1. Introduction

2. Problem Statement

3. Framework

3.4. Optimization

3.4.1. Stochastic Optimization

In the deep learning forecasting module, we have trained models that can predict user load (${\widehat{L}}_{u,t}$), market prices (${\widehat{p}}_t$), and the capacity of solar generation (${\widehat{P}}_{g,t}^{\max }$). In the validation dataset, we obtain the deviations of the models for these predictions, and their variances are denoted as $\widehat{\Sigma }{L}_u$, $\widehat{\Sigma }p$, and ${\widehat{\Sigma }}_{P_g}$, respectively. These values represent the level of uncertainty. To mitigate the impact of uncertainty, we propose a stochastic optimization method as shown in Figure 5 (b). We use the predicted values as means and uncertainty as variances, for example, ($\widehat{P}{g,t}^{\max }$, $\widehat{\Sigma }{P}_g$), ($\widehat{L}u,t$, $\widehat{\Sigma }{L}_u$) and ($\widehat{p}t$, $\widehat{\Sigma }p$), to perform Gaussian sampling. Through Gaussian sampling, we can obtain multiple scenarios, which are considered as a multi-scenario optimization problem. Assuming we have N scenarios, the n-th scenario can be represented as ($n\in {\mathcal{S}}_{\mathcal{N}}$):

$$\begin{array}{cc}\hfill {\left({\tilde{P}}_g^{\max }\right)}^n& =\left[{\left({\tilde{P}}_{g,1}^{\max }\right)}^n,{\left({\tilde{P}}_{g,2}^{\max }\right)}^n,\dots ,{\left({\tilde{P}}_{g,T}^{\max }\right)}^n\right],\hfill \\ \hfill {\left({\tilde{L}}_u\right)}^n& =\left[{\left({\tilde{L}}_{u,1}\right)}^n,{\left({\tilde{L}}_{u,2}\right)}^n,\dots ,{\left({\tilde{L}}_{u,T}\right)}^n\right],\hfill \\ \hfill {\left(\tilde{p}\right)}^n& =\left[{\left({\tilde{p}}_1\right)}^n,{\left({\tilde{p}}_2\right)}^n,\dots ,{\left({\tilde{p}}_T\right)}^n\right].\hfill \end{array}$$

Figure 5. The whole Optimization method framework. The subplot (a) represents the flowchart of prediction based on deep learning. The output of the prediction module serves as the input for the stochastic optimization module, as shown in (b). During the scheduling process, real-time data accumulates over time, and we update the predictions based on the real data, as demonstrated in (c), named the online data augmentation module. This framework enhances the robustness of scheduling under uncertain conditions.

Figure 5. The whole Optimization method framework. The subplot (a) represents the flowchart of prediction based on deep learning. The output of the prediction module serves as the input for the stochastic optimization module, as shown in (b). During the scheduling process, real-time data accumulates over time, and we update the predictions based on the real data, as demonstrated in (c), named the online data augmentation module. This framework enhances the robustness of scheduling under uncertain conditions.

Then, the objective function in our proposed stochastic optimization can be re-defined with:

$$\underset{X}{\mathrm{minimize}}\sum _{t=1}^T{\mathbb{E}}_{n\in {\mathcal{S}}_{\mathcal{N}}}{\left({\tilde{p}}_t\right)}^n·P_{\mathrm{grid},t}.$$

(5)

Constraint (1b) is refined as:

$$P_{g,t}^{\min }\le P_{g,t}\le {\left({\tilde{P}}_{g,t}^{\max }\right)}^{n}n\in {\mathcal{S}}_{\mathcal{N}},g\in \mathcal{G},t\in \mathcal{T}.$$

Constraint (1e) is refined as:

$${\displaystyle P_{\mathrm{grid},t}+\sum _{g\in \mathcal{G}}{P}_{g,t}+\sum _{s\in \mathcal{S}}{P}_{s,t}^{-}=\sum _{s\in \mathcal{S}}{P}_{s,t}^{+}+\sum _{u\in \mathcal{U}}{\left({\tilde{L}}_{u,t}\right)}^{n}n\in {\mathcal{S}}_{\mathcal{N}},t\in \mathcal{T}.}$$

Through solving the stochastic optimization problem (5), we get the scheduling plan: $\dot{X}=\{{\dot{P}}_{\mathrm{grid},t},{\dot{P}}_{g,t},{\dot{P}}_{s,t}^{+},{\dot{P}}_{s,t}^{-},{\dot{E}}_{s,t}\}$ .

3.4.2. Online Data Augmentation

In order to address the data drift problem, we propose the data augmentation method as shown in Figure 5 (c). The module contains two parts: pre-training/fine-tuning Scheme and rolling-horizon feedback correction.

Pre-training/Fine-tuning Scheme

In practice, the real-time energy dispatch processes as a periodic task (e.g., daily dispatch). Considering that the prediction models are trained based on historical data and future data may not necessarily follow the same distribution as the past, we perform online data augmentation. Online data augmentation consists of two parts: pre-training and fine-tuning. Firstly, we pre-train the neural network model using historical data to obtain a model capable of predicting $f_{L_u}$, $f_p$ and $f_{P_g}$. Secondly, we fine-tune the neural network using the accumulated online data. Specifically, in the fine-tuning process, we employ partial parameter fine-tuning to obtain the refined network ${\tilde{f}}_{L_u}$, ${\tilde{f}}_p$ and ${\tilde{f}}_{P_g}$.

Rolling-horizon Feedback Correction

In addition to updating the prediction models online, we also employ the rolling-horizon control technique. In the optimization process, we solve the optimization problem every horizon H (to incorporate the latest prediction models and trade-off computational time). This operation is repeated throughout the scheduling period.

4. Experiments

5. Conclusion

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