TW202036018A - Multi-stage constant current charging method for optimizing output current value using the optimal output current value to charge after the optimal output current value is obtained - Google Patents
Multi-stage constant current charging method for optimizing output current value using the optimal output current value to charge after the optimal output current value is obtained Download PDFInfo
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Abstract
Description
本發明係關於二次電池充電之方法,特別是一種基於多階段定電流充電法之二次電池充電之方法。 The present invention relates to a method for charging a secondary battery, in particular to a method for charging a secondary battery based on a multi-stage constant current charging method.
全球暖化及溫室效應加劇,使再生能源與電動車輛的開發與應用成為必然趨勢,由於這些系統的發展需要大量設置電池儲能與電能轉換管理系統,使得二次電池的製造材料技術、充電平衡技術、和電能轉換與管理技術發展備受矚目。 Global warming and the intensification of the greenhouse effect have made the development and application of renewable energy and electric vehicles an inevitable trend. Because the development of these systems requires a large number of battery energy storage and power conversion management systems, the manufacturing material technology and charge balance of secondary batteries The development of technology, power conversion and management technology has attracted much attention.
隨著二次電池相關技術的進步,二次電池已普遍應用於手機、筆記型電腦和平板電腦等產品中。在二次電池當中,鋰離子因具有高能量密度、循環壽命長、體積輕巧、無記憶效應、平均工作電壓高及自放電率低等特點,所以能成為二次電池中的主流。另外,許多大電力儲能系統也開始投入大容量鋰離子電池的研究與發展。 With the advancement of secondary battery-related technologies, secondary batteries have been widely used in products such as mobile phones, notebook computers, and tablet computers. Among the secondary batteries, lithium ion can become the mainstream of secondary batteries due to its high energy density, long cycle life, light weight, no memory effect, high average working voltage and low self-discharge rate. In addition, many large power storage systems have also begun to invest in the research and development of large-capacity lithium-ion batteries.
近十幾年來具有相對優異特性的鋰離子電池已經成為行動裝置電源的首選,電動車的動力電池和再生能源發電系統用之儲能裝置也是以配置鋰電池為主。目前也被大量應用於3C電子產品、再生能源發電儲能系統、電動車等需高壓高功率產業,因此鋰電池的應用與需求量逐年提升。 In the past ten years, lithium-ion batteries with relatively excellent characteristics have become the first choice for power sources for mobile devices. The power batteries of electric vehicles and the energy storage devices used in renewable energy power generation systems are also mainly equipped with lithium batteries. At present, it is also widely used in 3C electronic products, renewable energy power generation and energy storage systems, electric vehicles and other industries that require high voltage and high power. Therefore, the application and demand for lithium batteries are increasing year by year.
二次電池為求輕、薄致使電池容量受到限制,因此快速充電技術變得十分重要,然而為了追求快速充電而用大電流充電,將使二次電池的溫升遽增、電池循環壽命將減短。溫升對電池來說非常重要,充電時溫升過高除了有發生爆炸之安全顧慮以外,也會造成電池加速老化、電池組之間電量不平衡、容量衰退、和循環壽命減短等問題。上述老化之現象係因為在較高的操作電流下,電化學反應過度激烈,引起電池內阻逐漸變大所致。此外,如能讓串聯的電池組內每節電池之電量隨時維持均等,則電池組會有更多的充放電循環次數, 便能延長內建電池式行動裝置之使用時間,進而提升行動裝置的壽命與使用率。 The battery capacity of the secondary battery is limited in order to be lighter and thinner. Therefore, fast charging technology becomes very important. However, the high current charging in pursuit of fast charging will increase the temperature rise of the secondary battery and reduce the battery cycle life. short. Temperature rise is very important for batteries. Excessive temperature rise during charging may cause problems such as accelerated aging of the battery, imbalance between battery packs, capacity decline, and shortened cycle life. The above-mentioned aging phenomenon is caused by the excessively intense electrochemical reaction at a higher operating current, which causes the internal resistance of the battery to gradually increase. In addition, if the power of each battery in the battery pack in series can be maintained at any time, the battery pack will have more charge and discharge cycles. It can extend the use time of the built-in battery-type mobile device, thereby increasing the life and usage rate of the mobile device.
因此,充電技術對二次電池來說十分重要。充電技術關係到二次電池之充電速度、充電效率、電池溫升值,電池循環壽命等因素,目前最普遍被使用的鋰電池充電法為定電流定電壓充電法(Constant Current Constant Voltage,CC-CV),CC-CV充電一開始係使用定電流充電直到電池之額定上限電壓後,再使用額定上限電壓對電池進行充電,此時充電電流會因為電池端電壓與內電壓之差逐漸下降,當電流下降至額定截止電流時即為充飽。此方法之優點為簡單容易實現,缺點為充電時間較久。 Therefore, charging technology is very important for secondary batteries. The charging technology is related to the charging speed, charging efficiency, battery temperature rise, battery cycle life and other factors of the secondary battery. The most commonly used lithium battery charging method is the constant current constant voltage charging method (Constant Current Constant Voltage, CC-CV). ), CC-CV charging starts with constant current charging until the battery's rated upper limit voltage, and then uses the rated upper limit voltage to charge the battery. At this time, the charging current will gradually decrease due to the difference between the battery terminal voltage and the internal voltage. It is fully charged when it drops to the rated cut-off current. The advantage of this method is that it is simple and easy to implement, but the disadvantage is that the charging time is longer.
因此許多文獻提出改良之充電方法。有文獻利用雙迴路控制,使用正、負回授控制電池電壓,可以得到與CC-CV相似的充電曲線,且不需使用電流感測器,故較CC-CV充電法簡單且成本更低;有文獻提出一開始使用高於電池上限額定電壓(如4.3V)進行充電之升壓式定電流-定電壓充電法,在高定電壓週期過後切換至定電流定電壓充電法,此法能在短時間將電池充至額定容量的30%,所以充電時間較短,但缺點為充電前電池必須完全放電;亦有文獻提出主動式充電狀態結合模糊控制充電法及灰預測控制電池充電系統,可在相同時間內充入較多的電量;或有文獻提出以鎖相迴路控制為基礎的充電法,參考相位與輸出相位比較後產生相位誤差,誤差之相位會傳送到電流源去產生適合的電流對電池充電;為了改善鎖相迴路在定電壓模式的缺點,尚有文獻提出電流泵電池充電器,定電流模式時使用電流泵充電,而定電壓模式則使用脈衝電流充電。 Therefore, many documents propose improved charging methods. There are documents that use dual-loop control and use positive and negative feedback to control the battery voltage, which can obtain a charging curve similar to CC-CV, and does not need to use a current sensor, so it is simpler and lower in cost than the CC-CV charging method; Some literature proposes a step-up constant current-constant voltage charging method that initially uses a higher rated voltage of the battery (such as 4.3V) for charging, and then switches to the constant current and constant voltage charging method after the high constant voltage period. This method can be used in Charge the battery to 30% of the rated capacity in a short time, so the charging time is shorter, but the disadvantage is that the battery must be fully discharged before charging; there are also documents that propose active charging state combined with fuzzy control charging method and gray predictive control battery charging system. Charge more power in the same time; or some literature proposes a charging method based on phase-locked loop control, the reference phase is compared with the output phase to produce a phase error, and the error phase is transmitted to the current source to generate a suitable current Charge the battery; in order to improve the shortcomings of the phase-locked loop in the constant voltage mode, there are documents that propose a current pump battery charger, which uses current pump charging in the constant current mode, and uses pulse current charging in the constant voltage mode.
有文獻提出使用(0,1)-整數線性規劃(Integer Linear Programming,ILP)搜尋多階段電流及定電壓模式之最佳電池充電曲線;亦有文獻提出以智慧演算法決定多階段定電流充電法各階段之充電電流;或有文獻提出以電池模型為基礎之最佳化多階段充電法,其優點為用簡單數學運算決定充電時間為最短的充電電流,缺點為無法優化其他因素如充電損失、充電效率等;又有文獻透過改變電流大小和脈衝寬度及脈衝間的休息週期使充電的方法有多種變化;尚 有文獻提出模糊五階段鋰離子電池充電法,並使用田口方法來決定模糊控制之歸屬函數,藉此優化充電方法之性能表現。 Some literature proposes to use (0,1)-Integer Linear Programming (ILP) to search for the best battery charging curve for multi-stage current and constant voltage modes; some literature proposes to use smart algorithms to determine the multi-stage constant current charging method The charging current of each stage; or some literature proposes an optimized multi-stage charging method based on the battery model. Its advantage is that it uses simple mathematical calculations to determine the charging time as the shortest charging current. The disadvantage is that it cannot optimize other factors such as charging loss, Charging efficiency, etc.; there are also documents that change the charging method by changing the current size and pulse width and the rest period between pulses; Some literature proposes a fuzzy five-stage lithium-ion battery charging method, and uses Taguchi method to determine the attribution function of fuzzy control, thereby optimizing the performance of the charging method.
然而上述文獻皆需進行多次實際實驗以找出最佳化電流設定,因此本領域亟需一新穎的二次電池之充電方法。 However, the above-mentioned documents all require multiple actual experiments to find the optimal current setting. Therefore, a novel method for charging the secondary battery is urgently needed in the art.
本發明之一目的在於揭露一種最佳化輸出電流值之多階段定電流充電法,其係透過交流阻抗分析以建立電池等效模型,同時考量充電損失與充電時間,並利用粒子群演算法找尋有限區域中之最佳解,藉此實現最小化充電損失與時間之最佳化多階段充電法。 One purpose of the present invention is to disclose a multi-stage constant current charging method for optimizing the output current value, which uses AC impedance analysis to establish a battery equivalent model, while considering the charging loss and charging time, and uses the particle swarm algorithm to find The best solution in a limited area, thereby realizing an optimized multi-stage charging method that minimizes charging loss and time.
本發明之另一目的在於揭露一種最佳化輸出電流值之多階段定電流充電法,係利用粒子群演算法尋找最佳化充電電流設定值,僅需使用電池等效模型,而具有不需進行多次耗時費工之實際實驗即能得到最佳化電流設定之優點。 Another object of the present invention is to disclose a multi-stage constant current charging method for optimizing the output current value. The particle swarm algorithm is used to find the optimized charging current setting value. It only needs to use the battery equivalent model and has no need The advantages of optimized current setting can be obtained by carrying out many time-consuming and labor-intensive actual experiments.
本發明之再一目的在於揭露一種最佳化輸出電流值之多階段定電流充電法,於階段截止電壓為4.22V時,能將電池容量充至習知技術之CC-CV充電法之98%以上,且在溫升沒增加之前提下,充電時間能縮短22.77%,充電效率改善0.43%。 Another object of the present invention is to disclose a multi-stage constant current charging method that optimizes the output current value. When the stage cut-off voltage is 4.22V, the battery capacity can be charged to 98% of the conventional CC-CV charging method. Above, and before the temperature rise does not increase, the charging time can be shortened by 22.77%, and the charging efficiency can be improved by 0.43%.
為達前述目的,一種最佳化輸出電流值之多階段定電流充電法乃被提出,其係利用一控制電路實現,該充電法包括以下步驟:依一粒子群演算法初始化複數階段之各充電電流值I charge,s 及一階段截止電壓值V T (步驟a);對所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T 進行一運算以獲得一總充電時間T及一充電總損失,該運算包括:
其中,s為階段數,C eq 為電池之等效電容,R o 為電池串聯阻抗,R p 為電池並聯阻抗,V Ceq,s 為各階段之電池內電壓,L carge,s 為各階段之充電電流(步驟b);依一目前之總充電時間及充電總損失(T now ,L now )與一理想之總充電時間及充電總損失(T min ,L min )利用一適應值函數進行運算(步驟c);更新所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T 之一個別最佳值與一群體最佳值,以決定是否獲得一最佳輸出電流值(步驟d);以及應用該最佳之輸出電流值進行充電,再回到步驟b重複執行(步驟e)。 Among them, s is the number of stages, C eq is the equivalent capacitance of the battery, R o is the battery series impedance, R p is the battery parallel impedance, V Ceq,s is the battery voltage in each stage, and L carge,s is the battery Charging current (step b); according to a current total charging time and total charging loss ( T now , L now ) and an ideal total charging time and total charging loss ( T min , L min ), use a fitness function to calculate (Step c); update each of the charging current values I charge, s of the plurality of stages and one of the stage cut-off voltage values V T for an individual optimal value and a group optimal value to determine whether to obtain an optimal output current Value (step d); and apply the best output current value for charging, and then return to step b and repeat (step e).
在一實施例中,其中該適應值函數包括:
其中,α為權重值。 Among them, α is the weight value.
在一實施例中,該權重值α為0.5。 In an embodiment, the weight value α is 0.5.
在一實施例中,其中進一步包括利用一等效阻抗之擬合函數進行運算以確保電池內電壓不超過一預設之額定電壓,該等效阻抗之擬合函數包括:
在一實施例中,該預設之額定電壓為4.2V。 In one embodiment, the preset rated voltage is 4.2V.
在一實施例中,所述複數階段為5階段。 In one embodiment, the plural stages are 5 stages.
為使 貴審查委員能進一步瞭解本發明之結構、特徵及其目的,茲附以圖式及較佳具體實施例之詳細說明如後。 In order to enable your reviewer to further understand the structure, features and purpose of the present invention, drawings and detailed descriptions of preferred specific embodiments are attached as follows.
步驟a‧‧‧依一粒子群演算法初始化複數階段之各充電電流值I charge,s 及一階段截止電壓值V T Step a‧‧‧Initialize the charge current value I charge, s and the first-stage cut-off voltage value V T of the complex number stage according to a particle swarm algorithm
步驟b‧‧‧對所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T 進行一運算以獲得一總充電時間T及一充電總損失 Step b‧‧‧ Perform an operation on each charge current value I charge, s of the complex number stage and the stage cut-off voltage value V T to obtain a total charge time T and a total charge loss
步驟c‧‧‧依一目前之總充電時間及充電總損失(T now ,L now )與一理想之總充電時間及充電總損失(T min ,L min )利用一適應值函數進行運算 Step c‧‧‧Using a fitness function to perform calculations based on a current total charging time and total charging loss ( T now , L now ) and an ideal total charging time and total charging loss ( T min , L min )
步驟d‧‧‧更新所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T 之一個別最佳值與一群體最佳值,以決定是否獲得一最佳輸出電流值 Step d‧‧‧Update the respective optimal value of each charge current value I charge, s and the stage cut-off voltage value V T of the plurality of stages and a group optimal value to determine whether to obtain an optimal output current value
步驟e‧‧‧以及應用該最佳之輸出電流值進行充電,再回到步驟b重複執行 Step e‧‧‧ and apply the best output current value for charging, then go back to step b and repeat
圖1繪示本案之最佳化輸出電流值之多階段定電流充電法之步驟流程圖。 Fig. 1 shows the flow chart of the multi-stage constant current charging method with optimized output current value in this case.
圖2繪示習知技術之多階段定電流充電法之充電示意圖。 Fig. 2 shows a charging schematic diagram of the conventional multi-stage constant current charging method.
圖3繪示戴維寧電池等效模之示意圖。 Figure 3 shows a schematic diagram of an equivalent model of Thevenin battery.
圖4繪示電池之交流阻抗特性示意之奈氏圖。 Figure 4 shows a Nyquist diagram showing the AC impedance characteristics of the battery.
圖5繪示交流阻抗分析實驗系統之設置示意圖。 Figure 5 shows a schematic diagram of the setup of the AC impedance analysis experimental system.
圖6繪示不同剩餘容量之奈奎斯特阻抗圖。 Figure 6 shows the Nyquist impedance diagram for different remaining capacities.
圖7a繪示測得的串聯阻抗(R o )、並聯阻抗(R p )與等效阻抗(R eq )對電池剩餘容量百分比之關係曲線圖。 Figure 7a shows the measured series impedance ( R o ), parallel impedance ( R p ) and equivalent impedance ( R eq ) as a function of the percentage of battery remaining capacity.
圖7b繪示測得的測得的並聯電容(C p )對電池剩餘容量百分比之關係曲線圖。 Fig. 7b shows a graph of the relationship between the measured parallel capacitance ( C p ) and the percentage of remaining battery capacity.
圖7c繪示測得的開路電壓(V oc )對電池剩餘容量百分比之關係曲線圖。 Fig. 7c illustrates the relationship between the measured open circuit voltage ( V oc ) and the percentage of remaining battery capacity.
圖8繪示粒子群演算法之粒子在解空間移動之示意圖。 Figure 8 shows a schematic diagram of particles moving in the solution space of the particle swarm algorithm.
圖9繪示本案之電池剩餘容量(SOC)與等效阻抗(R eq )之擬合關係曲線圖。 FIG. 9 shows a curve diagram of the fitting relationship between the remaining battery capacity (SOC) and the equivalent impedance ( R eq ) of this case.
圖10繪示本案之適應值函數之定義示意圖。 Figure 10 shows the definition diagram of the fitness function in this case.
圖11繪示粒子群在空間移動軌跡之示意圖。 Fig. 11 is a schematic diagram showing the trajectory of particle swarms in space.
圖12繪示本案之實驗平台架構之示意圖。 Figure 12 shows a schematic diagram of the experimental platform architecture of this case.
圖13繪示習知技術之定電流定電壓充電法之電流、電壓實測波形圖。 Figure 13 shows the measured current and voltage waveforms of the conventional constant current and constant voltage charging method.
圖14繪示本案於階段截止電壓(VT=4.22V)之電流、電壓實測波形圖。 Figure 14 shows the measured current and voltage waveforms of the cut-off voltage (V T =4.22V) in this case.
請參照圖1,其繪示本案之最佳化輸出電流值之多階段定電流充電法之步驟流程圖。 Please refer to FIG. 1, which shows the flow chart of the multi-stage constant current charging method for optimizing the output current value of this case.
如圖所示,本案之最佳化輸出電流值之多階段定電流充電法,其係利用一控制電路實現,該充電法包括以下步驟:依一粒子群演算法初始化複數階段之各充電電流值I charge,s 及一階段截止電壓值V T ;(步驟a);對所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T
進行一運算以獲得一總充電時間T及一充電總損失,該運算包括:
其中,s為階段數,C eq 為電池之等效電容,R o 為電池串聯阻抗,R p 為電池並聯阻抗,V Ceq,s 為各階段之電池內電壓,I charge,s 為各階段之充電電流;(步驟b);依一目前之總充電時間及充電總損失(T now ,L now )與一理想之總充電時間及充電總損失(T min ,L min )利用一適應值函數進行運算;(步驟c);更新所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T 之一個別最佳值與一群體最佳值,以決定是否獲得一最佳輸出電流值;(步驟d);以及應用該最佳之輸出電流值進行充電,再回到步驟b重複執行;(步驟e)。 Where s is the number of stages, C eq is the equivalent capacitance of the battery, R o is the battery series impedance, R p is the battery parallel impedance, V Ceq, s is the battery voltage in each stage, I charge, s is the battery Charging current; (step b); based on a current total charging time and total charging loss ( T now , L now ) and an ideal total charging time and total charging loss ( T min , L min ), using a fitness function Operation; (Step c); Update the individual best value of each charge current value I charge, s and the phase cutoff voltage value V T of the complex number stage and a group best value to determine whether to obtain an optimal value Output current value; (step d); and apply the best output current value for charging, and then return to step b to repeat the execution; (step e).
該適應值函數包括:
其中,α為權重值,該權重值α例如但不限於為0.5。 Wherein, α is a weight value, and the weight value α is, for example, but not limited to 0.5.
其進一步包括利用一等效阻抗之擬合函數進行運算以確保電池內電壓不超過一預設之額定電壓,該等效阻抗之擬合函數包括:
該預設之額定電壓例如但不限於為4.2V;所述複數階段例如但不限於為5階段。 The preset rated voltage is, for example, but not limited to 4.2V; the plurality of stages is, for example, but not limited to, 5 stages.
以下將針對本案之原理進行說明:請參照圖2,其繪示習知技術之多階段定電流(Multi-Stage Constant Current,MSCC)充電法之充電示意圖。 The principle of this case will be explained as follows: Please refer to FIG. 2, which shows a charging diagram of the conventional multi-stage constant current (Multi-Stage Constant Current, MSCC) charging method.
如圖所示,多階段定電流充電法進行充電時,當電池電壓達到上限額定電壓4.2V時電流會切換到下一階段,然後使用小於上一階段的充電電流繼續充電。多階段定電流充電法之充電時間較短且電池溫升低,故可增加電池 的循環壽命。由於電池內部電化學特性相當複雜,因此難以使用習知技術得到最佳化充電電流,習知技術使每階段之充電電流能達到最佳化之方法,如使用模糊控制法係以充電時的電池溫升作為模糊控制的輸入,經過模糊控制計算後,輸出充電電流;或使用田口方法(Taguchi Methods,TM)來尋找最佳的充電電流;或使用蟻群系統(Ant colony system,ACS)求取最佳化充電電流。然而由於上述方法均需複雜運算,必須藉由電腦來實現。 As shown in the figure, when the multi-stage constant current charging method is used for charging, when the battery voltage reaches the upper limit rated voltage 4.2V, the current will switch to the next stage, and then continue to charge with a charging current smaller than the previous stage. The charging time of the multi-stage constant current charging method is shorter and the battery temperature rise is low, so the battery can be increased Cycle life. Because the internal electrochemical characteristics of the battery are quite complicated, it is difficult to use the conventional technology to optimize the charging current. The conventional technology can optimize the charging current at each stage, such as using the fuzzy control method to charge the battery Temperature rise is used as the input of fuzzy control, after fuzzy control calculation, output charging current; or use Taguchi Methods (TM) to find the best charging current; or use Ant colony system (ACS) to obtain Optimize charging current. However, since the above methods all require complex calculations, they must be implemented by computers.
鋰離子電池等效模型:Lithium ion battery equivalent model:
建立正確電池等效模型有利於實驗之分析,由於電池內部化學材料的影響會使得其輸出電壓隨使用時間增加而下降。因此,一個精確的電池等效模型必須考量自放電現象、電池內阻及暫態響應等因素。 Establishing a correct battery equivalent model is conducive to the analysis of the experiment, because the battery's internal chemical materials will cause its output voltage to drop with the increase of use time. Therefore, an accurate battery equivalent model must consider factors such as self-discharge, battery internal resistance, and transient response.
請參照圖3,其繪示戴維寧電池等效模之示意圖。 Please refer to FIG. 3, which shows a schematic diagram of an equivalent model of Thevenin battery.
如圖所示,該模型與線性電池模型不同處在於增加一組並聯電容(C p )及並聯阻抗(R p ),因為能藉由C p 與R p 模擬電池的動態響應,而在模擬電池之充放電時較為逼真,本案將以此模型來推導多階段定電流充電法之最佳化充電模式。 As shown in the figure, the difference between this model and the linear battery model is the addition of a set of parallel capacitors ( C p ) and parallel impedance ( R p ), because the dynamic response of the battery can be simulated by C p and R p , and the battery is simulated The charging and discharging process is more realistic. This case will use this model to derive the optimal charging mode of the multi-stage constant current charging method.
接著推導多階段定電流充電法之充電時間與充入電容量,該電池等效模型包括電池等效電容(C eq )、並聯阻抗(R p )與並聯電容(C p )及串聯阻抗(R o ),其中R p 與C p 為呈現電池之暫態響應,而C eq 上之初始電壓V Ceq 即為電池之開路電壓(Open-circuit voltage,OCV),此外模型內之相關參數皆與電池剩餘容量(state of charge,SOC)及溫度有關。 Then derive the charging time and charging capacity of the multi-stage constant current charging method. The battery equivalent model includes the equivalent battery capacitance ( C eq ), parallel impedance ( R p ) and parallel capacitance ( C p ) and series impedance ( R o ), where R p and C p represent the transient response of the battery, and the initial voltage V Ceq on C eq is the open-circuit voltage (OCV) of the battery. In addition, the relevant parameters in the model are related to the remaining battery The capacity (state of charge, SOC) is related to temperature.
其中,V T 為電池端點電壓(terminal voltage),亦為多階段定電流充電法之階段截止電壓,V Cp =V Rp ,根據克希荷夫電壓定律,V T 如方程示(1)所示。 Among them, V T is the battery terminal voltage (terminal voltage), which is also the stage cut-off voltage of the multi-stage constant current charging method, V Cp = V Rp , according to Kirchhoff's voltage law, V T is as shown in equation (1) Show.
其中,為電池之內電壓,如方程示(2)所示。 among them, Is the internal voltage of the battery, as shown in equation (2).
其中,s為階段數,當s=1時,I0=0,,為電池初 始開路電壓。因各階段為固定電流充電,其充電電流頻率極小,故並聯電容(C p )容抗極大可視為開路,則I RP I charge ,由於多階段定電流充電法之充電時間係由每一個階段之充電電流決定,因此所需總充電時間T如方程示(3)所示。 Among them, s is the number of stages, when s=1, I 0 =0, Is the initial open circuit voltage of the battery. Since each stage is charged with a fixed current, the frequency of the charging current is very small, so the parallel capacitor ( C p ) can be regarded as an open circuit when the capacitive reactance is large, then I RP I charge , since the charging time of the multi-stage constant current charging method is determined by the charging current of each stage, the required total charging time T is shown in equation (3).
經由算式推導,多階段定電流充電法之充電電容量總和Ah T ,如方程示(4)所示。 Derived from the formula, the total charge capacity Ah T of the multi-stage constant current charging method is shown in equation (4).
一般而言,五階段定電流充電法要將電池充飽,其第五階段電流,如方程示(5)所示。 Generally speaking, the five-stage constant current charging method needs to fully charge the battery, and the fifth stage current is shown in equation (5).
其中,V T_cut-off 為階段截止電壓、則為電池在充飽之後的內 電壓(如4.2V)。 Among them, V T_cut-off is the stage cut -off voltage, It is the internal voltage of the battery after being fully charged (such as 4.2V).
亦可求得充電能量總損失為如方程示(6)所示。 The total loss of charging energy can also be obtained as shown in equation (6).
鋰電池之交流阻抗分析:AC impedance analysis of lithium battery:
在二次電池之充放電技術中,交流阻抗(Alternating Current Internal Resistance,ACIR)分析係一種電化學分析之方式,主要為分析電池在不同狀態下之化學反應,藉此得到電池在不同狀態下之等效阻抗。而交流阻抗分析係利用 小振幅交流弦波電壓或電流對電池端電極進行擾動,從中獲取交流阻抗數據,並以此數據建立等效電路。此外,藉由改變交流弦波的頻率,可以得到實、虛阻抗對頻率之響應變化曲線,稱為電化學阻抗頻譜(Electrochemical Impedance Spectrum,EIS)或奈氏圖(Nyquist-plot)。 In the charging and discharging technology of secondary batteries, alternating current impedance (Alternating Current Internal Resistance, ACIR) analysis is a method of electrochemical analysis, mainly to analyze the chemical reaction of the battery in different states, so as to obtain the battery in different states. Equivalent impedance. And the AC impedance analysis department uses The small amplitude AC sine wave voltage or current disturbs the terminal electrodes of the battery, from which the AC impedance data is obtained, and an equivalent circuit is established from this data. In addition, by changing the frequency of the AC sine wave, the response curve of real and imaginary impedance to frequency can be obtained, which is called Electrochemical Impedance Spectrum (EIS) or Nyquist-plot.
請參照圖4,其繪示電池之交流阻抗特性示意之奈氏圖。 Please refer to FIG. 4, which shows a Nyquist diagram of the AC impedance characteristic of the battery.
如圖所示,電池之交流阻抗特性之奈氏圖可劃分為低頻、中頻及高頻三個部份加以探討,分別為低頻的質傳作用(Mass Transport Effects),中頻的荷傳及電雙層作用(Double-Layer Effects)以及高頻時電磁效應(Electric and Magnetic Effects)。 As shown in the figure, the Nyquist diagram of the AC impedance characteristics of the battery can be divided into three parts: low frequency, intermediate frequency and high frequency for discussion. They are the mass transport effects of low frequency (Mass Transport Effects), the charge transfer of intermediate frequency and Double-Layer Effects and High Frequency Electromagnetic Effects (Electric and Magnetic Effects).
為量測電池之交流阻抗參數,交流阻抗分析儀(Bio-Logic公司的多功能模組化恆電位儀)產生一組變頻弦波電壓訊號,電壓主動訊號即為將一主動變頻電壓訊號對電池做擾動,直到所有設定之擾動頻率處理完畢為止。而恆電壓模式下的擾動電壓不可過大,以避免干擾電池的平衡狀態,導致量測失真。在進行主動恆電位電壓擾動實驗時,電池因擾動電壓產生相對應之電流,因此可偵測出電流的振幅與相位角,並將該電流參數進行訊號調節及轉換。 To measure the AC impedance parameters of the battery, the AC impedance analyzer (Bio-Logic’s multifunctional modular potentiostat) generates a set of variable frequency sine wave voltage signals. The voltage active signal is an active variable frequency voltage signal to the battery Do disturbance until all set disturbance frequencies are processed. In the constant voltage mode, the disturbance voltage should not be too large to avoid disturbing the balance state of the battery and causing measurement distortion. In the active constant potential voltage perturbation experiment, the battery generates a corresponding current due to the perturbed voltage, so the amplitude and phase angle of the current can be detected, and the current parameters can be signal adjusted and converted.
如方程式(7)所示,利用擾動電壓之大小與相對應產生的電流可計算出阻抗與相角差,當完成所有頻率之響應量測後,則可執行交流阻抗參數分析。 As shown in equation (7), the impedance and phase angle difference can be calculated by the magnitude of the disturbance voltage and the corresponding current. After the response measurement of all frequencies is completed, the AC impedance parameter analysis can be performed.
確認電池規格符合實驗需求後,即可進行交流阻抗分析實驗,請參照圖5其繪示交流阻抗分析實驗系統之設置示意圖。 After confirming that the battery specifications meet the experimental requirements, the AC impedance analysis experiment can be carried out. Please refer to Figure 5 which shows the schematic diagram of the AC impedance analysis experiment system.
如圖五所示,首先將電腦與VSP連接,確認連線無誤後,新增電池測試迴路並設定自訂之測試步驟,之後再次確認設定參數與限制,如無誤便可開始測試。EC-Lab可進行定電流充/放電、定電壓充電、恆電位交流阻抗量測等測試;在限制部分也可以選擇每一段測試步驟裡電壓、電流或是時間限制;在資料儲存部分,EC-Lab能夠自動儲存每一次測試的電壓、電流、充/放 容量、時間等參數,並能夠藉此產生圖形。電池之剩餘容量又與電池交流阻抗大小有著相對應的關係,而在實驗過程中,電池剩餘容量精確度與實驗所需花費時間需要做權衡,因為每一個的測量都需要靜止約一小時後才能進行,所以測量1%作為間隔的所有資料,至少需花費100個小時的時間進行靜置。 As shown in Figure 5, first connect the computer to the VSP. After confirming that the connection is correct, add a battery test circuit and set a custom test procedure, then confirm the setting parameters and limits again, and start the test if there are no errors. EC-Lab can perform constant current charging/discharging, constant voltage charging, constant potential AC impedance measurement and other tests; in the limit part, you can also select the voltage, current or time limit in each test step; in the data storage part, EC- Lab can automatically store the voltage, current, charge/discharge of each test Parameters such as capacity and time can be used to generate graphics. The remaining capacity of the battery has a corresponding relationship with the AC impedance of the battery. During the experiment, the accuracy of the remaining capacity of the battery and the time required for the experiment need to be weighed, because each measurement needs to stand still for about an hour before you can Therefore, it takes at least 100 hours to stand still for all data measured at 1% as an interval.
請參照圖6,其繪示不同剩餘容量之奈奎斯特阻抗圖。 Please refer to Figure 6, which shows the Nyquist impedance diagram of different remaining capacities.
本案為考量到電池等效模型之精確度,將以每1%的電池剩餘容量作為交流阻抗分析之精度,當電池之交流阻抗測量完後,可得不同剩餘容量之奈奎斯特阻抗圖,如圖所示,由於本案使用戴維寧電池等效模型,因此縱座標軸之正值區域為兩個電阻R和一個電容C組成,以下僅針對正值區域進行交流阻抗之參數分析。 In this case, considering the accuracy of the battery equivalent model, each 1% of the remaining battery capacity will be used as the accuracy of the AC impedance analysis. After the AC impedance of the battery is measured, the Nyquist impedance diagrams of different remaining capacities can be obtained. As shown in the figure, because the Thevenin battery equivalent model is used in this case, the positive value area of the ordinate axis is composed of two resistors R and one capacitor C. The following only conducts parameter analysis of AC impedance for the positive value area.
請一併參照圖7a至7c,其中圖7a其繪示測得的串聯阻抗(R o )、並聯阻抗(R p )與等效阻抗(R eq )對電池剩餘容量百分比之關係曲線圖;圖7b其繪示測得的並聯電容(C p )對電池剩餘容量百分比之關係曲線圖;圖7c其繪示測得的開路電壓(V oc )對電池剩餘容量百分比之關係曲線圖。 Please refer to Figures 7a to 7c together, where Figure 7a shows the measured series impedance ( R o ), parallel impedance ( R p ), and equivalent impedance ( R eq ) versus the remaining battery capacity percentage; 7b is a graph showing the relationship between the measured parallel capacitance ( C p ) and the percentage of remaining battery capacity; Fig. 7c is a graph showing the relationship between the measured open circuit voltage ( V oc ) and the percentage of remaining battery capacity.
如圖所示,電池充飽後,以每1%容量放電後,再休息1小時後得到其開路電壓及量測交流阻抗,其中,等效阻抗(R eq )=串聯阻抗(R o )+並聯阻抗(R p )。 As shown in the figure, after the battery is fully charged and discharged at 1% capacity, the open circuit voltage and AC impedance are obtained after 1 hour of rest. The equivalent impedance ( R eq ) = series impedance ( R o ) + Parallel impedance ( R p ).
本案採用粒子群演算法尋找最佳化充電電流設定值:In this case, the particle swarm algorithm is used to find the optimal charging current setting value:
粒子群演算法之基本精神來自於群體動物的捕食行為,並將其用於搜尋最佳解之相關問題。在解空間中所有粒子都有本身所對應之適應值,並且每個粒子都知道自己目前為止之最佳適應值及其最佳位置,稱之為個體粒子的最佳值(Particle best value,pBest),這項資訊為每個粒子自己所擁有的經驗,同時每個粒子亦知道全部粒子之最佳解以及其位置,稱之為群體粒子的最佳值(Globe best value,gBest)。經過每次疊代更新,粒子會以個體經驗及群體經驗作為參考,並且更新個體之速度與位置。 The basic spirit of the particle swarm algorithm comes from the predation behavior of group animals, and it is used to search for the best solution to related problems. In the solution space, all particles have their own fitness value, and each particle knows its best fitness value and its best position so far, which is called the best value of individual particles (Particle best value, pBest ), this information is the experience of each particle, and each particle also knows the best solution and its position of all particles, which is called the best value of the group particle (gBest). After each iteration update, the particles will use individual experience and group experience as a reference, and update the individual's speed and position.
請參照圖8,其繪示粒子群演算法之粒子在解空間移動之示意圖。 Please refer to Figure 8, which shows a schematic diagram of particles moving in the solution space of the particle swarm algorithm.
如圖所示,一開始將所有粒子隨機散佈在解空間中,若有粒子能接近區域內最佳解附近,該區域的粒子將往此區域之最佳解進行搜尋,但此區域有可能只是區域最佳解,因此必須由各粒子群的搜索結果修正群體最佳的適應值及位置,進而接近全域最佳解。 As shown in the figure, at the beginning, all particles are randomly scattered in the solution space. If there are particles that can approach the best solution in the region, the particles in this region will search for the best solution in this region, but this region may only be The regional optimal solution, therefore, the optimal fitness value and position of the population must be corrected by the search results of each particle swarm to approach the global optimal solution.
粒子之移動速度如方程式(8)所示。 The moving speed of particles is shown in equation (8).
v ij (t+1)=w*v ij (t)+C 1 *rand1*[pBest ij (t)-x ij (t)]+C 2 *rand2*[gBest ij (t)-x ij (t)](8)
v ij ( t +1) = w * v ij ( t )+ C 1 *
粒子之位置更新機制如方程式(9)所示。 The particle position update mechanism is shown in equation (9).
x ij (t+1)=x ij (t)+v ij (t+1) (9) x ij ( t +1) = x ij ( t )+ v ij ( t +1) (9)
其中,w為權重值,C1和C2為個體和群體學習因子,x ij 表第i粒子j維度的位置,v ij 表第i粒子j維度的速度,rand1和rand2表亂數,pBest ij 表個體粒子最佳的位置,gBest ij 表群體最佳的位置。 Wherein, w is a weight value, C 1 and C 2 for the individual and community learning factor, x ij table position of the i-th particle j dimensions, velocity v ij Table i particles j dimensions, RAND1 and rand2 table nonce, pBest ij It represents the best position of individual particles, and gBest ij represents the best position of the population.
在取得鋰電池之交流阻抗後,接著運用粒子群演算法解決多階段最佳化電流設定值問題。在應用粒子群演算法前,須定義要解決之最佳化問題,本案以降低充電損失及縮短充電時間為目標,因此需找出有哪些因素會影響此目標。由多階段定電流充電模式之推導可知,影響充電時間及充電損失包含了各階段充電電流(I1~I5)與階段截止電壓(VT_cut-off)。 After obtaining the AC impedance of the lithium battery, the particle swarm algorithm is used to solve the multi-stage optimization current setting problem. Before applying the particle swarm algorithm, it is necessary to define the optimization problem to be solved. The goal of this case is to reduce the charging loss and shorten the charging time, so it is necessary to find out what factors will affect this goal. From the derivation of the multi-stage constant current charging mode, it can be seen that the charging time and the charging loss affect the charging current (I1~I5) and the stage cut-off voltage (VT_cut-off).
請參照圖9,其繪示本案之電池剩餘容量(SOC)與等效阻抗(R eq )之擬合關係曲線圖。 Please refer to FIG. 9, which shows a curve diagram of the fitting relationship between the remaining battery capacity (SOC) and the equivalent impedance ( R eq ) of this case.
如圖所示,本案之充電時間計算方式如方程式(3)所示,而充電損失與電池內阻有關,因此本案將所量測之交流阻抗數據利用曲線擬合功能建立剩餘容量與阻抗之擬合曲線,即可利用方程式(6)求得充電過程中的損失。本案之曲線擬合使用Gaussian加總函數模型如方程式(10)所示。 As shown in the figure, the charging time calculation method of this case is as shown in equation (3), and the charging loss is related to the internal resistance of the battery. Therefore, this case uses the measured AC impedance data to use the curve fitting function to establish a simulation of the remaining capacity and impedance. With the resultant curve, equation (6) can be used to find the loss during charging. The curve fitting in this case uses Gaussian summation function model as shown in equation (10).
其中,SOC為電池剩餘容量,R eq 為等效阻抗。 Among them, SOC is the remaining capacity of the battery, and R eq is the equivalent impedance.
適應值(fitness value)函數定義是粒子群演算法中最重要的一環,定義方式將會影響最後輸出結果,而本案考量了充電損失及充電時間為兩種不同單位的參數,因此必須提出方法將其正規化。 The definition of fitness value function is the most important part of the particle swarm algorithm. The definition method will affect the final output result. In this case, the charging loss and charging time are considered as two parameters of different units. Therefore, a method must be proposed. Its regularization.
請參照圖10,其繪示本案之適應值函數之定義示意圖。 Please refer to Figure 10, which illustrates the definition diagram of the fitness function in this case.
如圖所示,本案之適應值函數之定義為利用兩點間之直線距離做為適應值的數,圖中A點為目前之總充電時間及充電總損失,當A點(T now ,L now )與理想最佳解(T min ,L min )之距離d越小,意味著總充電時間及充電總損失越小,其適應值Objective評估越佳,而兩點間距離如方程式(11)所示。 As shown in the figure, the fitness value function in this case is defined as the number using the straight line distance between two points as the fitness value. Point A in the figure is the current total charging time and total charging loss. When point A ( T now , L The smaller the distance d between now ) and the ideal optimal solution ( T min , L min ) is, the smaller the total charging time and the total loss of charging, the better the objective evaluation of its fitness value, and the distance between the two points is as in equation (11) Shown.
其中,T代表充電時間,L代表充電損失。 Among them, T represents charging time and L represents charging loss.
為強調二參數之各別重要性,引入權重α來調配上式,可將方程式(11)改寫如方程式(12)所示。 In order to emphasize the respective importance of the two parameters, the weight α is introduced to adjust the above equation, and equation (11) can be rewritten as shown in equation (12).
本案使用所量測之交流阻抗數據,以MATLAB軟體模擬定電流定電壓充電法,而模擬條件為選用電池之技術手冊所提供的標準充電電流至最大充電電流,充電截止電流為0.02C所得之結果,正規化之參考資料點如表1所示。 This case uses the measured AC impedance data to simulate the constant current and constant voltage charging method with MATLAB software, and the simulation conditions are the results obtained from the standard charging current provided by the technical manual of the battery to the maximum charging current, and the charging cut-off current is 0.02C. , The reference data points of normalization are shown in Table 1.
從表1可得知,在0.5C條件下,充電時間為最大值(T max )8980秒、充電損失為最小值(L min )819.34焦耳;在2C條件下,充電時間為最小值(T min )3582秒、充電損失最大值(L max )2803.94焦耳。 It can be seen from Table 1 that under the condition of 0.5C, the charging time is the maximum value ( T max ) 8980 seconds and the charging loss is the minimum value ( L min ) 819.34 joules; under the condition of 2C, the charging time is the minimum value ( T min ) 3582 seconds, the maximum charge loss ( L max ) is 2803.94 Joules.
模擬結果:Simulation results:
本案模擬時選用電池之規格與適應值評估之參數如表2所示。 Table 2 shows the specifications and fitness evaluation parameters of the batteries selected in the simulation of this case.
其中,本案之權重值α設為0.5,表充電時間與充電損失具有相同的重要性。 Among them, the weight value α of this case is set to 0.5, indicating that the charging time and the charging loss have the same importance.
多階段定電流充電法影響充電時間與損失之因素包含各階段電流(I 1 ~I 5 )與階段截止電壓(V T ),一般各階段電流值介於0~1C間,階段截止電壓則設為4.2V。有文獻提到,若要確保最後一階段電流能將電池充飽,在內電壓不超過4.2V之前提下,可使用較高之階段截止電壓進行充電。 The factors that affect the charging time and loss of the multi-stage constant current charging method include the current ( I 1 ~ I 5 ) and the stage cut-off voltage ( V T ). Generally, the current value of each stage is between 0 and 1C, and the stage cut-off voltage is set It is 4.2V. It is mentioned in the literature that if you want to ensure that the last stage current can fully charge the battery, and the internal voltage does not exceed 4.2V, you can use a higher stage cut-off voltage for charging.
本案之粒子群範圍設定如表3所示。 The particle swarm range setting in this case is shown in Table 3.
表3
藉由所述之等效阻抗(R eq )之擬合曲線,可模擬充電過程中等效阻抗的變化,故能確保電池內電壓不超過額定電壓4.2V。 With the fitting curve of the equivalent impedance ( R eq ), the change of the equivalent impedance during the charging process can be simulated, so it can ensure that the battery voltage does not exceed the rated voltage of 4.2V.
請參照圖11,其繪示粒子群在解空間移動軌跡之示意圖。 Please refer to FIG. 11, which shows a schematic diagram of the movement trajectory of the particle swarm in the solution space.
如圖所示,本案分別先以兩種不同階段截止電壓V T (4.22V,4.25V)進行模擬,可得知,V T 越高時其適應值會越好。 As shown in the figure, this case is first simulated with two different phase cut-off voltages V T (4.22V, 4.25V). It can be seen that the higher the V T, the better the adaptation value.
本案之粒子群演算法之蒐尋結果,於階段截止電壓(VT=4.22V)之相關性能參數模擬結果如表4所示。 The search results of the particle swarm algorithm in this case and the simulation results of the relevant performance parameters of the phase cutoff voltage (VT=4.22V) are shown in Table 4.
本案於階段截止電壓(V T =4.25V)之相關性能參數模擬結果如表5所示。 Table 5 shows the simulation results of the relevant performance parameters of the cut-off voltage ( V T =4.25V) in this case.
請參照圖12,其繪示本案之實驗平台架構之示意圖。 Please refer to Figure 12, which shows a schematic diagram of the experimental platform architecture of this case.
如圖所示,本案電池之充放電實驗係採用WonATech公司出品之可程控充放電機WBCS3000及監控介面,而監控介面可設定多種充電法則,並能即時監控電池的電壓、電流及溫度等,電池皆放置在CIL-100恆溫箱內並控制在攝氏25度。 As shown in the figure, the charging and discharging experiment of the battery in this case uses the programmable charging and discharging machine WBCS3000 produced by WonATech and the monitoring interface, and the monitoring interface can set a variety of charging rules, and can monitor the voltage, current and temperature of the battery in real time. They are all placed in a CIL-100 incubator and controlled at 25 degrees Celsius.
本案與習知技術之實驗結果與比較:Experimental results and comparison between this case and conventional technology:
以下將針對本案與習知技術之定電流定電壓充電法與最佳化多階段定電流充電法進行比較,項目包含充電時間、充放電容量以及充電效率,以驗證本案之可行性和性能改善。 The following compares the constant current constant voltage charging method and the optimized multi-stage constant current charging method for this case and the conventional technology. The items include charging time, charging and discharging capacity, and charging efficiency to verify the feasibility and performance improvement of this case.
為作公平比較,將定電流定電壓充電法之定電流階段電流設為和五階段之I1相同。 For fair comparison, the current in the constant current phase of the constant current and constant voltage charging method is set to be the same as the five phase I1.
請參照圖13,其繪示習知技術之定電流定電壓充電法之電流、電壓實測波形圖。 Please refer to FIG. 13, which shows the measured current and voltage waveforms of the conventional constant current and constant voltage charging method.
如圖所示,習知技術之定電流定電壓充電法採用0.864C充電條件之總充電時間為7847秒。 As shown in the figure, the conventional constant current and constant voltage charging method adopts 0.864C charging conditions and the total charging time is 7847 seconds.
請參照圖14,其繪示本案於階段截止電壓(V T =4.22V)之電流、電壓實測波形圖。 Please refer to Figure 14, which shows the current and voltage measured waveforms of the cut-off voltage ( V T =4.22V) in this case.
如圖所示,本案於階段截止電壓(VT=4.22V)採用0.864C充電條件之總充電時間為6060秒,其實驗資料如表6所示。 As shown in the figure, in this case, the phase cut-off voltage (VT=4.22V) adopts 0.864C charging conditions and the total charging time is 6060 seconds. The experimental data is shown in Table 6.
兩種方法之實驗充電性能參數比較如表7所示,可看出本案之充電時間可縮短22.77%,充電效率改善0.43%。 The experimental charging performance parameters of the two methods are compared as shown in Table 7. It can be seen that the charging time in this case can be shortened by 22.77%, and the charging efficiency can be improved by 0.43%.
藉由前述所揭露的設計,本發明乃具有以下的優點: With the design disclosed above, the present invention has the following advantages:
1.本發明揭露一種最佳化輸出電流值之多階段定電流充電法,其係透過交流阻抗分析以建立電池等效模型,同時考量充電損失與充電時間,並利用粒子群演算法找尋有限區域中之最佳解,藉此實現最小化充電損失與時間之最佳化多階段充電法。 1. The present invention discloses a multi-stage constant current charging method for optimizing the output current value, which uses AC impedance analysis to establish an equivalent battery model, while taking into account the charging loss and charging time, and uses the particle swarm algorithm to find a limited area The best solution in this way can realize an optimized multi-stage charging method that minimizes charging loss and time.
2.本發明揭露一種最佳化輸出電流值之多階段定電流充電法,係利用粒子群演算法尋找最佳化充電電流設定值,僅需使用電池等效模型,而具有不需進行多次耗時費工之實際實驗即能得到最佳化電流設定之優點。 2. The present invention discloses a multi-stage constant current charging method for optimizing the output current value. The particle swarm algorithm is used to find the optimized charging current setting value. Only the battery equivalent model is used, and there is no need to perform multiple times Time-consuming and labor-intensive actual experiments can get the advantages of optimized current settings.
3.本發明揭露一種最佳化輸出電流值之多階段定電流充電法,於階段截止電壓為4.22V時,能將電池容量充至習知技術之定電流定電壓充電法之98%以上,且在溫升沒增加之前提下,充電時間能縮短22.77%,充電效率改善0.43%。 3. The present invention discloses a multi-stage constant current charging method with optimized output current value. When the stage cut-off voltage is 4.22V, the battery capacity can be charged to more than 98% of the conventional constant current and constant voltage charging method. And before the temperature rise does not increase, the charging time can be shortened by 22.77%, and the charging efficiency can be improved by 0.43%.
本發明所揭示者,乃較佳實施例,舉凡局部之變更或修飾而源於本發明之技術思想而為熟習該項技藝之人所易於推知者,俱不脫本發明之專利權範疇。 The disclosure of the present invention is a preferred embodiment, and any partial changes or modifications that are derived from the technical idea of the present invention and can be easily inferred by those familiar with the art will not depart from the scope of the patent right of the present invention.
綜上所陳,本發明無論就目的、手段與功效,在在顯示其迥異於習知之技術特徵,且其首先發明合於實用,亦在在符合發明之專利要件,懇請貴審查委員明察,並祈早日賜予專利,俾嘉惠社會,實感德便。 In summary, no matter the purpose, means, and effects of the present invention, it is showing its technical characteristics that are very different from the conventional ones, and its first invention is suitable for practical use, and it is also in compliance with the patent requirements of the invention. I sincerely ask your examiner to observe it carefully, and Pray that the patent will be granted as soon as possible to benefit the society.
步驟a‧‧‧依一粒子群演算法初始化複數階段之各充電電流值I charge,s 及一階段截止電壓值V T Step a‧‧‧Initialize the charge current value I charge,s and the first-stage cut-off voltage value V T of the complex number stage according to a particle swarm algorithm
步驟b‧‧‧對所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T 進行一運算以獲得一總充電時間T及一充電總損失 Step b‧‧‧ Perform an operation on each charge current value I charge,s of the complex number stage and the stage cut-off voltage value V T to obtain a total charge time T and a total charge loss
步驟c‧‧‧依一目前之總充電時間及充電總損失(T now ,L now )與一理想之總充電時間及充電總損失(T min ,L min )利用一適應值函數進行運算 Step c‧‧‧Using a fitness function to perform calculations based on a current total charging time and total charging loss ( T now , L now ) and an ideal total charging time and total charging loss ( T min , L min )
步驟d‧‧‧更新所述複數階段之各充電電流值I charge,s 及所述階段截止電壓值V T 之一個別最佳值與一群體最佳值,以決定是否獲得一最佳輸出電流值 Step d‧‧‧Update the individual best value of each charge current value I charge,s and the phase cutoff voltage value V T of the plurality of stages and a group best value to determine whether to obtain an optimal output current value
步驟e‧‧‧以及應用該最佳之輸出電流值進行充電,再回到步驟b重複執行 Step e‧‧‧ and apply the best output current value for charging, then go back to step b and repeat
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