Smart grid energy scheduling based on improved dynamic programming algorithm and LSTM

LSTM algorithm considering environmental factors

LSTM has found extensive application in natural language processing, where it addresses the long dependency problem in model training compared to RNN. The LSTM process is roughly divided into three steps. The first step is to determine what information to discard from the cell state, which is done through the oblivion gate. The second step is to determine what information is stored in the cell state, which is determined by the input gate. Finally, determine which information to output, which is determined by the output gate result and the cell state. However, to enable accurate prediction of energy consumption of a node in the power grid, LSTM requires ample data and an appropriate experimental setup. In reality, the variation of grid energy consumption is not only linked to the load but also to the environment where the grid is situated. To this end, this study collects the daily average data of wind speed, precipitation, temperature, and humidity in a city and trains them simultaneously with daily electricity consumption. Specifically, wind speed, precipitation, temperature, and humidity are input as influencing features of electricity consumption to the LSTM model. In this article, four kinds of environmental data of T City in 2020 and data of a node of the power grid are collected and organized in the form of matrix. The input feature structure is depicted in Fig. 2.

Modeling of smart grid energy storage systems

The initial step towards addressing the smart grid energy consumption dispatching issue through dynamic programming is to develop a model for the energy storage system of the smart grid. The fundamental configuration of the smart grid energy storage system is displayed in Fig. 3. The energy storage system of the smart grid, studied in this article, comprises primarily three components: the battery system, supercapacitor system, and DC/DC DC converter. Among these, the battery system is connected in parallel to the DC bus via the DC converter. The Rint model is used for the battery, and the internal resistance model is employed for the supercapacitor, with the internal resistance of both remaining constant. In conventional states, single state variables can describe state characteristics, but in smart power grids, the states of batteries and supercapacitors are equally important, so single state variables cannot fully describe their changes.

Assuming that the power demand of a node of the smart grid at the k discrete event interval is P_req(k), then the energy flow relationship of its on-board hybrid energy storage system is shown in Eq. (1). (1)${\displaystyle P_{req}\left(k\right)=\left\{\begin{array}{c}\left(I_b\left(k\right)U_b\left(k\right)-I_b^2\left(k\right)\eta +I_{sc}\left(k\right)U_{sc}\left(k\right)-I_{sc}^2\left(k\right)R_{sc}\right.P_{req}\left(k\right)>0\hfill \\ \frac{I_b\left(k\right)U_b\left(k\right)+I_b^2\left(k\right)R_b}{\eta }+I_{sc}\left(k\right)U_{sc}\left(k\right)+I_{sc}^2\left(k\right)R_{sc}{P}_{req}\left(k\right)<0\hfill \end{array}\right.}$

where U_b(k) is the battery no-load voltage, I_b(k) is the battery current, U_sc(k) is the supercapacitor no-load voltage, I_sc(k) is the supercapacitor current; η is the efficiency of the DC converter; P_req(k) > 0 indicates the smart grid in operating state; P_req(k) < 0 indicates the smart grid in energy-saving state.

Equation (1) indicates that during normal operation mode of the smart grid, the system loss comprises two major components: the internal resistance thermal loss of the battery and supercapacitor, and the DC/DC DC converter loss.

The no-load voltage of the battery is considered as a function of the battery charge state (SOC), and the following functional relationship is obtained by conducting experiments on the hybrid power pulse characteristics of the battery monomer, performing parameter discrimination and fourth-order polynomial fitting: (2)${\displaystyle U_b\left(k\right)=aSO{C}_b^4\left(k\right)+bSO{C}_b^3\left(k\right)+cSO{C}_b^2\left(k\right)+dSO{C}_b\left(k\right)+e}$

where, a ∼ e is the polynomial fit coefficient; SOC_b(k) is the charge state of the battery at the k-th discrete time interval.

Redefining the charge state of a supercapacitor as the ratio of the square of the voltage value in a certain state to the square of the voltage value in a fully charged state, the function of the no-load voltage of a supercapacitor with respect to its charge state is as follows: (3)${\displaystyle U_{sc}\left(k\right)=\sqrt{U_{sc,N}\cdot SO{C}_{sc}\left(k\right)}}$

where, U_sc(k) is the voltage of the supercapacitor under full charge; SOC_sc(k) is the charged state of the ultracapacitor at the k discrete time interval.

Two-state variable based DPA

The concept of state variables pertains to variables that articulate the inherent state of a process at the outset of each stage within a DPA. Furthermore, the input state variable in each stage is contingent on the output state variable of the preceding stage. While the traditional DPA employs single-state variables to represent the process, such an approach imposes certain limitations in adequately capturing the intricacies of electricity consumption scheduling within the framework of a smart grid. To address this issue, our article proposes the use of dual-state variables to enhance the effectiveness of the DPA.

The grid energy consumption scheduling process is deemed a problem-solving process, which is segmented into n stages based on the time sequence of the demanded power during system operation. In the context of smart grid energy consumption scheduling, the state of charge of energy storage devices, namely, the battery and supercapacitor, serves as an indicator of the entire system’s state. Therefore, the SOC of battery and supercapacitor are taken as the state variables of the system z₁(k) and z₂(k) , and the decision variable j(k) is taken as the output power of battery P_b(k), then the output power of supercapacitor can be determined as: (4)${\displaystyle P_{sc}\left(k\right)=P_{req}\left(k\right)-u\left(k\right).}$

The discrete situation of the state equation of the smart grid energy storage system is shown in Eq. (5), where the state variables in the k + 1-th phase are determined by the state variables and decision variables in the k-th phase. (5)${\displaystyle \left\{\begin{array}{c}{z}_1\left(k\right)=f_1\left(z_1\left(k\right),u\left(k\right)\right)\hfill \\ z_2\left(k\right)=f_2\left(z_2\left(k\right),u\left(k\right)\right)\hfill \end{array}\right.}$

where f₁ and f₂ are the transfer functions for the state variables z₁(k) and z₂(k), respectively.

Equations (6) and (6) depict the present computation for the battery and supercapacitor, along with the state transfer equations. (6)${\displaystyle \left\{\begin{array}{c}{I}_b\left(k\right)=\frac{U_b\left(k\right)-\sqrt{U_b^2\left(k\right)-4R_{b}u\left(k\right)}}{2R_b}\hfill \\ z_1\left(k+1\right)=z_1\left(k\right)-\frac{I_b\left(k\right)\Delta t\left(k\right)}{Q_{b,N}}\hfill \end{array}\right.}$ (7)${\displaystyle \left\{\begin{array}{c}{I}_{sc}\left(k\right)=\frac{U_{sc}\left(k\right)-\sqrt{U_{sc}^2\left(k\right)-4R_{sc}{P}_{sc}\left(k\right)}}{2R_{sc}}\hfill \\ z_2\left(k+1\right)=z_2\left(k\right)-\frac{P_{sc}\left(k\right)I_{sc}^2\left(k\right)R_{sc}}{\frac{1}{2}{C}_{sc,N}{U}_{sc,N}^2}\hfill \end{array}\right.}$

where, Δt(k) indicates the duration of the k phase; Q_b,N is the rated capacity of the battery; C_sc,N is the rated capacitance of the supercapacitor; and U_sc,N is the rated voltage of the supercapacitor.

The expression of the optimal objective function for a certain state variable at the n-th stage is: (8)${\displaystyle J\left(z_1\left(n\right),z_2\left(n\right)\right)=\underset{u\left(n\right)}{min}\left(L\left(z_1\left(n\right),z_2\left(n\right),u\left(n\right)\right)\right)}$

where L represents the cost function, which is the loss value of the smart grid energy storage system.

The optimal objective function used to determine the optimal decision in the k-th phase, when the state variables are determined, is shown in Eq. (9). The meaning is: the total loss value of the grid energy storage system from the departure of the k-th state to the last state process. (9)${\displaystyle J\left(z_1\left(k\right),z_2\left(k\right)\right)=\underset{u\left(k\right)}{min}\left(L\left(z_1\left(k\right),z_2\left(k\right),u\left(k\right)\right)\right)+J\left(z_1\left(k+1\right),z_2\left(k+1\right)\right)}$

where z₁(k) and z₂(k) are the state variables of smart grid, and u(k) isthe decision variable.

Electricity consumption prediction

The following are the evaluation metrics used to assess the LSTM approach that incorporates environmental factors:

(1)

MAPE (Mean absolute percentage error), sensitive to relative error, does not change due to global scaling of the target variable: (10)${\displaystyle MAPE\left(y,\sim y\text{\%}\right)=\frac{1}{n_{samples}}\sum _{i=0}^{n_{amples}-1}\frac{|y_i-\sim y_i\text{\%}|}{max\left(\varepsilon ,\left|y_i\right|\right)}}$

(2)

MSE (Mean squared error), the mean of the absolute squared errors of the predicted and true values: (11)${\displaystyle MSE\left(y,\sim y\text{\%}\right)=\frac{1}{n_{samples}}\sum _{i=0}^{n_{samples}-1}{\left(y_i-\sim y_i\text{\%}\right)}^2}$

This experiment aims to validate the effectiveness of using LSTM models for electricity consumption prediction after integrating environmental factors. Specifically, the experiment involves training a model that combines environmental variables and comparing its performance against a model trained using only electricity consumption data as input. The comparison of the two models’ performance in terms of evaluation metrics is presented in Table 1. Among them, only “ours” combines environmental variables, and the rest methods only use electricity consumption data for training. The results demonstrate that after combining environmental factors, the LSTM model’s MAPE reduces by 0.553%, from 4.565% to 4.014%, compared to training with ordinary electricity consumption data. Additionally, after combining environmental factors, the LSTM model’s MSE decreases from 0.2846 to 0.2645, a reduction of 0.0201. Furthermore, we compared the performance of other time series models, namely the recurrent neural network (RNN) and CNN-LSTM, against the LSTM model with environmental factors. The LSTM model with environmental factors outperformed both the RNN and CNN-LSTM models, with the latter being the second-best performer. These findings support the notion that incorporating environmental factors can enhance the time series forecasting model’s electricity consumption prediction capabilities compared to using only raw data.

Figure 4 presents a comparison of the predicted electricity consumption using the LSTM method with environmental factors proposed in this article and the curve fit of the test set. The red part of the plot represents the prediction result of the training process, the blue part represents the prediction result of the test set, and the green curve is the original data. The plot illustrates that both the training and test data align closely with the curve of the original data set,. The curve is almost completely fitted to the training set, but there are slight errors in the fitting to the original data set. This finding demonstrates that the LSTM method combined with environmental factors accurately predicts the electricity consumption of a smart grid.

Energy consumption scheduling

The experimentation was conducted using MATLAB (MathWorks, Inc., Natick, MA, USA), where a total of ten generation modules were simulated. Ablation experiments were devised to test the efficacy of the proposed smart grid energy consumption scheduling system’s two components. Firstly, the dynamic programming scheduling algorithm was omitted, and secondly, the traditional DPA was used for scheduling optimization. Thirdly, the two-state variable improved DPA was employed, and fourthly, the two-state variable DPA was combined with the LSTM electricity consumption prediction method, taking into account environmental factors. Comparison experiments were also conducted to validate the overall system’s effectiveness, where the particle swarm optimization algorithm, the ant colony algorithm, and the random forest algorithm were compared to the same type of energy consumption scheduling algorithms.

Table 1 presents the results of the ablation experiments, where ten power generation modules were utilized for simulation, and Table 1 displays the average energy consumption values over a specific period. Furthermore, line graphs were plotted to showcase the different methods’ performances on various generation modules. As shown in Table 2 and Fig. 5, the two methods proposed in this article reduced the smart grid system’s energy consumption to varying degrees. The addition of the LSTM method with environmental factors proposed in this article reduced the mean energy consumption of ten generation modules by 6.2 mkJ compared to the traditional DPA. By combining the two-state variable DPA, the overall system saved 14.8 mkJ compared to the traditional DPA, amounting to approximately 23% of energy loss. The data in Fig. 5 shows that the method presented in this article had a comparable effect on different power generation modules, reducing energy loss in varying degrees.

Table 3 and Fig. 6 depict the results of the comparison experiments. The data presented in Table 3 shows that our proposed method exhibits varying degrees of improvement when compared to the three machine learning algorithms typically used in energy scheduling: random forest, the ant colony algorithm (ACO), and the particle swarm algorithm (PSO). Our method achieves an energy reduction of 15.7 mkJ on a simulation experiment of a power generation module, as compared to the worst-performing random forest algorithm. In comparison to the second-best performing PSO algorithm, our method achieves a positive improvement of 2.7 mkJ less. In summary, using the method proposed in this article for energy scheduling in smart grids can significantly reduce energy consumption across power-using devices of varying power levels.

Discussion

Based on the results of the ablation experiments conducted on the time series model, the LSTM method incorporating environmental factors outperforms the original LSTM and RNN, and even surpasses the CNN-LSTM, which has been previously shown to outperform the LSTM. These findings highlight the significance of incorporating multiple factors in grid electricity consumption prediction. In terms of the overall scheduling algorithm, adding the LSTM incorporating environmental variables and the two-state variable DPA have varying degrees of performance improvement for the overall algorithm, and the effectiveness of both algorithms has been demonstrated in this article. The final comparison experiments confirm that the whole system can reduce energy consumption to varying degrees for different power generation modules, and the performance of energy consumption reduction is similar, with even more energy consumption reduction achieved in the lowest power module 5. These results underscore the universality and practical significance of the method presented in this article.