Low voltage ride through induced oscillation analysis method based on phase plane method

Abstract

The invention belongs to the field of power system stability analysis, and particularly relates to a low-voltage ride-through induced oscillation analysis method based on a phase plane method. In recent years, oscillation instability phenomena of multi-time crossing control participation and repeated fluctuation of voltage and active power output occur at home and abroad, and primary analysis finds that the oscillation instability phenomena correspond to switching oscillation participated in a low-crossing control link. In order to analyze boundary conditions of the low-pass induced oscillation, a simplified switching system established based on a current loop is converted into a general second-order switching system; calculating and discussing the allowable balance point position and property of the general second-order switching system; and according to the position and the property of the balance point, analyzing a low-pass induced oscillation mechanism of the second-order switching system under positive damping, and giving a general conclusion. According to the method, a detailed new solution thought is provided for the boundary conditions of low-voltage-ride-through induced oscillation caused by unreasonable balance points, and a theoretical reference is provided for dispatching and operation parameter giving of new energy wind power connected to a power grid through a converter.

Description

Technical Field

[0001] The present invention belongs to the field of power system stability analysis, and in particular relates to a low voltage ride through induced oscillation analysis method based on a phase plane method. Background Art

[0002] In response to fossil energy depletion, climate change and environmental problems, my country has vigorously developed new energy. By the end of December 2024, China's installed capacity of new energy power generation, including wind power, solar power generation and biomass power generation, reached 1.45 billion kilowatts, exceeding the installed capacity of thermal power for the first time.

[0003] Centralized renewable energy bases are often located at the end of the grid structure, making them prone to voltage instability and other issues. In actual operation, oscillatory instability, characterized by repeated fluctuations in voltage and active power output, has occurred with the participation of ride-through control. Preliminary research indicates that the mathematical mechanism of this voltage instability corresponds to a non-smooth bifurcation, which differs from both the physical and mathematical mechanisms of traditional voltage instability, such as saddle-node bifurcations. For example, voltage oscillation instability in a grid-connected wind power system in the northern Hebei power grid caused widespread disconnection of wind turbines, resulting in a maximum loss of 476,000 kW of wind power output and a voltage drop below 0.9 pu. Notably, the voltage instability in this new energy station's output system exhibited repeated and dramatic fluctuations in the grid connection point voltage between 0.9 and 1.05 pu, and repeated fluctuations in wind power active power output. Furthermore, field data indicates that the wind farm's control method was constantly switching, resulting in repeated in-and-out low-voltage ride-through conditions. Traditional voltage instability typically manifests as reactive power fluctuations with relatively stable active power output, with minimal control involvement. This phenomenon is significantly different from traditional voltage instability.

[0004] In addition, mathematically, when the control switches, the mathematical model describing the system becomes a switching dynamic system (non-smooth dynamic system), and the above-mentioned voltage oscillation instability phenomenon corresponds to the dynamic properties of the non-smooth system. Furthermore, from the perspective of parameter space, the emergence of the above-mentioned voltage oscillation instability corresponds to the occurrence of non-smooth bifurcation in the switching system. Traditionally, for power systems without switching participation, their voltage instability often corresponds to the smooth bifurcation of smooth systems, especially saddle-node bifurcation. Therefore, the oscillations with control participation in the above-mentioned new energy stations are different from traditional voltage instabilities not only in the physical process, but also in their mathematical mechanisms. Existing studies attribute its mechanism to an oscillation induced by a low voltage ride-through strategy.

[0005] Therefore, in order to understand and prevent the low voltage ride-through induced oscillation phenomenon that may occur in new energy stations, the present invention proposes a low voltage ride-through induced oscillation analysis method based on the phase plane method, aiming to provide an engineering reference for analyzing the special oscillations that occur in such new energy stations under positive damping conditions. Summary of the Invention

[0006] The purpose of the present invention is to provide a low voltage ride through induced oscillation analysis method based on the phase plane method. The method has rigorous logic and is easy to implement. It can accurately determine whether low voltage ride through induced oscillation occurs in a simplified second-order system of new energy and provide sufficient conditions for the occurrence of low voltage ride through induced oscillation. It has theoretical innovation and practicality.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A low voltage ride-through induced oscillation analysis method based on a phase plane method, the method comprising:

[0009] Step 1: Convert the simplified switching system of the new energy source based on the current loop into a general second-order switching system in control theory;

[0010] Step 2: Calculate and discuss the location and properties of the admissible equilibrium points of a general second-order switching system;

[0011] Step 3: Analyze the low-throughput induced oscillation mechanism of the second-order switching system under positive damping based on the position and properties of the equilibrium point, and give a general conclusion: the voltage corresponding to the normal system equilibrium point is lower than the low-throughput voltage threshold, which is a sufficient but not necessary condition for the occurrence of low-throughput induced oscillation.

[0012] It can be seen from the technical solution provided by the present invention that the above analysis method has clear logic and is of great practical value for predicting whether low-breakthrough-induced oscillation occurs. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the implementation process. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0014] Figure 1 The impact of the voltage value corresponding to the normal system balance point provided by the embodiment of the present invention on the system allowable balance point;

[0015] Figure 2 The voltage phase trajectory and physical quantity time domain response of the system when the normal system equilibrium point voltage is higher than the low breakdown voltage threshold provided by the embodiment of the present invention: converges to the stable focus y EP0 ;

[0016] Figure 3 The voltage phase trajectory and physical quantity time domain response of the system provided in the embodiment of the present invention when the normal system equilibrium point voltage is lower than the low breakdown voltage threshold: converge to a non-smooth limit cycle;

[0017] Figure 4 The embodiment of the present invention provides a special case where the voltage phase trajectory and physical quantity time domain response of the system when the normal system equilibrium point voltage is higher than the low breakdown voltage threshold: convergence to a non-smooth limit cycle. DETAILED DESCRIPTION

[0018] The method of the present invention is demonstrated below with examples.

[0019] In order to present the analysis method more concisely and clearly, the present invention focuses on the voltage stability problem of renewable energy, ignores the PLL loop and control outer loop of the VSC on the grid side of the direct-drive wind turbine, and builds a second-order system that considers the current inner loop and its dual line link. The system is composed of a subsystem under normal operation and a subsystem under low-through state. Specifically: when the voltage at the PCC point negatively crosses into the low-through voltage V LVRTin When the voltage goes through the positive direction, the normal system switches to the low-through voltage system. LVRTout When the low penetration system switches to the normal system. The details are as follows:

[0020]

[0021] The subscripts “0” and “1” represent the system in which the state quantity is in normal operation and the low voltage ride-through strategy is in effect, respectively.

[0022] The state equations of the second-order switching system with dq axis current as the state quantity for the normal system and the low-throughput system are given below:

[0023] 0Normal system

[0024]

[0025] 1Low penetration system

[0026]

[0027] In the above system, the physical meaning and typical values ​​of the parameters are classified as follows in Table 1:

[0028] Table 1 Meaning and typical values ​​of various physical quantities

[0029]

[0030] Perform step 1: transform the simplified switching system of the new energy source based on the current loop into a general second-order switching system in control theory;

[0031] For the second-order system and the new state quantity y (scalar), if there is the following relationship

[0032]

[0033] Among them, KT is a 1×2 matrix, which represents the correspondence between x (second-order quantity) and y (first-order scalar quantity).

[0034] V c =V s +I d R g -I q ω s L g (4)

[0035] y=V c (PCC point voltage), K T =[R g ,-ω s L g ],y0=V s .

[0036] Since the input u here is a scalar that is independent of time and its differential with respect to time is 0, its first and second order derivatives are:

[0037]

[0038] According to the Cayley-Halmilton theorem, a non-singular square matrix A must satisfy its own characteristic equation. In particular, for a second-order square matrix,

[0039]

[0040] Where tr(A) is the trace of matrix A, and det(A) is the determinant of matrix A. Substituting the last equation into the second-order derivative term of (5), we can finally deduce:

[0041]

[0042] Substituting the relationship between y and its derivative and x in (3) and (5) into (7), we can finally obtain the second-order system equation about y in the form of

[0043]

[0044] In this way, we deduce that x=[x1,x2] T It is the transformation of the state equation of the second-order state quantity to the scalar y. d ,I q ] and y=V c And the related matrix parameters are brought in, and finally we can get the V c The second-order system is as follows:

[0045]

[0046] By applying the above switching logic, the final switching system can be obtained as follows:

[0047]

[0048] The matrices A, B, and u of the normal operating system and the low-throughput system need to change their values ​​according to the 0 / 1 subscript during the switching process.

[0049] Proceed to step 2: Calculate and discuss the locations and properties of the admissible equilibrium points of a general second-order switching system;

[0050] For a second-order system of the general form

[0051]

[0052] Expanding the derivative value, we have

[0053]

[0054] The slope of the trajectory tangent at the equilibrium point is an indefinite value, so the equilibrium point satisfies:

[0055]

[0056] That is, the first-order derivative and the second-order derivative of the state quantity at the equilibrium point are both 0. Therefore, the equilibrium point must be located on the horizontal axis.

[0057] Step 2.1 Equilibrium point of normal system

[0058] According to the above derivation, the state equation satisfied by the system under normal operation is:

[0059]

[0060] Bring in the parameters, specifically:

[0061]

[0062] Obviously, The position of the equilibrium point of the normal system in the phase plane space is

[0063]

[0064] The characteristic root of the equilibrium point can be solved by equation (15), which is

[0065]

[0066] It can be seen that the equilibrium point of a normal system must be a stable focus mathematically. Under free conditions, the phase trajectory will converge to the equilibrium point y as an inward spiral. EP0 Under the typical parameters chosen, the pair of conjugate negative real roots are: -2±j4.

[0067] Step 2.2: Low penetration of the system's equilibrium point

[0068] Similarly, the state space equation satisfied by the system under the low-penetration strategy satisfies:

[0069]

[0070] Substituting A1, B1, and u1 parameters, the second-order system is:

[0071]

[0072] Obviously, it is easy to find the position of the equilibrium point of the low-penetration system on the phase plane:

[0073]

[0074] The corresponding voltage is compared with the voltage V LVRTout Do the difference:

[0075]

[0076] Therefore, we can draw a conclusion: the voltage corresponding to the equilibrium point of the low-throughput system is greater than the voltage at which the system exits the low-throughput. Therefore, the equilibrium point of the low-throughput system is not within its scope and is a virtual equilibrium point (VEP).

[0077] The characteristic root of the equilibrium point can be solved by solving the characteristic equation of formula (19), and we can get

[0078]

[0079] Now let’s discuss the properties of characteristic roots.

[0080] Among them, due to the low-throughput reactive dynamic current coefficient K L The value is generally 1.5 to 3.0, and the allowable overflow coefficient I N The value is generally 1.0 to 1.1. The value in “()” in the result is less than 0. Therefore, the characteristic root should also be the conjugate complex root of the negative real part, that is,

[0081]

[0082] Under given typical parameters, the characteristic root is -4.3056±j 4.8092, and the corresponding equilibrium point is also a stable focus.

[0083] Step 2.3 Existence of equilibrium point of the overall system

[0084] According to the above analysis, we can conclude that under different normal system equilibrium point corresponding voltages, the existence of the equilibrium point is as follows: Figure 1shown.

[0085] Figure 1 Specific instructions:

[0086] Since the balance point of the low-throughput system has nothing to do with the voltage corresponding to the balance point of the normal system and it is always a virtual balance point, the entire process is a dotted line.

[0087] (1) When the voltage corresponding to the normal system balance point When , the normal system has one allowable equilibrium point in region 1; the low-penetration system has one virtual equilibrium point in region 1. The entire system has only one allowable equilibrium point in region 1.

[0088] (2) When the voltage corresponding to the normal system balance point When , the normal system has one allowable equilibrium point in region 2, and the low-penetration system has one virtual equilibrium point in region 1. The entire system has only one allowable equilibrium point in region 2.

[0089] (3) When the voltage corresponding to the normal system balance point When the normal system has a virtual equilibrium point in region 3, the low-throughput system has a virtual equilibrium point in region 1. At this time, all equilibrium points of the entire system are virtual equilibrium points, and there are no permissible equilibrium points. The system may have a new stable mode different from the equilibrium point.

[0090] The relationship between the equilibrium point voltage and the equilibrium point existence is summarized in Table 2 below.

[0091] Table 2 Correspondence between normal system balance point voltage and allowable balance point

[0092]

[0093] Proceed to step 3: Analyze the low-throw induced oscillation mechanism of the second-order switching system under positive damping based on the location and properties of the equilibrium point, and give a general conclusion: the voltage corresponding to the normal system equilibrium point is lower than the low-throw voltage threshold, which is a sufficient but not necessary condition for the occurrence of low-throw induced oscillation;

[0094] According to the previous analysis, under the selected typical parameters, the two equilibrium points of the overall system are both conjugate negative real roots, and the property of the overall equilibrium point of the system is positive damping.

[0095] In addition, both Case 1 and Case 2 are cases of an admissible equilibrium point and a virtual equilibrium point, and can essentially be attributed to V EP0 >V LVRTin Condition.

[0096] Step 3.1 A case where the normal system equilibrium point voltage is greater than the low-breakdown voltage threshold: V EP0 >V LVRTin

[0097] Set the initial system input, that is, the current reference value (I dref0 ,I qref0 )=(0.9,0.1), the corresponding PCC point voltage This corresponds to y0 in the phase plane; thereafter, at 1s, the dispatching operation is simulated to increase the reactive power output of the system. Through the active / reactive power outer loop, the final current reference value becomes (I dref ,I qref )=(0.9,0.2), the corresponding voltage V EP0 =0.845>V LVRTin =0.80, corresponding to y in the phase plane EP0 The phase plane response and time domain response can be plotted as Figure 2 .

[0098] Figure 2 It shows that: under given parameters, the equilibrium point of the normal system is a stable focus, and in this case it is an admissible equilibrium point. The low-penetration system must have a virtual stable focus, the coordinates of which can be calculated as y EP0 =(V EP0 ,0)=(0.845,0).

[0099] In addition, the operating trend is analyzed: from the initial moment to 1 second, the system operates at the initial set equilibrium point, corresponding to a stable focus at (0.945, 0) (the vertical axis in the figure is not 0); 1 second later, the system's set equilibrium point is adjusted to (0.845, 0), and its V EP0 >V LVRTin , is an admissible equilibrium point. The system converges to y along the blue spiral trajectory. EP0 .

[0100] Step 3.2 Normal system equilibrium point voltage is less than the low breakdown voltage threshold: V EP0 <V LVRTin

[0101] Keep the initial equilibrium point y0 unchanged and set the equilibrium point y EP0 Adjust to y EP0 =(V EP0 ,0)=(0.795,0), that is, the voltage is lower than V LVRTin The phase plane response and time domain response can be plotted, as well as the first swing phase trajectory of the normal system and the low-throughput system if there is no low-throughput switching link. Figure 3 .

[0102] Figure 3It shows that: when the equilibrium point of the normal system changes due to the position change and becomes a virtual equilibrium point, the nature of the equilibrium point remains unchanged and it is still a stable focus. LVRTin When , the system switches to a low-throughput system, the state quantity does not change, so the voltage remains unchanged, but due to the changes in the Jacobian matrix A and the input quantity correlation matrix B and u, the first-order derivative of the voltage changes suddenly.

[0103] Since the equilibrium point y of the low-penetration system EP1 is a virtual stable focus, so when the trajectory moves to V LVRTout When the system exits the low penetration and returns to the normal system, it will continue to move towards y EP0 Movement, repeating the above process, forming a stable non-smooth limit cycle (SLC), and then generating repeated oscillations of voltage, that is, the oscillation phenomenon induced by the low-penetration strategy, referred to as low-penetration induced oscillation.

[0104] It is not difficult to find that the stable focus of the normal system is in the low-penetration system. When it becomes a virtual equilibrium point, it will definitely lead to low-penetration induced oscillation. Therefore, the equilibrium point y of the normal system is EP0 The virtual equilibrium point is a sufficient condition for the occurrence of voltage oscillation induced by the low voltage ride-through strategy, that is,

[0105] Step 3.3 Special Case: V EP0 >V LVRTin Low penetration induced oscillation still occurs

[0106] Keep the voltage corresponding to the initial equilibrium point y0 unchanged ((I dref0 ,I qref0 )=(0.95,0.1)), the equilibrium point y of the normal operation system EP0 Adjust to y EP0 =(V EP0 ,0)=(0.82,0)((I dref ,I qref )=(1.00,0.23), does not exceed the overcurrent condition), at this time the equilibrium point voltage is higher than V LVRTin Draw the phase plane response and time domain response, as well as the first swing phase trajectory of the normal system and the low-throughput system if there is no low-throughput switching link. Figure 4 .

[0107] Figure 4 It shows that when the normal system equilibrium point is higher than the low-breakdown voltage threshold, such voltage oscillations may still occur. That is, when the overall system has an allowable equilibrium point, some initial equilibrium points (for the system after 1 second, they are initial values) may also converge to the limit cycle rather than the allowable virtual focus.

[0108] Therefore, we can draw the general conclusion that VEP0 <V LVRTin It is a sufficient but not necessary condition for the occurrence of low-voltage wear-through induced oscillation, that is, under normal circumstances, when the voltage corresponding to the system's equilibrium point is lower than the low-voltage threshold, low-voltage wear-through induced oscillation will inevitably occur.

[0109] It should be noted that the contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0110] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A low voltage ride through induced oscillation analysis method based on the phase plane method, characterized in that: The following steps are involved: Step 1: Convert the simplified switching system of the new energy source based on the current loop into a general second-order switching system in control theory; Step 2: Calculate and discuss the location and properties of the admissible equilibrium points of a general second-order switching system; Step 3: Analyze the low-throughput induced oscillation mechanism of the second-order switching system under positive damping based on the position and properties of the equilibrium point, and give a general conclusion: the voltage corresponding to the normal system equilibrium point is lower than the low-throughput voltage threshold, which is a sufficient but not necessary condition for the occurrence of low-throughput induced oscillation.

2. The low voltage ride through induced oscillation analysis method based on the phase plane method according to claim 1 is characterized by: In step 1, the second-order switching system with dq current as state variables established according to the common low-throughput strategy is converted into a second-order switching system with common state variables of the control system and their derivatives as system variables.

3. The low voltage ride through induced oscillation analysis method based on the phase plane method according to claim 1 is characterized by: For a normal system, the equilibrium point is: And the characteristic root of its equilibrium point is: It can be seen that the equilibrium point of a normal system must be a stable focus mathematically. Under free conditions, the phase trajectory will converge to the equilibrium point y as an inward spiral. EP0 . The position of the equilibrium point of the low-penetration system on the phase plane is The corresponding voltage is compared with the voltage V LVRTout Do the difference: Therefore, we can draw a conclusion: the voltage corresponding to the equilibrium point of the low-throughput system is greater than the voltage at which the system exits the low-throughput. Therefore, the equilibrium point of the low-throughput system is not within its scope and is a virtual equilibrium point (VEP). (1) When the voltage corresponding to the normal system balance point When , the normal system has one allowable equilibrium point in region 1; the low-penetration system has one virtual equilibrium point in region 1. The entire system has only one allowable equilibrium point in region 1. (2) When the voltage corresponding to the normal system balance point When , the normal system has one allowable equilibrium point in region 2, and the low-penetration system has one virtual equilibrium point in region 1. The entire system has only one allowable equilibrium point in region 2. (3) When the voltage corresponding to the normal system balance point When the normal system has a virtual equilibrium point in region 3, the low-throughput system has a virtual equilibrium point in region 1. At this time, all equilibrium points of the entire system are virtual equilibrium points, and there are no permissible equilibrium points. The system may have a new stable mode different from the equilibrium point.

4. The low voltage ride through induced oscillation analysis method based on the phase plane method according to claim 1 is characterized by: In step 3, the system may have different stable forms under positive damping depending on the voltage corresponding to the normal system equilibrium point. Under normal circumstances, when the voltage corresponding to the system equilibrium point is lower than the low-breakthrough voltage threshold, low-breakthrough induced oscillation will inevitably occur. However, under normal circumstances, when the voltage corresponding to the system equilibrium point is higher than the low-breakthrough voltage threshold, low-breakthrough induced oscillation may also occur depending on the initial value. Therefore, a general conclusion can be drawn: V EP0 <V LVRTin It is a sufficient but not necessary condition for the occurrence of low-penetration induced oscillation.

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