# Power Battery Scheduling Optimization Based on Double DQN Algorithm with Constraints
## 1 Introduction
### Regression Model Based on Deep Learning  
Since early battery degradation does not immediately lead to capacity degradation but is reflected in the discharge voltage curve, incremental capacity (_IC_) curve analysis is considered an effective method to study battery degradation mechanisms [22], as shown in Figure 3. The graph reveals that there is no complete way to describe the _IC_ curve using simple linear functions. Therefore, it is advisable for us to select health indicators (HIs)  
Figure 1: A charging protocol during cyclic aging of battery (taking 3C-60%-4C as an example): R represents relaxation, CC1V means constant current charging by C1 (Q1)-C2 (80%)-1C, CVC represents constant voltage charging by 3.6 V, and CCD means constant current discharging by 4C, CVD means constant voltage discharging by 2 V constant voltage discharge. with actual physical correlation to the aging state as information in deep learning, which can calculate capacity Q more accurately. For data\(-\)driven capacity prediction, the extraction of HI is an important step in determining the estimation accuracy and reliability [23]. Select CH5, CH11, CH17, CH22, and CH32 files in the original data set. The \(dQ/dV\) corresponding to voltage is calculated according to Equation (4) to obtain the \(IC\) curve of the loop. Calculate the variance(var), skewness(ske), and kurtosis(kur) as battery health indicators to assess the health status of the battery [24,25]. Furthermore, in order to explore the relationship between the proposed HIs and the actual capacity, the Pearson correlation coefficient (PCC) and Spearman correlation coefficient (SCC) are used for correlation analysis [26]. \[IC=\frac{dQ}{dV}=\frac{\triangle Q}{\triangle V}=\frac{Q_{k+1}-Q_{k}}{V_{k+1}- V_{k}} \tag{4}\]  
The linear correlations between the extracted health indicators var, ske, kur, and capacity are calculated using the equations and battery data files, as shown in Table 1. PCC analysis is a better method to reflect the linear correlation between HIs and capacity, while SCC analysis is better to assess the monotonicity between HIs and capacity. The results  
Figure 3: \(IC\) curves under different cycle periods. Figure 2: SOC curves of the same batteries under different discharge protocols. indicate that the variance, skewness, and kurtosis of the \(IC\) curve have high correlations with capacity (both PCC and SCC are more significant than 0.9), which can reflect the attenuation characteristics of battery capacity well. The neural network layer of deep learning covers a wide range by transmitting the known information in the learning dataset, which can theoretically map to arbitrary functions and can solve very complex problems. This paper passes a pre\(-\)trained degradation model of HIs sequences to a test battery using LSTM. Figure 4a shows the structure of the LSTM network model used in this article, including the input layer, hidden layer, fully connected layer, and output layer. The apparent advantage of the LSTM chosen is that it can extract the backward and forward dependencies between samples and better handle time series problems, alleviating the \"gradient disappearance\" disadvantage caused by backpropagation during training [27; 28]. Figure 4b shows the detailed structure of the LSTM used in this paper. As shown in the figure, the forget gate retains the information that the previous memory is beneficial for this output and discards the useless information; the update gate is responsible for generating new important information, which is related to the past memory and the current memory, whilst the output gate generates the final information to be output. The network parameters are continuously adjusted in order to make the output optimal.