Subsynchronous oscillation positioning method and platform for grid-connected wind power system based on instantaneous power
By detecting instantaneous voltage and current in wind power grid-connected systems and calculating the DC and AC components of the secondary term of instantaneous power, the complexity and misjudgment problems of subsynchronous oscillation positioning in existing technologies are solved, achieving accurate oscillation source positioning and real-time monitoring. This method is applicable to wind power grid-connected systems with different control methods.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTH CHINA ELECTRIC POWER UNIV
- Filing Date
- 2024-08-20
- Publication Date
- 2026-05-12
AI Technical Summary
Existing methods for locating subsynchronous oscillations in wind power grid-connected systems suffer from computational complexity, high error rates, and poor adaptability. In particular, in the phase-locked loop and droop control loop of wind turbine units, voltage and current disturbances cause changes in instantaneous power frequency components, making it difficult to accurately identify the oscillation source.
By detecting the instantaneous voltage and current at the wind power grid connection point, calculating the DC component and AC component of the secondary term of the instantaneous power, and using the subsynchronous period and instantaneous power criteria to determine whether the wind turbine is a subsynchronous oscillation source, a positioning method based on instantaneous power is provided, which simplifies the calculation process and reduces misjudgments.
It enables precise positioning of subsynchronous oscillation sources in wind power grid-connected systems, reduces calculation time and workload, is applicable to power systems under different control methods, improves practicality and accuracy, and supports real-time monitoring and suppression of subsynchronous oscillations.
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Figure CN119029931B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power systems and their automation technology, and in particular to a method and platform for locating subsynchronous oscillations in a wind power grid-connected system based on instantaneous power. Background Technology
[0002] Large-scale wind power grid-connected systems have triggered subsynchronous oscillations in Scotland, Australia, and Northwest China. The measured instantaneous voltage and current harmonic frequencies in various regions have largely covered the subsynchronous frequency band. Furthermore, the widespread propagation of these subsynchronous oscillations poses a serious threat to the safety and stable operation of the power grid. The most important method for suppressing forced oscillations is to promptly locate and disconnect the oscillation source after it occurs.
[0003] With the widespread application of WAMS measurement systems, data-based oscillation source localization methods have gradually matured. Existing oscillation source localization methods based on measurement data can be broadly categorized into machine learning methods, energy flow methods, and subsynchronous power methods. Machine learning-based artificial intelligence methods learn the connection between oscillation characteristics and oscillation source location by inputting massive amounts of data. However, the interpretability of the machine learning computation process is poor, and its physical meaning is unclear. Furthermore, the acquisition of massive amounts of oscillation event data is limited, making it difficult to achieve the requirement of complete system observability; therefore, its adaptability and accuracy in practical power systems require further research. Energy flow methods first use signal processing methods such as mode decomposition to filter relevant signals within the subsynchronous frequency range, and then calculate the sign and magnitude of dissipated energy to identify the oscillation source. However, this method cannot distinguish between oscillating generator units and units that only contribute negative damping, and its theoretical basis needs further refinement.
[0004] Compared to other methods, the subsynchronous power method based on instantaneous power has a clear physical meaning, and the data acquisition is simple and easy to measure, meeting the requirements for online real-time oscillation monitoring. However, in wind power grid-connected systems, the voltage and current at the subsynchronous frequency can cause disturbances in phase generation stages such as phase-locked loops and droop control, further affecting the voltage and current and generating multi-mode harmonic components, causing changes in the frequency components of the instantaneous power. In addition, the subsynchronous power contains additional power frequency voltage and current related terms generated by phase angle disturbances. When the power flow or active power droop coefficient is large, it can generate large power frequency voltage and current terms in non-oscillating source units, canceling out the true subsynchronous power and leading to misjudgment of the oscillation source. Summary of the Invention
[0005] In order to solve the problems in the prior art, the present invention provides a subsynchronous oscillation positioning method for wind power grid-connected systems based on instantaneous power, which is accurate in positioning, simple in calculation, short in time, low in workload, and highly applicable.
[0006] To achieve the above-mentioned objectives, this invention provides a method for locating subsynchronous oscillation sources in a wind power grid-connected system based on instantaneous power, comprising the following steps:
[0007] When a subsynchronous oscillation disturbance occurs, the instantaneous voltage and instantaneous current at the wind power grid connection point are detected;
[0008] The instantaneous power of the wind power grid connection point is obtained based on the instantaneous voltage and the instantaneous current.
[0009] The subsynchronization period is obtained based on the instantaneous power.
[0010] The DC component and the AC component of the second term after disturbance are obtained based on the subsynchronization period and the instantaneous power.
[0011] The subsynchronous power is obtained based on the subsynchronous period, the disturbed DC component, and the disturbed quadratic AC component.
[0012] The subsynchronous power is used to determine whether the wind turbine is a subsynchronous oscillation source.
[0013] Furthermore, the subsynchronous power is:
[0014] ;
[0015] In the formula, For secondary synchronous power, The DC component after disturbance. The quadratic component after the disturbance is the commutative component. For the secondary synchronization period, This represents steady-state active power.
[0016] when When the value is greater than 0, the wind turbine is a subsynchronous oscillation source;
[0017] when When <0, the wind turbine is not a subsynchronous oscillation source.
[0018] Furthermore, the disturbed DC component is:
[0019] ;
[0020] In the formula, The DC component after disturbance. For instantaneous power at arrive Points within a time period Instantaneous power This is the secondary synchronization period.
[0021] Furthermore, the alternating quadratic component after disturbance is:
[0022] ;
[0023] In the formula, The quadratic component after the disturbance is the commutative component. For the secondary synchronization period, For time, For time Instantaneous power at time For time Instantaneous power at time For time Instantaneous power at time For time Instantaneous power at that time.
[0024] Furthermore, the step of obtaining the subsynchronization period is as follows:
[0025] Construct an absolute average value model of the instantaneous power difference based on the instantaneous power;
[0026] The minimum value of the absolute average value of the instantaneous power difference is obtained based on the aforementioned model of the absolute average value of the instantaneous power difference;
[0027] The subsynchronization period is obtained based on the minimum value.
[0028] Furthermore, the instantaneous power difference absolute average value model is as follows:
[0029] ;
[0030] In the formula, Angular frequency is The absolute average value of the instantaneous power difference at time, The sampling period is , The instantaneous power start time, The instantaneous power end time, For sampling time is Instantaneous power at time For sampling time is Instantaneous power at time Angular frequency, Let be the time of the i-th sampling.
[0031] Furthermore, the step of obtaining the subsynchronization period is as follows:
[0032] The time of the i-th sampling, the start time of the instantaneous power, and the end time of the instantaneous power are obtained and input into the absolute average value model of the instantaneous power difference;
[0033] The minimum value is obtained by running the instantaneous power difference absolute average value model;
[0034] The sampling period corresponding to the minimum value is obtained based on the model of the minimum value and the absolute average value of the instantaneous power difference;
[0035] The subsynchronization period is obtained based on the sampling period corresponding to the minimum value.
[0036] Furthermore, the formula for obtaining the subsynchronization period based on the sampling period corresponding to the minimum value is as follows:
[0037] ;
[0038] In the formula, For the secondary synchronization period, The sampling period is the minimum value of the absolute average value of the instantaneous power difference.
[0039] Furthermore, after obtaining the subsynchronization period, the subsynchronization frequency is obtained according to the subsynchronization frequency calculation formula.
[0040] Furthermore, the formula for calculating the subsynchronous frequency is as follows:
[0041] ;
[0042] In the formula, For secondary synchronization frequency, This is the secondary synchronization period.
[0043] A platform includes a processor and a memory, the memory storing computer-readable instructions, the processor executing the computer-readable instructions, which, when executed, perform the subsynchronous oscillation positioning method for wind power grid-connected systems based on instantaneous power.
[0044] An apparatus includes a processor and a memory, the memory storing computer-readable instructions, the processor being configured to execute the computer-readable instructions, wherein the computer-readable instructions, when executed, perform the subsynchronous oscillation positioning method for wind power grid-connected systems based on instantaneous power.
[0045] The beneficial effects of this invention are:
[0046] 1. This invention proposes a precise location criterion for subsynchronous oscillation sources in wind power grid-connected systems based on instantaneous power frequency components, providing support for real-time monitoring and effective suppression of subsynchronous oscillations. The proposed method can directly utilize the measured values of instantaneous voltage and instantaneous current in broadband measurement systems.
[0047] 2. The method proposed in this invention is entirely based on measurement data, requiring no internal parameters of the wind turbine or transmission line parameters. It avoids the computational burden of time-frequency conversion by utilizing instantaneous power characteristics, meets the requirements for online monitoring of subsynchronous oscillations, and has good feasibility in practical online system applications. It is of great significance for the safe and stable operation of new power systems.
[0048] 3. In this invention, the subsynchronous frequency can be calculated using basic arithmetic, without the need for auxiliary components such as filters. Furthermore, the calculation of the subsynchronous oscillation source criterion, i.e., the subsynchronous power, is simple and straightforward, greatly reducing calculation time and workload, and demonstrating good practicality in power systems under different grid connection control methods.
[0049] 4. Compared with existing subsynchronous oscillation location methods, the method proposed in this invention can prevent misjudgment of subsynchronous oscillation sources and has important engineering application value in actual power systems. Attached Figure Description
[0050] Figure 1 This is a schematic diagram illustrating the principle of the present invention;
[0051] Figure 2 This is the result of extracting the subsynchronous frequency of the grid-connected wind turbine.
[0052] Figure 3 for =20Hz Subsynchronous frequency extraction result of grid-type wind turbine;
[0053] Figure 4 for =52Hz Subsynchronous frequency extraction result of grid-type wind turbine;
[0054] Figure 5 This is a topology diagram of the IEEE-39 node;
[0055] Figure 6 The subsynchronous oscillation source location results for Example 1 are as follows: the subsynchronous oscillation source is a grid-following wind turbine, where (a) is a grid-following wind turbine and (b) is a grid-connected wind turbine.
[0056] Figure 7 The subsynchronous oscillation source location results for example 2 are as follows: the subsynchronous oscillation source is a grid-type wind turbine, where (a) is a grid-following wind turbine and (b) is a grid-type wind turbine. Detailed Implementation
[0057] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to describe the solution.
[0058] This invention provides a method for locating subsynchronous oscillations in a wind power grid-connected system based on instantaneous power, comprising the following steps:
[0059] When a subsynchronous oscillation disturbance occurs, the instantaneous voltage and instantaneous current at the wind power grid connection point are detected;
[0060] The instantaneous power of the wind power grid connection point is obtained based on the instantaneous voltage and the instantaneous current.
[0061] The subsynchronization period is obtained based on the instantaneous power.
[0062] The DC component and the AC component of the second term after disturbance are obtained based on the subsynchronization period and the instantaneous power.
[0063] The subsynchronous power is obtained based on the subsynchronous period, the disturbed DC component, and the disturbed quadratic AC component.
[0064] The subsynchronous power is used to determine whether the wind turbine is a subsynchronous oscillation source.
[0065] This invention enables the direct use of instantaneous voltage and instantaneous current measurements in a broadband measurement system, providing support for real-time monitoring and effective suppression of subsynchronous oscillations.
[0066] Furthermore, the subsynchronous power is:
[0067] ;
[0068] In the formula, For secondary synchronous power, The DC component after disturbance. The quadratic component after the disturbance is the commutative component. For the secondary synchronization period, For steady-state active power, The amplitude of the subsynchronous frequency current. The voltage amplitude at the subsynchronous frequency. The phase of the current at the subsynchronous frequency. The voltage phase is the subsynchronous frequency.
[0069] when When the value is greater than 0, the wind turbine is a subsynchronous oscillation source;
[0070] when When <0, the wind turbine is not a subsynchronous oscillation source.
[0071] An oscillating source unit is a wind turbine that acts as a subsynchronous oscillator. When subsynchronous oscillation occurs, it generates a subsynchronous frequency voltage and current, which in turn supplies instantaneous power components to the system. The oscillating source unit can be located by detecting the subsynchronous power at the wind turbine's output. When K > 0, the wind turbine inputs instantaneous power to the system, and the wind turbine is a subsynchronous oscillating source; when K < 0, the wind turbine absorbs instantaneous power from the system, and the wind turbine is not a subsynchronous oscillating source.
[0072] This invention can directly utilize the measured values of instantaneous voltage and instantaneous current in a broadband measurement system to obtain the subsynchronous power through basic arithmetic calculations, and use the subsynchronous power as the criterion for the subsynchronous oscillation source, which greatly reduces the calculation time and workload. It has demonstrated good practicality in power systems under different grid-connected control and is applicable to wind power grid-connected systems with various synchronous control methods.
[0073] Synchronization control methods for wind power grid-connected systems can be broadly categorized into two types: grid-following (GFL) and grid-forming (GFM). GFL collects voltage data from the grid connection point and uses a phase-locked loop (PLL) to achieve grid synchronization. GFM, on the other hand, collects active power data and uses droop control, VSG, and other control strategies to achieve phase self-generation of the wind turbines. Due to the different control structures in the phase generation process, the phase angle of wind turbines in grid-following and grid-forming systems will exhibit different disturbed frequency components after subsynchronous oscillation.
[0074] 1) For grid-connected wind turbines, the instantaneous power-frequency characteristics are analyzed as follows:
[0075] In a wind power grid-connected system, assuming that a subsynchronous frequency voltage and current are generated after the grid-connected wind turbine generator experiences subsynchronous oscillation, the three-phase voltage at the subsynchronous frequency is as shown in equation (1):
[0076] (1)
[0077] In the formula, The voltage of phase a at the grid connection point is... The voltage of phase b at the grid connection point. The voltage of phase c at the grid connection point. The nominal angular frequency, For secondary synchronization frequency, For time, This represents the amplitude of the power frequency phase voltage. This represents the initial phase of the power frequency phase voltage. The amplitude of the subsynchronous frequency voltage. This is the initial phase of the subsynchronous frequency voltage;
[0078] The dq-axis components corresponding to the subsynchronous frequency voltage are shown below:
[0079] (2)
[0080] in:
[0081] (3)
[0082] (4)
[0083] In the formula, The d-axis component of the grid connection point voltage. The q-axis component of the grid connection point voltage. The phase angle is Park transform, The phase angle is The transpose of the Park transform. This is the phase angle output by the phase-locked loop before it is disturbed. This represents the d-axis component of the fundamental frequency voltage. The d-axis component of the subsynchronous frequency voltage. This represents the q-axis component of the fundamental frequency voltage. This is the q-axis component of the subsynchronous frequency voltage. The nominal angular frequency, For secondary synchronization frequency, For time, This represents the amplitude of the power frequency phase voltage. This represents the initial phase of the power frequency phase voltage. The amplitude of the subsynchronous frequency voltage. This is the initial phase of the subsynchronous frequency voltage.
[0084] After the subsynchronous frequency voltage is transformed by Park, the resulting frequency component is: of and The phase-locked loop (PLL) achieves zero steady-state error tracking of the grid phase by controlling the q-axis voltage. When the voltage is disturbed, the PLL output phase angle will change. The disturbance at the same frequency is shown in the following formula:
[0085] (5)
[0086] (6)
[0087] In the formula, This represents the slight increase in phase angle after the phase-locked loop is disturbed. To determine the amplitude of the phase angle of the phase-locked loop (PLL) for the grid-type wind turbine under disturbance. The nominal angular frequency, For secondary synchronization frequency, For time, The phase angle of the disturbed phase-locked loop is the phase angle. The amplitude of the subsynchronous frequency voltage. For the Laplace operator, This is the proportional gain of the phase-locked loop. The integral coefficients of the phase-locked loop are... This represents the amplitude of the power frequency phase voltage. The initial phase of the power frequency phase voltage, It is the imaginary unit.
[0088] The amplitude of the phase angle of the phase-locked loop of the grid-type wind turbine under disturbance The magnitude is affected by the amplitude of the subsynchronous frequency voltage. The magnitude and amplitude of the subsynchronous frequency voltage are affected by the phase-locked loop (PLL) PI parameters. same.
[0089] Therefore, after the voltage is disturbed, the phase angle of the phase-locked loop output will become:
[0090] (7)
[0091] In the formula, This is the phase angle output by the phase-locked loop before it is disturbed. This represents the phase angle output by the phase-locked loop after it is disturbed. This represents the slight increase in phase angle after the phase-locked loop is disturbed;
[0092] The changing phase angle, after being fed back to the phase-locked loop voltage input, , , This will generate new perturbed frequency components in the dq coordinate system, as shown in the following equation:
[0093] (8)
[0094] In the formula, The grid connection point voltage d-axis component after the phase-locked loop is disturbed. This represents the q-axis component of the grid connection point voltage after the phase-locked loop is disturbed. The phase angle is Park transform, The voltage of phase a at the grid connection point is... The voltage of phase b at the grid connection point. The voltage of phase c at the grid connection point. This is the phase angle output by the phase-locked loop before it is disturbed. This represents the d-axis component of the fundamental frequency voltage. The d-axis component of the subsynchronous frequency voltage. This represents the q-axis component of the fundamental frequency voltage. This is the q-axis component of the subsynchronous frequency voltage. This represents the d-axis component of the fundamental frequency voltage generated after the phase-locked loop is disturbed. This refers to the d-axis component of the subsynchronous frequency voltage generated after the phase-locked loop is disturbed. This refers to the q-axis component of the fundamental frequency voltage generated after the phase-locked loop is disturbed. This refers to the q-axis component of the subsynchronous frequency voltage generated after the phase-locked loop is disturbed.
[0095] In the formula, , , , The disturbance generated by the dq-axis voltage after the phase-locked loop is disturbed is shown in the following formula:
[0096] (9)
[0097] In the formula, This is the amplitude of the fundamental frequency current. This is the amplitude of the fundamental frequency voltage. The amplitude of the subsynchronous frequency current. The voltage amplitude at the subsynchronous frequency. To determine the amplitude of the phase angle of the phase-locked loop (PLL) for the grid-type wind turbine under disturbance. The nominal angular frequency, For secondary synchronization frequency, For time, The phase of the fundamental frequency current. The phase of the fundamental frequency voltage. The phase of the current at the subsynchronous frequency. The voltage phase at the subsynchronous frequency. The phase angle of the disturbed phase-locked loop;
[0098] According to the three-phase instantaneous power theory, the instantaneous reactive power of each phase in a three-phase circuit does not contribute to the total instantaneous power. The three-phase instantaneous active power is the sum of the instantaneous power of each phase, which equals the three-phase instantaneous power. Therefore, the following text will not distinguish between instantaneous active power and instantaneous power, and will refer to them collectively as instantaneous power. In this article, the AC component of the primary term represents the frequency. The alternating component of the quadratic term represents the frequency. The alternating components, the cubic alternating components represent frequencies of... The alternating component, and thus, the alternating component of order k represents the frequency. The amount of communication;
[0099] After the occurrence of subsynchronous oscillation, the instantaneous power of the grid-connected wind turbine is:
[0100] (10)
[0101] In the formula, To match the instantaneous power of grid-connected wind turbines, The grid connection point voltage d-axis component after the phase-locked loop is disturbed. This represents the q-axis component of the grid connection point voltage after the phase-locked loop is disturbed. This represents the d-axis component of the grid-connected current after the phase-locked loop is disturbed. This represents the q-axis component of the grid-connected current after the phase-locked loop is disturbed. To track the DC component of the instantaneous power of grid-connected wind turbines, To match the primary AC component of the instantaneous power of the grid-type wind turbine, To compare with the AC component of the second term of the instantaneous power of the grid-type wind turbine, The instantaneous power of the grid-connected wind turbine is the third term AC component; that is, after the subsynchronous oscillation occurs, the instantaneous power of the grid-connected wind turbine consists of 4 components. According to equations (1)-(10), the 4 components of the instantaneous power of the grid-connected wind turbine are as follows:
[0102] (11)
[0103] (12) (13)
[0104] (14)
[0105] It can be seen that the DC component of the instantaneous power of the grid-type wind turbine is... It is mainly generated by the combined effects of power frequency voltage and current and subsynchronous frequency voltage and current, and its order of magnitude is the same as that of steady-state active power; similar to the AC component of the primary term of the instantaneous power of a grid-type wind turbine. It is generated by the interaction of power frequency voltage and current and subsynchronous frequency voltage and current; and is related to the AC component of the second term of the instantaneous power of the grid-type wind turbine. It is generated by the combined effects of power frequency voltage and current and subsynchronous frequency voltage and current after being disturbed by a phase-locked loop; and is related to the third AC component of the instantaneous power of the grid-type wind turbine. It is generated by the interaction of power frequency voltage and current and subsynchronous frequency voltage and current after being disturbed by a phase-locked loop. At the same time, as the frequency of the instantaneous power component increases, its corresponding amplitude decreases.
[0106] 2) For grid-connected wind power systems, the instantaneous power-frequency characteristics are analyzed as follows:
[0107] Grid-connected wind power systems collect active power from the transmission line and generate the wind turbine phase angle through power control mechanisms such as droop control and VSG (Voltage-to-Groove) control. The output phase angle is affected by active power disturbances. After a subsynchronous oscillation occurs, the instantaneous power of the grid-connected wind power system will exhibit frequency components different from those of the voltage and current, resulting in drastically different output phase angle changes. Common power control mechanisms in grid-connected wind power systems include droop control, droop control via an LPF (low-pass filter), and VSG control. - To achieve stable operation of the grid-connected wind power system, the changes in output phase angle and active power of the grid-connected wind power system can be obtained.
[0108] The change in output phase angle of a grid-connected wind power system is:
[0109] (15)
[0110] In the formula, For grid-connected wind power systems, the output phase angle change is... This refers to the instantaneous change in active power of a grid-connected wind power system. This is the droop control coefficient. For the Laplace operator, The LPF cutoff frequency, The nominal angular frequency, For the virtual rotational inertia of the VSG, The virtual damping coefficient of the VSG;
[0111] The change in active power of a grid-connected wind power system is:
[0112]
[0113]
[0114]
[0115] (16)
[0116] In the formula, The change in active power of a grid-connected wind power system. The grid connection point voltage d-axis component after the phase-locked loop is disturbed. This represents the q-axis component of the grid connection point voltage after the phase-locked loop is disturbed. This represents the d-axis component of the grid-connected current after the phase-locked loop is disturbed. This represents the q-axis component of the grid-connected current after the phase-locked loop is disturbed. This represents the d-axis component of the fundamental frequency voltage. This represents the q-axis component of the fundamental frequency voltage. This is the amplitude of the fundamental frequency current. This is the amplitude of the fundamental frequency voltage. The amplitude of the subsynchronous frequency current. The voltage amplitude at the subsynchronous frequency. The phase of the fundamental frequency current. The phase of the fundamental frequency voltage. The phase of the current at the subsynchronous frequency. The voltage phase at the subsynchronous frequency. The phase angle of the disturbed phase-locked loop, Nominal angular frequency; For secondary synchronization frequency, For time;
[0117] Furthermore, the instantaneous power disturbance of the grid-connected wind turbine is controlled by a droop control circuit to generate a phase angle that includes both DC and primary AC components. The phase angle change of the instantaneous power disturbance output by the grid-connected wind turbine after the droop control circuit is:
[0118] (17)
[0119] In the formula, The instantaneous power disturbance output of a grid-connected wind turbine is the phase angle change after passing through the droop control circuit. To output the AC component of the phase angle change, To output the DC component of the phase angle change, Nominal angular frequency; For secondary synchronization frequency, For time, The phase angle corresponding to the AC component of the droop control output phase angle change; in equation (13):
[0120] (18)
[0121] (19)
[0122] In the formula, This is the droop control coefficient. For the Laplace operator, It is the imaginary unit.
[0123] It can be seen that the AC component of the output phase angle change Amplitude order of magnitude and The same applies to the DC component of the output phase angle change. Amplitude order of magnitude and Similarly, the output phase angle disturbance is mainly The resulting AC disturbance. And the droop control coefficient. The order of magnitude is usually set to The phase angle fluctuation of grid-connected wind turbines is orders of magnitude smaller than that of parallel-connected wind turbines when disturbances occur. Furthermore, the power control loop bandwidth of grid-connected wind turbines is typically designed in the 2-10Hz range, far smaller than the phase-locked loop bandwidth of parallel-connected wind turbines. When the subsynchronous frequency of the disturbance exceeds the power control loop bandwidth, grid-connected wind turbines cannot respond to disturbance changes in a timely manner. Therefore, the instantaneous power after subsynchronous oscillation in a grid-connected wind power system exhibits significant multi-timescale characteristics.
[0124] After knowing or obtaining the subsynchronous frequency, the following analysis is further performed on the grid-connected wind turbine:
[0125] (1) When At that time, i.e., the current synchronization frequency The bandwidth of the power control loop is greater than that of grid-connected wind turbines. hour:
[0126] Control mechanisms such as droop cannot respond to disturbance changes in a timely manner. Therefore, the voltage and current only have power frequency components and subsynchronous frequency components, and the voltage and current at this time are expressed by the following formula:
[0127] (20)
[0128] The resulting instantaneous power is not affected by the phase generation stage. The instantaneous power only includes the DC component and the primary AC component. That is, when the subsynchronous frequency is greater than the bandwidth of the power control stage of the grid-connected wind turbine, the instantaneous power of the grid-connected wind turbine is:
[0129] (twenty one)
[0130] In the formula, The DC component of the grid-type wind turbine is defined as the frequency of the subsynchronous circuit being greater than the bandwidth of the power control loop. The AC component of the primary term of the grid-type wind turbine is defined as follows: when the subsynchronous frequency is greater than the bandwidth of the power control loop of the grid-type wind turbine.
[0131] (twenty two)
[0132] (twenty three)
[0133] visible, It is mainly generated by the combined effects of power frequency voltage and current and subsynchronous frequency voltage and current, and its order of magnitude is the same as that of steady-state active power. It is generated by the interaction of power frequency voltage and current and subsynchronous frequency voltage and current.
[0134] (2) When At that time, i.e., the current synchronization frequency The bandwidth of the power control loop is smaller than that of grid-connected wind turbines. hour:
[0135] At this time, the secondary synchronization frequency is within the bandwidth of the power control loop of the grid-connected wind turbine. The voltage and current input from the secondary synchronization frequency into the active power control loop generate a disturbance of [value missing]. The output phase angle changes, and the changed output phase angle will lead to... A new perturbation frequency component is generated in the dq coordinate system:
[0136] (twenty four)
[0137] (25)
[0138] Similarly, A new disturbance is also generated in the dq coordinate system, and the instantaneous power generated after interacting with the voltage is:
[0139] (26)
[0140] Similar to grid-connected wind turbines, as the frequency of the instantaneous power component increases, its amplitude decreases by an order of magnitude; among which:
[0141] (27)
[0142] (28)
[0143] (29)
[0144] (30)
[0145] As can be seen from the above analysis, during subsynchronous oscillations, the instantaneous power of grid-connected wind turbines simultaneously contains DC components and AC components of primary, secondary, and tertiary terms, similar to the composition of instantaneous power in grid-connected wind turbines. This is further supported by changes in the droop control parameters. It can effectively affect the amplitude of each AC component of the primary term. In addition, due to the influence of the bandwidth of the power control links such as droop, grid-connected wind turbines cannot respond to higher frequency subsynchronous frequencies. After being disturbed by higher frequencies, the instantaneous power of grid-connected wind turbines only contains DC components and primary AC components.
[0146] Since the period of the AC component of the instantaneous power of the wind power grid-connected system is always... / k, which is k times the instantaneous power. The period of the frequency component is / k, by calculating instantaneous power time-series data in The integral value within the period can effectively filter out the AC component contained in the instantaneous power and extract the DC component after disturbance. The disturbed DC component is:
[0147] ;
[0148] In the formula, The DC component after disturbance. For instantaneous power at arrive Points within a time period Instantaneous power For the secondary synchronization period, This represents the DC component of the instantaneous power.
[0149] In grid-connected wind turbines: see equation (11):
[0150]
[0151] It can be seen that the DC component of the instantaneous power of a grid-connected wind turbine consists of four components: the power frequency voltage-current interaction component, the subsynchronous frequency voltage-current interaction component, the power frequency voltage-current interaction after being disturbed by the phase-locked loop, and the subsynchronous frequency voltage-current interaction after being disturbed by the phase-locked loop. The main component is the power frequency voltage-current interaction component, whose value is similar to that of the steady-state active power component. same:
[0152] ;
[0153] To successfully separate the subsynchronous power, it is also necessary to extract the interaction components of voltage and current after phase-locked loop perturbation in the DC component of the instantaneous power. After the subsynchronous oscillation occurs, the voltage and current at the power frequency and the subsynchronous frequency will generate DC components in the instantaneous power. Since the AC components of the frequency components have the same amplitude, the voltage-current interaction component after being disturbed by the phase-locked loop can be separated from the DC component using the amplitude of the instantaneous power quadratic term. The simplified quadratic term of the instantaneous power AC component is as follows.
[0154] ;
[0155] In the formula, ,
[0156] ;
[0157] It is evident that the DC component of the voltage-current interaction after phase-locked loop perturbation has the same amplitude as the AC component of the secondary synchronization power frequency. By extracting the AC component amplitude of the instantaneous power secondary term, the DC component of the voltage-current interaction at the secondary synchronization frequency can be separated.
[0158] In alternating current components, the amplitude decreases by an order of magnitude as the frequency increases. The amplitude of the first term is much larger than that of the second term, while the amplitude of the third term is not significantly different from that of the second term. To accurately separate the second-order component in instantaneous power, it is necessary to effectively filter out the first and third terms. Therefore, with... By sampling the instantaneous power time-series data at a period of / 2, we can obtain:
[0159]
[0160] p(t)+p(t+ / 2) This allows for the filtering of first-order and third-order terms, thereby achieving the separation of the second-order term of instantaneous power. Furthermore, it eliminates the DC component in the instantaneous power time-series data, as shown below.
[0161]
[0162] calculate The integral value of the instantaneous power time-series data within a 4-cycle period is shown below. From this, the amplitude of the second harmonic is obtained, achieving quadratic term separation. The disturbed AC component of the quadratic term is:
[0163] ;
[0164] ;
[0165] In the formula, The quadratic component after the disturbance is the commutative component. For the secondary synchronization period, For time, For time Instantaneous power at time For time Instantaneous power at time For time Instantaneous power at time For time Instantaneous power at time This is the AC component of the quadratic term of the instantaneous power.
[0166] The above analysis, taking grid-type control as an example, proposes a subsynchronous oscillation source location criterion based on instantaneous power. Under the grid-type control strategy, the above location criterion is still applicable.
[0167] (1) Assuming that the subsynchronous frequency is not within the bandwidth of the drooping equal power control link, the instantaneous power of the grid-type wind turbine only has DC component and primary AC component, and there is no secondary AC component. It only includes steady-state active power and instantaneous power generated by subsynchronous frequency voltage and current.
[0168] (2) Assuming that the subsynchronous frequency voltage and current can generate phase angle disturbances in the droop control loop, the instantaneous power of the grid-connected wind turbine will include a DC component and AC components of first to third terms. Unlike grid-connected wind turbines, after the subsynchronous oscillation of the grid-connected wind turbine, the output phase angle will generate an additional DC disturbance component, but its amplitude differs from the AC disturbance component by 1 to 2 orders of magnitude, and its impact on the instantaneous power is limited. The main components of the DC component in the instantaneous power are the power components generated by the undisturbed power frequency and subsynchronous frequency voltage and current, and the power components generated by the droop control loop. The power components generated by the power frequency and subsynchronous frequency voltage and current after AC disturbance have an instantaneous power component composition that is basically similar to that of grid-connected wind turbines.
[0169] Furthermore, since the active power droop factor is typically set to the order of magnitude... Under the same conditions, its output phase angle disturbance is much smaller than that of the grid-connected wind turbine. The instantaneous power components generated by the voltage and current after the phase angle disturbance are much smaller than those generated without the disturbance. In the DC component, only the power component generated by the disturbance of the power frequency voltage and current is close in order of magnitude to the DC component generated by the interaction of the subsynchronous frequency voltage and current. The AC component of the second term of the instantaneous power can be simplified as:
[0170] ;
[0171] In the formula,
[0172] ,
[0173] .
[0174] The correctness of the above analysis and conclusions is verified and evaluated based on the IEEE-39 node standard model, and its topology is as follows: Figure 5 As shown, grid-connected and grid-connected wind turbines are connected to nodes 32 and 34, respectively. The grid-connected wind turbines use a phase-locked loop (PLL) for grid connection, while the grid-connected wind turbines use droop power control. The effectiveness of the proposed subsynchronous oscillation source location criterion is verified based on the following two mathematical examples. In both examples, the number of grid-connected and grid-connected wind turbines aggregated is 400, and the instantaneous power measurement point is set at the grid connection point of the aggregated wind turbine model. Subsynchronous oscillation sources are set at both the grid-connected and grid-connected wind turbines to verify the applicability of the subsynchronous oscillation source location criterion in wind power grid-connected systems under different control conditions.
[0175] Example 1: The subsynchronous oscillation source is a grid-following wind turbine.
[0176] The parameter settings for Example 1 are described below. The rated active power of the grid-connected and grid-connected wind turbines is set to 10MW. At 3s, a subsynchronous oscillation occurs in the grid-connected wind turbine at node 32, with an oscillation frequency of 20Hz. The subsynchronous frequency in the system is calculated to be 20Hz, and the instantaneous power before and after the oscillation at the grid connection point of the grid-connected and grid-connected wind turbines is calculated. , and The oscillation positioning criterion K, i.e., the secondary synchronous power, is calculated for the instantaneous power of grid-connected and grid-connected wind turbines. Its time-domain data is as follows: Figure 6 As shown, Figure 6 (a) is a grid-connected wind turbine. Figure 6 (b) is a grid-type wind turbine.
[0177] Comparing the time-domain waveforms of grid-connected and grid-connected wind turbines, it can be seen that the K value of both is less than zero before the subsynchronous oscillation. Oscillation occurs at 3 seconds, with the K value becoming positive for the grid-connected wind turbine and remaining negative for the grid-connected wind turbine. Based on the subsynchronous oscillation source location criterion, the grid-connected wind turbine is the oscillation source of the system's subsynchronous oscillation, inputting positive subsynchronous power into the system. This result is mutually verified with the simulation results, confirming the effectiveness of the oscillation location criterion in the grid-connected wind turbine.
[0178] Example 2: The subsynchronous oscillation source is a grid-type wind turbine.
[0179] The parameter settings for Example 2 are described below. The rated active power of both the grid-connected and grid-connected wind turbines is set to 80MW. At 3s, a subsynchronous oscillation occurs in the grid-connected wind turbine at node 34, with an oscillation frequency of 10Hz. The subsynchronous frequency of the system is calculated to be 10Hz, and the instantaneous power before and after the oscillation at the grid connection point of both the grid-connected and grid-connected wind turbines is calculated. , and The oscillation positioning criterion K, i.e., the secondary synchronous power, is calculated for the instantaneous power of grid-connected and grid-connected wind turbines. Its time-domain data is as follows: Figure 7 As shown, Figure 7 (a) is a grid-connected wind turbine. Figure 7 (b) is a grid-type wind turbine.
[0180] The time-domain waveforms of both grid-connected and grid-connected wind turbines show that the K value is less than zero before the subsynchronous oscillation. After the oscillation occurs, the K value becomes positive for the grid-connected wind turbine and remains negative for the grid-connected wind turbine. Based on the subsynchronous oscillation source location criterion, the grid-connected wind turbine is the oscillation source of the system's subsynchronous oscillation, inputting positive subsynchronous power into the system. This result is verified by the simulation settings, confirming the applicability of the oscillation location criterion in grid-connected wind turbines.
[0181] Compared to voltage and current components, the instantaneous power of both oscillating and non-oscillating sources consists of a DC component and a frequency of ( ). It consists of AC components that are integer multiples of 1 / 2 ohm. The subsynchronous period is defined. =2 π / ( ), then the instantaneous power exists at k times ( The period of the frequency component is / k. The instantaneous power is sampled using the next synchronization period as follows.
[0182] ;
[0183] Calculate the instantaneous power difference p(t+) )-p(t). From the frequency characteristics of the AC component, it can be seen that when The instantaneous power difference is equal to zero. Based on the instantaneous power frequency characteristics, an absolute average value model of the instantaneous power difference is constructed to obtain the subsynchronous period. The steps are as follows:
[0184] Construct an absolute average value model of the instantaneous power difference based on the instantaneous power; the absolute average value model of the instantaneous power difference is as follows;
[0185] ;
[0186] In the formula, Angular frequency is The absolute average value of the instantaneous power difference at time, The sampling period is The instantaneous power start time, The instantaneous power end time, For sampling time is Instantaneous power at time For sampling time is Instantaneous power at time For sampling time is Time This represents the absolute value of the instantaneous power difference over the sampling period. Angular frequency, Let be the time of the i-th sampling.
[0187] The minimum value of the absolute average value of the instantaneous power difference is obtained based on the aforementioned model of the absolute average value of the instantaneous power difference; specifically:
[0188] The time of the i-th sampling, the start time of the instantaneous power, and the end time of the instantaneous power are obtained and input into the absolute average value model of the instantaneous power difference;
[0189] The minimum value is obtained by running the instantaneous power difference absolute average value model;
[0190] The sub-synchronization period is obtained based on the minimum value, specifically:
[0191] The sampling period corresponding to the minimum value is obtained based on the model of the minimum value and the absolute average value of the instantaneous power difference;
[0192] The secondary synchronization period is obtained based on the sampling period corresponding to the minimum value, and the calculation formula is as follows:
[0193] ;
[0194] In the formula, For the secondary synchronization period, The sampling period is the minimum value of the absolute average value of the instantaneous power difference.
[0195] Furthermore, after obtaining the subsynchronization period, the subsynchronization frequency is obtained according to the subsynchronization frequency calculation formula, which is:
[0196] ;
[0197] In the formula, For secondary synchronization frequency, This is the secondary synchronization period.
[0198] This invention also provides a platform including a processor and a memory. The memory stores computer-readable instructions, and the processor is used to run the computer-readable instructions. When the computer-readable instructions are run, they execute a subsynchronous oscillation positioning method for wind power grid-connected systems based on instantaneous power.
[0199] This invention also provides a device including a processor and a memory. The memory stores computer-readable instructions, and the processor is used to execute the computer-readable instructions. When the computer-readable instructions are executed, they perform a subsynchronous oscillation positioning method for wind power grid-connected systems based on instantaneous power.
[0200] The correctness of the derived subsynchronous frequency was verified using the official PSCAD GFM / GFL two-unit interconnection model. The model includes two 100MVA wind turbines, which can freely choose between grid-connected or grid-connected operation modes, and the two wind turbines are interconnected via transmission lines.
[0201] 1) Verification of obtaining subsynchronous frequency based on grid-connected wind turbines:
[0202] The grid-connected wind turbines are connected to the grid using phase-locked loops, with a grid-connected capacity of 400 units. Subsynchronous oscillations are induced in the grid-connected wind turbines at 3 seconds, with an oscillation frequency of 20Hz. The instantaneous power at the outlet of the grid-connected wind turbines is extracted, and the instantaneous power values are calculated under different sampling periods, such as... Figure 2 As shown. Comparing different frequencies, it can be seen that the instantaneous power difference is 0 at 20Hz, 40Hz, 50Hz, and 55Hz, respectively. This corresponds to the instantaneous power frequency components being 0 at 40Hz, 60Hz, 10Hz, and 5Hz. This proves that the instantaneous power difference is minimized when sampling the instantaneous power sequence with a period of k(1 / (60-20)), i.e., the subsynchronous frequency is 20Hz. Spectral analysis of the instantaneous power shows that the power contains components at 40Hz, 60Hz, 10Hz, and 5Hz. 40Hz, 3 The 40Hz AC component gradually decreases in magnitude as the frequency order increases, verifying the correctness of the derivation of the instantaneous power frequency response characteristics of the grid-connected wind turbine.
[0203] 2) Verification of obtaining subsynchronous frequency based on grid-connected wind turbines:
[0204] Grid-connected wind turbines are connected to the grid using droop control, with 400 turbines connected. Subsynchronous oscillations are induced in the grid-connected wind turbines at 3 seconds, with oscillation frequencies of 20Hz and 8Hz. The instantaneous power characteristics of the grid-connected wind turbines at different oscillation frequencies are analyzed.
[0205] (1) At 3s, a subsynchronous oscillation with a frequency of 20Hz is induced in the grid-type wind turbine. The instantaneous power at the outlet of the grid-type wind turbine is extracted, and the instantaneous power value under different sampling periods is calculated, such as... Figure 3 As shown. Comparing the instantaneous power difference at different frequencies, it can be seen that the instantaneous power difference is smallest at period k(1 / (60-20)), i.e., the subsynchronous frequency is 20Hz. Comparing the spectrum results of grid-connected and grid-connected wind turbines after injection at 20Hz, it can be seen that because the subsynchronous frequency is greater than the droop control bandwidth, the droop control cannot respond to disturbance changes in time. The values of the quadratic and cubic terms of instantaneous power are much smaller than the instantaneous power components at the same oscillation frequency as the grid-connected wind turbine. This verifies the correctness of the derivation of the instantaneous power frequency response characteristics of the grid-connected wind turbine when subjected to high-frequency disturbances (for power).
[0206] (2) At 3s, a subsynchronous oscillation with a frequency of 8Hz is induced in the grid-type wind turbine. The instantaneous power at the outlet of the grid-type wind turbine is extracted, and the instantaneous power value under different sampling periods is calculated, such as... Figure 4As shown. Comparing the instantaneous power differences at different frequencies, it can be seen that the instantaneous power difference is smallest at period k(1 / (60-8)), i.e., the subsynchronous frequency is 8Hz. From the instantaneous power spectrum analysis, it can be seen that after being subjected to low-frequency disturbances, grid-type wind turbines also have AC components of the first, second, and third terms, and their orders of magnitude gradually decrease with the increase of frequency order.
[0207] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for locating subsynchronous oscillations in a wind power grid-connected system based on instantaneous power, characterized in that, Includes the following steps: When a subsynchronous oscillation disturbance occurs, the instantaneous voltage and instantaneous current at the wind power grid connection point are detected; The instantaneous power of the wind power grid connection point is obtained based on the instantaneous voltage and the instantaneous current. The subsynchronization period is obtained based on the instantaneous power. The DC component and the AC component of the second term after disturbance are obtained based on the subsynchronization period and the instantaneous power. The disturbed DC component is: ； In the formula, The DC component after disturbance. For instantaneous power at arrive Points within a time period Instantaneous power This is the secondary synchronization period; The disturbed quadratic term's AC component is: ； In the formula, The quadratic term after the disturbance is the commutative component. For the secondary synchronization period, For time, For time Instantaneous power at time For time Instantaneous power at time For time Instantaneous power at time For time Instantaneous power at time; The subsynchronous power is obtained based on the subsynchronous period, the disturbed DC component, and the disturbed quadratic AC component. Determine whether the wind turbine is a source of subsynchronous oscillation based on the subsynchronous power. The subsynchronous power is: ； In the formula, For secondary synchronous power, The DC component after disturbance. The quadratic term after the disturbance is the commutative component. For the secondary synchronization period, This represents steady-state active power. when When the value is greater than 0, the wind turbine is a subsynchronous oscillation source; when When <0, the wind turbine is not a subsynchronous oscillation source.
2. The method for locating subsynchronous oscillations in a wind power grid-connected system based on instantaneous power as described in claim 1, characterized in that, The steps to obtain the sub-synchronization period are as follows: Construct an absolute average value model of the instantaneous power difference based on the instantaneous power; The minimum value of the absolute average value of the instantaneous power difference is obtained based on the aforementioned model of the absolute average value of the instantaneous power difference; The subsynchronization period is obtained based on the minimum value.
3. The method for locating subsynchronous oscillations in a wind power grid-connected system based on instantaneous power according to claim 2, characterized in that, The model for the absolute average value of the instantaneous power difference is: ； In the formula, Angular frequency is The absolute average value of the instantaneous power difference at time, The sampling period is , The instantaneous power start time, The instantaneous power end time, For sampling time is Instantaneous power at time For sampling time is Instantaneous power at time Angular frequency, Let be the time of the i-th sampling.
4. The method for locating subsynchronous oscillations in a wind power grid-connected system based on instantaneous power according to claim 3, characterized in that, The steps to obtain the sub-synchronization period are as follows: The time of the i-th sampling, the start time of the instantaneous power, and the end time of the instantaneous power are obtained and input into the absolute average value model of the instantaneous power difference; The minimum value is obtained by running the instantaneous power difference absolute average value model; The sampling period corresponding to the minimum value is obtained based on the model of the minimum value and the absolute average value of the instantaneous power difference; The subsynchronization period is obtained based on the sampling period corresponding to the minimum value.
5. The subsynchronous oscillation positioning method for wind power grid-connected systems based on instantaneous power according to claim 4, characterized in that, The formula for obtaining the sub-synchronization period based on the sampling period corresponding to the minimum value is: ； In the formula, For the secondary synchronization period, The sampling period is the minimum value of the absolute average value of the instantaneous power difference.
6. The method for locating subsynchronous oscillations in a wind power grid-connected system based on instantaneous power according to any one of claims 1-5, characterized in that, After obtaining the subsynchronization period, the subsynchronization frequency is obtained according to the subsynchronization frequency calculation formula.
7. A platform comprising a processor and a memory, characterized in that, The memory stores computer-readable instructions, and the processor is used to run the computer-readable instructions. When the computer-readable instructions are run, they execute the subsynchronous oscillation positioning method for wind power grid-connected systems based on instantaneous power as described in any one of claims 1-6.