The power batteries serving as the power supply for electric vehicles (EVs) have direct effects on the overall performance of EVs, and the battery overcharge may cause overheating or even an explosion, while the battery over-discharge may result in accelerated aging and permanently reduced capacity [1
]. Concerning the issues of safety usage, the state estimation of batteries available for safety precautions can facilitate the elimination of safety hazards, which means the state of charge (SOC) and state of health (SOH) joint estimation is of great significance for the research on power batteries [2
Lots of scholars have proposed many SOC estimation methods, such as the open circuit voltage method [3
], the Coulomb counting method [5
], the neural network method [6
] and the Kalman filtering algorithm [7
]. Among them, the open circuit voltage method was to first establish a corresponding function of the open circuit voltage and the SOC and then obtain the SOC by measuring the open circuit voltage after the battery was stationary [8
]; the Coulomb integral method, which discretizes the current flowing through the battery and sums it up, and obtains the SOC value by simple division [9
]; the neural network method optimizes the relevant parameters of the SOC estimation algorithm and solves complex abstract problems through autonomous learning [7
]; a series of Kalman filtering algorithms based on the extended Kalman filtering algorithm optimize autoregressive data processing, which can make the optimal estimation in the minimum variance sense for the state of the dynamic system [10
The estimation methods in the SOH are mainly divided into two categories: One is to start with the characteristic parameters of the battery, and the other is to analyze the aging characteristics and electrochemical reaction characteristics of the battery [12
]. The former mainly uses the direct measurement method, obtaining the current SOH by obtaining aging characteristic parameters such as capacity and ohmic internal resistance [8
]. There are also methods such as neural networks [14
] and fuzzy logic [15
], which can directly estimate the SOH of the battery through data training without an a priori model. The latter uses an electrochemical model method [12
] that models the internal physical and chemical reactions during the charging process and designs an estimator for SOH estimation. There is also a method based on an equivalent circuit model [16
] that establishes a circuit that reflects internal variables for SOH estimation.
All of the above algorithms are only a single estimate for the SOC or the SOH, ignoring the close relationship between the SOC and the SOH. The SOC estimate is affected by battery aging—as the battery ages, inaccurate SOC estimates can affect the SOH correction. Therefore, a joint estimate of the SOC and the SOH is necessary. The literature proposes an online SOH estimation method for the lithium battery using the constant-voltage (CV) charge current, as proposed in reference document [17
], which can ensure the estimation error of less than 2.5%. However, it is difficult to accurately estimate the true state of the lithium battery by merely estimating the value of the SOH. Another SOC and SOH joint estimation method applicable to the cycle life of lithium-ion batteries for EVs, as proposed in reference document [18
], involves an SOC and SOH identification using offline state estimators with different time scales; this requires substantial data to ensure asymptotic convergence without the real-time update.
Reference document [19
] analyzed the error sources from the four angles of measurement, model, algorithm and state parameters for the SOC estimation. Finally, the author put forward new concerns in the practical application of SOC estimation. A multi-time-scale observer of the SOC and the SOH for a lithium-ion battery with coupled fast and slow dynamics was proposed in the reference document [16
]. The authors used a deterministic transformation of the extended Kalman filter. The paper made an effective estimation of the SOC and the SOH by strictly characterizing the stability of estimation error. Three model-based filtering algorithms [20
] were used to estimate the SOC, and the tracking accuracy, calculation time, robustness, etc., were analyzed and compared. Experimental results showed the advantages of three algorithms; the unscented Kalman filtering (UKF) algorithm has a good stability and the Particle filter (PF) algorithm, in the early stage has extreme rapidity. This article gave a combination of the two algorithms to improve the accuracy of the research direction.
In this paper, full consideration was given to the estimation error caused by the change in ohmic resistance during the service of power batteries, and the constant ohmic resistance was replaced by that of gentle variations resistance so as to propose a joint estimation algorithm of the power battery SOC and SOH based on a fuzzy control trace-free Kalman filter. This algorithm uses two complete fuzzy unscented Kalman filtering (F-UKF) algorithms to estimate the SOC and ohmic resistance of the battery at the same time. First of all, the use of a fuzzy controller can effectively reduce the impact of observation noise under complex conditions and to further improve the accuracy of battery SOC estimation. Secondly, the fuzzy controller is used to make a real-time correction of the variance matrix of the observed noise so as to finally realize the estimation of the battery ohmic internal resistance; experiments show that the joint estimation algorithm is not affected by the initial value of SOC, and it still has good convergence speed and tracking accuracy under complex conditions.
The rest of this paper is organized as follows: Section 2
introduces the model of lithium battery, open circuit voltage, SOC calibration experiment, and parameter identification. Section 3
reviews the implementation method of traceless Kalman filtering, fully considers the intrinsic coupling relationship between the SOC and the SOH, puts forward the fuzzy and traceless Kalman filter algorithm on the basis of traceless Kalman filtering, and uses two F-UKF algorithms to estimate the SOC and ohmic internal resistance at the same time. Section 4
discusses the relevant experimental process and conclusions, and Section 5
summarizes the full text.
4. Experimental Verification and Result Analysis
The ITS5300-based battery test platform available to verify the proposed SOC and SOH joint estimation algorithm is shown in Figure 8
. The nominal capacity of a single lithium iron phosphate battery is 40 Ah, and the corresponding performance parameters are shown in Table 3
. In order to measure the terminal voltage and working current of the battery, the software of IT9320 battery test system (ITECH ELECTRONIC CO., LTD, Nanjing, China) was used to simulate the discharge conditions with constant-current pulses and the urban dynamometer driving schedule (UDDS) driving cycles, and the MATLAB software was adopted for the simulation verification and analysis of the joint estimation algorithm proposed in this paper.
4.1. Sensitivity Verification of the F-UKF Algorithm against Initial Values
Concerning the estimation of the battery SOC and ohmic resistance using the F-UKF algorithm, it was difficult to obtain the accurate initial values of battery SOC, but the values of ohmic resistance were relatively stable without violent fluctuations. The lithium iron phosphate battery was charged until the battery SOC reached 85% of the initial state before the experiment. Under the discharge conditions with constant-current pulses, the different initial values of the battery SOC were set to verify the F-UKF sensitivity against initial values. In the MATLAB software, the respective initial values of the SOC were set to 40%/0% and 85% for the F-UKF algorithm and the ampere-hour integration method, with the sampling period and discharge rate set to 1 s and 0.5 C (20 A) for the 500-second simulation experiment.
The simulations under discharge conditions with constant-current pulses shown in Figure 9
and Figure 10
indicate that the different initial values of battery SOC converged to the vicinity of reference value after a period of filtering iteration. Though the greater deviation of SOC initial values resulted in a longer convergence time, the stabilized values could follow the reference value well, and the estimation error was extremely small. Therefore, the F-UKF algorithm proposed in this paper is insensitive to the initial values.
4.2. Joint Simulation Verification of UDDS Driving Cycles
The lithium iron phosphate battery was charged until the battery SOC reached 85% of the initial state before the experiment.
The software of IT9320 battery test system was used to compile the pulse current driving cycles before the acquisition of terminal voltage and working current from UDDS driving cycles. In the MATLAB software, the initial values of SOC were set to 80% for the F-UKF and joint estimation algorithms and 85% for the ampere-hour integration method, respectively. The initial value of ohmic resistance was set to 1.50 mΩ for the joint estimation algorithm, which was greater than the reference value of 1.278 mΩ.
The simulations of UDDS driving cycles shown in Figure 11
indicate that the convergence time of SOC from the initial 80% to the vicinity of reference value based on the F-UKF algorithm was about 170 s, while the UKF algorithm was about 185 s. The SOC estimation error of the F-UKF algorithm after convergence could be controlled within 2.82%, while the estimation error of the UKF algorithm was about 2.93%. Since the noise of UKF was random white noise, the F-UKF algorithm that introduces adaptive technology was to adjust the noise instead of eliminating the noise. It can be seen that the convergence performance of the F-UKF algorithm was not only better than the UKF algorithm, but the estimation accuracy was also relatively improved in complex conditions.
The simulations of UDDS driving cycles shown in Figure 12
a indicate that the convergence time of SOC from the initial 80% to the vicinity of reference value based on the F-UKF algorithm was about 170 s, while the corresponding convergence time with an increased rising velocity based on the joint estimation algorithm was about 120 s. Therefore, the convergence performance of the joint estimation algorithm was better than that of the F-UKF algorithm under complex conditions. Figure 12
b shows that the respective SOC estimation errors of the F-UKF algorithm and the joint estimation algorithm after convergence were less than 2.82% and 1.76%. Therefore, the tracking performance of the joint estimation algorithm was better than that of the F-UKF algorithm in terms of the SOC estimation.
The simulations of UDDS driving cycles shown in Figure 13
and Figure 14
indicate that the convergence time of ohmic resistance from 1.50 mΩ to the vicinity of reference value (1.278 mΩ) based on the joint estimation algorithm was about 140 s, and the corresponding battery SOH was about 89.87% of the reference value after stabilization. Figure 15
shows that the maximum SOH estimation error based on the joint estimation algorithm was 1.61%, and the SOH estimation error was less than 1.20% over time.