^{1}

^{1}

^{1}

^{1}

^{1}

^{2}

^{2}

^{2}

^{1}

^{2}

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

A two-stage robust planning method for energy storage in distribution networks based on load prediction is proposed to address the uncertainty of active load in energy storage planning. First, considering the uncertainty of active load, a short-term load forecasting model combining the mutual information method and BiLSTM is established based on k-means++ clustering. Second, based on the results of load forecasting, a comprehensive norm-constrained uncertainty set is constructed, and a two-stage robust model for distribution network energy storage planning is established. The first stage aims to minimize the annual investment cost of the energy storage system, while the second stage aims to minimize the daily operating cost of the distribution network. At the same time, a second-order cone relaxation transformation model with non-convex constraints is introduced to ultimately achieve the optimal economy of the distribution network in energy storage planning. Finally, the effectiveness of the proposed method and model is validated on the IEEE 33-node distribution network model using the MATLAB platform.

For the development of a high-proportion renewable energy source (RES), the access of a large number of RESs and the increase in load demand have brought new challenges for the flexible and efficient operation of the power system, and energy storage technology is considered to be an important means to solve the instability of RES output and demand (

At present, there is a lot of research on energy storage planning conducted by many scholars.

At this stage, the main methods of dealing with uncertainty problems in power systems are stochastic optimization (SO) (

Regardless of the method of uncertainty, one source of data is based on the predicted value. In the work of

To sum up, considering the shortcomings of the existing research, this paper proposes a two-stage robust planning method for energy storage in a distribution network based on load prediction. First, in order to extract effective and comprehensive forecasting information from load fluctuations and improve forecasting accuracy, a mutual information (MI) method and BiLSTM short-term load forecasting model considering feature importance fluctuations are established based on k-means++ clustering. Based on load prediction, a DRO uncertainty set with comprehensive norm constraints is constructed to establish a two-stage distribution network energy-storage planning model. The first stage aims at the minimum annual investment cost of energy storage, the second stage aims at the minimum daily operating cost of the distribution network, and the second-order cone relaxation transformation model is introduced. Finally, the economy and effectiveness of the proposed model and method are verified on the IEEE 33-node distribution network model.

One of the characteristics of a power system load is its periodicity. Developing short-term load forecasting based on the periodic characteristics of the load is the basis for improving the forecasting accuracy. The periodicity of the load is reflected in the overall change law of 24 h a day with a similar trend (

As an improvement of k-means, k-means++ is used to make the distance between the initial cluster centers as far as possible in the process of cluster initialization to avoid the problem of local optimization of cluster centers to select relatively better cluster centers. The k-means++ algorithm effectively solves the initial center selection problem of the k-means algorithm, but it does not provide an effective solution for the selection of cluster number k.

This cluster takes meteorological characteristics as input to subdivide the daily load scenarios. Meteorological features include different types of data, such as temperature and humidity. Since temperature is a significant factor affecting the variation of daily load, the temperature of a day is selected as the input of clustering, and the final result of daily load scene division is obtained.

The MI method is used to measure the importance of input features, and the extracted MI value is used to represent the importance value of the input features. The greater the MI value, the greater the correlation between the input features and load, that is, the greater the importance value. MI comes from the concept of entropy in information theory, which reflects the correlation between any two random variables. The MI value between the input feature and the load is used to characterize the importance value of the input feature. Therefore, based on dividing different daily load scenarios from the original database, the importance value fluctuation matrix of the input features is extracted for the specific scenarios.

The formula for calculating the MI value

The steps for constructing the importance fluctuation matrix are as follows:

According to the clustering result of the daily load scenario, the load data are divided into n groups according to the number of load sampling points in a day. Then, the output load dataset is as follows:

The input feature matrix

The MI value

t iteratively solves the input importance values at different moments from 1 to n and obtains the input importance fluctuation matrix

Considering that there is a certain relationship between the load in the current period and the load in the previous and later periods in short-term load forecasting, BiLSTM, which considers two-way time information, is chosen as the underlying model of short-term load forecasting. The calculation formula of BiLSTM is as follows:

The process of the short-term load forecasting method based on MI-BiLSTM is shown in

Flow chart of load forecast.

Based on the load prediction results of each scenario and combined with the comprehensive norm constraints in DRO (including 1-norm and infinite norm), the uncertainty set of predicted load values is constructed to enhance the robustness of the power system operation (

Meanwhile, the probability distribution of the load scenario satisfies the following confidence constraints:

Based on the constructed load uncertainty set, a two-stage energy storage planning model of a distribution network is established (

The first-stage model aims to minimize the annual investment cost of energy storage, and the specific expression is as follows:

The objective function of the second-stage model is the lowest daily operating cost

(1) Power flow constraint

Here, equation 21 uses second-order cone relaxation to deal with nonlinearity (

(2) Current constraint

(3) Voltage constraint

(4) Energy storage constraints

According to equations

The robust model in equation

MP is shown as follows:

SP is used to solve the lowest daily operating cost of the distribution network under the worst scenario probability distribution when the variables are given in the first stage, as follows:

Since the variables and constraints in equation

The process of solving the two-stage robust model can be seen in

Solution flow chart.

Here, the grid parameters of IEEE 33 nodes are used, among which the 16th node is connected to the photovoltaic and the 20th node is connected to the fan. The allowable voltage range of nodes is 0.95–1.05 pu. The specific network architecture is shown in

33-node network architecture.

Output of wind turbines and photovoltaics.

Annual load curve.

The annual load data of a region in the east of China are used as daily k-means++ clustering, and the four best types of scenarios and the probability of each scenario are divided by simulation, as shown in

Load clustering scenario and its probability.

Four different models, LSTM, BiLSTM, MI-LSTM, and MI-BiLSTM, are selected for comparison. Since the main work of prediction is to extract the importance value fluctuation matrix and modify the original input features, the relevant parameters of the deep neural network model should be controlled to remain unchanged during comparison, and the original input features and modified features should be observed to change the accuracy of prediction by substituting them into the model. Therefore, the parameter settings of the LSTM and MI-LSTM models are consistent, and the parameter settings of the BiLSTM and MI-BiLSTM models are also consistent. The hyperparameters of the LSTM and BiLSTM models are optimized by the control variable method. MAPE and RMSE are recorded under different daily load scenarios. The prediction results under the four methods are shown in

Comparison of the prediction results of different models under different scenarios.

Scenario | LSTM | BiLSTM | MI-LSTM | MI-BiLSTM | ||||
---|---|---|---|---|---|---|---|---|

MAPE (%) | RMSE (kw) | MAPE (%) | RMSE (kw) | MAPE (%) | RMSE (kw) | MAPE (%) | RMSE (kw) | |

1 | 6.52 | 103.21 | 6.09 | 96.16 | 5.09 | 79.67 | 4.07 | 64.91 |

2 | 6.32 | 100.37 | 5.28 | 82.96 | 4.85 | 76.28 | 4.15 | 65.94 |

3 | 7.20 | 117.17 | 5.95 | 95.25 | 5.21 | 82.88 | 4.43 | 70.47 |

4 | 7.49 | 114.83 | 6.28 | 97.54 | 5.96 | 92.79 | 5.03 | 78.00 |

Average | 6.88 | 108.89 | 5.90 | 92.98 | 5.28 | 82.90 | 4.42 | 69.83 |

As can be seen from

In scenarios one to four, the MAPE of the MI-BiLSTM model was 2.45%, 2.17%, 2.77%, and 2.46%, respectively. Compared with other models in all the scenarios, the average value of the MI-BiLSTM model is the lowest, and so is its RMSE.

The comparison of the results of different models is shown in

Comparison of load forecasting under different scenarios.

In order to verify the effectiveness and economy of energy storage planning, the following three schemes were compared.

Considering neither energy storage planning nor incorporating wind turbines or photovoltaics.

Considering incorporating WT and PV without considering energy storage planning.

Considering incorporating wind turbines, photovoltaics, and energy storage.

The indicators, energy storage capacity configuration results, and node position pairs under different schemes are shown in

According to

As can be seen from

It is not difficult to see that the implementation of energy storage planning for the distribution network on the basis of load forecasting has improved the operating costs, voltage fluctuations, and network losses of the distribution network.

Comparison of the indicators and configuration results.

Case | C_{1} (10^{4} yuan) |
C_{2} (yuan) |
C_{5} (yuan) |
C_{3} (yuan) |
Capacity (MWh) | Node |
---|---|---|---|---|---|---|

1 | — | 35,631.004 | 35,073.653 | 557.351 | — | — |

2 | — | 23,588.062 | 22,636.892 | 951.170 | — | — |

3 | 121.125 | 22,117.791 | 20,979.319 | 878.206 | 1.793 | 27 |

Voltage fluctuations of different cases.

To verify the advantages of the DRO energy storage planning presented in this article, the results of DRO are compared with those of SO and RO. Among them, SO is optimized based on the expected value of the load forecast, while RO considers the worst case based on the expected value of the load forecast, and the expected value of the load forecast fluctuates ±10%.

Comparison of the energy storage planning results under different uncertain methods.

Method | C_{1} (10^{4} yuan) |
C_{2} (yuan) |
C_{5} (yuan) |
C_{3} (yuan) |
C_{4} (yuan) |
Capacity (MWh) | Node |
---|---|---|---|---|---|---|---|

SO | 119.92 | 21,819.64 | 20,678.81 | 883.16 | 257.67 | 1.78 | 20 |

DRO | 121.13 | 22,117.79 | 20,979.32 | 878.21 | 260.27 | 1.79 | 27 |

RO | 119.83 | 24,440.52 | 23,326.73 | 856.31 | 257.48 | 1.77 | 18 |

Comparison of generation power in the distribution network under different uncertainty methods.

Comparison of energy storage charging and discharging under different uncertain methods.

As can be seen from

RO ignored the distribution information of the load and only considered the worst-case system operation, which led to an increase in the cost of power purchase to meet the load demand. Second, the configured energy storage charge and discharge cannot meet the worst-case load at all times, so the energy storage capacity decreases, which also increases the power generation of the distribution network unit.

In contrast, SO considers only a single empirical distribution, while DRO considers the worst distribution of load compliance in an uncertain concentration, which results in the lowest daily operating costs in SO.

In summary, the DRO model presented here takes into account the distribution information in the known load sample data and optimizes it for the worst-case scenario, effectively balancing robustness and economy.

In order to track the fluctuation of the importance value of input features and further improve the prediction accuracy, a MI-BiLSTM short-term load forecasting method considering the fluctuation of importance value of the features is proposed on the basis of k-means++ clustering. Then, based on load forecasting, a comprehensive norm-constrained uncertainty set is constructed. A two-stage robust model for energy storage planning of a distribution network is constructed to optimize the network loss. After a case analysis, the following conclusions are reached:

1) The MI-BiLSTM short-term load forecasting method using a feature importance value fluctuation matrix can make up for the defects of LSTM and improve the forecasting accuracy.

2) Under various daily load scenarios, the prediction methods presented in this paper show higher prediction accuracy. This shows that the method is not limited to a specific scenario and has good adaptability and stability.

3) Based on load prediction, energy storage planning for a distribution network not only reduces the daily operating cost of the distribution network but also improves the power flow distribution of the system, further reduces network loss, and improves voltage fluctuation, which is of practical significance.

4) For uncertainty, the DRO method based on comprehensive norm can improve the robustness of the uncertainty set, and compared with SO and RO, this method has a better performance in planning and economic problems and the effect is stable.

The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding authors.

YH: writing–review and editing and data curation. YM: writing–original draft.

The authors declare that financial support was received for the research, authorship, and/or publication of this article. This work was supported by the Science and Technology Project of State Grid Shanghai Electric Power Company (No. 52090022004J).

Authors MY, HZ, KJ, YL, and XT were employed by State Grid Shanghai Electric Company.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors declare that this study received funding from Science and Technology Project of State Grid Shanghai Electric Power Company (No. 52090022004J). The funder had the following involvement: study design, collection, analysis, interpretation of data, the writing of this article.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.