A stability analysis method and system for DC microgrid system based on SOFC

Abstract

The present invention relates to the technical field of direct current (DC) microgrid systems, and in particular to a method for analyzing the stability of a DC microgrid system based on an SOFC. Specifically, the method comprises the following steps: establishing a DC microgrid equivalent model based on the DC microgrid system; applying the mixed potential function theory based on the DC microgrid equivalent model to establish a mixed potential function of the system, then converting the mixed potential function into a unified expression of the mixed potential function, and finally deriving a system stability condition based on the third stability theorem; constructing a large-disturbance stability criterion function of the DC microgrid system based on the system stability condition and a control loop expression obtained by adopting a double-closed-loop control strategy for an SOFC converter and a lithium battery pack converter; and performing a stability analysis on the DC microgrid system based on the large-disturbance stability criterion function of the DC microgrid system. Through the above steps, the stability boundary of a large load disturbance can be calculated, thereby accurately and effectively performing a stability analysis on the DC microgrid system.

Description

Technical Field

[0001] The present invention relates to the technical field of direct current microgrids, and in particular to a stability analysis method for a direct current microgrid system based on SOFC. Background Art

[0002] Fuel cell power generation technology is a future trend in low-carbon energy. Among fuel cells, solid oxide fuel cells (SOFCs) offer high-temperature fuel cell performance and greater fuel flexibility, making them suitable for use in DC microgrid systems. However, if a large disturbance in the DC grid is connected to the system, the busbar voltage becomes unstable, impacting the normal operation of the entire system and, in severe cases, causing system failure. Therefore, analyzing the stability of DC microgrids remains a major research challenge.

[0003] Currently, research on DC grid stability primarily focuses on small-signal stability and large-signal stability. Small-signal stability analysis typically employs frequency-domain methods, such as the Nyquist plot-based impedance criterion and small-disturbance characteristic analysis. Large-signal stability analysis typically employs time-domain analysis. However, DC grids are often used in complex applications with numerous nonlinear loads. Small-signal analysis methods are limited to systems with constant-power loads and fail to fully capture system characteristics. Large-signal analysis methods based on traditional mixed potential function criteria are also hampered by inadequate modeling, resulting in the loss of converter parameter information during analysis. This is particularly true in SOFC-based DC microgrid systems, where the power supply characteristics of the SOFC are considered, resulting in large voltage drops and slow power tracking. Furthermore, under heavy loads, the SOFC's poor tracking performance can lead to bus voltage instability. Therefore, effective stability analysis of SOFC-based DC microgrids is crucial. Summary of the Invention

[0004] To address the above-mentioned deficiency in the prior art that DC microgrids cannot perform stability analysis, the present invention provides a stability analysis method for a DC microgrid system based on SOFC, comprising the following steps:

[0005] Establish a DC microgrid equivalent model based on the DC microgrid system;

[0006] The DC microgrid system includes at least an SOFC, an SOFC converter, a lithium battery pack, a lithium battery pack converter, a DC bus, a load, and a load converter. The SOFC is connected to the input side of the DC bus through the SOFC converter, and the lithium battery pack is connected to the input side of the DC bus through the lithium battery pack converter. The load is connected to the output side of the DC bus through the load converter. The SOFC converter and the lithium battery pack converter use a dual closed-loop control strategy to regulate the DC bus voltage and current.

[0007] Based on the DC microgrid equivalent model, the hybrid potential function of the system is established by applying the hybrid potential function theory, and then the hybrid potential function is converted into a unified expression of the hybrid potential function. Finally, the system stability condition is obtained according to the third stability theorem.

[0008] According to the system stability conditions and the control loop expressions obtained by adopting the double closed-loop control strategy of SOFC converter and lithium battery pack converter, the large disturbance stability criterion function of DC microgrid system is constructed.

[0009] The stability analysis of the DC microgrid system is carried out based on the large disturbance stability criterion function of the DC microgrid system.

[0010] In some embodiments, the load includes a variable power load and a constant power load, and the load converter includes a variable power load converter and a constant power load converter; the variable power load is connected to the output side of the DC bus through the variable power load converter; the constant power load is connected to the output side of the DC bus through the constant power load converter.

[0011] In some embodiments, the DC microgrid equivalent model includes the current transmitted from the SOFC to the DC bus through the SOFC converter being equivalent to a current source i1; the current transmitted from the lithium battery pack to the DC bus through the lithium battery pack converter being equivalent to a current source i2; the current transmitted from the DC bus to the variable power load through the variable power load converter being equivalent to a current source i d The current transmitted from the DC bus to the constant power load through the constant power load converter is equivalent to the current source i R .

[0012] In some embodiments, a mixed potential function of the system is established by applying the mixed potential function theory according to the DC microgrid equivalent model, and then the mixed potential function is converted into a unified expression of the mixed potential function. Finally, the system stability condition is derived according to the third stability theorem, including the following steps:

[0013] Establish the current potential function according to the DC microgrid equivalent model;

[0014] The voltage and current product function of the capacitive branch is established based on the DC microgrid equivalent model;

[0015] The mixed potential function of the system is obtained by summing the current potential function and the voltage and current product function of the capacitive branch;

[0016] The mixed potential function is transformed into a unified expression of the mixed potential function, and the characteristics of the unified expression of the mixed potential function are applied to the third stability theorem to obtain the system stability condition.

[0017] In some embodiments, the current potential function is expressed as:

[0018]

[0019] Where μ is the branch number (μ=1,···,r+s), r is the number of inductive branches, s is the number of capacitive branches; u dc is the DC bus voltage; P R is the input power of the constant power load, P M is the input power of the variable power load;

[0020] The product function of voltage and current of each capacitive branch is expressed as:

[0021]

[0022] Where U σ 、i σ are the capacitor voltage and capacitor current respectively.

[0023] The mixed potential function is expressed as:

[0024]

[0025] The unified expression of the mixed potential function is:

[0026]

[0027] Then the system stability condition is expressed as:

[0028]

[0029] Where τ1 and τ2 are the two eigenvalues ​​of the mixed potential function, and τ1 and τ2 are the minimum eigenvalues ​​of the second-order partial derivative matrices of A(i) and B(u) in the unified expression of the mixed potential function.

[0030] In some embodiments, the control loop expression obtained by adopting a dual closed-loop control strategy for the SOFC converter and the lithium battery pack converter is:

[0031]

[0032]

[0033] Where, They are the current set values ​​of SOFC and lithium battery pack respectively; is the voltage given value of the DC bus; i FC 、i B are SOFC current and lithium battery pack current respectively; u dc is the DC bus voltage; d1 and d2 are the differential gain coefficients of SOFC and lithium battery pack respectively; k svp 、k Sviare the proportional coefficient and integral coefficient of the SOFC converter voltage outer loop respectively; k sip 、k Bvi are the proportional coefficient and integral coefficient of the inner loop of the SOFC converter current respectively; k Bvp 、k Bvi are the proportional coefficient and integral coefficient of the voltage outer loop of the lithium battery pack converter respectively; k Bip 、k Bvi They are the proportional coefficient and integral coefficient of the inner current loop of the lithium battery pack converter respectively.

[0034] In some embodiments, the large disturbance stability criterion function of the DC microgrid system is expressed as:

[0035]

[0036] Where u FC 、u B are the SOFC power supply voltage and the lithium battery pack power supply voltage respectively; R FC 、R B They are the SOFC converter resistance and the lithium battery pack converter resistance respectively.

[0037] In some embodiments, the following steps are also included:

[0038] The stability analysis of the DC microgrid system is conducted based on the large disturbance stability criterion function of the DC microgrid system and the fact that the load power is less than the maximum power that the DC microgrid system can provide.

[0039] The expression for the load power being less than the maximum power the system can provide is:

[0040] i FC u FC +i B u B >P M +P R

[0041] Where i FC 、u FC are the output current and output voltage of SOFC respectively; i B 、u B are the output current and output voltage of the lithium battery pack respectively; P M 、P R They are the power of variable power load and the power of constant power load respectively.

[0042] In some embodiments, the method further comprises the step of: verifying the correctness of the mixed potential function using a verification formula; the verification formula is expressed as:

[0043]

[0044] Where P(i,u) is the mixed potential function; C is the DC bus capacitance.

[0045] The present invention further provides a DC microgrid system, which adopts the stability analysis method of the SOFC-based DC microgrid system as described in any of the above embodiments.

[0046] Based on the above, compared with the prior art, the stability analysis method for a SOFC-based DC microgrid system provided by the present invention utilizes an equivalent model to construct an equivalent circuit diagram and, based on the Brayton-Moser hybrid potential function theory, derives the SOFC-lithium battery DC microgrid potential function. This method then derives a large-signal stability criterion for the system. Based on this criterion, the stability boundary for large load disturbances is calculated, effectively predicting the magnitude of the disturbance under which the bus voltage can remain stable. The present method is highly practical, does not require complex calculations, is simple and easy to implement, and has promising application prospects.

[0047] Other features and beneficial effects of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The objectives and other beneficial effects of the present invention can be achieved and obtained by the structures particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work. The positional relationships described in the drawings in the following description are based on the directions of the components drawn in the diagrams, unless otherwise specified.

[0049] Figure 1 Flowchart of the steps of the stability analysis method of a DC microgrid system based on SOFC provided by one embodiment of the present invention

[0050] Figure 2 A structural block diagram of a DC microgrid system provided by one embodiment of the present invention;

[0051] Figure 3 A structural block diagram of a DC microgrid system provided by another embodiment of the present invention;

[0052] Figure 4 A current principle diagram of a DC microgrid equivalent model provided by one embodiment of the present invention;

[0053] Figure 5 A flowchart of step S2 provided in one embodiment of the present invention;

[0054] Figure 6 A block diagram of a voltage-current dual closed-loop control system according to an embodiment of the present invention;

[0055] Figure 7 This is the circuit schematic diagram of the equivalent model of the ship DC microgrid system;

[0056] Figure 8 The waveform diagram of the simulation results of the ship DC microgrid at different working points. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments; the technical features designed in different implementation modes of the present invention described below can be combined with each other as long as they do not conflict with each other; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0058] In the description of the present invention, it should be noted that all terms used in the present invention (including technical terms and scientific terms) have the same meanings as those generally understood by ordinary technicians in the field to which the present invention belongs, and should not be understood as limiting the present invention; it should be further understood that the terms used in the present invention should be understood to have meanings consistent with the meanings of these terms in the context of this specification and in the relevant fields, and should not be understood in an idealized or overly formal sense, unless explicitly defined as such in the present invention.

[0059] This paper addresses the issue of bus oscillations caused by pulsed load disturbances in DC microgrids, proposing a stability analysis method for SOFC-based DC microgrid systems. By applying mixed potential function theory to the SOFC power system, this method derives a large-disturbance stability criterion for the SOFC-lithium battery DC microgrid, and derives the load power stability boundary for the DC microgrid system. This method effectively controls the parameters of the converters and the output power of each power supply in the DC microgrid system, addressing the question of whether the SOFC-lithium battery DC microgrid system can maintain bus voltage stability under large disturbances.

[0060] The stability analysis method of a DC microgrid system based on SOFC provided by an embodiment of the present invention is described in detail below through specific implementation methods and accompanying drawings.

[0061] Specifically, if Figure 1As shown, the stability analysis method of a DC microgrid system based on SOFC provided by an embodiment of the present invention includes the following steps:

[0062] Step S1: establishing a DC microgrid equivalent model based on the DC microgrid system.

[0063] like Figure 2 As shown, the DC microgrid system includes at least an SOFC, a SOFC converter, a lithium battery pack, a lithium battery pack converter, a DC bus, a load, and a load converter. The SOFC is connected to the input side of the DC bus via the SOFC converter, and the lithium battery pack is connected to the input side of the DC bus via the lithium battery pack converter. The load is connected to the output side of the DC bus via the load converter. The SOFC converter and the lithium battery pack converter use a dual closed-loop control strategy to regulate the DC bus voltage and current. In specific implementations, the SOFC converter uses a boost converter, and the lithium battery pack converter uses a bidirectional converter. A proportional-integral (PI) controller is designed between the two to implement the dual closed-loop control strategy.

[0064] Of course, in actual application, the DC microgrid system can also include other energy components according to actual needs, such as photovoltaic power generation components, wind power generation components, diesel generator sets and other structures, and improve energy efficiency and reduce operating costs through the design of a multi-energy hybrid system. This embodiment is not limited to this.

[0065] Furthermore, load classification can be selected based on actual needs, allowing for the construction of corresponding models for each, thereby effectively improving the accuracy of DC microgrid system stability assessments. In this embodiment, the loads include variable power loads and constant power loads, and the load converters include variable power load converters and constant power load converters. The variable power loads are connected to the output side of the DC bus via the variable power load converters, while the constant power loads are connected to the output side of the DC bus via the constant power load converters. The variable power loads and constant power loads are designed appropriately based on actual operating conditions. A variable power load refers to a load whose power demand changes with operating conditions or operational requirements during the operation of the DC microgrid system, while a constant power load refers to a load whose power demand remains relatively stable during the operation of the DC microgrid system. Taking a shipboard DC microgrid system as an example, a variable power load can be a propulsion motor connected to the DC bus via a motor controller inverter. A constant power load can be a control room load or other loads such as lighting, communications, or navigation.

[0066] It should be noted that the present embodiment is Figure 2 The DC microgrid system provided only provides one set of SOFC, one set of lithium battery pack, and one set of load, but those skilled in the art can construct multiple sets of SOFC and lithium battery packs according to actual needs, which all fall within the scope of protection of the present invention. For example, see Figure 3 The DC microgrid system can be equipped with two groups of SOFC, two groups of lithium battery and two groups of load, each of which is connected to the DC bus. One group can be used as a common system and the other group can be used as a backup system. The two are controlled by the bus tie switch to form a dual system to cope with different working conditions.

[0067] According to the structure of the above actual DC microgrid system, an equivalent circuit model can be effectively established to study the influence of system parameters on the stability of the DC microgrid system.

[0068] The lithium battery pack and SOFC models can be reasonably established as equivalent models suitable for stability analysis based on actual needs, and will not be elaborated here. For example, the SOFC system dynamic model can be established based on the following. Specifically, the fuel's electrical response time starting from the fuel input can be simply expressed as a first-order lag model with a time constant. The SOFC dynamic structure system uses multiple inertial links to simulate the various reaction links within the fuel cell. Therefore, the Nernst voltage can be obtained based on the SOFC open-circuit electromotive force as follows: Where, E 0,cell It consists of a constant term and a temperature dependency; R is the gas constant; T is the stack operating temperature (K); F is the Faraday constant; are the pressures of hydrogen, oxygen, and water in the fuel cell stack, respectively. Applying the Nernst equation and Ohm's law to consider ohmic losses, the voltage of the SOFC can be expressed as V Fc =E cell -E ohm , where V Fc is the single cell output voltage of SOFC, E cell is the Nernst voltage of SOFC, E ohm is the ohmic voltage of SOFC.

[0069] Furthermore, due to the presence of an inner-loop current controller in the source converter, it has the characteristics of a controllable current source. When the voltage on the power supply side decreases or increases, the current changes, further exacerbating voltage fluctuations. Therefore, the converter on the load side can also be equivalent to a controlled current source.

[0070] Based on the above, please continue to refer to Figure 4The DC microgrid equivalent model provided in this embodiment may include four capacitor branches, wherein a capacitor C1 is connected in parallel between the output of the SOFC and SOFC converter and the DC bus to form a capacitor branch; a capacitor C2 is connected in parallel between the output of the lithium battery pack and the lithium battery pack converter and the DC bus to form a capacitor branch; a capacitor C3 is connected in parallel between the input of the variable power load and the variable power load converter and the DC bus to form a capacitor branch; and a capacitor C4 is connected in parallel between the input of the constant power load and the constant power load converter and the DC bus to form a capacitor branch. Since the DC microgrid system is generally used in scenarios with short lines, without considering the line impedance, the total capacitance can be equivalent to the DC bus capacitance C = C1 + C2 + C3 + C4.

[0071] On this basis, the current transmitted from SOFC to DC bus through SOFC converter is equivalent to current source i1; the current transmitted from lithium battery pack to DC bus through lithium battery pack converter is equivalent to current source i2; the current transmitted from DC bus to variable power load through variable power load converter is equivalent to current source i d The current transmitted from the DC bus to the constant power load through the constant power load converter is equivalent to the current source i R .

[0072] Of course, according to the concept of the present invention, when the input side and input side of the DC bus in the DC microgrid system also include other power generation components or loads, those skilled in the art can also equate other power generation components or loads to corresponding capacitors and current sources according to actual needs, and this embodiment is not limited to this.

[0073] In step S2, a mixed potential function of the system is established by applying the mixed potential function theory according to the DC microgrid equivalent model, and then the mixed potential function is converted into a unified expression of the mixed potential function. Finally, the system stability condition is obtained according to the third stability theorem.

[0074] Specifically, based on the hybrid potential function theory, the influence of nonlinear control links such as the SOFC control link is considered to construct the system's hybrid potential function, and then the stability criterion of the DC microgrid is derived. Therefore, step S2 may specifically include the following steps:

[0075] Step S21: establishing a current potential function according to a DC microgrid equivalent model.

[0076] In specific implementation, a suitable current potential function can be established according to the current distribution and flow state of each component in the actual DC microgrid equivalent model. In this embodiment, the current source i1, current source i2, current source i3, and current source i4 equivalent to the non-energy storage components in each input and output component are d , current source i REstablish a current potential function. In this embodiment, the current potential function is expressed as:

[0077]

[0078] Where μ is the branch number (μ=1,···,r+s), r is the number of inductive branches, s is the number of capacitive branches; u dc is the DC bus voltage; p R is the input power of the constant power load, P M is the input power of the variable power load. Specifically, r and s are set according to the number of inductor branches and capacitor branches in the actual DC microgrid equivalent model and are not limited here.

[0079] Step S22: Establish a voltage and current product function for the capacitor branch based on the DC microgrid equivalent model, wherein the hybrid potential function is obtained by summing the current potential function of the non-energy storage element and the voltage and current product of the capacitor branch.

[0080] Therefore, in this embodiment, the voltage and current product function of the capacitor branch is expressed as:

[0081]

[0082] Where U σ 、i σ are the capacitor voltage and capacitor current respectively.

[0083] In step S23, the current potential function and the voltage and current product function of the capacitive branch are summed to obtain a mixed potential function of the system. The mixed potential function obtained by summing the current potential function and the voltage and current product function of the capacitive branch can be expressed as:

[0084]

[0085] In a preferred embodiment, the method further comprises the step of verifying the correctness of the mixed potential function using a verification formula; wherein the verification formula is expressed as:

[0086]

[0087] Where P(i,u) is the mixed potential function; C is the DC bus capacitance.

[0088] Based on the above verification formula, the correctness of the mixed potential function can be effectively verified, the accuracy of the DC microgrid system in stability analysis can be improved, and errors can be avoided.

[0089] Step S24 , converting the mixed potential function into a unified expression of the mixed potential function, and applying the third stability theorem to the characteristics of the unified expression of the mixed potential function to obtain a system stability condition.

[0090] In this embodiment, the unified expression of the mixed potential function based on the above mixed potential function conversion is:

[0091]

[0092] Since the mixed potential function conforms to the third stability theorem, the system stability condition can be expressed as follows based on the unified expression of the mixed potential function:

[0093]

[0094] Where τ1 and τ2 are the two eigenvalues ​​of the mixed potential function, and τ1 and τ2 are the minimum eigenvalues ​​of the second-order partial derivative matrices of A(i) and B(u) in the unified expression of the mixed potential function.

[0095] Step S3: constructing a large disturbance stability criterion function of the DC microgrid system according to the system stability condition and the control loop expression obtained by adopting the double closed-loop control strategy of the SOFC converter and the lithium battery pack converter.

[0096] In the specific embodiment, a dual closed-loop control strategy can be realized by designing a proportional-integral controller, such as Figure 6 As shown, the transfer function of the current loop and the voltage loop is expressed as G i (S) = k ip +k ii / s,G v (S) = k vp +k vi / s. Then the control loop expression obtained by adopting the dual closed-loop control strategy for SOFC converter and lithium battery pack converter is:

[0097]

[0098]

[0099] Where, They are the current set values ​​of SOFC and lithium battery pack respectively; is the voltage given value of the DC bus; i FC 、i B are SOFC current and lithium battery pack current respectively; u dc is the DC bus voltage; d1 and d2 are the differential gain coefficients of SOFC and lithium battery pack respectively; k Svp 、k svi are the proportional coefficient and integral coefficient of the SOFC converter voltage outer loop respectively; k sip 、k Bvi are the proportional coefficient and integral coefficient of the inner loop of the SOFC converter current respectively; kBvp 、k Bvi are the proportional coefficient and integral coefficient of the voltage outer loop of the lithium battery pack converter respectively; k Bip 、k Bvi They are the proportional coefficient and integral coefficient of the inner current loop of the lithium battery pack converter respectively.

[0100] Therefore, in this embodiment, combining the above control loop expression and system stability conditions, the large disturbance stability criterion function of the DC microgrid system can be expressed as:

[0101]

[0102] Where u FC 、u B are the SOFC power supply voltage and the lithium battery pack power supply voltage respectively; R FC 、R B They are the SOFC converter resistance and the lithium battery pack converter resistance respectively.

[0103] Step S4: performing stability analysis on the DC microgrid system based on the large disturbance stability criterion function of the DC microgrid system, thereby effectively solving the large disturbance stability condition of the DC microgrid system when encountering load mutation and impact load conditions.

[0104] In a preferred embodiment, the DC microgrid system stability analysis can also be performed based on the large disturbance stability criterion function of the DC microgrid system and in combination with the load power being less than the maximum power that the DC microgrid system can provide. The expression for the load power being less than the maximum power that the system can provide is:

[0105] i FC u FC +i B u B >P M +P R

[0106] Where i FC 、u FC are the output current and output voltage of SOFC respectively; i B 、u B are the output current and output voltage of the lithium battery pack respectively; P M 、P R They are the power of variable power load and the power of constant power load respectively.

[0107] The embodiment of the present invention improves a stability analysis method for a DC microgrid system based on SOFC as described above, and can accurately determine the grid bus oscillation problem caused by the DC microgrid's susceptibility to load interference while taking into account the characteristics of the SOFC power supply. It is particularly beneficial for application in stability analysis of ship DC microgrid systems.

[0108] Based on the above, in order to verify the correctness of the above stability criterion, a case analysis is conducted on the SOFC converter and lithium battery converter using dual closed-loop control in the ship DC microgrid system. Figure 7 The simulation of the actual operation of the ship in the equivalent model of the ship DC microgrid system shown needs to be verified by considering the ship speed problem caused by the change of the sea area. Specifically, during the initial voyage, the power of the constant power load on the ship is set to 20kW, and the propulsion motor load power is set to 30kW. When the horsepower of the propulsion motor needs to be increased, the propulsion motor load power increases by 30kW, that is, the variable power load increases by 30kW. The maximum disturbance of the system is set to: T = 4s. Here, 4 groups of system parameters are used to correspond to 4 working conditions respectively, and the DC microgrid system stability analysis method based on SOFC provided in the embodiment of the present invention is used to simulate this case to obtain the following Figure 8 The waveform diagram of the simulation results of the ship DC microgrid at different operating points is shown.

[0109] In addition, the parameters of each component in the ship DC microgrid system are set as shown in the following table:

[0110]

[0111]

[0112] According to the parameters in the table above, it can be obtained that under the above large disturbance, the boundary condition for stable operation of load power is 169260>P M +P R .

[0113] When setting the DC bus voltage reference value u dc =600V, by Figure 8 (A) It can be seen that when the parameters of working condition A are at T=4s, due to the small increase in the propulsion motor power, that is, when ΔPM=40kW, the voltage fluctuates slightly and quickly converges to the equilibrium point, and the system maintains stable operation. Therefore, the simulation results of working condition A are consistent with the stability analysis results. Similarly, when working conditions B and working conditions C occur, that is, when large-capacity loads are put into operation, the system bus voltage drop also increases due to the increase in the power of the set impact load, and the convergence speed slows down, which meets the stability analysis results. And it can be seen from the criterion that as the impact load increases and gets closer to the critical stability value, the time for the system to converge to the equilibrium point also increases. If the DC bus voltage Figure 8 (B) Figure 8 (C) shown.

[0114] However, in working condition D, the impact load step change in the system is large, which does not meet the conditions of the large signal stability criterion function of the DC microgrid and exceeds the critical value of large signal stability. Figure 8 (D) As can be seen, after the step change at T = 4s, the system gradually oscillates significantly, then decays. Ultimately, it can no longer maintain stable operation. Therefore, the simulation results for operating condition D are consistent with the stability analysis results.

[0115] The present invention also provides a DC microgrid system, which uses the SOFC-based DC microgrid system stability analysis method described in any of the above embodiments. The DC microgrid system can be applied to various fields, such as a ship DC microgrid system.

[0116] In summary, compared with the prior art, the stability analysis method for a SOFC-based DC microgrid system provided by the present invention utilizes an equivalent model to construct an equivalent circuit diagram. Based on the Brayton-Moser hybrid potential function theory, the SOFC-lithium battery DC microgrid potential function is derived, thereby obtaining a large-signal stability criterion for the system. Based on this criterion, the stability boundary for large load disturbances is calculated, enabling accurate and effective prediction of the magnitude of the disturbance under which the bus voltage can remain stable. This method is highly practical, does not require complex calculations, is simple and easy to implement, and has promising application prospects.

[0117] In addition, those skilled in the art should understand that, although there are many problems in the prior art, each embodiment or technical solution of the present invention may be improved in only one or several aspects, without having to simultaneously solve all the technical problems listed in the prior art or background art. Those skilled in the art should understand that any content not mentioned in a claim should not be construed as limiting the claim.

[0118] Although terms such as DC microgrid system, SOFC, SOFC converter, lithium battery pack, lithium battery pack converter, load, DC bus, constant power load, and variable power load are frequently used herein, the use of other terms is not excluded. These terms are used solely to more conveniently describe and explain the essence of the present invention; interpreting them as any additional limitations is contrary to the spirit of the present invention. The terms "first" and "second" (if any) in the description and claims of the embodiments of the present invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or precedence.

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing the stability of a DC microgrid system based on SOFC, characterized in that: The following steps are involved: Establish a DC microgrid equivalent model based on the DC microgrid system; The DC microgrid system includes at least an SOFC, an SOFC converter, a lithium battery pack, a lithium battery pack converter, a DC bus, a load, and a load converter; the SOFC is connected to the input side of the DC bus through the SOFC converter, the lithium battery pack is connected to the input side of the DC bus through the lithium battery pack converter; the load is connected to the output side of the DC bus through the load converter; wherein the SOFC converter and the lithium battery pack converter adopt a dual closed-loop control strategy to regulate the DC bus voltage and current; According to the DC microgrid equivalent model, a mixed potential function of the system is established by applying the mixed potential function theory, then the mixed potential function is converted into a unified expression of the mixed potential function, and finally the system stability condition is obtained according to the third stability theorem; specifically, the following steps are included: Establishing a current potential function according to the DC microgrid equivalent model; Establishing a voltage and current product function for a capacitor branch according to the DC microgrid equivalent model; Summing the current potential function and the voltage and current product function of the capacitance branch to obtain a mixed potential function of the system; Converting the mixed potential function into a unified expression of the mixed potential function, and applying the third stability theorem to the characteristics of the unified expression of the mixed potential function to obtain a system stability condition; The current potential function is expressed as: Where, Number the branch ( ,···, ), is the number of inductor branches, is the number of capacitor branches; is the DC bus voltage; is the input power of the constant power load, is the input power of the variable power load; The voltage and current product function of each of the capacitive branches is expressed as: Where, are the capacitor voltage and capacitor current respectively; 、 are equivalent current sources, is equivalent to the current transmitted from the SOFC to the DC bus through the SOFC converter, Equivalent to the current transmitted by the lithium battery pack converter to the DC bus; The mixed potential function is expressed as: The unified expression of the mixed potential function is expressed as: Then the system stability condition is expressed as: Where, 、 are the two eigenvalues ​​of the mixed potential function, and are the unified expressions of the mixed potential function. and The smallest eigenvalue of the second-order partial derivative matrix; Constructing a large disturbance stability criterion function of the DC microgrid system according to the system stability condition and the control loop expression obtained by adopting a double closed-loop control strategy for the SOFC converter and the lithium battery pack converter; The stability of the DC microgrid system is analyzed based on a large disturbance stability criterion function of the DC microgrid system.

2. The method for analyzing stability of a DC microgrid system based on SOFC according to claim 1, characterized in that: The load includes a variable power load and a constant power load, and the load converter includes a variable power load converter and a constant power load converter; the variable power load is connected to the output side of the DC bus through the variable power load converter; the constant power load is connected to the output side of the DC bus through the constant power load converter.

3. The method for analyzing stability of a DC microgrid system based on SOFC according to claim 2, characterized in that: The DC microgrid equivalent model includes the current transmitted from the SOFC to the DC bus through the SOFC converter being equivalent to a current source ; The current transmitted from the lithium battery pack to the DC bus through the lithium battery pack converter is equivalent to a current source. The current transmitted from the DC bus to the variable power load through the variable power load converter is equivalent to a current source The current transmitted from the DC bus to the constant power load through the constant power load converter is equivalent to a current source .

4. The method for analyzing stability of a DC microgrid system based on SOFC according to claim 1, characterized in that: The control loop expression obtained by adopting the dual closed-loop control strategy of the SOFC converter and the lithium battery pack converter is: Where, 、 are respectively the current set values ​​of the SOFC and the current set values ​​of the lithium battery pack; is a given value of the voltage of the DC bus; 、 are the SOFC current and the lithium battery pack current respectively; is the DC bus voltage; 、 are the differential gain coefficient of the SOFC and the differential gain coefficient of the lithium battery pack respectively; 、 are respectively the proportional coefficient and the integral coefficient of the voltage outer loop of the SOFC converter; 、 are respectively the proportional coefficient and the integral coefficient of the inner current loop of the SOFC converter; 、 are respectively the proportional coefficient and the integral coefficient of the voltage outer loop of the lithium battery pack converter; 、 are respectively the proportional coefficient and the integral coefficient of the inner current loop of the lithium battery pack converter.

5. The method for analyzing stability of a DC microgrid system based on SOFC according to claim 4, characterized in that: The large disturbance stability criterion function of the DC microgrid system is expressed as: Where, 、 are the SOFC power supply voltage and the lithium battery pack power supply voltage respectively; 、 They are respectively the SOFC converter resistor and the lithium battery pack converter resistor.

6. The method for analyzing stability of a DC microgrid system based on SOFC according to claim 1, characterized in that: The following steps are also included: Performing a stability analysis on the DC microgrid system according to a large disturbance stability criterion function of the DC microgrid system and in combination with the fact that the power of the load is less than the maximum power that the DC microgrid system can provide; The power of the load is less than the maximum power that the system can provide. Where, 、 are the output current and output voltage of the SOFC, respectively; 、 are the output current and output voltage of the lithium battery pack respectively; 、 are the load of the variable power load and the power of the constant power load respectively.

7. The method for analyzing stability of a DC microgrid system based on SOFC according to claim 6, characterized in that: The method further comprises the steps of: using a verification formula to verify the correctness of the mixed potential function; the verification formula is expressed as: Where, is the mixed potential function; is the DC bus capacitor.

8. A DC microgrid system, characterized by: A stability analysis method for a DC microgrid system based on SOFC is adopted as described in any one of claims 1 to 7.

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