using the following formula:

[0173] ;

[0174] In the formula, This refers to the DC-side current of the grid-side portion. This is the matrix of the dq components of the grid-connected current on the grid side. This is the equivalent capacitance on the DC side of the grid side.

[0175] In step 5, based on the above formula, and using the modified expression for the machine side, the entire control block diagram is transformed to the actual coordinate system of the system, effectively enhancing the accuracy of the model block diagram. Further, the machine side model block diagram of the dq axis can be obtained as follows: Figure 8 As shown in the diagram, the current is fed into the DC bus of the grid-side converter. For output, the AC parameters and control parameters are converted, focusing the variable on the change in current at the PCC point. , Network-side modulation wave variation Current flowing into the busbar The relationships are organized to obtain the organized network-side model block diagram as follows: Figure 9 As shown, the AC parameters are then completely converted to DC parameters by unifying the small-signal expression of the SPWM modulation of the grid-side converter, thus realizing the construction of the system transfer function from the perspective of the DC bus. Finally, the DC admittance model of the grid side is obtained as follows:

[0176] ;

[0177] ;

[0178] ;

[0179] ;

[0180] ;

[0181] ;

[0182] In the formula, For the network-side admittance, For grid-side DC circuit admittance, For grid-side AC loop admittance, For grid-side control loop admittance, This is the matrix of the dq components of the grid-connected current on the grid side. This is the AC / DC coupling matrix for the small-signal network side. The equivalent impedance matrix of the power grid. Here is the impedance matrix of the filter circuit. This is the equivalent matrix of the dual closed-loop control branch on the small-signal network side.

[0183] In step 6, based on the pumped storage unit's small-system admittance model and grid-side small-signal admittance model established in steps 3 and 5, their reciprocals are converted into an impedance model, as shown in the following formula:

[0184] ;

[0185] In the formula, Z sdc For the impedance on the machine side, Z gdc This represents the impedance on the grid side.

[0186] The electrical parameters (main circuit parameters, motor speed, and rotor position) and control parameters (machine-side converter control parameters, grid-side converter control parameters, and phase-locked loop parameters) under steady-state operation are substituted into the impedance model, and the Laplace operator is also included. Replace with , to obtain the response frequency The impedance frequency domain model is used as a variable. By changing the response frequency... The numerical Bode plot shows the intersection of the amplitudes of the two impedance frequency domain models. If the phase difference at the intersection point is less than 90°, the machine-side and grid-side components will not experience interactive instability on the DC side; otherwise, interactive instability will occur. The Bode plot is drawn based on the respective impedance models of the machine-side and grid-side components, and both Bode plots are plotted on the same coordinate system.

[0187] Example 2

[0188] To verify the accuracy of the admittance models of the two small systems mentioned above, a simulation model of a full-power pumped storage unit was built on the Matlab / Simulink simulation platform. With all parameters designed within a reasonable range, the system operated at a steady-state operating point to verify the accuracy of the model.

[0189] The verification method is as follows: Based on the averaged model, a series of single-frequency voltage disturbances are injected into the DC side. The admittance characteristic curves of the simulation model are obtained by measuring the frequency response of each subsystem, and then compared with the mathematical model established under the corresponding operating conditions. Furthermore, given that the system exhibits different admittance characteristics under different operating conditions, frequency sweep verification was performed for both pumping and generation conditions to ensure the model's effectiveness and accuracy across the entire operating range. The frequency sweep results and analytical results of the two subsystems of the pumped-storage unit under generation and pumping conditions are as follows: Figure 10 , Figure 11 As shown. Frequency sweep results indicate that the impedance curves of the small systems on both sides of the grid intersect at 38Hz, regardless of whether the system is generating or pumping. In the generating condition, a 120° phase difference and positive damping characteristics ensure system stability; however, in the pumping condition, a 196° phase difference (exceeding 180°) meets the instability condition of the Nyquist criterion, indicating a significant interactive stability problem under this condition. Therefore, waveforms of the DC-side voltage and current under both conditions are provided, as shown below. Figure 12 As shown in the waveform diagram, the DC electrical parameters are stable under power generation conditions, while under pumping conditions, a 38Hz AC component appears in the DC electrical parameters, consistent with the model analysis. Comparing the two results, it can be seen that the frequency sweep result and the analytical result match well from low frequency to high frequency bands. The segmented modeling method and DC bus stability analysis method for full-power pumped storage units under grid-connected control designed in this invention can describe the amplitude-frequency characteristics of each part of the small system under different operating conditions, and can also effectively reveal the interactive stability of the two DC parts of the small system.

[0190] In summary, as can be seen from the embodiments and accompanying drawings, the segmented small-signal modeling method and DC bus stability analysis method for full-power pumped storage units provided by the present invention can effectively reduce the modeling difficulty and complexity of full-power pumped storage units, improve the accuracy of small-signal modeling of pumped storage units, and specifically analyze the system interaction stability at the DC bus, helping to conduct stability assessment of the DC bus of full-power pumped storage units, and solving the problems of unit parameter sensitivity analysis and tracing the source of unit broadband oscillation.

Claims

1. A method for judging the stability of the DC bus of a full-power pumped storage unit, characterized in that, include: The DC bus capacitor is equivalent to two parallel equal capacitors, and the pumped storage unit is divided into a machine-side part and a grid-side part with the parallel connection point as the boundary. For the turbine side, small-signal models of the turbine system, synchronous motor, turbine-side converter, turbine-side modulation circuit, and turbine-side control loop are constructed respectively. Based on the small-signal models, a first admittance model is constructed; based on the first admittance model, a first impedance model is constructed. For the grid-side portion, small-signal models of the grid-side converter, AC-side main circuit, grid-side modulation element, and grid-side control loop are constructed respectively. Based on the small-signal models, a second admittance model is constructed; based on the second admittance model, a second impedance model is constructed. Substitute the electrical parameters and control parameters into the first impedance model and the second impedance model respectively to construct the corresponding first impedance frequency domain model and second impedance frequency domain model. Bode plots are drawn according to the first impedance model and the second impedance model in the same coordinate system; Adjust the response frequency to determine the amplitude intersection point of the first impedance frequency domain model and the second impedance frequency domain model in the Bode plot; Under the same operating conditions, if the phase difference at the intersection point is less than 180°, interactive instability will not occur on the DC bus; otherwise, interactive instability will occur. The small-signal model of the turbine system is shown in the following formula: ； In the formula, Indicates a small semaphore. This refers to the mechanical torque consumed by the turbine system through the main shaft. The time parameter for the water hammer effect in the turbine system. For the Laplace operator, This refers to the proportional coefficient in PID control. The integral coefficient in PID control. The time constant of the blade servo system control delay. This refers to the output power of the synchronous motor; The small-signal model of a synchronous motor is shown in the following formula: ； In the formula, Let be the stator voltage of the synchronous motor in the dq coordinate system. Let be the matrix corresponding to the small-signal stator current of the armature reaction of the synchronous motor in the dq coordinate system. Let be the stator current of the synchronous motor in the dq coordinate system. Let be the matrix corresponding to the small signal of the synchronous motor's armature response and electrical angular velocity in the dq coordinate system. This refers to the electrical angular velocity of the synchronous motor. The small-signal model of the generator-side converter is shown in the following formula: ； In the formula, This refers to the DC-side current of the machine-side section. This is the dq component matrix of the modulated wave on the machine side. This is the matrix of the dq components of the stator current on the machine side. This is the equivalent capacitance on the DC side of the machine side. DC side voltage Indicates transpose; The small-signal model of the machine-side modulation stage is shown in the following formula: ； In the formula, The modulation gain coefficient; The small-signal model of the machine-side control loop is shown in the following formula: ； In the formula, This represents the transfer function matrix of the inner current loop on the machine side. This is the decoupling matrix for the stator current under small-signal conditions. This is the decoupling matrix for the motor angular velocity under small signal conditions. This is the transfer function matrix for the outer loop of the engine-side rotational speed.

2. The method for judging the stability of a full-power pumped storage unit's DC bus as described in claim 1, characterized in that, In the small-signal model of the synchronous motor: ； ； In the formula, Let be the d-axis component of the armature inductance in the dq coordinate system. Let be the q-axis component of the armature inductance in the dq coordinate system. Let q be the q-axis component of the stator current of the synchronous motor in the dq coordinate system. Let d be the d-axis component of the stator current of the synchronous motor in the dq coordinate system. Equivalent magnetic flux; In the small-signal model of the machine-side control loop: ； ； ； ； In the formula, This is the transfer function of the inner loop of the speed PI controller in the machine-side control loop. The transfer function for the outer loop of the PI controller in the engine-side control loop is given. For the armature inductance of the motor, This is the damping coefficient of the synchronous motor.

3. The method for judging the stability of a full-power pumped storage unit's DC bus as described in claim 2, characterized in that, The formula for the first admittance model is as follows: ； ； ； ； ； In the formula, For the machine-side admittance, This is the admittance of the DC capacitor on the machine side. For the machine-side AC circuit admittance, For the machine-side control loop admittance, Here is the impedance matrix of the filter circuit. This is the equivalent matrix of the dual closed-loop control branch on the lower side of the small signal. This is the conversion matrix from stator current to electric angular velocity.

4. The method for judging the stability of a full-power pumped storage unit's DC bus as described in claim 1, characterized in that, For the grid-side portion, small-signal models are constructed for the grid-side converter, AC-side main circuit, grid-side modulation stage, and grid-side control loop, respectively: (1) Construct the small-signal model of the grid-side converter, as shown in the following formula: ； In the formula, Indicates a small semaphore. This refers to the DC-side current of the grid-side portion. This is the dq component matrix of the modulated wave on the network side. This is the matrix of the dq components of the grid-connected current on the grid side. This is the equivalent capacitance on the DC side of the grid side. This is the DC side voltage; (2) Construct the small-signal model of the AC side main circuit, as shown in the following formula: ； ； ； In the formula, This represents the d-axis component of the grid-side converter port voltage under the actual phase of the power system. This represents the q-axis component of the grid-side converter port voltage under the actual phase of the power system. The equivalent impedance matrix of the power grid. Here is the impedance matrix of the filter circuit. This represents the d-axis component of the grid-connected current under the actual phase of the power system. This represents the q-axis component of the grid-connected current under the actual phase of the power system. For the Laplace operator, The equivalent inductance of the power grid, The equivalent capacitance of the power grid to ground. For filtering inductors, The rotational angular velocity of the grid connection point coordinate transformation obtained by the phase-locked loop; (3) Construct the small-signal model of the network-side modulation stage, as shown in the following formula: ； In the formula, This is the dq component matrix of the grid-side converter port voltage; (4) Construct the small-signal model of the grid-side control loop, as shown in the following formula: ； ； ； ； In the formula, This represents the dq component matrix of the modulated wave on the network side under actual phase. The modulation gain coefficient of the machine-side converter. This is the transformation matrix for the actual phase transition to the dq component of the voltage at the PCC point under the corresponding controller phase in the phase-locked loop. This is the transformation matrix for the actual phase transition to the modulated wave dq component under the phase-locked loop corresponding controller phase. This is the transformation matrix for the actual phase transition to the current dq component at the PCC point under the corresponding controller phase in the phase-locked loop. This represents the transfer function matrix of the inner loop current on the grid side. This is the decoupling matrix for the grid connection point current under small-signal conditions. The outer loop transfer function matrix of the grid-side voltage section. This is the dq component matrix of the grid-connected voltage on the grid side under the actual phase. This is the matrix of the dq components of the grid-connected current on the grid side under the actual phase. Let be the transfer function of the inner loop of the speed PI controller in the grid-side control loop. This is the transfer function of the outer loop of the DC voltage PI in the grid-side control loop.

5. The method for judging the stability of a full-power pumped storage unit's DC bus as described in claim 4, characterized in that, The formula for the second admittance model is as follows: ； ； ； ； ； ； In the formula, For the network-side admittance, For grid-side DC loop admittance, For grid-side AC loop admittance, For grid-side control loop admittance, This is the matrix of the dq components of the grid-connected current on the grid side. This is the dq component matrix of the modulated wave on the network side. This is the AC / DC coupling matrix for the small-signal network side. The equivalent impedance matrix of the power grid. Here is the impedance matrix of the filter circuit. This is the equivalent matrix of the dual closed-loop control branch on the small-signal network side.

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