A fast solution method for MMC harmonic power flow

Abstract

The present invention discloses a method for quickly solving MMC harmonic power flow, which belongs to the field of direct current transmission. Aiming at the shortcoming that the time domain simulation method is difficult to conveniently solve the harmonic power flow, the present invention firstly establishes a complete MMC harmonic state space model taking into account the control links such as the V / F control outer loop, the current inner loop, the grid voltage feedforward loop, and the circulating current suppression loop based on the harmonic state space theory. Subsequently, aiming at the shortcoming that the time for solving the steady-state power flow in the time domain simulation is too long, based on the characteristics of the periodic time-varying system in the frequency domain, the present invention proposes a frequency shift factor, which can greatly reduce the dimension of the MCC model and speed up the iterative solution speed of the harmonic power flow.

Description

Technical Field

[0001] The invention relates to the field of direct current power transmission, and in particular to a method for quickly solving MMC harmonic power flow. Background Art

[0002] In order to reduce the large amount of energy loss generated during long-distance transmission of electricity, high-voltage direct current transmission technology using voltage source converters has emerged, namely flexible direct current transmission technology. Flexible direct current transmission technology is a high-voltage direct current transmission technology based on modular multilevel converters (MMC), which has inherent advantages in application fields such as wind power access and island power supply. At present, flexible direct current transmission technology has been fully developed and applied in wind power transmission, grid interconnection, large-capacity long-distance transmission and other scenarios. The solution of its harmonic flow results is a key link in realizing system stability analysis and small signal modeling, but most of the current related studies use time domain simulation methods to calculate the steady-state flow results, which is not only time-consuming, but also cannot conveniently obtain the content of each harmonic. Therefore, how to develop a harmonic flow solution algorithm to achieve fast and accurate solution of MMC steady-state harmonic flow is one of the current difficulties. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for quickly solving MMC harmonic power flow.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A method for quickly solving MMC harmonic power flow includes the following steps:

[0006] S1. Construct the harmonic state space equation of MMC system based on harmonic state space theory;

[0007] S2. Simplify the harmonic state space equation obtained in S1 by using the delay factor, and set the simplified harmonic state space equation as an iteration initial value.

[0008] S3, construct the Jacobian matrix, bring the initial value calculated by S2 into the constructed Jacobian matrix and iterate using the Newton-Raphson algorithm;

[0009] S4, subtract the result of S3 iteration from the result of the previous iteration, compare the obtained error with the set accuracy, and output the harmonic state power flow result if it meets the accuracy requirement. If not, return to step S3 and iterate again until the result meets the accuracy requirement.

[0010] Furthermore, the harmonic state space equation in S1 is expressed as:

[0011]

[0012] In the formula, is the state variable, is the input variable, For output, , , and is the coefficient A, B, C and D The Toeplitz matrix form of , and:

[0013]

[0014] In the formula, Represents the A matrix in the frequency domain h Subharmonic coefficients.

[0015] Furthermore, the specific method of simplifying the harmonic state space equation obtained by S1 by using the delay factor in S2 is:

[0016]

[0017] In the formula, For delay, is the delayed offset signal, P is the delay matrix, is the state quantity at time t.

[0018] Furthermore, the Jacobian matrix in S3 is expressed as:

[0019]

[0020] In the formula, is the N×N Jacobian matrix, △x is the change in the state variable during iteration, i Represents the i Iterations, x represents each state variable.

[0021] Furthermore, the specific method of iterating using the Newton-Raphson algorithm in S3 is:

[0022]

[0023] Where J is the N×N Jacobian matrix, Δy is the column vector of mismatch after simultaneous equations, △x is the change in state variables during iteration, i Represents the i Iterations, x represents each state variable.

[0024] The present invention has the following beneficial effects:

[0025] 1. The harmonic state space model of MMC is derived, which effectively realizes the accurate calculation of MMC harmonic power flow.

[0026] 2. The derived delay factor is used to avoid repeated modeling of redundant signals, which greatly improves the calculation rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The figure is a flow chart of the method for quickly solving the MMC harmonic power flow of the present invention.

[0028] Figure 2 This is a topological diagram of phase A of the MMC main circuit according to an embodiment of the present invention.

[0029] Figure 3 Schematic diagram of the MMC baseband control loop according to an embodiment of the present invention.

[0030] Figure 4 Schematic diagram of the MMC circulation suppression ring according to an embodiment of the present invention.

[0031] Figure 5 The figure is a schematic diagram of the harmonic power flow solution process according to an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0033] A fast solution method for MMC harmonic power flow, such as Figure 1 As shown, the following steps are included:

[0034] S1. Construct the harmonic state space equation of MMC system based on harmonic state space theory;

[0035] In this embodiment, based on the harmonic state space theory, a complete MMC harmonic state space model is established, which takes into account the control links such as the V / F control outer loop, the current inner loop, the grid voltage feedforward loop, and the circulating current suppression loop.

[0036] The state space model of a linear time-varying periodic system can be established as:

[0037] (1)

[0038] in x ( t )and u ( t) represents state variables and input variables. A ( t ), B ( t ), C( t )and D ( t ) is the period T 0 The coefficient matrix of A ( t + T 0 ) = A ( t ), t Represents time.

[0039] Based on Fourier transform theory, x ( t ) can be written as:

[0040] (2)

[0041] in X h ( t )express x ( t )of h The Fourier series, ω 0 =2π / T 0 represents the fundamental frequency angular velocity, j Represents the imaginary unit.

[0042] In formula (2), X h ( t ) can be expressed as:

[0043] (3)

[0044] Will x ( t ) can be written in matrix form:

[0045] (4)

[0046] in:

[0047] (5)

[0048] So x ( t ) can be derived as follows:

[0049] (6)

[0050] in ,and N for:

[0051] (7)

[0052] Substituting formula (4) and formula (6) into formula (1), we can get the equation in the form of harmonic state space (HSS):

[0053] (8)

[0054] in , , and is the coefficient A, B, C and D The Toeplitz matrix form of , the subsequent expressions have this meaning, The specific form of is shown in formula (9).

[0055] (9)

[0056] In the formula, Represents the A matrix in the frequency domain h Subharmonic coefficients.

[0057] like Figure 2 The figure shows the A-phase equivalent circuit of the MMC of this embodiment, u dcu and u dcl Respectively represent the positive and negative DC voltages, each is 1 / 2u dc ,u dc is the DC voltage; i dc is the DC side current; i uA 、i lA and u cumA 、u clmA Represent the upper arm current and lower arm voltage respectively; i cA is the circulating current; u 2A 、i 2A are the voltage and current of phase A on the AC side; R arm and L arm are the equivalent arm resistance and inductance.

[0058] Depend on Figure 2 The circuit topology in can be used to write the MMC main circuit parameter calculation formula as follows:

[0059] (10)

[0060] Where n uAand n lA are the modulation signals of the upper arm and lower arm of phase A respectively; N m is the number of submodules.

[0061] According to equations (1) to (9), the harmonic state space model of the A-phase main circuit of the MMC can be expressed as:

[0062] (11)

[0063] Expanding the above formula to three phases yields:

[0064] (12)

[0065] In the formula, the subscripts A, B, and C all represent three-phase A, B, and C circuits.

[0066] The base frequency control loop of MMC is as follows Figure 3 As shown, it includes a V / F control outer loop, a current inner loop and a feedforward control loop. The three-phase voltage and current of A, B and C need to be converted to the dq domain through park transformation, and the formula is as follows:

[0067] (13)

[0068] where u 2d , u 2q and i 2d, i 2q It is MMC on PCC. 2ABC and i 2ABC In the subsequent analysis, the subscript dq represents the dq axis component, and the subscript ref represents the reference value. Then the V / F control can be derived as:

[0069] (14)

[0070] In formula (14), x u2 is the integral state variable; U 2ref and i 2ref is the voltage reference and current reference; U base is the base voltage value of MMC; k mmcp and k mmci are the proportional and integral parameters of the PI controller in AC voltage control.

[0071] Depend on Figure 3 It can be seen that the internal current control can be written as:

[0072] (15)

[0073] In the formula, x i2 I is the integral state variable of the current control; base and Zbase are the current base value and impedance base value respectively; U MMC is a 50Hz modulation signal; k p and k i are the proportional and integral parameters of the PI controller used for current control.

[0074] The final conversion to the base frequency control output signal HSS formula in the three-phase coordinate system is:

[0075] (16)

[0076] U gA1 , U gB1 , U gC1 It is the A, B, and C phase control signal applied to the bridge arm by the base frequency control loop.

[0077] The control block diagram of the circulating current suppression loop is as follows: Figure 4 As shown, the corresponding HSS equation can be written as:

[0078] (17)

[0079] The HSS equation of the control link can be written as:

[0080] (18)

[0081] where x cir is the integral state variable in CCSC control; U cir is a 100Hz modulation signal; in CCSC control, k cirp and k ciri are the proportional and integral parameters of the PI controller, EI is the identity matrix.

[0082] The final formula of the double frequency control output signal HSS converted to the three-phase coordinate system is:

[0083] (19)

[0084] U cirA , U cirB , U cirC It is the A, B, and C phase control signal applied to the bridge arm by the double frequency control loop.

[0085] S2. Simplify the harmonic state space equation obtained in S1 by using the delay factor, and set the simplified harmonic state space equation as an iteration initial value.

[0086] Assume that the dynamic periodic variable shown in equation (2) x ( t ) Existence time τThe delay of the delayed offset signal is x( t - τ ), whose expression is:

[0087] (20)

[0088] Set delay offset φ = ω 0 τ , and let the coefficient X n ( t - t )= X n e -jnj It can be seen that the phase delay of the time domain dynamic signal is only expressed as the Fourier coefficient in the frequency domain X n The vector rotates, and the offset is the harmonic order n The linear function of . That is, the delay relationship of the harmonic signal in the frequency domain is:

[0089] (twenty one)

[0090] in P is the delay matrix:

[0091] (twenty two)

[0092] Furthermore, the delay equation of HSS can be derived from equation (11):

[0093] (twenty three)

[0094] From (21) and (23), we can see that through the delay matrix P It can eliminate the influence of phase offset between different dynamic signals, and then establish a unified dynamic equation to avoid repeated modeling of redundant signals, which can significantly improve the computational efficiency of complex nonlinear systems.

[0095] After considering the phase shift, the following relationship exists:

[0096] (twenty four)

[0097] According to formula (21), formula (12) can be written as follows:

[0098] (25)

[0099] The Toeplitz form of the baseband Park transform and inverse transform matrices is the same as equation (13) and equation (16)

[0100] According to formula (22), formula (13) can be rewritten as:

[0101] (26)

[0102] From this we can get

[0103] (27)

[0104] Similarly, according to formula (22), we can deduce i d , i q for:

[0105] (28)

[0106] From this we can get:

[0107] (29)

[0108] The voltage outer loop PI link equation is the same as equation (14), and the corresponding current inner loop PI link is the same as equation (15).

[0109] The three-phase base frequency modulation signal is:

[0110] (30)

[0111] The double frequency Park transform and inverse transform matrices are the same as equations (24) and (25)

[0112] The following relationship also exists:

[0113] (31)

[0114] Then in the above formula i cir_d , i cir_q To simplify:

[0115] (32)

[0116] After simplification, we can get

[0117] (33)

[0118] Then the three-phase double frequency modulation signal is:

[0119] (34)

[0120] It can be seen that all three-phase signals can be represented by a single phase, which greatly reduces the number of iterative equations and the number of global equations, and significantly reduces the amount of calculation.

[0121] S3, construct the Jacobian matrix, bring the initial value calculated by S2 into the constructed Jacobian matrix and iterate using the Newton-Raphson algorithm;

[0122] The Jacobian matrix The formula for obtaining is:

[0123] (35)

[0124] △x is the change in the state variable during iteration, i Represents the i iterations, x represents each state variable.

[0125] The iterative process of the Newton-Raphson algorithm is as follows:

[0126] (36)

[0127] Where J is the N×N Jacobian matrix, and Δy is the column vector of mismatch after the simultaneous equations.

[0128] In this embodiment, if Figure 5 shown.

[0129] S4, subtract the result of S3 iteration from the result of the previous iteration, compare the obtained error with the set accuracy, and output the harmonic state power flow result if it meets the accuracy requirement; if not, return to step S3 and iterate again until the result meets the accuracy requirement;

[0130] The error can be obtained by subtracting the current iteration value from the previous iteration value, that is, .

[0131] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0132] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for quickly solving MMC harmonic power flow, characterized in that: The steps include: S1. Based on the harmonic state space theory, the harmonic state space equation of the MMC system is constructed. The harmonic state space equation is expressed as: In the formula, is the state variable, is the input variable, For output, , , and is the coefficient A, B, C and D The Toeplitz matrix form of , where: In the formula, Represents the A matrix in the frequency domain h Subharmonic coefficients; S2. Use the delay factor to simplify the harmonic state space equation obtained in S1. The specific method is: In the formula, For delay, is the delayed offset signal, P is the delay matrix, is the state quantity at time t; And set the simplified harmonic state space equation as the initial value of iteration; S3, construct the Jacobian matrix, bring the initial value calculated by S2 into the constructed Jacobian matrix and iterate using the Newton-Raphson algorithm; S4, subtract the result of S3 iteration from the result of the previous iteration, compare the obtained error with the set accuracy, and output the harmonic state power flow result if it meets the accuracy requirement. If not, return to step S3 and iterate again until the result meets the accuracy requirement.

2. A method for quickly solving MMC harmonic power flow according to claim 1, characterized in that: The Jacobian matrix in S3 is expressed as: In the formula, is the N×N Jacobian matrix, △x is the change in the state variable during iteration, i Represents the i iterations, x represents each state variable.

3. A method for quickly solving MMC harmonic power flow according to claim 1, characterized in that: The specific method of iterating using the Newton-Raphson algorithm in S3 is: Where J is the N×N Jacobian matrix, Δy is the column vector of mismatch after simultaneous equations, △x is the change in state variables during iteration, i Represents the i iterations, x represents each state variable.

Images