A stability analysis method for energy storage system with pulse constant power load

Abstract

The present application discloses a stability analysis method for a pulsed constant power load energy storage system, which relates to the technical field of power systems, including: establishing a PCPL-ESS simplified equivalent circuit, dividing the system into two modes of loading and unloading, and establishing state equations for the two modes of loading and unloading; using a mixed potential energy method to construct a mixed potential function for the two modes, and constructing a stability domain criterion for the Lyapunov function expression; drawing the PCPL-ESS system stability domain boundary, dividing the load operation safety domain according to the PCPL-ESS load performance requirements; using the load operation safety domain to impose secondary constraints on the system stability domain boundary, and determining the optimal system operation peak power. The use of a mixed evaluation function does not require the system to be simulated, and is universal. The optimal system operation peak power can be determined based on the on-site equipment parameters, and appropriate equipment parameters can also be selected when the peak power is fixed.

Description

Technical Field

[0001] The present application relates to the technical field of power systems, and in particular to a stability analysis method for a pulse constant power load energy storage system. Background Art

[0002] ‌PCPL-ESS (Pulse constant power load-Energy Storage System) is a typical independent power system, which is mainly used to deal with pulse loads with periodic disturbances and strong nonlinear characteristics. This type of system is widely used in fully electrified vehicles and ship power systems, but due to its unique operating characteristics, it poses a major challenge to the stability and safety of the system. The main characteristics of the pulse constant power load energy storage system include: Periodic disturbances: The pulse load has strong nonlinearity and will cause periodic disturbances to the system, thereby causing fluctuations in the bus voltage and frequency. Strong nonlinearity: The operating characteristics of the pulse load cause the system to exhibit unstable operating behaviors in multiple modes, including unstable phenomena such as Hope bifurcation and catastrophic bifurcation.

[0003] In traditional technology, there are a lot of literatures that have conducted large signal stability analysis on conventional constant power loads, and have achieved good research results. For example, the Lyapunov direct method, the mixed potential energy method, the TS method, etc. The power system with pulse constant power loads has strong dynamic characteristics, and the system itself has high power quality specifications for the voltage and current of the actual operation of the equipment. Compared with the constant power load system with single loading as the research object, it requires more stringent stability restrictions.

[0004] However, most of the above-mentioned studies on the stability of power systems with pulsed constant power loads are still based on time domain simulation methods. Through a large number of actual or simulation tests, the trend of changes in system stability and key parameters can only be found in the current equipment test environment. Due to the lack of completeness and universality, it is impossible to accurately judge the stability of energy storage systems with pulsed constant power loads. Summary of the invention

[0005] In order to solve the above technical problems, this application proposes the following technical solutions:

[0006] In a first aspect, an embodiment of the present application provides a stability analysis method for a pulsed constant power load energy storage system, comprising:

[0007] The simplified equivalent circuit of PCPL-ESS is established, the system is divided into two modes: loading and unloading, and the state equations for the two modes are established;

[0008] Use the mixed potential energy method to construct the mixed potential function for the two modes and construct the stability domain criterion of the Lyapunov function expression;

[0009] Draw the PCPL-ESS stability domain boundary and divide the load operation safety domain according to the PCPL-ESS load performance requirements;

[0010] The load operation safety region is used to impose secondary constraints on the system stability region boundary to determine the optimal system operation peak power.

[0011] In a possible implementation, the PCPL-ESS simplified equivalent circuit is established to divide the system into two modes: loading and unloading. State equations are established for the two modes: loading and unloading. The two modes include:

[0012] The PCPL-ESS is considered as two sub-mode periodic switching operations of constant power load loading PLSM and load shedding PLM;

[0013] To set the inductor current i L and capacitor voltage u C is the system state variable, and the state equations of the two modes are determined respectively:

[0014]

[0015] in d 1=1- d g , d g Driving signal for DC / DC converter s g Duty cycle; R C is the equivalent resistance of the normal load, u s is the output voltage of the energy storage unit, r s is the internal resistance of the power supply, L , C are the input inductance and output capacitance of the converter respectively; P PL is the peak power of the pulse load, the pulse signal g PL ( t ) is expressed as follows:

[0016] (2)

[0017] in, T PL is the pulse period, pulse frequency f PL =1 / T PL , D PL is the pulse duty cycle.

[0018] In one possible implementation, the equilibrium points of the two modes are calculated based on formula (1): x e :

[0019] (3)

[0020] The Jacobi matrices of the two modes are obtained respectively. For the nonlinear terms in the Jacobi matrix of the PLM mode, Taylor expansion is performed at the equilibrium point:

[0021] (4)

[0022] It follows that:

[0023] (5)

[0024] Solve for the eigenvalues ​​of the two modes:

[0025] (6)

[0026] (7)

[0027] According to the Lyapunov stability judgment condition, the preliminary stability criterion is obtained:

[0028] (8)

[0029] Load power P C = u Ce 2 / R C， It turns out that:

[0030] Load power P C = u Ce 2 / R C， It turns out that:

[0031] (9).

[0032] In a possible implementation, the use of the mixed potential energy method to construct a mixed potential function for two modes and construct a stability domain criterion of the Lyapunov function expression includes:

[0033] The hybrid potential function for the two modes is constructed first in the PLM mode, where the current potential function is:

[0034] (10)

[0035] The voltage potential function of the output circuit is:

[0036] (11)

[0037] The energy function of a capacitor is:

[0038] (12)

[0039] The mixed potential function of the PLM mode is obtained:

[0040] (13)

[0041] Corresponding to the standard formula, we get:

[0042] get

[0043] Get the minimum eigenvalue

[0044] Constructing Lyapunov function expression :

[0045] (14)

[0046] According to the third stability theorem of hybrid potential, it should satisfy μ 1+ μ 2>0, the judgment is:

[0047] (15)

[0048] when P PL When this criterion is met, further μ 1+ μ 2=0, the critical voltage is obtained , substituting it into equation (14) to obtain the critical Lyapunov function

[0049] (16)

[0050] (16) is positive definite and its time derivative is always less than 0, thus satisfying the asymptotic stability condition. The asymptotic stability domain of the PLM mode is obtained. :

[0051] (17)

[0052] The mixed potential function for constructing PLSM modes is:

[0053] (18)

[0054] Solve to get the minimum eigenvalue μ 1. μ 2;

[0055] Construct the Lyapunov function expression:

[0056] (19)

[0057] Satisfy the conditions μ 1+ μ 2>0, the stability domain of the PLSM mode is the entire domain, and the stability domain of the two modes of the combined system is the RASPLM of formula (17).

[0058] In a possible implementation, drawing the PCPL-ESS stability domain boundary and dividing the load operation safety domain according to the PCPL-ESS load performance requirements includes:

[0059] Asymptotically stable region RAS PLM Draw, select parameters and substitute them into formula (14), and draw in the whole domain P * ( i , u ), and the critical value min P * ( i , u Cmin ) to obtain the domain boundary Ω B ;

[0060] Draw and compare the domain boundary plots at different peak powers with fixed parameters and the domain boundary plots for different parameters with fixed peak power.

[0061] In a possible implementation, the use of the load operation safety region to perform secondary constraints on the system stability region boundary to determine the optimal system operation peak power includes:

[0062] Combined with the load performance requirements, the evaluation function is obtained based on the mixed potential method f ( x ):

[0063] (20)

[0064] by δi L , δuC RES boundary value for step sampling x RES_ij :

[0065] (twenty one)

[0066] in, j =1-4, representing 4 boundary lines; , They are the maximum values ​​of current and voltage fluctuations allowed by the load respectively;

[0067] Take different P PL Calculate the RES boundary in the evaluation function The mapping value of If it is greater than 0, the appropriate peak power can be obtained.

[0068] In the embodiment of the present application, a hybrid evaluation function is used, which does not require system simulation and is universal. The optimal system operating peak power can be determined based on the on-site equipment parameters. At the same time, appropriate equipment parameters can also be selected when the peak power is fixed. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 A schematic flow chart of a stability analysis method for a pulsed constant power load energy storage system provided in an embodiment of the present application;

[0070] Figure 2 A schematic diagram of the PCPL-ESS equivalent circuit provided in an embodiment of the present application;

[0071] Figure 3 The hybrid potential energy method RAS provided in the embodiment of the present application PLM Graph of the solution process;

[0072] Figure 4 RAS provided in the embodiment of the present application PLM Domain boundary and different pulse load power P PL Simulation diagram of the value;

[0073] Figure 5 RAS provided in the embodiment of the present application PLM Domain boundaries and different energy storage components LC value Simulation diagram of

[0074] Figure 6 A quadratic constraint simulation diagram of the device parameters for RAS provided in the embodiment of the present application;

[0075] Figure 7 The test waveform and phase trajectory diagram provided for the embodiments of the present application. DETAILED DESCRIPTION

[0076] The present solution is described below in conjunction with the accompanying drawings and specific implementation methods.

[0077] See also Figure 1 The stability analysis method of the energy storage system containing pulse constant power load provided in the embodiment of the present application includes:

[0078] S101, establish the simplified equivalent circuit of PCPL-ESS, divide the system into two modes: loading and unloading, and establish the state equations for the two modes.

[0079] The battery energy storage system with pulse constant power load generally takes pulse load as the main load, supplemented by some conventional loads. The energy storage unit with higher stability is selected as the power supply, which is connected to the DC bus through DC / DC boost conversion to supply power to the pulse load and conventional load on the DC side. The focus is on retaining the nonlinearity and constant power characteristics of the pulse load, and simplifying the PCPL-ESS system as follows Figure 2 The equivalent circuit shown in the figure, in which the battery energy storage unit is connected to the DC bus through the DC / DC converter Boost. Figure 2 middle, Output voltage of the energy storage unit; is the internal resistance of the power supply; L , C are the input inductance and output capacitance of the converter respectively; T For IGBT, D is a diode; For normal load; pulse switch for pulse load Switching signal by pulse Control. In order to ensure the effectiveness of the pulse peak power of the pulse load equipment, a controller is generally used to ensure the constancy of the pulse power peak. Therefore, the pulse load is often manifested as a "pulse constant power load".

[0080] The PCPL-ESS is considered as two sub-mode periodic switching operations of constant power load loading PLSM and load shedding PLM;

[0081] To set the inductor current i L and capacitor voltage u C is the system state variable, and the state equations of the two modes are determined respectively:

[0082]

[0083] in d 1=1- d g , d g Driving signal for DC / DC converters g Duty cycle; R C is the equivalent resistance of the normal load, u s is the output voltage of the energy storage unit, r s is the internal resistance of the power supply, L , C are the input inductance and output capacitance of the converter respectively; P PL is the peak power of the pulse load, the pulse signal g PL ( t ) is expressed as follows:

[0084] (2)

[0085] in, T PL is the pulse period, pulse frequency f PL =1 / T PL , D PL is the pulse duty cycle.

[0086] S102, using the mixed potential energy method to construct a mixed potential function for the two modes, and constructing a stability domain criterion for the Lyapunov function expression.

[0087] The eigenvalue method is the most basic method for power system stability. Based on formula (2), the equilibrium points of the two modes of PCPL-ESS are calculated: x e :

[0088] (3)

[0089] It can be seen that the equilibrium point of the two modes x e_PLSM ≠ x e_PLM , the PCPL-ESS system is a nonlinear system with two modes and two equilibrium points. Then, the Jacobi matrices of the two modes are obtained respectively. It can be seen that the PLM modal Jacobi matrix has nonlinear terms. f ( u C )=- P PL / C u C , Taylor expansion is performed at the equilibrium point, and we have:

[0090] (4)

[0091] This gives the Jacobi matrix of the two modes:

[0092] (5)

[0093] Solve the PLSM modal eigenvalues:

[0094] (6)

[0095] Since the component parameters are all positive, the real part of the eigenvalue is negative, so it can be concluded that the PLSM mode of PCPL-ESS is at the equilibrium point x e_PLSM Stable.

[0096] Solve the PLM modal eigenvalues:

[0097] (7)

[0098] According to the Lyapunov stability criteria, the PLM mode should be at the equilibrium point x e_PLM If it is stable at the point, the real part of the eigenvalue must be negative, so the preliminary stability criterion I is obtained:

[0099] (8)

[0100] Among them, the normal load power P C = u Ce 2 / R C , the above formula can be written as

[0101] (9)

[0102] in accordance with Figure 2 The circuit structure and formula (2) construct the mixed potential function of the PLM mode. Among them, the current potential function of the DC / DC converter input loop is:

[0103] (10)

[0104] The voltage potential function of the output circuit is:

[0105] (11)

[0106] The energy function of a capacitor is:

[0107] (12)

[0108] Get the mixed potential function of the PLM modeP ( i , u )for:

[0109] (13)

[0110] verify P ( i , u ) is correct:

[0111]

[0112] Satisfying formula (9), prove P ( i , u ) is correct. By matching formula (10) with standard formula (8), we have

[0113]

[0114] From this we get

[0115]

[0116] Further get the minimum eigenvalue μ 1. μ 2:

[0117]

[0118] Constructing Lyapunov function expression P* ( i , u ):

[0119] (14)

[0120] According to the third stability theorem of mixed potential, to ensure the large signal stability of the system, the condition should be met first μ 1+ μ 2>0, we get the judgment:

[0121] (15)

[0122] Comparing with formula (9), it can be seen that this criterion is the same as the preliminary criterion I obtained by the eigenvalue method. P PL When this criterion is met, further μ 1+ μ 2=0, the critical voltage is obtained

[0123]

[0124] Substituting into equation (14) we get the critical Lyapunov function

[0125] (16)

[0126] It can be seen that the above formula is positive, and its time derivative d can be proved to be P *( i , u ) / d t <0, so the Lyapunov function and its derivatives all satisfy the asymptotic stability conditions. The asymptotic stability region RASPLM of the PLM mode (pulse power loading) of the PCPL-ESS system can be obtained:

[0127] (17)

[0128] S103, draw the PCPL-ESS stability domain boundary, and divide the load operation safety domain according to the PCPL-ESS load performance requirements.

[0129] According to inequality (17), the stability region RAS (Region of Asymptotic Stability) of the PLM mode under pulse load can be plotted, see Figure 3 (a).

[0130] Similarly, the mixed potential function of the PLSM mode is obtained as follows:

[0131] (18)

[0132] Solve to get the minimum eigenvalue μ 1. μ 2:

[0133]

[0134] Construct the Lyapunov function expression:

[0135] (19)

[0136] Obviously meet the conditions μ 1+ μ 2>0, that is, all state variables in the PLSM mode are steady state, that is, RAS PLSM It is the whole domain. PLM <RAS PLSM Therefore, the modal stability region of the PCPL-ESS system PLM and PLSM is taken as RAS PLM .

[0137] Based on the above-mentioned stability analysis conclusion of the hybrid potential energy function method, it can be seen that the PLSM mode of the PCPL-ESS system is globally stable, and the PLM mode has an asymptotically stable region RAS, then RAS PLM This is the system stability region.

[0138] Select the parameter settings as shown in Table 1. Substituting the simulation parameter values ​​into equation (13), the stability domain boundary RAS of the PLM mode can be plotted: PLM .

[0139] Table 1 Simulation model parameters

[0140]

[0141] According to criterion I, the initial stability critical value can be calculated: P PL ≤ 13.26kW, substitute the simulation parameter values ​​in Table 1 into formula (8), and obtain the system stability condition according to criterion I: P PL <13.26kW. P PL = 8kW as an example, based on the conclusion of mixed potential, the parameters are substituted into formula (14) and the whole domain is plotted. P * ( i , u )like Figure 3 (a) shows; calculate the critical voltage u Cmin =465.31V, we get P * ( i , u Cmin )like Figure 3 As shown in (b), the critical value min is further obtained. P * ( i , u Cmin ) = 1.7226e +06; Based on formula (18), the asymptotic stability region RAS of the PLM mode can be obtained PLM ,like Figure 3 (cd) Shown in dark blue.

[0142] Domain Boundary RAS PLM It can be seen from the solution and drawing process that the mixed potential function P * ( i , u ) is a three-dimensional surface with a concave bottom. Its vertical axis value is P * ( i ,u Cmin ) is compared, if it is less than the critical value, it is a stable domain, otherwise it is an unstable domain, mapped to i L ~ u C The coordinate plane can obtain the blue plane domain, such as Figure 3 (d). If inequality (17) is taken as an equation, the domain boundary Ω can be obtained B :

[0143] (17)

[0144] When the system parameters are set, the pulse load power P PL With domain boundary Ω B One-to-one correspondence, that is, different P PL The values ​​correspond to different domain boundaries.

[0145] Based on the previous derivation process, it can be seen that the asymptotic stability region RAS of the PLM mode is related to the system parameters (pulse peak power P PL 、DC / DC converter energy storage elements LC ) are closely related.

[0146] Select P PL =1W→13kW, draw the PLM modal RAS domain boundaries as follows Figure 4 shown.

[0147] It can be seen that:

[0148] ① Pulse load power P PL The larger it is, the smaller the system RAS is;

[0149] ② Especially when P PL =13kW, close to the critical value of 13.26kW, RAS is very small. If it continues to increase P PL Value, min P * ( i , u Cmin ) will be less than P * ( i , u ) minimum value, that is, it cannot be Figure 3 (a) An intersection is generated, that is, Ω in formula (2-16) is empty;

[0150] ③ PPL takes 0W as the PLSM mode, and the critical voltage of formula (14) uC min=0V, uC min as the divisor term results in P *( i , uC min) produces Nan value (infinity), which means that the PLSM mode is stable in the whole domain.

[0151] S104, using the load operation safety region to perform secondary constraints on the system stability region boundary, and determining the optimal system operation peak power.

[0152] Based on the preliminary stability criterion I, it can be seen that reducing the inductance value of the converter L , or increase the capacitance value C , can increase the pulse peak power P PL The above figure shows that P PL =13kW RAS range is very small, in this case, by reducing the inductance value L , or increase the capacitance value C To increase the RAS range. Figure 5 As shown, Figure 5 (a) is a fixed capacitance value C= 940 uF, gradually reduce the inductance value L , it can be seen that the RAS range increases accordingly; Figure 5 (b) is a fixed inductance value L= 2.6 mH, gradually increase the capacitance value C , it can be seen that the RAS range increases accordingly.

[0153] According to the eigenvalue method, the peak power of the pulse load can be preliminarily obtained P PL The upper limit of value: P PL <13.26kW; the peak power is further calculated by the hybrid potential function method P PL Corresponding ( i L , u C ) Stable operation of domain RAS, and Figure 4 show, P PL The larger the value, the smaller the stability domain, especially when P PL When the critical value is approached, RAS shrinks to a domain where it cannot operate normally. P PLHow should the value be selected to ensure that the PCPL-ESS system operates within a safe and stable range, and that the system does not have to bear too much redundancy. Combined with the actual performance requirements of the equipment, the equipment operation safety region RES (Region of Equipment Safety) is divided to ensure that the system ( i L , u C ) The actual operating range is all within the stable domain, that is, RES∈RAS, achieving the purpose of quadratic constraint RAS domain, thus finding P PL The appropriate value can reduce the redundancy of the system load. The specific process is as follows:

[0154] Combined with the load performance requirements, the evaluation function is obtained based on the mixed potential method f ( x ):

[0155] (20)

[0156] It is known that P PL After deciding, P * ( i , u ) is a three-dimensional surface with a concave bottom, min P * ( i , u Cmin ) is a fixed value, and in three-dimensional coordinates it is a plane with a fixed Z value, that is, the critical surface, such as Figure 6 (a). And Eq. f ( x )=0 is the domain boundary Ω of the stable domain RAS B , Figure 6 (a) When mapped onto a plane, it is Figure 6 (b) shown.

[0157] Known system equilibrium point x e =( i Le , u Ce ), comprehensively evaluate the system equipment performance requirements and the actual circuit components' tolerance (such as the maximum voltage and maximum current that the switching device IGBT can withstand), and obtain the safety domain RES, that is, the state parameter ( i L , u C )Operation Range( i Le ±Δi L , u Ce ±Δ u C ).by δi L , δu C RES boundary value for step sampling x RES_ij :

[0158] (twenty one)

[0159] in, j =1~4, representing 4 boundary lines; Δ i L , Δ u C They are the maximum values ​​of current and voltage fluctuations allowed by the load respectively.

[0160] (1) Starting from the critical value P PL , calculate the RES boundary in the evaluation function f ( x )'s mapping value, just judge f ( x RES_ij ) is greater than 0. P PL When it is the critical value, RAS is almost reduced to the equilibrium point. f ( x RES_ij ) are all > 0, RAS RES, which means that the boundaries of RES are all in the unstable region;

[0161] (2) δP PL To reduce the step size P PL ( P PL = P PL - δP PL ), and judge again f ( x RES_ij ) is greater than 0, if yes f ( x RES_ij )>0, then continue to decrease P PL value;

[0162] It can be seen that with P PLThe decrease of RAS causes the domain boundary of RAS to expand outward from the equilibrium point. When RAS intersects with the domain boundary of RES, f ( x RES_ij ) values ​​are partially ≥ 0 and partially < 0;

[0163] (3) When all f ( x RES_ij )≤0, then stop decreasing P PL Value, at this time P PL The value is P PL_RES .

[0164] all f ( x RES_ij )≤0, then RES RAS means that the RES boundary has entered the stable region, and the system is stable if it runs within the RES. P PL value, the system load will be redundant.

[0165] The above process is based on the device component parameters, such as LC, which are constant values. The pulse peak power PPL_RES suitable for system operation is obtained through the secondary constraint of RES on RAS. Figure 5 It shows that the RAS domain increases with the increase of L or C value. Therefore, if the PPL has been determined, the L or C value can be gradually reduced through the above process to obtain the appropriate value of L or C of the system energy storage element and reduce the redundancy of the system energy storage element.

[0166] Taking the experimental research object of this embodiment as an example, the equilibrium point value of the PLM mode is calculated as follows: xe_PLM=((20+PPL / 600)A, 600V). The load equipment performance requires that the DC voltage uC fluctuation rate is ≤±10%, that is, ΔuC=60V; at the same time, considering the equipment performance and the actual requirements of the components, ΔiL=100A is obtained, and the system safety domain RES is obtained as follows Figure 5 As shown in the red rectangle, the quadratic constraint step is adopted, PPL=13kW is taken, the decreasing step size δPPL=200W is used, and the mixed evaluation function f(xRES) of the boundary points of the stable domain RAS and RES is gradually compared.

[0167] When PPL = [11.4kW 13kW], RAS RES, RES boundary points xRES_ij are all located on the critical surface, then all f(xRES_ij)>0;

[0168] When PPL=(6.2kW 11.4kW), RAS and RES intersect, part of the RES boundary is inside RAS, and part is outside. Taking PPL=10kW as an example, the blue dotted part of the figure is f(xRES)≤0, and the red solid line is f(xRES)>0;

[0169] When PPL<6.2kW, RES RAS, then all f(xRES_ij)≤0.

[0170] Finally, PPL=6.2kW is the peak power PPL_RES suitable for system operation.

[0171] Based on the actual experimental platform, Figure 2 Parameters, source end battery storage unit, used to output a stable 400V DC voltage u s ; Bus DC / DC converter is mainly used for Boost ( u Ce = 600V), using a duty cycle d 1 (1 / 3) Direct control. Equipment performance requirements: bus voltage fluctuation rate ≤ ±10%.

[0172] According to the above conclusions, set the pulse load peak P PL = 3 groups of tests were conducted at 4kW, 6kW and 8kW to test the DC voltage of the equipment respectively. u C , DC / DC input side current i L (Also the source output current i s ) and load current i Load The real-time waveform data of (total current of normal load and pulse load) is obtained by using YOKOGAWA oscilloscope recorder DL850E. Figure 7 As shown, channel 3 (CH3) is used to calculate the actual load power in real time. p Load = u C × i Load Waveform data.

[0173] The blue curve is u C ~ i L Phase domain diagram, representing the DC / DC converter output voltage and input current ( i L It is also the source output current is )’s actual operating status; the red curve is u C ~ i Load Phase domain diagram, characterizing the output state of the DC / DC converter. Table 2 lists the measurement and analysis results of the three groups of test waveform data.

[0174] Table 2 Group test parameters and measurement results

[0175]

[0176] Through the analysis of waveform data and phase domain diagram, we can know that:

[0177] (1) P PL =4kW(< P PL_RES ), the voltage and current u C , i L The actual operating waveform fully meets the equipment performance requirements, and at this time RES RAS, the system has a certain amount of redundancy;

[0178] (2) P PL =6kW, voltage and current u C , i L The actual operating waveform basically meets the equipment performance requirements (the voltage slightly exceeds the limit), and at this time RES RAS, the system is in a critical state;

[0179] (3) P PL =8kW(> P PL_RES )hour, u C The operating range is >±60V (±10%), which seriously exceeds the RES domain boundary. At this time, RES intersects with RAS, indicating that part of the operating trajectory is in an unstable area.

[0180] The above conclusions show that the quadratic constraint obtained based on the mixed evaluation function method P PL_RES=6.2kW is used to determine whether the system has load redundancy, which is closer to the actual situation. It proves that this method is universal in evaluating the stability of energy storage systems with pulsed constant power loads and can be used as a theoretical basis for actual production.

[0181] In the embodiments of the present application, "at least one" refers to one or more, and "plurality" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Among them, A and B can be singular or plural. The character " / " generally indicates that the previous and subsequent associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c can be represented by: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple.

[0182] The above is only a specific implementation of the present application. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. The protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A stability analysis method for a pulse constant power load energy storage system, characterized in that: include: The simplified equivalent circuit of PCPL-ESS is established, the system is divided into two modes: loading and unloading, and the state equations for the two modes are established; Use the mixed potential energy method to construct the mixed potential function for the two modes and construct the stability domain criterion of the Lyapunov function expression; Draw the PCPL-ESS stability domain boundary and divide the load operation safety domain according to the PCPL-ESS load performance requirements; The load operation safety region is used to impose secondary constraints on the system stability region boundary to determine the optimal system operation peak power, including: Combined with the load performance requirements, the evaluation function is obtained based on the mixed potential method f ( x ): by δi L , δu C RES boundary value for step sampling x RES_ij : in, is the Lyapunov function expression, is the inductor current, is the capacitor voltage, Critical voltage, The system equilibrium point The inductor current balance point value; The system equilibrium point The capacitor voltage value, j =1-4, represents 4 boundary lines, and It is the sampling of the current values ​​of the four boundary lines of RES. and Sampling of voltage values ​​of the four boundary lines of RES; , They are the maximum values ​​of current and voltage fluctuations allowed by the load respectively; Take different Calculate the RES boundary in the evaluation function The mapping value of If it is greater than 0, the appropriate peak power can be obtained; Starting from the critical value P PL , calculate the RES boundary in the evaluation function f ( x )'s mapping value, just judge f ( x RES_ij ) is greater than 0, we know P PL When it is the critical value, RAS is almost reduced to the equilibrium point. f ( x RES_ij ) are greater than 0, RAS RES, which means that the boundaries of RES are all in the unstable region; by δP PL To reduce the step size P PL , judge again f ( x RES_ij ) is greater than 0, if yes f ( x RES_ij ) is greater than 0, then continue to decrease P PL value; along with P PL The decrease of RAS causes the domain boundary of RAS to expand outward from the equilibrium point. When RAS intersects with the domain boundary of RES, f ( x RES_ij ) values ​​are partly greater than or equal to 0 and partly less than 0; When all f ( x RES_ij ) is less than or equal to 0, then stop decreasing P PL Value, at this time P PL The value is P PL_RES ; all f ( x RES_ij ) is less than or equal to 0, then RES RAS means that the RES boundary has entered the stable region. The system is stable if it continues to decrease. P PL value, the system load will be redundant.

2. The stability analysis method of the pulse constant power load energy storage system according to claim 1 is characterized in that: The PCPL-ESS simplified equivalent circuit is established, the system is divided into two modes: loading and unloading, and state equations are established for the two modes: loading and unloading, including: The PCPL-ESS is considered as two sub-mode periodic switching operations of constant power load loading PLSM and load shedding PLM; To set the inductor current i L and capacitor voltage u C is the system state variable, and the state equations of the two modes are determined respectively: in d 1=1- d g , d g Driving signal for DC / DC converter s g Duty cycle; R C is the equivalent resistance of the normal load, u s is the output voltage of the energy storage unit, r s is the internal resistance of the power supply, L , C are the input inductance and output capacitance of the converter respectively; P PL is the peak power of the pulse load, the pulse signal g PL ( t ) is expressed as follows: (2) in, T PL is the pulse period, pulse frequency f PL =1 / T PL , D PL is the pulse duty cycle.

3. The stability analysis method of the energy storage system containing pulse constant power load according to claim 2 is characterized in that: Based on formula (1), the equilibrium points of the two modes are calculated x e : (3) The Jacobi matrices of the two modes are obtained respectively. For the nonlinear terms in the Jacobi matrix of the PLM mode, Taylor expansion is performed at the equilibrium point: (4) It follows that: (5) Solve for the eigenvalues ​​of the two modes: (6) (7) According to the Lyapunov stability judgment condition, the preliminary stability criterion is obtained: (8) Load power P C = u Ce 2 / R C， It turns out that: Load power P C = u Ce 2 / R C， It turns out that: (9)。 4. The stability analysis method of the energy storage system containing pulse constant power load according to claim 3 is characterized in that: The method of using the mixed potential energy method to construct a mixed potential function for two modes and construct a stable domain criterion of the Lyapunov function expression includes: The mixed potential functions are constructed for the two modes, first the PLM mode, where the current potential function is: (10) The voltage potential function of the output circuit is: (11) The energy function of a capacitor is: (12) The mixed potential function of the PLM mode is obtained: (13) Corresponding to the standard formula, we get: get Get the minimum eigenvalue Constructing Lyapunov function expression : (14) According to the third stability theorem of hybrid potential, it should satisfy μ 1+ μ 2 > 0, the criterion is: (15) when P PL When this criterion is met, further μ 1+ μ 2=0, the critical voltage is obtained , substituting it into equation (14) to obtain the critical Lyapunov function (16) (16) is positive definite and its time derivative is always less than 0, thus satisfying the asymptotic stability condition. The asymptotic stability domain of the PLM mode is obtained. : (17) The mixed potential function for constructing PLSM modes is: (18) Solve to get the minimum eigenvalue μ 1. μ 2; Construct the Lyapunov function expression: (19) Satisfy the conditions μ 1+ μ 2>0, the stability domain of the PLSM mode is the entire domain, and the stability domain of the two modes of the combined system is the formula (17) .

5. The stability analysis method of the energy storage system containing pulse constant power load according to claim 4 is characterized in that: The PCPL-ESS stability domain boundary is drawn, and the load operation safety domain is divided according to the PCPL-ESS load performance requirements, including: Asymptotically stable region RAS PLM Draw, select parameters and substitute them into formula (14), and draw in the whole domain , and the critical value min P * ( i , u C min ) to obtain the domain boundary Ω B ; Draw and compare the domain boundary plots at different peak powers with fixed parameters and the domain boundary plots for different parameters with fixed peak power.

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