Modeling and Experiment Validation of the DC/DC Converter for Online AC Impedance Identification of the Lithium-Ion Battery.
by：HGB
2020-06-04
In today\'s world, energy crisis and environmental pollution are becoming more and more serious.
Due to features such as high energy density [1] [2] and low emissions, lithium-ion batteries have received worldwide attention, and lithium-ion batteries have been used in a variety of applications, such as packaging in battery electric vehicles and hybrid electric vehicles [3] [4.
Electrical impedance mirror, abbreviated as EIS, it has been widely used in lithium-ion battery studies related to aging status and its impact on applications and temperature estimation and expansion [5] [6] [7.
The principle of the EIS method is that at certain frequencies, a small voltage or current signal is superimposed on the battery, and then after the voltage and current signals are obtained at the same time, the two signals can be passed.
The EIS method has three basic assumptions, namely, linear, Casualty, and stability [8].
The linearity of the battery is ensured by controlling the magnitude of the increased current or voltage fluctuation signal.
Casualties are obvious because the corresponding signal cannot be measured without increasing the excitation signal.
Stability means that the system can return to normal when the added signal is removed, which is satisfied.
Under normal circumstances, the impedance acquisition of the battery can be divided into two categories, namely, the impedance measurement method and the online estimation method.
The impedance measurement method depends on the experimental equipment. After measurement, it is important to estimate the physical parameters of the battery.
The impedance properties of the battery depend on the battery conditions such as the state of charge, the temperature, the current, and the history of the final previous [5] [9] [10].
The charging state of the battery has a high impedance change in this frequency range, so the impedance-
[11] a methodology-based approach is proposed.
The relationship between physical parameters and impedance spectra can be established by equivalent circuit models such as randles model and transmission line model [12] [13.
In [14], it is said that the real part of the battery impedance is related to the battery temperature, and the sensitivity analysis shows that for the low frequency, the impedance varies greatly with the temperature.
The effect of charging method on battery life was studied, and the battery was characterized by using EIS method [15], and a comparative study between charging techniques was introduced.
The online estimation method of impedance parameters takes into account the significant changes in battery properties during life due to aging [16.
In this set, the filter technique is a commonly used method, which is a recursive estimator for [15.
Based on the equivalent circuit model [17], a single filter can be used to estimate the charging status of the battery.
To take into account the non-linearity in the battery model, an advanced version of Kalmanfilter, such as an extended filter or a sigmapoint filter, is adopted.
Some recent publications have taken into account the non-linearity between the charging state and the open-circuit voltage [18] [19] [20.
Although great progress has been made in impedance acquisition, the application of these methods in actual battery packs is limited in many ways.
Impedance measurement requires expensive laboratory equipment, which cannot be borne in the actual system.
Online estimation requires a large number of calculations, including matrix operations and implementation on a common low level
The cost micro-controller is actually difficult to achieve.
In addition, complex matrix operations can lead to numerical instability of [16.
Therefore, the combination of the online measurement of impedance and the online estimation method will be very meaningful.
In order to achieve this goal, the first thing that needs to be done is to design the equipment used for impedance online measurement.
However, there are not many known literature in this regard.
[21] The study in proposes a solution that uses a power converter to motivate the battery at any operating point for impedance spectrum, which is performed by the control system without additional power hardware
The limitation of this method is that the output current of the battery is much smaller than the actual current of the vehicle battery pack.
Similar work for online impedance measurement can also be found in the field of hydrogen polymer electrolyte membrane fuel cell systems.
[22] The vehicle fuel cell AC impedance measurement system is proposed and passed on-
The function of the system has been verified.
However, in addition to the key frequency points where the excitation frequency is 300Hz, no more information is provided about the controllable high voltage DC/DC converter.
Power converters do not exist in all applications
Therefore, a New Impedance measurement method is proposed in this paper, which produces a wide range of frequencies, and the method is suitable for various battery systems without increasing the cost of the system.
To this end, the topology of the impedance measurement system is given, including a power converter for excitation signal generation and a unit voltage monitoring device for obtaining the signal and calculating the impedance.
The average state space equation of the power converter is derived to check the controllable and observable nature of the converter\'s target input current.
Based on these state-space equations, a small signal model is derived to calculate the gain amplitude of the fluctuating current signal relative to the unique control variable, that is, the duty cycle of the power semiconductor PWM.
This helps design control algorithms and allows validation of the proposed system topology.
By establishing the model of power system in Matlab/Simulink, the function of the system is verified.
After designing the power converter, experiments were carried out on the high-power lim2 battery and the feasibility of the converter\'s online impedance measurement was verified in a wide frequency range.
The organization of the paper is as follows.
The second section introduces the system structure and mathematical model of the power converter in detail.
Then, the function of the system is verified according to the gain amplitude of the excitation current signal, and the calculated impedance is compared with the theoretical equivalent circuit model in Section III.
Subsequently, the power converter and battery voltage monitor were designed and implemented into a high-power battery pack, and validation of the converter model and on-line impedance measurement was obtained in section 4.
Section V concludes.
Starting with the system model, the system configuration is described, including DC/DC converters, lithium-
Ion battery pack and load.
Then there\'s a hot drawing of lithium.
Ion batteries and converters have been introduced.
On-line AC impedance recognition system with lithium configuration
As shown in Figure 1, the Ion battery consists of lithium-
Ion battery assembly with BMS (battery management system), battery voltage monitor, sequencer, electronic load and DC/DC converter, and power consumption resistance. The lithium-
The ion battery pack of BMS is considered to be a voltage source for DC/DC converters and electronic loads.
BMS helps monitor the normal operating status of batterypack, which provides information such as temperature, charging status, and health status.
The electronic load is controlled to draw constant current from the battery pack, like a constant current receiver.
Typically, a DC/DC converter is a power conversion device, but in this system it is implemented to generate a current excitation signal that will be superimposed on the battery pack.
This current signal is the sum of the sine current part and the DC part because the input current of the converter cannot be lower than zero.
The controller of the converter is responsible for the implementation of the function.
Because the power conversion of the DC/DC converter is not effectively utilized, but only generates heat, the operation time should be as short as possible, and if used in the actual system, the DC part should be as low as possible.
To measure the voltage of each battery, a battery voltage monitor was developed.
The shunt resistor measures the output current of batterypack and converts the current signal to a voltage signal that can be amplified by the battery voltage monitor.
Combined with battery voltage monitoring and shunt resistance, the output voltage and current of each battery can be obtained at the same time. after recording these signals, the impedance spectrum can be calculated using FFT technology.
Unlike the traditional analog signal processing circuit, the unit voltage monitor must be able to extract weak fluctuation signals from large DC current and voltage at a stable operating point.
On the basis of battery voltage monitoring and DC/DC converter, the work of this paper can proceed smoothly. Lithium-
When studying the electrical impedance spectrum, the Ion battery model,
Ion batteries are considered to be linear systems around their operating points.
In order to adapt to the impedance spectrum, many equivalent circuits have been tried, with two commonly used models, the randles model and the model with Warburg elements, as shown in Figure 2 () figure 2 (B) is shown ). The term [E. sub.
N] is the nerster voltage based on thermodynamics and term [R. sub.
M] is the sum of contact resistance, internal ion transfer resistance, and wire resistance. The term [R. sub.
C] refers to the faradic resistance and terminology at the electro-chemical interface [C]sub.
D1] indicates a double-layer capacitor.
When considering the limited proliferation process,
The double-layer capacitor inside the battery is replaced with the Warburg element [Z. sub. w].
DC/DC converter modeling as shown in Figure 3 (a), DC/DC converter is a general purpose boostconverter consisting of an inductor [L]sub.
1], switching power supply-
Semiconductor module [G. sub. 1], a diode [D. sub.
1] and a capacitor [C. sub. 1].
Resistance [R. sub. L1] and [R. sub.
1C] is considered to be a parasitic power consumption similar to the inductor [L]sub.
1] and capacitor [C. sub. 1] respectively. The turn-on and turn-
Power failure of module [G]sub.
1] and diode [D. sub.
1] are all included in the resistor [R. sub.
Because these processes are complex, there is, in fact, no exact equation that can be used to describe them quantitatively.
The resistor R represents the load requirement of the converter.
The control converter injects a fluctuating current signal into the battery pack.
The fluctuating current signal can be any waveform, but in order to ensure a high signal-to-noise ratio, the sine current interference signal is selected as the target waveform.
In the case of inherent limitations of the DC/DC converter, the frequency of the interference signal is expanded as widely as possible, one of which is the switching frequency of the module [G]sub.
1], the full range of spectrum is realized.
The principle of DC/DC converter is based on pulse width modulation (PWM), and duty cycle D and switching frequency are two key parameters of PWM.
When the module [G. sub.
As shown in Figure 3 (B), the converter works in one way and the equation of state is described by Equation 1.
When the module [G. sub.
1] as shown in Figure 3 (c), the converter works in another way, and the equation of state is described by Equation 2.
[Mathematical expression non-reproducible] (1) [Mathematical expression non-reproducible] (2) [Mathematical expression non-reproducible] (3) where [U. sub.
In] = input voltage of the converter [I. sub.
In] = input current of Converter [usub.
O] = output voltage of Converter [sub.
C1] = voltage on the capacitor [C. sub.
After considering the duty cycle D, the average state equation is deduced as Equation 3. The re-
Equation 4 describes the equations of arrangement in order to obtain input variables X, state variables U, and output variables iin, as well as corresponding coefficient matrices A, B, C, and T.
[Mathematical expressions cannot be reproduced] (4) the state space equation can be described by Equation 5 according to equation 4, and all variables and coefficient matrices can be described by Equation 6.
[Mathematical expression non-reproducible] (5) [Mathematical expression non-reproducible] (6) the controllable matrix Q is described by Equation 7, and the observable matrix R is described by Equation 8.
It is easy to find that this system is completely controllable but not observable because of the theoretical voltagesub.
C1 of capacitor [C. sub.
1] is not measurable.
For DC/DC converters, the directly adjustable parameter is the duty cycle. to achieve the generation of periodic current waves, a small signal model of DC/DC converters needs to be established first.
Then analyze the amplitude gain of the cycle current signal relative to the cycle change around its stability value, which helps to better understand the system properties in this special application.
[Non-reproducible mathematical expressions] (7) [non-reproducible mathematical expressions] (8) [non-reproducible mathematical expressions] (9) [non-reproducible mathematical expressions] (10) (11) to derive the small signal model, the small dynamic signal is added to all relevant parameters and variables as Equation 9. The term[l. sub.
Compared to the stable value [L], in] represents a dynamic signal with a small amplitudesub. in]. The term [u. sub. 0], [u. sub. C1], d and[u. sub.
In] are dynamic small signals of output voltage, capacitor voltage, duty cycle and input voltage, respectively.
At the same time terms [Americansub. o], [U. sub. C1], [D. sub. 0] and [U. sub.
In] represents the corresponding output voltage, capacitor voltage, duty cycle, and stability value of the input voltage.
When equation 9 is substituted into equation 4, the sum of the stable variables in each equation is zero, and a small signal model can be proposed by ignoring the second-order infinite small term.
However, by simply analyzing equation 4, duty cycle D is one of the supports of all coefficient matrices, and it takes a lot of effort to perform Taylor expansion on these matrices, however, it does not have much impact on what needs to be emphasized and will be analyzed later.
Therefore, in order to simplify the equation of state space, it is assumed that the equivalent internal resistance of the capacitor [C]sub.
1] can be ignored, which means the term [R. sub.
C1] equal to zero.
Then [America]sub.
C1] is equal to [u. sub.
O] and the state space is-
Expressed as equation 10.
After simplification, the small signal model obtained is equation 11.
The input current [l] is obtained by carrying out a LA\'s transformation of equation 11. sub.
And small input voltage [u. sub.
And small output voltage [U. sub.
0] is expressed as equation 12.
[Non-reproducible mathematical expressions] (12) [non-reproducible mathematical expressions] (13) [non-reproducible mathematical expressions] (14) [non-reproducible mathematical expressions] (15) [Mathematical expression non-reproducible] (16) [Mathematical expression non-reproducible] (17) if the term [United States of America]sub.
When] (s) is 0, equation 12 becomes equation 13.
This is reasonable when the input voltage source of the DC/DC converter is an ideal device. The gain [G. sub.
Id] (s) is defined as the scale. sub. In (s) to d (s ). If the term [u. sub.
In] (s) equals--[R. sub. in][l. sub.
In] (s), equation 12 becomes equation 14.
This is reasonable when the input voltage source is not an ideal device and there is an internal resistor.
In fact, if the input source is lithium-
Ion battery, term [R. sub.
In] is a function of the angular frequency, which leads to the impedance spectrum of the battery, which is just the object of our work.
Although the word [R . ]sub.
In] represents the characteristic of the voltage source, and its only contribution can be considered mathematically as part of the internal resistance of the inductor.
In practical applications, the value of the load resistance R is much larger than the value of [R. sub.
In and [R. sub.
L1], that is, R [(1-D). sup. 2]>>[R. sub. L1]+[R. sub.
So even if the term [R. sub.
With the change of the angular frequency, it has little effect on the amplitude and phase of the gain [G]sub. id](s).
Gain [G] when the excitation frequency of the small signal duty cycle is close to zero or infinite. sub.
The id] (s) is described in Equation 15 ).
At other angular frequencies, the s = j [ω] = j2 [pi] f is substituted into equation 14 and another equation 16 is obtained.
The change trend of gain [G] amplitude is obtained. sub.
Id] (j2 [pi] f), first-
The maximum and minimum values can be solved as a sequential derivation of equation 17.
[Mathematical expressions cannot be reproduced] (18) [mathematical expressions cannot be reproduced] (19) [mathematical expressions cannot be reproduced] (20) conclusions can be drawn, the solution of equation 17 reaches the extreme value only when the frequency f approaches the critical value [f. sub.
C] The size of these parameters is described by Equation 18.
Equation 18 shows that the DC/DC converter continuously changes the frequency of a conventional circuit consisting of an inductor and capacitor by multiplying an invalid duty cycle.
At the critical frequency [f. sub.
C], the amplitude of the gain [G. sub.
Equation 19 describes id] (j2 [pi] f ).
Comparing equation 19 with equation 15, the derivation results of equation 20 are obtained.
[Non-reproducible mathematical expressions] (21) [non-reproducible mathematical expressions] (22) [non-reproducible mathematical expressions] (23) [non-reproducible mathematical expressions] (24) [Mathematical expression non-reproducible] (25) when designing a DC/DC converter, adhere to some of the basic principles described in equation 21 to ensure that the DC/DC converter works in continuous current mode, the ripple current and voltage are relatively small. The term [f. sub.
S represents the switching frequency.
Function Ratio ([f. sub.
C) increases in monotony as the variable [f] increases. sub. C].
If the function ratio ([f. sub.
C]) greater than 1, the following inequalities can be obtained when Equation 22 is established, and the solution of equation 23 can be obtained.
After converting equation 21 to a form close to equation 23, Equation 24 is obtained.
According to the principle of DC/DC converter, frequency [f. sub.
The output current signal must be lower than the switching frequency of the module [G. sub. 1].
When equation 25 is satisfied, the interference current signal will have a good signal-to-noise ratio.
Another key point based on the small signal model is that in each cycle of the current excitation signal, the more switching cycles are included, the better the quality of the current signal.
This paper assumes that equation 23 is satisfied.
Therefore, when the frequency is far from the critical point, the amplitude of the gain [G]sub.
As shown in figure 4, id] (j2 [pi] f) dropped significantly.
The gain function of the periodic disturbance current signal to the periodic fluctuation duty cycle is the basis for generating the target current signal by applying the DC/DC converter.
Since the critical frequency is lower than the switching frequency, it cannot be avoided that the critical frequency is within the relevant range of the impedance spectrum.
Therefore, near the critical frequency, the amplitude of the current disturbance signal will be very high, which may affect the stability of the converter control, which requires attention.
However, measures can be taken to change the critical frequency, such as adjusting the capacitor value online at an additional hardware cost based on the target current fluctuation signal.
Verification of DC/DC converter model in order to verify the exported small signal model of DC/DC converter
Loop control is used to adjust the duty cycle command.
To demonstrate the desired functionality of the converter, turn off-
Loop control is used to adjust the amplitude of the current excitation signal in an achievable frequency range.
The work is shown below.
The state-space equations of control algorithm design DC/DC converters are not complex, they are built from the perspective of an average model that does not pay much attention to the dynamic response during the switching cycle, because ripple current cannot be avoided.
The proposed control algorithm is shown in figure 5. The term[i. sub. in_ref], [D. sub. Model], [D. sub. PID], D and [i. sub.
In] represents the target input current of the DC/DC converter, via feed-
Forward Control, off-
Loop duty cycle calculated by PID controller, actual duty cycle of module [G]sub.
1] and the actual input current of the converter.
In order to ensure fast and dynamic, the model-
Based on nonlinear feedback
Calculate a stable target duty cycle using forward control.
Usually, feed
The forward control method has nothing to do with time, and it relies on the accuracy of the mathematical model by assuming that the dynamic term in the state space equation is zero.
When the accuracy is high enough, the error of the actual input current of the DC/DC converter from the target will be very small.
However, it is limited by the inaccurate physical model of the module [G. sub. 1] and diode [D. sub.
1] the PID controller is used to ensure the stable convergence of the controller to the target value.
According to the control theory, the step response of the PID controller always has some overtuning.
On the one hand, in order to reduce overtones, it will be at a disadvantage of slow dynamic response.
On the other hand, in order to achieve a fast dynamic response, it will sacrifice a large tune.
Therefore, the combination of the model-
Based on nonlinear feedback
Taking into account the dynamic response and static error, the forward and PID controllers are more acceptable.
In this way, the time constant of the pid controller can be a little longer.
The control system of the controller, like a micro-controller, is usually discrete, and the highest control frequency is the switching frequency of the module [G. sub. 1].
Of course, the PID controller is discrete.
In order to verify the function of the DC/DC converter, Matlab/Simulink is set up in the system, as shown in figure 6.
To simplify, the randles model is used to simulate the electrical properties of lithium, a common circuit in the field of electrochemistryionbattery.
The electronic load in the system is regarded as a constant current source, and this component needs to be controlled in the software, so a signal source is added as a control unit.
The model of frequency converter is established by using power electronic technology and passive components.
After considering the actual operation process, some other elements such as resistance [R] were placed. sub.
1] contactor [S. sub. 1] and [S. sub. 2].
Parameters for all components are shown in Table 1.
The internal resistance of the capacitors C and L is usually at the milliliters level described by the manufacturer.
The constant current generated by the controllable current source is 100 A and the equivalent voltage of the battery is 100 V.
According to the mathematical model and component parameters of the above DC/DC converter, the change of the theoretical amplitude of the gain function [G. sub.
As shown in Figure 7, the id with frequency is calculated and plotted] (2 [pi] f ).
The critical frequency is 145.
42Hz, the approximation based on equation 18 is 145.
28Hz, so the two values are very close to each other and the error is within 0. 1%.
In equation 18, the term [R. sub. L1] + [R. sub.
In] only for sum R [(1-D). sup. 2] +[R. sub. L1] + [R. sub.
When considering the size of the term [R]sub. L1] + [R. sub. in] and R[(1-D). sup. 2].
Therefore, this approximation makes sense for quickly finding critical frequencies with high accuracy.
In the derivation of the small signal model of the converter, in order to reduce the amount of computation, the internal resistance of the capacitor is assumed to be zero.
The rationality of the hypothesis is verified according to the system parameters, and the description is as follows.
In the effective matrix, the term [R. sub. C1][C. sub. 1]+[DRC. sub.
Exist in the rulers.
The term DR is about 10 [OMEGA] and [R. sup. C1] isjust 0.
001 [OMEGA], so the term [R. sub. C1][C. sub.
1] The impact is not big and can be ignored.
For example, the simulation process consists of five parts, as shown in Figure 9.
First, the current source starts drawing alinearly-
Increase the battery current, then the battery is stable on the target current for a period of time [S] of the contactorsub. 1]and [S. sub.
2] all closed.
No input current flows through the DC/DC converter.
The second is the contactor [S. sub.
1] on, the battery starts charging the inductor. sub.
1] and capacitor [C. sub.
1] and resistance R for a period of time.
Resistance r1 is used as a damping device to weaken the severe oscillation caused by serial inductor [L. sub.
1] and capacitor [C. sub.
But there is no way to avoid this oscillation.
Again, the duty cycle D of the contactor S, module [G. sub.
1] gradually increase until the input current of the converter reaches the target stability value of the fluctuation current signal superposition.
Fourth, after working for a period of time in the third part, the target of current signal fluctuation is increased, and the duty cycle d changes periodically.
Fifth, with the cancellation of the fluctuating current signal, the input current returns a stable value.
The stability value of the input current is 20 A, and the amplitude of the disturbance current signal is 2.
5 A, the frequency range is 0. 1Hz to 1k Hz.
Below, the current fluctuation signal at0.
1Hz, 10Hz, 100Hz, 200Hz, 500Hz, Hz and 1 k Hz are simulated and the results are given.
Another important thing to check is the ratio of the amplitude of the current fluctuation signal to the periodic amplitude
The changed duty cycle is consistent with the theoretical value calculated using the converter mathematical model.
Therefore, in the model built in Matlab/Simulink,
Loop feedback controller is invalid, only modelbased feed-
Realize forward control and view detailed current response of the converter.
In this way, the amplitude of the fluctuation duty cycle is almost the same in all frequency ranges.
Figure 10 shows the simulation results at 100Hz.
By performing fftoff on the current signal starting from 0. 5s to 0.
At 7 s, the calculated amplitude of the disturbance current signal is 10. 4 A.
The fluctuation range of duty cycle is about 0. 0315.
Then the ratio between the last two values is about 330.
The error between the simulation results and the theoretical results is about 7.
27% and the theoretical value is 307. 8.
Table 2 lists the results at different frequencies.
The results show that the theoretical gain ratio is close to the simulation value and the error is less than 8% in the wide frequency range.
The exception to 1 k Hz is that this frequency is only 10% of the switching frequency of the module [G. sub.
It uses only ten points to simulate a sine wave.
In addition, when considering the theoretical gain ratio, the ripple current is the same size as the fluctuating input current.
At the same time, when frequencies such as 100Hz and 200Hz surround the critical point, the analog amplitude of the input current is almost 50% of the stable value, which is far from the foundation of the small signal model.
However, the interference current signal can still be generated well, which proves the feasibility of the converter function.
In addition to the above three frequencies, the analog input current at most frequencies is about 2.
It is the control target of the converter.
In order to achieve the target current, the PI controller takes effect again, and the simulation results are as follows.
Based on these research results, the target current of the model-based feed-
The forward controller is adjusted according to the amplitude gain ratio at different frequencies.
It should be noted in practical application that the amplitude of the fluctuating duty cycle cannot be too large, resulting in the failure of the DC/DC converter, especially when the current changes are very drastic.
Figure 11 shows the simulation results of the battery output current and voltage at 100Hz frequency.
For simplicity, only the waveform of the fourth part described in Figure 9 is shown, and the filtered output current is also included.
It can be seen that the stable output current of the battery is combined with the fluctuating current, and there is a corresponding voltage response in the stable output voltage.
In order to calculate the impedance, FFT technology is applied and the results are listed in Table 3.
Figure 12 shows the simulation results at 10Hz frequency.
For convenience, a specific output signal at these frequencies is not displayed here.
Table 3 also lists the calculated impedance at 10Hz and other frequencies.
The data show that the DC/DC converter can be well controlled to inject a sine current signal into the battery.
Experimental verification of the system function in the experiment, LiMn [O. sub.
2] 5 Series 35 Ahparalleled batteries and 24 series batteries were selected as the subjects of study.
The battery capacity is 175Ah and the nominal voltage is 100 volts.
Table 1 lists the parameters of the DC/DC converter.
The electronic load BTS600 from Digatron power electronics corporation acts as a constant current load and the current extracted from the battery is 75a.
Another electronic load of ITECs operates in constant resistance mode with a value of 20 [ω] when the experiment starts, the initial charging state of the battery is about 75%, then about 55% when the AC impedance recognition experiment is activated.
The ambient temperature is about 23 degrees.
Compare the theoretical gain amplitude with the experimental results, set the target duty cycle calculated offline based on the mathematical model in the micro-controller unit, and control the output of pwm to DC/DC converter through appearance
Table for duty cycle.
The duty cycle organizes asEquation 26 in the following form, and the fluctuation range of the duty cycle is 7.
38% of the stability value satisfies the hypothesis of the small signal model.
[Mathematical expression non-reproducible] (26) [Mathematical expression non-reproducible] (27) stable input current of the converter at D = 0.
With an input voltage of 592 V and a converter efficiency of 100, 100% is about 30 Aon.
The input current will be reduced to 27 A when the efficiency is only 90%.
In addition, when the input voltage is also reduced to 90 volts, the input current will be reduced to about 24.
This can be explained by Equation 27, and the term [eta] represents efficiency.
The measured steady current is 25. 7 A.
The experiment was performed at frequencies of 1000Hz, 500Hz, 200Hz, 100Hz, 40Hz, 10Hz, and 6. 4Hz and 1Hz.
With the help of the embedded signal analyzer, the actual signal of the current is sampled and the stable current is filtered to extract the weak and changing parts.
The phase offset and amplitude attenuation caused by the analyzer need to be calibrated.
In terms of the actual parameters of the analyzer, only high-
The pass filter should be compensated, and the other parts of the analyzer have little effect on the amplitude.
Gain amplitude at 200Hz with a value of 245.
712 is designated as a standard, and for simplicity, the ratio of other frequencies is calculated only in this paper.
The current signals obtained at these frequencies are shown in Figure 13 and Figure 14.
At most frequency points, in addition to the 1Hz frequency with a sample number of 500, the number of samples for the micro-controller unit is 400.
The frequency is 0.
The target frequency range from 1 hz to less than 10Hz is 2Hz, the range from 10Hz to less than 100Hz is 2Hz, and the range from 100Hz to 1 k Hz is 20Hz.
The comparison between the experimental results and the theoretical results is shown in Table 4.
The experimental results are calculated with ffttechnology.
The THD (total harmonic distortion) value is defined as the ratio of the root values of all frequencies other than the base frequency values and the root values of all frequencies.
It can be found that the error of only 1000Hz and 500Hz is within 7%, and the error is greater than 20%.
The reason is based on the predefined amplitude 0.
Only when the theoretical gain amplitude is less than 60, the fluctuation duty cycle of 0437 will get the amplitude of the disturbance current signal less than 2.
5 A, only 10% of the stable current.
It is clear that the gain amplitude at other frequencies is much larger than 60.
When the frequency is lower than 40Hz, the error is kept at about 24%, and the gain amplitude is almost unchanged in this frequency range.
However, when a frequency such as 100Hz and 200Hz approaches a critical frequency of 118.
At 62Hz, the error becomes very significant and dominates the nonlinear properties of the converter.
Although there is an error between the experimental and theoretical results, the total harmonic distortion value of most frequency points is less than 5%.
As for the THD values of 1 k Hz and 500Hz, this is generated by the basic principle of the converter, and the switching frequency is only 10 k Hz.
In order to produce a sine wave with a high signal-to-noise ratio, the target frequency should be far away from the switching frequency, which is easy to understand.
The relatively low THD values demonstrate the feasibility of the signal analyzer and the feasibility of injecting a sine current signal into the battery using a converter.
Although the amplitude of the measured fluctuating current is greater than 2 at most frequencies.
5 A, all of which are below 10 A, which is in line with the basic assumptions for conducting an AC impedance recognition method.
AC impedance recognition results the measured current and voltage of the signal analyzer after filtration at 10Hz and 100Hz are shown in Figure 15 and Figure 16.
It can be seen that the fluctuating current signal is well injected into the battery, and the signal analyzer is able to measure the voltage response of the battery.
The period of these signals is very certain, and the noise does not have much effect on the quality of the target signal.
For the correct selection of shunt resistors, the conversion voltage signal of the current is the same as the voltage response of each single battery.
In this way, when calculating the impedance, the transfer function of the signal analyzer can be omitted, because the transfer function exists in the measurement of the voltage and current of the single battery at the same time.
Current fluctuation signal in 500 hz, 400Hz, 320Hz, 200Hz, 100Hz, 80Hz, 64Hz, 50Hz, 40Hz, 32Hz of frequency under, 20Hz, 10Hz, 8Hz, 6.
4Hz, 5Hz, 4Hz.
When the frequency is higher than 500Hz, the current changes too fast and the power semiconductor cannot tolerate it.
When the frequency is lower than 4Hz, it takes a long time to collect these signals, and the internal state of the battery changes, so the measured impedance is very dispersed.
Figure 17 shows the measured AC impedance of batteries 9, 14, 16 and 22, respectively.
Zview test software is used to fit the experimental data. the equivalent circuit is a circuit with aWarburg components.
The fitting line is compared with the experimental data, and the experimental data is consistent with the fitting line to a certain extent. The non-
The uniformity of these single cells can be seen from this figure.
Summary/conclusion the focus of this work is to identify the AC impedance of lithium
Through a DC/DC converter in parallel with the battery output, the ion battery is online.
The main function of the DC/DC converter is to inject fluctuating current signals into the battery while the battery is working.
The working principle of the boost DC/DC converter is analyzed and the average state space equation is established.
It is found that the converter is completely controllable, but it can be partially observed.
Based on the average state space equation, a small signal model is derived to calculate the gain function of the fluctuation current signal relative to the fluctuation duty cycle of the converter.
When the frequency increases from zero to the switching frequency of the power semiconductor, there is a resonance frequency in this gain function, and attention should be paid to avoid running around the resonance frequency.
The equivalent circuit model and controller model of the battery are then established in Matlab/Simulink to verify the state space equation.
The simulation results show that the possibility of applying this converter to identify the AC impedance within a wide frequency range that the converter can withstand.
After the functional verification of the system, the converter was designed and the lithium-
Ion batteries with high voltage and high current.
The fluctuating current signal and the voltage response of the single cell are measured using a signal analyzer.
The biggest obstacle is to extract weak AC signals from important DC signals and solve this problem by implementing special signal processing circuits.
Measure the AC impedance of a single battery and install it into the equivalent circuit model of the battery.
The experimental results also show that
Uniformity of each single cell.
Therefore, the converter can be used online to identify the AC impedance of lithium
The proposed method is feasible.
On this basis, research methods for estimating other parameters of batteries can be enriched, especially in practical applications, such as in transportation systems.
The future work is to refine the signal quality and optimize the control algorithm of the controller. References(1.
) Felix Christian, Waag Wladislaw, Hahn Hans-
\"Martin, soldek Uve ,\"
Line adaptive battery impedance parameters and state estimation considering the physical principle of reduced-order equivalent circuit battery model: Part 1 requirements, key reviews of methods and modeling.
Power magazine, 260 (2014): 276-291. (2.
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See KhayWai, \"fading Kalman filter-based real-
Estimated time status of lithium ion battery charging
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Ion battery based on battery impedance model.
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Moynot Valerie, \"develop an empirical aging model for Li-
Ion batteries and applications to evaluate vehicle impactto-
Power grid strategy for battery life.
Energy application, 172 (2016): 398-407. (5.
) Waag Wladislaw, sauitz Stefan, saudirk Uwe, \"Experimental study of lithium
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J. van LamellenP. M. Lammers,M. J. G. , \"Sensor-
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Power magazine, 247 (2014): 539-544. (7.
) Feng xunning, Sun Jing, Ouyang Minggao and he Xiangming, \"the representation of large-format lithium-ion batteries exposed to extremely high temperature \".
Power magazine, 272 (2014): 457-467. (8.
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) Schmidt, January, Philip, Arnold Stefan, Logan Andre, Weiner Daniel, \"measurement of temperature inside the cell: evaluation and application of a new method.
Power magazine, 243 (2013): 110-117. (15.
) Monet Mohammed Abdul, Trad Heem, Omar noshen, Haji Omar, \"Lithium-
Ion batteries: Evaluation study of different charging methods based on aging process.
Energy application, 152 (2015): 143-155. (16.
) Waag Wladislaw, Fleischer Christian, saudirk Uwe, \"online estimation of lithium
Ion battery impedance parameters using a new variable parameter
Parameter method.
Journal of Energy, 237 (2013): 260-269. (17. ) Li J. , Jia B. , Mazzola M. , Xin M. , \"On-
Line batterystate with Gaussian-estimated charge
Hermite orthogonal filter.
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Battery SOC and capacity estimation.
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, \"Adaptive trace-free kalmanfilter for charge state estimation of lithium-
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) Depernet Daniel, Ba Oumar, Berthon Alain, \"online impedance spectrum of lead-acid batteries for storage management in independent power plants.
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1088,2010, doi: 10. 4271/2010-01-1088.
Contact Information Dr. Hong KongD.
State Key Laboratory of automotive safety and energy, Department of Automotive Engineering, Tsinghua University, Haidian district, Beijing, Room 213, China Hong p09 @ 163.
The work was funded by the National Natural Science Foundation of China (China National Natural Science Foundation)
No. 51576113 and U1564209 are approved by the Ministry of Science and Technology of China.
No, no.
There is no dfg71590.
205bag06b01, Z02-by independent research program-
Tsinghua University awarded No. 1
20151080411 and national key laboratory of automotive safety and energyZZ2014-034.
Pu Hong, Hong Liangjiang, Jian Qiuli, Xu liangfei and minggaogou Yangzhong University all have: 10. 4271/2017-01-
Due to features such as high energy density [1] [2] and low emissions, lithium-ion batteries have received worldwide attention, and lithium-ion batteries have been used in a variety of applications, such as packaging in battery electric vehicles and hybrid electric vehicles [3] [4.
Electrical impedance mirror, abbreviated as EIS, it has been widely used in lithium-ion battery studies related to aging status and its impact on applications and temperature estimation and expansion [5] [6] [7.
The principle of the EIS method is that at certain frequencies, a small voltage or current signal is superimposed on the battery, and then after the voltage and current signals are obtained at the same time, the two signals can be passed.
The EIS method has three basic assumptions, namely, linear, Casualty, and stability [8].
The linearity of the battery is ensured by controlling the magnitude of the increased current or voltage fluctuation signal.
Casualties are obvious because the corresponding signal cannot be measured without increasing the excitation signal.
Stability means that the system can return to normal when the added signal is removed, which is satisfied.
Under normal circumstances, the impedance acquisition of the battery can be divided into two categories, namely, the impedance measurement method and the online estimation method.
The impedance measurement method depends on the experimental equipment. After measurement, it is important to estimate the physical parameters of the battery.
The impedance properties of the battery depend on the battery conditions such as the state of charge, the temperature, the current, and the history of the final previous [5] [9] [10].
The charging state of the battery has a high impedance change in this frequency range, so the impedance-
[11] a methodology-based approach is proposed.
The relationship between physical parameters and impedance spectra can be established by equivalent circuit models such as randles model and transmission line model [12] [13.
In [14], it is said that the real part of the battery impedance is related to the battery temperature, and the sensitivity analysis shows that for the low frequency, the impedance varies greatly with the temperature.
The effect of charging method on battery life was studied, and the battery was characterized by using EIS method [15], and a comparative study between charging techniques was introduced.
The online estimation method of impedance parameters takes into account the significant changes in battery properties during life due to aging [16.
In this set, the filter technique is a commonly used method, which is a recursive estimator for [15.
Based on the equivalent circuit model [17], a single filter can be used to estimate the charging status of the battery.
To take into account the non-linearity in the battery model, an advanced version of Kalmanfilter, such as an extended filter or a sigmapoint filter, is adopted.
Some recent publications have taken into account the non-linearity between the charging state and the open-circuit voltage [18] [19] [20.
Although great progress has been made in impedance acquisition, the application of these methods in actual battery packs is limited in many ways.
Impedance measurement requires expensive laboratory equipment, which cannot be borne in the actual system.
Online estimation requires a large number of calculations, including matrix operations and implementation on a common low level
The cost micro-controller is actually difficult to achieve.
In addition, complex matrix operations can lead to numerical instability of [16.
Therefore, the combination of the online measurement of impedance and the online estimation method will be very meaningful.
In order to achieve this goal, the first thing that needs to be done is to design the equipment used for impedance online measurement.
However, there are not many known literature in this regard.
[21] The study in proposes a solution that uses a power converter to motivate the battery at any operating point for impedance spectrum, which is performed by the control system without additional power hardware
The limitation of this method is that the output current of the battery is much smaller than the actual current of the vehicle battery pack.
Similar work for online impedance measurement can also be found in the field of hydrogen polymer electrolyte membrane fuel cell systems.
[22] The vehicle fuel cell AC impedance measurement system is proposed and passed on-
The function of the system has been verified.
However, in addition to the key frequency points where the excitation frequency is 300Hz, no more information is provided about the controllable high voltage DC/DC converter.
Power converters do not exist in all applications
Therefore, a New Impedance measurement method is proposed in this paper, which produces a wide range of frequencies, and the method is suitable for various battery systems without increasing the cost of the system.
To this end, the topology of the impedance measurement system is given, including a power converter for excitation signal generation and a unit voltage monitoring device for obtaining the signal and calculating the impedance.
The average state space equation of the power converter is derived to check the controllable and observable nature of the converter\'s target input current.
Based on these state-space equations, a small signal model is derived to calculate the gain amplitude of the fluctuating current signal relative to the unique control variable, that is, the duty cycle of the power semiconductor PWM.
This helps design control algorithms and allows validation of the proposed system topology.
By establishing the model of power system in Matlab/Simulink, the function of the system is verified.
After designing the power converter, experiments were carried out on the high-power lim2 battery and the feasibility of the converter\'s online impedance measurement was verified in a wide frequency range.
The organization of the paper is as follows.
The second section introduces the system structure and mathematical model of the power converter in detail.
Then, the function of the system is verified according to the gain amplitude of the excitation current signal, and the calculated impedance is compared with the theoretical equivalent circuit model in Section III.
Subsequently, the power converter and battery voltage monitor were designed and implemented into a high-power battery pack, and validation of the converter model and on-line impedance measurement was obtained in section 4.
Section V concludes.
Starting with the system model, the system configuration is described, including DC/DC converters, lithium-
Ion battery pack and load.
Then there\'s a hot drawing of lithium.
Ion batteries and converters have been introduced.
On-line AC impedance recognition system with lithium configuration
As shown in Figure 1, the Ion battery consists of lithium-
Ion battery assembly with BMS (battery management system), battery voltage monitor, sequencer, electronic load and DC/DC converter, and power consumption resistance. The lithium-
The ion battery pack of BMS is considered to be a voltage source for DC/DC converters and electronic loads.
BMS helps monitor the normal operating status of batterypack, which provides information such as temperature, charging status, and health status.
The electronic load is controlled to draw constant current from the battery pack, like a constant current receiver.
Typically, a DC/DC converter is a power conversion device, but in this system it is implemented to generate a current excitation signal that will be superimposed on the battery pack.
This current signal is the sum of the sine current part and the DC part because the input current of the converter cannot be lower than zero.
The controller of the converter is responsible for the implementation of the function.
Because the power conversion of the DC/DC converter is not effectively utilized, but only generates heat, the operation time should be as short as possible, and if used in the actual system, the DC part should be as low as possible.
To measure the voltage of each battery, a battery voltage monitor was developed.
The shunt resistor measures the output current of batterypack and converts the current signal to a voltage signal that can be amplified by the battery voltage monitor.
Combined with battery voltage monitoring and shunt resistance, the output voltage and current of each battery can be obtained at the same time. after recording these signals, the impedance spectrum can be calculated using FFT technology.
Unlike the traditional analog signal processing circuit, the unit voltage monitor must be able to extract weak fluctuation signals from large DC current and voltage at a stable operating point.
On the basis of battery voltage monitoring and DC/DC converter, the work of this paper can proceed smoothly. Lithium-
When studying the electrical impedance spectrum, the Ion battery model,
Ion batteries are considered to be linear systems around their operating points.
In order to adapt to the impedance spectrum, many equivalent circuits have been tried, with two commonly used models, the randles model and the model with Warburg elements, as shown in Figure 2 () figure 2 (B) is shown ). The term [E. sub.
N] is the nerster voltage based on thermodynamics and term [R. sub.
M] is the sum of contact resistance, internal ion transfer resistance, and wire resistance. The term [R. sub.
C] refers to the faradic resistance and terminology at the electro-chemical interface [C]sub.
D1] indicates a double-layer capacitor.
When considering the limited proliferation process,
The double-layer capacitor inside the battery is replaced with the Warburg element [Z. sub. w].
DC/DC converter modeling as shown in Figure 3 (a), DC/DC converter is a general purpose boostconverter consisting of an inductor [L]sub.
1], switching power supply-
Semiconductor module [G. sub. 1], a diode [D. sub.
1] and a capacitor [C. sub. 1].
Resistance [R. sub. L1] and [R. sub.
1C] is considered to be a parasitic power consumption similar to the inductor [L]sub.
1] and capacitor [C. sub. 1] respectively. The turn-on and turn-
Power failure of module [G]sub.
1] and diode [D. sub.
1] are all included in the resistor [R. sub.
Because these processes are complex, there is, in fact, no exact equation that can be used to describe them quantitatively.
The resistor R represents the load requirement of the converter.
The control converter injects a fluctuating current signal into the battery pack.
The fluctuating current signal can be any waveform, but in order to ensure a high signal-to-noise ratio, the sine current interference signal is selected as the target waveform.
In the case of inherent limitations of the DC/DC converter, the frequency of the interference signal is expanded as widely as possible, one of which is the switching frequency of the module [G]sub.
1], the full range of spectrum is realized.
The principle of DC/DC converter is based on pulse width modulation (PWM), and duty cycle D and switching frequency are two key parameters of PWM.
When the module [G. sub.
As shown in Figure 3 (B), the converter works in one way and the equation of state is described by Equation 1.
When the module [G. sub.
1] as shown in Figure 3 (c), the converter works in another way, and the equation of state is described by Equation 2.
[Mathematical expression non-reproducible] (1) [Mathematical expression non-reproducible] (2) [Mathematical expression non-reproducible] (3) where [U. sub.
In] = input voltage of the converter [I. sub.
In] = input current of Converter [usub.
O] = output voltage of Converter [sub.
C1] = voltage on the capacitor [C. sub.
After considering the duty cycle D, the average state equation is deduced as Equation 3. The re-
Equation 4 describes the equations of arrangement in order to obtain input variables X, state variables U, and output variables iin, as well as corresponding coefficient matrices A, B, C, and T.
[Mathematical expressions cannot be reproduced] (4) the state space equation can be described by Equation 5 according to equation 4, and all variables and coefficient matrices can be described by Equation 6.
[Mathematical expression non-reproducible] (5) [Mathematical expression non-reproducible] (6) the controllable matrix Q is described by Equation 7, and the observable matrix R is described by Equation 8.
It is easy to find that this system is completely controllable but not observable because of the theoretical voltagesub.
C1 of capacitor [C. sub.
1] is not measurable.
For DC/DC converters, the directly adjustable parameter is the duty cycle. to achieve the generation of periodic current waves, a small signal model of DC/DC converters needs to be established first.
Then analyze the amplitude gain of the cycle current signal relative to the cycle change around its stability value, which helps to better understand the system properties in this special application.
[Non-reproducible mathematical expressions] (7) [non-reproducible mathematical expressions] (8) [non-reproducible mathematical expressions] (9) [non-reproducible mathematical expressions] (10) (11) to derive the small signal model, the small dynamic signal is added to all relevant parameters and variables as Equation 9. The term[l. sub.
Compared to the stable value [L], in] represents a dynamic signal with a small amplitudesub. in]. The term [u. sub. 0], [u. sub. C1], d and[u. sub.
In] are dynamic small signals of output voltage, capacitor voltage, duty cycle and input voltage, respectively.
At the same time terms [Americansub. o], [U. sub. C1], [D. sub. 0] and [U. sub.
In] represents the corresponding output voltage, capacitor voltage, duty cycle, and stability value of the input voltage.
When equation 9 is substituted into equation 4, the sum of the stable variables in each equation is zero, and a small signal model can be proposed by ignoring the second-order infinite small term.
However, by simply analyzing equation 4, duty cycle D is one of the supports of all coefficient matrices, and it takes a lot of effort to perform Taylor expansion on these matrices, however, it does not have much impact on what needs to be emphasized and will be analyzed later.
Therefore, in order to simplify the equation of state space, it is assumed that the equivalent internal resistance of the capacitor [C]sub.
1] can be ignored, which means the term [R. sub.
C1] equal to zero.
Then [America]sub.
C1] is equal to [u. sub.
O] and the state space is-
Expressed as equation 10.
After simplification, the small signal model obtained is equation 11.
The input current [l] is obtained by carrying out a LA\'s transformation of equation 11. sub.
And small input voltage [u. sub.
And small output voltage [U. sub.
0] is expressed as equation 12.
[Non-reproducible mathematical expressions] (12) [non-reproducible mathematical expressions] (13) [non-reproducible mathematical expressions] (14) [non-reproducible mathematical expressions] (15) [Mathematical expression non-reproducible] (16) [Mathematical expression non-reproducible] (17) if the term [United States of America]sub.
When] (s) is 0, equation 12 becomes equation 13.
This is reasonable when the input voltage source of the DC/DC converter is an ideal device. The gain [G. sub.
Id] (s) is defined as the scale. sub. In (s) to d (s ). If the term [u. sub.
In] (s) equals--[R. sub. in][l. sub.
In] (s), equation 12 becomes equation 14.
This is reasonable when the input voltage source is not an ideal device and there is an internal resistor.
In fact, if the input source is lithium-
Ion battery, term [R. sub.
In] is a function of the angular frequency, which leads to the impedance spectrum of the battery, which is just the object of our work.
Although the word [R . ]sub.
In] represents the characteristic of the voltage source, and its only contribution can be considered mathematically as part of the internal resistance of the inductor.
In practical applications, the value of the load resistance R is much larger than the value of [R. sub.
In and [R. sub.
L1], that is, R [(1-D). sup. 2]>>[R. sub. L1]+[R. sub.
So even if the term [R. sub.
With the change of the angular frequency, it has little effect on the amplitude and phase of the gain [G]sub. id](s).
Gain [G] when the excitation frequency of the small signal duty cycle is close to zero or infinite. sub.
The id] (s) is described in Equation 15 ).
At other angular frequencies, the s = j [ω] = j2 [pi] f is substituted into equation 14 and another equation 16 is obtained.
The change trend of gain [G] amplitude is obtained. sub.
Id] (j2 [pi] f), first-
The maximum and minimum values can be solved as a sequential derivation of equation 17.
[Mathematical expressions cannot be reproduced] (18) [mathematical expressions cannot be reproduced] (19) [mathematical expressions cannot be reproduced] (20) conclusions can be drawn, the solution of equation 17 reaches the extreme value only when the frequency f approaches the critical value [f. sub.
C] The size of these parameters is described by Equation 18.
Equation 18 shows that the DC/DC converter continuously changes the frequency of a conventional circuit consisting of an inductor and capacitor by multiplying an invalid duty cycle.
At the critical frequency [f. sub.
C], the amplitude of the gain [G. sub.
Equation 19 describes id] (j2 [pi] f ).
Comparing equation 19 with equation 15, the derivation results of equation 20 are obtained.
[Non-reproducible mathematical expressions] (21) [non-reproducible mathematical expressions] (22) [non-reproducible mathematical expressions] (23) [non-reproducible mathematical expressions] (24) [Mathematical expression non-reproducible] (25) when designing a DC/DC converter, adhere to some of the basic principles described in equation 21 to ensure that the DC/DC converter works in continuous current mode, the ripple current and voltage are relatively small. The term [f. sub.
S represents the switching frequency.
Function Ratio ([f. sub.
C) increases in monotony as the variable [f] increases. sub. C].
If the function ratio ([f. sub.
C]) greater than 1, the following inequalities can be obtained when Equation 22 is established, and the solution of equation 23 can be obtained.
After converting equation 21 to a form close to equation 23, Equation 24 is obtained.
According to the principle of DC/DC converter, frequency [f. sub.
The output current signal must be lower than the switching frequency of the module [G. sub. 1].
When equation 25 is satisfied, the interference current signal will have a good signal-to-noise ratio.
Another key point based on the small signal model is that in each cycle of the current excitation signal, the more switching cycles are included, the better the quality of the current signal.
This paper assumes that equation 23 is satisfied.
Therefore, when the frequency is far from the critical point, the amplitude of the gain [G]sub.
As shown in figure 4, id] (j2 [pi] f) dropped significantly.
The gain function of the periodic disturbance current signal to the periodic fluctuation duty cycle is the basis for generating the target current signal by applying the DC/DC converter.
Since the critical frequency is lower than the switching frequency, it cannot be avoided that the critical frequency is within the relevant range of the impedance spectrum.
Therefore, near the critical frequency, the amplitude of the current disturbance signal will be very high, which may affect the stability of the converter control, which requires attention.
However, measures can be taken to change the critical frequency, such as adjusting the capacitor value online at an additional hardware cost based on the target current fluctuation signal.
Verification of DC/DC converter model in order to verify the exported small signal model of DC/DC converter
Loop control is used to adjust the duty cycle command.
To demonstrate the desired functionality of the converter, turn off-
Loop control is used to adjust the amplitude of the current excitation signal in an achievable frequency range.
The work is shown below.
The state-space equations of control algorithm design DC/DC converters are not complex, they are built from the perspective of an average model that does not pay much attention to the dynamic response during the switching cycle, because ripple current cannot be avoided.
The proposed control algorithm is shown in figure 5. The term[i. sub. in_ref], [D. sub. Model], [D. sub. PID], D and [i. sub.
In] represents the target input current of the DC/DC converter, via feed-
Forward Control, off-
Loop duty cycle calculated by PID controller, actual duty cycle of module [G]sub.
1] and the actual input current of the converter.
In order to ensure fast and dynamic, the model-
Based on nonlinear feedback
Calculate a stable target duty cycle using forward control.
Usually, feed
The forward control method has nothing to do with time, and it relies on the accuracy of the mathematical model by assuming that the dynamic term in the state space equation is zero.
When the accuracy is high enough, the error of the actual input current of the DC/DC converter from the target will be very small.
However, it is limited by the inaccurate physical model of the module [G. sub. 1] and diode [D. sub.
1] the PID controller is used to ensure the stable convergence of the controller to the target value.
According to the control theory, the step response of the PID controller always has some overtuning.
On the one hand, in order to reduce overtones, it will be at a disadvantage of slow dynamic response.
On the other hand, in order to achieve a fast dynamic response, it will sacrifice a large tune.
Therefore, the combination of the model-
Based on nonlinear feedback
Taking into account the dynamic response and static error, the forward and PID controllers are more acceptable.
In this way, the time constant of the pid controller can be a little longer.
The control system of the controller, like a micro-controller, is usually discrete, and the highest control frequency is the switching frequency of the module [G. sub. 1].
Of course, the PID controller is discrete.
In order to verify the function of the DC/DC converter, Matlab/Simulink is set up in the system, as shown in figure 6.
To simplify, the randles model is used to simulate the electrical properties of lithium, a common circuit in the field of electrochemistryionbattery.
The electronic load in the system is regarded as a constant current source, and this component needs to be controlled in the software, so a signal source is added as a control unit.
The model of frequency converter is established by using power electronic technology and passive components.
After considering the actual operation process, some other elements such as resistance [R] were placed. sub.
1] contactor [S. sub. 1] and [S. sub. 2].
Parameters for all components are shown in Table 1.
The internal resistance of the capacitors C and L is usually at the milliliters level described by the manufacturer.
The constant current generated by the controllable current source is 100 A and the equivalent voltage of the battery is 100 V.
According to the mathematical model and component parameters of the above DC/DC converter, the change of the theoretical amplitude of the gain function [G. sub.
As shown in Figure 7, the id with frequency is calculated and plotted] (2 [pi] f ).
The critical frequency is 145.
42Hz, the approximation based on equation 18 is 145.
28Hz, so the two values are very close to each other and the error is within 0. 1%.
In equation 18, the term [R. sub. L1] + [R. sub.
In] only for sum R [(1-D). sup. 2] +[R. sub. L1] + [R. sub.
When considering the size of the term [R]sub. L1] + [R. sub. in] and R[(1-D). sup. 2].
Therefore, this approximation makes sense for quickly finding critical frequencies with high accuracy.
In the derivation of the small signal model of the converter, in order to reduce the amount of computation, the internal resistance of the capacitor is assumed to be zero.
The rationality of the hypothesis is verified according to the system parameters, and the description is as follows.
In the effective matrix, the term [R. sub. C1][C. sub. 1]+[DRC. sub.
Exist in the rulers.
The term DR is about 10 [OMEGA] and [R. sup. C1] isjust 0.
001 [OMEGA], so the term [R. sub. C1][C. sub.
1] The impact is not big and can be ignored.
For example, the simulation process consists of five parts, as shown in Figure 9.
First, the current source starts drawing alinearly-
Increase the battery current, then the battery is stable on the target current for a period of time [S] of the contactorsub. 1]and [S. sub.
2] all closed.
No input current flows through the DC/DC converter.
The second is the contactor [S. sub.
1] on, the battery starts charging the inductor. sub.
1] and capacitor [C. sub.
1] and resistance R for a period of time.
Resistance r1 is used as a damping device to weaken the severe oscillation caused by serial inductor [L. sub.
1] and capacitor [C. sub.
But there is no way to avoid this oscillation.
Again, the duty cycle D of the contactor S, module [G. sub.
1] gradually increase until the input current of the converter reaches the target stability value of the fluctuation current signal superposition.
Fourth, after working for a period of time in the third part, the target of current signal fluctuation is increased, and the duty cycle d changes periodically.
Fifth, with the cancellation of the fluctuating current signal, the input current returns a stable value.
The stability value of the input current is 20 A, and the amplitude of the disturbance current signal is 2.
5 A, the frequency range is 0. 1Hz to 1k Hz.
Below, the current fluctuation signal at0.
1Hz, 10Hz, 100Hz, 200Hz, 500Hz, Hz and 1 k Hz are simulated and the results are given.
Another important thing to check is the ratio of the amplitude of the current fluctuation signal to the periodic amplitude
The changed duty cycle is consistent with the theoretical value calculated using the converter mathematical model.
Therefore, in the model built in Matlab/Simulink,
Loop feedback controller is invalid, only modelbased feed-
Realize forward control and view detailed current response of the converter.
In this way, the amplitude of the fluctuation duty cycle is almost the same in all frequency ranges.
Figure 10 shows the simulation results at 100Hz.
By performing fftoff on the current signal starting from 0. 5s to 0.
At 7 s, the calculated amplitude of the disturbance current signal is 10. 4 A.
The fluctuation range of duty cycle is about 0. 0315.
Then the ratio between the last two values is about 330.
The error between the simulation results and the theoretical results is about 7.
27% and the theoretical value is 307. 8.
Table 2 lists the results at different frequencies.
The results show that the theoretical gain ratio is close to the simulation value and the error is less than 8% in the wide frequency range.
The exception to 1 k Hz is that this frequency is only 10% of the switching frequency of the module [G. sub.
It uses only ten points to simulate a sine wave.
In addition, when considering the theoretical gain ratio, the ripple current is the same size as the fluctuating input current.
At the same time, when frequencies such as 100Hz and 200Hz surround the critical point, the analog amplitude of the input current is almost 50% of the stable value, which is far from the foundation of the small signal model.
However, the interference current signal can still be generated well, which proves the feasibility of the converter function.
In addition to the above three frequencies, the analog input current at most frequencies is about 2.
It is the control target of the converter.
In order to achieve the target current, the PI controller takes effect again, and the simulation results are as follows.
Based on these research results, the target current of the model-based feed-
The forward controller is adjusted according to the amplitude gain ratio at different frequencies.
It should be noted in practical application that the amplitude of the fluctuating duty cycle cannot be too large, resulting in the failure of the DC/DC converter, especially when the current changes are very drastic.
Figure 11 shows the simulation results of the battery output current and voltage at 100Hz frequency.
For simplicity, only the waveform of the fourth part described in Figure 9 is shown, and the filtered output current is also included.
It can be seen that the stable output current of the battery is combined with the fluctuating current, and there is a corresponding voltage response in the stable output voltage.
In order to calculate the impedance, FFT technology is applied and the results are listed in Table 3.
Figure 12 shows the simulation results at 10Hz frequency.
For convenience, a specific output signal at these frequencies is not displayed here.
Table 3 also lists the calculated impedance at 10Hz and other frequencies.
The data show that the DC/DC converter can be well controlled to inject a sine current signal into the battery.
Experimental verification of the system function in the experiment, LiMn [O. sub.
2] 5 Series 35 Ahparalleled batteries and 24 series batteries were selected as the subjects of study.
The battery capacity is 175Ah and the nominal voltage is 100 volts.
Table 1 lists the parameters of the DC/DC converter.
The electronic load BTS600 from Digatron power electronics corporation acts as a constant current load and the current extracted from the battery is 75a.
Another electronic load of ITECs operates in constant resistance mode with a value of 20 [ω] when the experiment starts, the initial charging state of the battery is about 75%, then about 55% when the AC impedance recognition experiment is activated.
The ambient temperature is about 23 degrees.
Compare the theoretical gain amplitude with the experimental results, set the target duty cycle calculated offline based on the mathematical model in the micro-controller unit, and control the output of pwm to DC/DC converter through appearance
Table for duty cycle.
The duty cycle organizes asEquation 26 in the following form, and the fluctuation range of the duty cycle is 7.
38% of the stability value satisfies the hypothesis of the small signal model.
[Mathematical expression non-reproducible] (26) [Mathematical expression non-reproducible] (27) stable input current of the converter at D = 0.
With an input voltage of 592 V and a converter efficiency of 100, 100% is about 30 Aon.
The input current will be reduced to 27 A when the efficiency is only 90%.
In addition, when the input voltage is also reduced to 90 volts, the input current will be reduced to about 24.
This can be explained by Equation 27, and the term [eta] represents efficiency.
The measured steady current is 25. 7 A.
The experiment was performed at frequencies of 1000Hz, 500Hz, 200Hz, 100Hz, 40Hz, 10Hz, and 6. 4Hz and 1Hz.
With the help of the embedded signal analyzer, the actual signal of the current is sampled and the stable current is filtered to extract the weak and changing parts.
The phase offset and amplitude attenuation caused by the analyzer need to be calibrated.
In terms of the actual parameters of the analyzer, only high-
The pass filter should be compensated, and the other parts of the analyzer have little effect on the amplitude.
Gain amplitude at 200Hz with a value of 245.
712 is designated as a standard, and for simplicity, the ratio of other frequencies is calculated only in this paper.
The current signals obtained at these frequencies are shown in Figure 13 and Figure 14.
At most frequency points, in addition to the 1Hz frequency with a sample number of 500, the number of samples for the micro-controller unit is 400.
The frequency is 0.
The target frequency range from 1 hz to less than 10Hz is 2Hz, the range from 10Hz to less than 100Hz is 2Hz, and the range from 100Hz to 1 k Hz is 20Hz.
The comparison between the experimental results and the theoretical results is shown in Table 4.
The experimental results are calculated with ffttechnology.
The THD (total harmonic distortion) value is defined as the ratio of the root values of all frequencies other than the base frequency values and the root values of all frequencies.
It can be found that the error of only 1000Hz and 500Hz is within 7%, and the error is greater than 20%.
The reason is based on the predefined amplitude 0.
Only when the theoretical gain amplitude is less than 60, the fluctuation duty cycle of 0437 will get the amplitude of the disturbance current signal less than 2.
5 A, only 10% of the stable current.
It is clear that the gain amplitude at other frequencies is much larger than 60.
When the frequency is lower than 40Hz, the error is kept at about 24%, and the gain amplitude is almost unchanged in this frequency range.
However, when a frequency such as 100Hz and 200Hz approaches a critical frequency of 118.
At 62Hz, the error becomes very significant and dominates the nonlinear properties of the converter.
Although there is an error between the experimental and theoretical results, the total harmonic distortion value of most frequency points is less than 5%.
As for the THD values of 1 k Hz and 500Hz, this is generated by the basic principle of the converter, and the switching frequency is only 10 k Hz.
In order to produce a sine wave with a high signal-to-noise ratio, the target frequency should be far away from the switching frequency, which is easy to understand.
The relatively low THD values demonstrate the feasibility of the signal analyzer and the feasibility of injecting a sine current signal into the battery using a converter.
Although the amplitude of the measured fluctuating current is greater than 2 at most frequencies.
5 A, all of which are below 10 A, which is in line with the basic assumptions for conducting an AC impedance recognition method.
AC impedance recognition results the measured current and voltage of the signal analyzer after filtration at 10Hz and 100Hz are shown in Figure 15 and Figure 16.
It can be seen that the fluctuating current signal is well injected into the battery, and the signal analyzer is able to measure the voltage response of the battery.
The period of these signals is very certain, and the noise does not have much effect on the quality of the target signal.
For the correct selection of shunt resistors, the conversion voltage signal of the current is the same as the voltage response of each single battery.
In this way, when calculating the impedance, the transfer function of the signal analyzer can be omitted, because the transfer function exists in the measurement of the voltage and current of the single battery at the same time.
Current fluctuation signal in 500 hz, 400Hz, 320Hz, 200Hz, 100Hz, 80Hz, 64Hz, 50Hz, 40Hz, 32Hz of frequency under, 20Hz, 10Hz, 8Hz, 6.
4Hz, 5Hz, 4Hz.
When the frequency is higher than 500Hz, the current changes too fast and the power semiconductor cannot tolerate it.
When the frequency is lower than 4Hz, it takes a long time to collect these signals, and the internal state of the battery changes, so the measured impedance is very dispersed.
Figure 17 shows the measured AC impedance of batteries 9, 14, 16 and 22, respectively.
Zview test software is used to fit the experimental data. the equivalent circuit is a circuit with aWarburg components.
The fitting line is compared with the experimental data, and the experimental data is consistent with the fitting line to a certain extent. The non-
The uniformity of these single cells can be seen from this figure.
Summary/conclusion the focus of this work is to identify the AC impedance of lithium
Through a DC/DC converter in parallel with the battery output, the ion battery is online.
The main function of the DC/DC converter is to inject fluctuating current signals into the battery while the battery is working.
The working principle of the boost DC/DC converter is analyzed and the average state space equation is established.
It is found that the converter is completely controllable, but it can be partially observed.
Based on the average state space equation, a small signal model is derived to calculate the gain function of the fluctuation current signal relative to the fluctuation duty cycle of the converter.
When the frequency increases from zero to the switching frequency of the power semiconductor, there is a resonance frequency in this gain function, and attention should be paid to avoid running around the resonance frequency.
The equivalent circuit model and controller model of the battery are then established in Matlab/Simulink to verify the state space equation.
The simulation results show that the possibility of applying this converter to identify the AC impedance within a wide frequency range that the converter can withstand.
After the functional verification of the system, the converter was designed and the lithium-
Ion batteries with high voltage and high current.
The fluctuating current signal and the voltage response of the single cell are measured using a signal analyzer.
The biggest obstacle is to extract weak AC signals from important DC signals and solve this problem by implementing special signal processing circuits.
Measure the AC impedance of a single battery and install it into the equivalent circuit model of the battery.
The experimental results also show that
Uniformity of each single cell.
Therefore, the converter can be used online to identify the AC impedance of lithium
The proposed method is feasible.
On this basis, research methods for estimating other parameters of batteries can be enriched, especially in practical applications, such as in transportation systems.
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Contact Information Dr. Hong KongD.
State Key Laboratory of automotive safety and energy, Department of Automotive Engineering, Tsinghua University, Haidian district, Beijing, Room 213, China Hong p09 @ 163.
The work was funded by the National Natural Science Foundation of China (China National Natural Science Foundation)
No. 51576113 and U1564209 are approved by the Ministry of Science and Technology of China.
No, no.
There is no dfg71590.
205bag06b01, Z02-by independent research program-
Tsinghua University awarded No. 1
20151080411 and national key laboratory of automotive safety and energyZZ2014-034.
Pu Hong, Hong Liangjiang, Jian Qiuli, Xu liangfei and minggaogou Yangzhong University all have: 10. 4271/2017-01-
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