A performance analysis method for AC / DC hybrid power distribution system based on power balance

Abstract

The present invention provides a performance analysis method for an AC / DC hybrid power distribution system based on power balance, which belongs to the field of power distribution and includes: proposing a stability criterion based on power balance according to the passivity theory; establishing a DC side equivalent power model, analyzing the power distribution of each part based on the DC side equivalent power model, and establishing a stability criterion based on power balance on the DC side according to the stability criterion based on power balance proposed according to the passivity theory in step 1; establishing an equivalent power model considering power transmission on the AC side, considering the power transmission characteristics of the converter from the AC side to the DC side, analyzing the power distribution of each part based on the equivalent power model of the AC side power transmission, and establishing a stability criterion considering power transmission on the AC side according to the stability criterion, which together with the DC side equivalent power model constitutes a stability analysis framework for the entire AC / DC hybrid power distribution system. The present invention improves the systematicness of the instability mechanism analysis method of the AC / DC hybrid power distribution system.

Description

Technical Field

[0001] The present invention belongs to the field of power distribution, and in particular relates to a performance analysis method of an AC / DC hybrid power distribution system based on power balance. Background Art

[0002] At present, facing the high proportion of distributed power sources and DC loads, the distribution system is undergoing a disruptive change. The AC / DC hybrid distribution system combines the advantages of both AC and DC grids, with the characteristics of fewer power conversion links, low losses, and high power supply quality. It has unique advantages in compatibility with large-scale distributed power sources and DC loads, and has broad application prospects.

[0003] However, there are significant stability issues in AC / DC hybrid power distribution systems: Since the core devices in the system are all power electronic converters, their weak damping and low inertia characteristics restrict their stable and efficient operation. In addition, the device topology and control strategies are different, and the complexity of the dynamic characteristics makes their interaction mechanism with the DC network more complicated. The existence of constant power loads further exacerbates this complexity, because they have impedance characteristics, which leads to the formation of positive feedback that enhances the disturbance signal when the system is disturbed, thereby reducing the stability of the system. Although the commonly used stability analysis criteria can quantitatively calculate the stability boundary of the system, they often rely on complex mathematical models and calculations, and the criteria themselves lack the connection with the key physical quantities of the dynamic process, so it is difficult to reveal the physical mechanism of the poor interaction between the power electronic converter and the DC network resonant mode and the general law of system instability.

[0004] Therefore, in order to reveal the general law of instability of AC / DC hybrid distribution systems, it is urgent to propose a performance analysis method for AC / DC hybrid distribution systems based on power balance. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a performance analysis method for an AC / DC hybrid distribution system based on power balance. The method applies the passivity theory, redefines the system stability problem as a power imbalance problem, simplifies the stability analysis process, provides an analysis framework suitable for different types of power electronic converters, and improves the systematicness of the instability mechanism analysis method of the AC / DC hybrid distribution system.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme:

[0007] A method for analyzing performance of an AC / DC hybrid power distribution system based on power balance comprises the following steps:

[0008] Step 1: Propose a stability criterion based on power balance according to the passivity theory;

[0009] Step 2: Establish a DC side equivalent power model to simplify the DC side of the AC / DC hybrid distribution network, analyze the power distribution of each part based on the DC side equivalent power model, and establish a DC side stability criterion based on power balance according to the stability criterion based on the passivity theory proposed in step 1;

[0010] Step 3: Establish an equivalent power model considering the power transmission on the AC side, consider the power transmission characteristics of the converter from the AC side to the DC side, analyze the power distribution of each part based on the equivalent power model of the power transmission on the AC side, and establish a stability criterion considering the power transmission on the AC side according to the stability criterion based on power balance proposed according to the passivity theory in step 1. Together with the DC side equivalent power model established in step 2, it constitutes the stability analysis framework of the entire AC / DC hybrid distribution system.

[0011] Beneficial effects:

[0012] 1. The present invention simplifies the stability analysis process by converting complex system dynamics into a power balance problem, avoids solving complex high-order differential equations, and makes the analysis more intuitive and easy to handle.

[0013] 2. The present invention is not only applicable to a simple two-terminal AC-DC hybrid power distribution system, but can also be extended to a complex AC-DC hybrid power distribution system containing a DC-DC converter, and has wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A flow chart of a method for analyzing performance of an AC / DC hybrid power distribution system based on power balance provided by the present invention;

[0015] Figure 2 It is the equivalent circuit diagram of the DC side of the AC / DC hybrid distribution network;

[0016] Figure 3 It is the equivalent circuit diagram of VSC in AC / DC hybrid distribution network. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0018] like Figure 1 As shown, the present invention provides a method for analyzing performance of an AC / DC hybrid power distribution system based on power balance, comprising the following steps:

[0019] Step 1: Propose a stability criterion based on power balance according to the passivity theory, including:

[0020] For a nonlinear system described by the state-space expression (1) If there exists a continuously differentiable semi-positive definite storage function S:D→R such that (2) For any input signal If all of them hold, then the nonlinear system represented by equation (1) is called passive. Equation (2) is called the dissipative inequality. R represents the set of real numbers, R p represents the p-dimensional real number space.

[0021] Among them, the state vector , D represents The domain of is the subset of n-dimensional real space containing the origin or the entire space; is the state vector The derivative of , which represents the state vector rate of change over time; and are input signal and output signal respectively; and They are the state equation and the output equation, which are about the state vector and input signal The superscript T indicates the transpose of the matrix. S is the storage function. t indicates the time variable, indicating that the integration is performed from time 0 to time t; s is the integral variable; x(0) indicates the state vector at the initial time (i.e., t=0); It means that for any time t, equation (2) holds.

[0022] If there exists a positive definite function P(x), the dissipation inequality is:

[0023] (3)

[0024] For any input signal If all of them hold, then the nonlinear system represented by equation (1) is said to be strictly passive.

[0025] Deriving equation (2) and equation (3) respectively, we get:

[0026] For a passive system, if there exists a smooth and differentiable storage function S that satisfies:

[0027] (4)

[0028] For a strictly passive system, if there exists a storage function S that satisfies:

[0029] (5)

[0030] When considering the input signal u=0, For a strictly passive system, as long as the Lyapunov stability condition is met, that is, there is a smooth, differentiable and positive definite storage function, then the state vector x=0 is the asymptotically stable equilibrium point of the system.

[0031] For circuit systems, passivity can be expressed by the power balance equation. The input signal u is the system voltage, the output signal y is the current, the system storage function S represents the sum of the energy on all energy storage components such as capacitors and inductors, and the positive definite function P(x) represents the energy dissipated on components such as system resistors. A strictly passive system satisfies the requirement that the rate of change of stored energy is never greater than the sum of its supply rate and dissipation rate, which is a prerequisite for system stability.

[0032] Step 2: Establish the DC side equivalent power model (i.e. Figure 1 DC side equivalent circuit modeling in ), including:

[0033] Step 21: Establish the equivalent power model of each part of the DC side:

[0034] The equivalent circuit of the DC side of the AC / DC hybrid distribution system is as follows: Figure 2 As shown. Among them, the voltage source converter VSC1 adopts constant DC voltage control and is the input power supply of the circuit; the voltage source converter VSC2 adopts constant active power control and can be equivalent to a constant power load. v is the DC side output voltage of VSC1, u dc is the DC bus voltage, i is the current flowing through the equivalent inductance and resistance of VSC1, L and R are the equivalent inductance and resistance of the voltage source converter VSC1, C is the DC bus capacitance of the voltage source converter VSC1, L out and R out is the equivalent inductance and resistance of the DC bus, R CPL is the equivalent resistance of the constant power load, i load For the flow through R CPL The current of the entire circuit flows out from the voltage source converter VSC1, passes through the resistor R, inductor L, capacitor C, resistor R out 、Inductance L out , and finally reaches the constant power load VSC2.

[0035] Next, the DC side of the AC / DC hybrid distribution system is equivalently modeled from the perspective of power balance.

[0036] (1) Establish system equivalent circuit model:

[0037] From circuit theory we can get:

[0038] (6)

[0039] in, and are first-order and second-order differential operators used to represent the derivatives of variables with respect to time. A0, A1, and A2 represent the rows of the coefficient matrix, respectively.

[0040] (2) Establishing a supply function model:

[0041] The supply function describes the power flowing into the circuit at any time, reflecting the energy exchange between the circuit and the external environment. The supply function describing the energy inflow is expressed through the port variables of the circuit (usually voltage and current), which can be expressed as:

[0042] (7)

[0043] Among them, S in is the supply function; A0 and A2 represent the first and third rows of the coefficient matrix, respectively.

[0044] (3) Establish a storage function model:

[0045] The storage function describes the storage and flow of energy in a circuit. It represents the energy stored in the energy storage elements (i.e., inductors and capacitors) in the circuit and can be expressed as:

[0046] (8)

[0047] Among them, S stored is a storage function; A1 and A2 represent the second and third rows of the coefficient matrix respectively.

[0048] (4) Establishing dissipation function model:

[0049] The dissipation function describes the portion of the circuit that dissipates energy, specifically the process of converting electrical energy into heat energy through resistive components, and can be expressed as:

[0050] (9)

[0051] Among them, S dissipation is the dissipation function; A2 represents the third row of the coefficient matrix; P CPL is the power of the constant power load.

[0052] Step 22: Derive stability criteria based on power balance theory, including:

[0053] According to formula (5), select (10)

[0054] Substituting equations (6), (7), (8) and (9) into equation (10), the system stability condition can be calculated as:

[0055] (11)

[0056] After step 21 and step 22, by obtaining the circuit topology and related parameters, the DC side equivalent power model is established, and by substituting the model parameters into equation (11), it is determined whether the inequality is satisfied. If satisfied, it indicates that the AC / DC hybrid distribution system is stable on the DC side; if not satisfied, the system may have stability problems, thereby realizing the stability analysis of the AC / DC hybrid distribution system (i.e. Figure 1 Derived stability criterion in ).

[0057] Step 3: Establish an equivalent power model considering AC side power transmission, including:

[0058] Step 31: Calculate the power delivered to the DC side using coordinate transformation and power analysis:

[0059] The equivalent circuit on the AC side is as follows Figure 3 As shown, the current flows out of the AC grid, and the three-phase voltage synthesis vector of the grid is recorded as v ac , through the resistor R s and inductor L s , reaches the voltage source converter VSC1, and the three-phase voltage synthesis vector on the bridge arm grid side is recorded as v p , the voltage source converter VSC1 controls the output voltage v to achieve AC-DC conversion. Taking the AC grid-side current flowing from the grid to the bridge arm as the reference direction, the Kirchhoff voltage law KVL equation of the VSC (voltage source converter) grid side in the dq coordinate system is:

[0060] (12)

[0061] Among them, v pd and v pq are the d-axis component and q-axis component of the three-phase voltage synthesis vector on the grid side of the VSC bridge arm, respectively. acd and v acq are the d-axis component and q-axis component of the three-phase voltage synthesis vector of the AC power grid, respectively. acd and i acq are the d-axis component and q-axis component of the three-phase current synthesis vector of the AC power grid, is the angular frequency.

[0062] Multiply both sides of (a) of formula (12) by , multiply both sides of (b) of formula (12) by , while considering , we can get:

[0063] (13)

[0064] Adding equation (13) (a) and (13) (b) together, we get:

[0065] (14)

[0066] Let the composite vector v of the d-axis and the three-phase voltage of the power grid be ac If they overlap, then v acd =v ac , then in the dq coordinate system, the active power p generated by the power grid can be s , reactive power q s And the power p transmitted to the DC side by the voltage source converter VSC bridge arm t It is expressed as:

[0067] (15)

[0068] Among them, i pd and i pq They are the d-axis and q-axis components of the three-phase current synthesis vector on the grid side of the VSC bridge arm.

[0069] So we get:

[0070] (16)

[0071] Since the strength of the AC distribution network is relatively large, it is assumed that the AC side grid of the VSC has ideal voltage source characteristics, v ac The amplitude is a constant, denoted as V ac . Formula (16) can be written as follows:

[0072] (17)

[0073] The power transferred from the VSC bridge arm to the DC side is denoted as p t , and taking into account the definition of the instantaneous power on the AC side of the VSC bridge arm in equation (15), substituting equations (15) and (17) into equation (14), we have:

[0074] (18)

[0075] Step 32: Derive the stability criterion considering the AC side power transmission, that is, considering the AC side power transmission, the supply function S in The power p that can be transferred to the DC side by the voltage source converter VSC bridge arm t Indicates that S in =p t , according to formula (5), the condition for system stability can be re-expressed as:

[0076] (19) .

Claims

1. A performance analysis method for an AC / DC hybrid power distribution system based on power balance, characterized in that: The steps include: Step 1: Propose a stability criterion based on power balance according to the passivity theory, including: For a nonlinear system described by the state-space expression , if there exists a continuously differentiable semi-positive definite storage function S:D→R, and there exists a positive definite function P(x) such that (3) For any input signal If all of them hold true, then the nonlinear system represented by equation (1) is strictly passive; Among them, the state vector , D represents the domain of x, which is a subset of the n-dimensional real space containing the origin or the entire space; is the derivative of the state vector x, which represents the rate of change of the state vector x over time; R represents a real number set, R p represents p-dimensional real space; u and y are input signal and output signal respectively; f(x,u) and h(x,u) are state equation and output equation respectively, which are functions of state vector x and input signal u; t represents time variable; s is integral variable; x(0) represents the state vector at the initial moment; It means that for any time t>0, equation (3) holds true, and the superscript T represents the transpose of the matrix; Derivation of formula (3) yields: For a strictly passive system, if there exists a storage function S that satisfies (5) When considering the input signal u=0, , for a strictly passive system, as long as the Lyapunov stability condition is met, that is, there is a smooth, differentiable and positive definite storage function, then the state vector x = 0 is the asymptotically stable equilibrium point of the nonlinear system shown in equation (1); Step 2: Establish a DC side equivalent power model to simplify the DC side of the AC / DC hybrid distribution network. Analyze the power distribution of each part based on the DC side equivalent power model. According to the stability criterion based on power balance proposed based on the passivity theory in step 1, establish the stability criterion based on power balance on the DC side, including: Step 21: Establish equivalent power models of various parts on the DC side; Step 22: Derive stability criteria based on power balance theory; Step 3: Establish an equivalent power model considering the power transmission on the AC side, consider the power transmission characteristics of the converter from the AC side to the DC side, analyze the power distribution of each part based on the equivalent power model of the power transmission on the AC side, and establish a stability criterion considering the power transmission on the AC side according to the stability criterion based on power balance proposed according to the passivity theory in step 1. Together with the DC side equivalent power model established in step 2, it constitutes the stability analysis framework of the entire AC / DC hybrid distribution system.

2. The method for analyzing performance of an AC / DC hybrid power distribution system based on power balance according to claim 1, characterized in that: The step 21 comprises: (1) Establish system equivalent circuit model: From circuit theory we get: (6) Where, v is the output voltage of the voltage source converter VSC1, u dc is the DC bus voltage, i is the current flowing through the equivalent inductance and resistance of VSC1, L and R are the equivalent inductance and resistance of VSC1, C is the DC bus capacitance of VSC1, L out and R out is the equivalent inductance and resistance of the DC bus, R CPl is the equivalent resistance of the constant power load, i load For the flow through R CPL The current, and are first-order and second-order differential operators used to represent the derivatives of variables with respect to time, and A0, A1, and A2 represent the rows of the coefficient matrix respectively; (2) Establishing a supply function model: The supply function describing the energy inflow is expressed by the port variables of the circuit; the port variables are voltage and current; (3) Establish a storage function model: The storage function describes the storage and flow of energy in a circuit, and represents the energy stored in the energy storage element in the circuit; the energy storage elements are inductors and capacitors; (4) Establishing dissipation function model: The dissipation function describes the portion of a circuit that dissipates energy, the process of converting electrical energy into heat through resistive components.

3. The method for analyzing performance of an AC / DC hybrid power distribution system based on power balance according to claim 2, characterized in that: The step 22 comprises: According to formula (5), select (10) Among them, S in , S stored , S dissipation They represent supply function, storage function, and dissipation function respectively; The stability condition of the computing system is: (11) Where, L and R are the equivalent inductance and resistance of VSC1, C is the DC bus capacitance of VSC1, L out and R out is the equivalent inductance and resistance of the DC bus, R CPL is the equivalent resistance of the constant power load, i load For the flow through R CPL The current, and are first-order and second-order differential operators used to represent the derivative of a variable with respect to time, L out and R out are the equivalent inductance and equivalent resistance of the DC bus, P CPL is the power of the constant power load; After step 21 and step 22, the circuit topology and related parameters are obtained, and the DC side equivalent power model is established. By substituting the model parameters into equation (11), it is determined whether equation (11) is satisfied; if satisfied, it indicates that the AC / DC hybrid distribution system is stable on the DC side; if not satisfied, the AC / DC hybrid distribution system has stability problems.

4. The method for analyzing performance of an AC / DC hybrid power distribution system based on power balance according to claim 3, characterized in that: The step 3 comprises: Step 31: Calculate the power delivered to the DC side using coordinate transformation and power analysis, that is, the supply function S in The power p transmitted to the DC side by the voltage source converter VSC bridge arm t express; Step 32: The stability condition of the AC / DC hybrid distribution system is re-expressed as: (19) Among them, p s and q s are the active power and reactive power generated by the AC power grid, V ac is the composite vector amplitude of the three-phase voltage of the AC power grid, R s and L s are the equivalent resistance and inductance of the AC side of VSC1 respectively; L and R are the equivalent inductance and resistance of VSC1, C is the DC bus capacitance of VSC1, L out and R out is the equivalent inductance and resistance of the DC bus, R CPL is the equivalent resistance of the constant power load, i load For the flow through R CPL The current, and are first-order and second-order differential operators used to represent the derivative of a variable with respect to time, L out and R out are the equivalent inductance and equivalent resistance of the DC bus, P CPL is the power of the constant power load.

5. The method for analyzing performance of an AC / DC hybrid power distribution system based on power balance according to claim 4, characterized in that: The step 31 comprises: Taking the AC grid-side current flowing from the grid to the bridge arm as the reference direction, the Kirchhoff voltage law KVL equation on the VSC grid side in the dq coordinate system is: (12) Among them, v pd and v pq are the d-axis and q-axis components of the three-phase voltage synthesis vector on the grid side of the VSC bridge arm, respectively. acd and v acq are the d-axis and q-axis components of the three-phase voltage synthesis vector of the AC power grid, i acd and i acq are the d-axis and q-axis components of the three-phase current synthesis vector of the AC power grid, R s and L s are the equivalent resistance and inductance of the AC side of VSC1, is the angular frequency; Multiply both sides of (a) of formula (12) by , multiply both sides of (b) of formula (12) by , while considering , adding the two equations together, we get: (14) Let the composite vector v of the d-axis and the three-phase voltage of the power grid be ac If they overlap, then v acd =v ac , then in the dq coordinate system, the active power p generated by the power grid is s , reactive power q s And the power p transmitted to the DC side by the voltage source converter VSC bridge arm t It is expressed as: (15) Among them, i pd and i pq They are the d-axis and q-axis components of the three-phase current synthesis vector of the VSC bridge arm grid side; Assuming that the AC side grid of the VSC has ideal voltage source characteristics, v ac The amplitude is a constant, denoted as V ac ; So we get: (17) The power transferred from the VSC bridge arm to the DC side is denoted as p t , and taking into account the definition of the instantaneous power on the AC side of the VSC bridge arm in equation (15), substituting equations (15) and (17) into equation (14), we have: (18) 。

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