To address the scheduling problem involving energy storage systems and uncertain energy, we propose a method based on multi-stage robust optimization. This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method, which helps overcome the limitations of traditional methods in terms of time scale. The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day. To achieve this, a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power. The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem. By decomposing the problem into a series of sub-objectives, the system scale is effectively reduced, and the algorithm’s convergence ability is improved. Compared with other algorithms, the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

The vigorous development of renewable energy sources such as new energy has gradually weakened the status of traditional energy. Mbungu et al. [

The new integrated energy system covers multiple energy sources. The development of energy sources including natural gas and heat energy has become an important development direction for the current national response to the energy crisis [

Robustness optimization is an optimization method that makes use of interval disturbance information to make the best decision under the worst disturbance condition. Recently, it has been applied to the dispatching decision of power systems because of its advantages such as easily available basic data, high computational efficiency, and suitability for solving large-scale systems. Based on this, this paper studies the regulation method of energy storage systems based on multi-stage robust optimization. Aiming at robust optimization parameters, wind power uncertainty, photovoltaic power generation uncertainty parameters, renewable energy output uncertainty model, and load uncertainty model, multi-stage robust optimization of energy storage is carried out. By constructing a multilevel robust optimal allocation model, the upper optimization model and the lower optimization model are refined. By applying decision constraints, the performance of the energy storage power station system is improved, resulting in enhanced system efficiency and reduced computation time. The use of generalized Benders Decomposition facilitates coordinated operation and eliminates unnecessary power data. Taking into account the coordinated operation among different systems, the power dispatch plan should be developed to enhance the visibility of renewable energy contribution and avoid operational delays. Experimental results demonstrate that this method can adjust the uncertain set boundaries by introducing various constraint parameters. It effectively addresses the conservativeness issue commonly encountered in other robust optimization approaches, enabling a more reasonable reduction in energy storage capacity within the power system. Consequently, it enhances the responsive capabilities of large-scale renewable energy integration into the grid.

The primary objective of power system dispatch is to ensure a balance between the total energy generated and the total energy consumed by the load. With the presence of renewable energy, the static balance of the power system evolves into a dynamic equilibrium over time. That is, in the process of power dispatching, it is necessary to maintain the energy regulation capacity of the system is greater than the fluctuation range of the energy consumption load.

Robust optimization is an optimization method for uncertainties. In the process of system operation, assuming that the value range of uncertainties is fixed, the purpose of the optimal solution is to make the values of any uncertainties meet the constraint requirements of the system [

The establishment of a good set of uncertainties is the key to solving the problem of inconsistencies. In the power dispatching problem, renewable energy is the main source of system uncertainty. Various factors, including seasonal changes and environmental conditions, can impact wind energy. Therefore, it is important to enhance the accuracy of wind power output prediction. Similarly, the output of photovoltaic systems is influenced by factors such as day-night cycles, solar intensity, and cloud conditions. These factors contribute to more intense fluctuations in the short-term output of photovoltaic systems.

The main influencing factor of the fan output is the size of the wind speed. In the case of a certain air quality, the power generated by the fan

where,

The fan’s specific output is influenced by factors such as wind speed, wind direction, air pressure, and temperature. The uncertainty associated with these factors leads to fluctuations in the actual output of the fan around its theoretical value. Additionally, due to the non-linear relationship between wind speed and wind output power, the distribution of wind power output power varies under different wind speed conditions.

The situation of solar power generation is mainly determined by the intensity of light at the time of power output [

where,

In addition to the impact of light intensity, factors such as air temperature, cloud cover, and atmospheric conditions also affect the output power of photovoltaic power generation systems. Therefore, it has obvious output uncertainty.

With the development of multi-energy systems, the share of renewable energy sources in the electricity mix is steadily rising. However, the unpredictable, fluctuating, and sporadic nature of renewable energy output presents considerable challenges to the power system. These factors can significantly impact the stability and safety of the power system.

The uncertainty related to renewable energy sources like wind and photovoltaics can be characterized by the disparity between forecasts and actual output. Thus the model _{k}

where,

By establishing an uncertain regulation model, the multi-energy composite system is represented as:

where,

For renewable energy, the ability to regulate its output also has certain uncertainties. Its uncertainty can be expressed in the model as:

where,

In a diverse energy system, uncertainties exist not only in the output of renewable energy sources but also in the load. The load variation in such systems is influenced by uncertain factors like weather conditions, energy prices, and behavioral patterns, resulting in load uncertainty [

In the operation of multi-energy systems, the presence of various uncertain disturbances can significantly impact system stability. Evaluating the compatibility between energy load demand and system stability in uncertain conditions is of utmost importance. Furthermore, developing an uncertain load model is critical for ensuring the safety and reliability of the system during its operation. The model for constructing the load level

where,

Given the inherent unpredictability of renewable energy sources, the integration of energy storage systems plays a vital role in enhancing the flexibility of power systems during power dispatch. By storing surplus energy generated from renewables during high production periods and releasing it during low production periods, energy storage systems help mitigate fluctuations and ensure a stable and dependable power supply [

When dealing with short-term and ultra-short-term economic scheduling problems, it is important to consider the calculation method used. A typical approach is to employ a forward-looking economic scheduling model with a rolling time scale. To ensure accurate solutions, the time scale for this method typically falls between half an hour and two hours. This does not meet the requirements of economy and effectiveness for economic dispatch that needs to cover the whole day. Therefore, a multi-stage scheduling model is required to ensure system accuracy.

The multi-stage robust optimization model for the daily scheduling model can optimize the energy storage resources for a relatively long time. It can provide the system with extreme situations, making the decision-maker’s decision-making more forward-looking [

Given the uncertain parameters and influences within the system, historical data does not need to be taken into account during system operation [

where,

Decision objective

where,

In order to effectively cope with the robustness of increasing loads, and fully consider the role of uncertain output and uncertain loads. The setting of the objective function is the maximum fluctuation of the indeterminant. The objective function after optimization of the configuration is:

For a multi-objective optimization process, the influence of different factors needs to be considered comprehensively. Consider the conflict between the various uncertainties and weigh the objectives according to their importance. You can optimize a multi-objective problem as a single-objective problem, expressed as:

where,

Another optimization goal of the model is to ensure the economics of the distribution system. Thus the optimized objective function is the lowest power purchase cost for the distribution network, expressed as:

where,

where,

Uncertain output constraint of photovoltaic power generation system, expressed as:

where,

Operation limit of power station, expressed as:

In an equalized circuit system, it is assumed that the state of charge changes in each battery are consistent. This means that the output characteristics of the battery pack are equivalent to the output of a single battery. As a result, the battery pack can be simplified using the Thevenan model [

where,

Energy balance constraint, expressed as:

where,

Thermal power unit operation constraints, expressed as:

Generally, the fuel cost characteristics of thermal power units are approximated by a smooth quadratic function, and a pulse is superimposed on the unit energy consumption curve considering the threshold effect. The output constraint is shown in

where,

Energy storage system operation constraints, expressed as:

In energy storage systems, the state of charge in each period is affected by both the previous state of charge and the current charge and discharge amounts. To ensure the sustainable operation of the energy storage system, it is essential for the total charge and discharge power to balance out over the entire scheduling period:

where,

Uncertain delay constraint, expressed as:

The uncertain delay is treated by delay dependence, and the margin of preset delay is constrained to minimize to evaluate the robustness of closed-loop systems with different delays. The delay meets the following conditions:

where,

For multi-stage robust optimization problems, the model needs to be solved by generalized Benders Decomposition. This decomposes the problems in the model into sub-problems [

A flowchart of the decomposition method is shown in

After the decomposition of the model, the main requirements to solve the problems include economic optimization problems, feasibility problems and planning optimization problems.

The test system was obtained after modification of the PJM 5-bus system. The system consists of four thermal power units, one wind farm, one photovoltaic power station and one energy storage system. The specific parameters of the test system are as follows: the rated voltage is 10.60 kV, the maximum allowable voltage of a single node is 1.97 pu, the maximum allowable current of the corresponding branch is 1.20 kA, and the minimum required voltage value of the standby is 0.25 pu, the minimum allowable current of the corresponding branch is the minimum. The value is 0.15 kA. Among them, the rated capacity of traditional units is 1000 MW, the proportion of new energy photovoltaic power generation is 20%, the rated power of energy storage power station is 20 MW, and the total power is set at 20 MW·h. The parameters of the generator set are shown in

Unit | Power range (MW) | RU/RD (MW/h) | Unit cost (yuan/MW·h) |
---|---|---|---|

G1 | 0~180 | 80 | 9800 |

G2 | 0~200 | 68 | 25000 |

G3 | 0~50 | 16 | 9000 |

G4 | 0~500 | 208 | 19000 |

For thermal power sets, the cost function is considered to be a linear change. The penalty cost per unit cut load is 120 yuan/kW·h. The penalty cost of not meeting the standard for uncertain energy consumption is 30 yuan/kW·h.

Set the battery energy storage device of the energy storage power station as a lithium iron phosphate material battery. The unit capacity cost of the battery is 2100 yuan/kW·h, the power cost is set to 1600 yuan/kW·h, and the operation and maintenance cost accounts for 1% of the total investment. Set the fluctuation deviation of renewable energy storage to 10%.

Schedule the analysis results

The method of this paper, the method of reference [

As shown in

Considering the worst-case scenario in which the power output in the system is uncertain, the system scheduling scenario is shown in

As can also be seen in

Algorithm comparison

In order to prove the superiority of this model, it is compared with the methods of reference [

The methods of reference [ |
The methods of reference [ |
Methods of this paper | |
---|---|---|---|

Fuel cost (million yuan) | 185.35 | 198.35 | 178.14 |

Load abandonment cost (10,000 yuan) | 1.42 | 10.06 | 0.98 |

Cut load cost (10,000 yuan) | 0 | 16.23 | 0 |

Total cost (10,000 yuan) | 186.77 | 240.35 | 179.12 |

It can be seen from the results in

Uncertainty analysis

To verify the influence of uncertain source loads on power system dispatching. According to the different deviations of renewable energy fluctuations, the robust dispatching model is analyzed to ensure that the deviation of load fluctuations is less than 10%. Set the fluctuation deviation of renewable energy to 0%–30%. In this scenario, compare the operating cost fluctuation range of the methods in this paper [

It can be seen from

When the fluctuation of uncertain energy sources is small, the system can effectively ensure its economy on the basis of ensuring robustness. In actual scheduling, the staff needs to ensure the economy of the scheduling system according to the fluctuation deviation.

To address the scheduling challenges related to energy storage systems and uncertain energy sources, this research proposes a regulation method based on multi-stage robust optimization. The study constructs an optimal allocation model for energy storage in power systems and employs the multi-stage robust optimization approach to address the limitations of traditional methods in terms of time scale. By doing so, it aims to tackle system issues arising from the fluctuations of uncertain environmental energy and unpredictable load variations. The generalized bending decomposition method is utilized to optimize the parameters of the target solution model, reducing the system size and ensuring algorithm convergence. Comparative analysis demonstrates that the proposed model exhibits favorable economic performance when compared to other models. Additionally, the study highlights the significant impact of fluctuation deviations on the system’s operating cost and robustness. This model can effectively enhance the economic efficiency of power systems containing uncertain energy and energy storage systems, making it suitable for guiding the regulation and control of related power systems. Future research can further explore the uncertainty on the power side and investigate the coordinated configuration of energy storage and reactive power compensation equipment with 100% renewable energy supply and support for new energy stations.

None.

The authors received no specific funding for this study.

The authors confirm contribution to the paper as follows: study conception and design, data collection: Zaihe Yang, Shuling Wang; analysis and interpretation of results: Runhang Zhu, Jiao Cui, Ji Su; draft manuscript preparation: Zaihe Yang, Liling Chen. All authors reviewed the results and approved the final version of the manuscript.

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

The authors declare that they have no conflicts of interest to report regarding the present study.