Constraint Generation Algorithm Research Articles

Risk-averse electrolyser sizing in industrial parks: An efficient stochastic-robust approach

Hydrogen is called to be one of the most important energy vectors in future energy systems. Nowadays, its use in the industry sector is prominent, finding multiple applications in fertilizer production or oil refining. In this sense, some industry sectors demand a considerable amount of hydrogen for their processes. In many cases, hydrogen must be purchased externally, which supposes a challenge due to hydrogen transportation is costly and few efficient. In this context, local hydrogen production through mature electrolysis technology may suppose an attractive alternative in industrial parks. This paper focuses on this topic, in particular, a risk-averse electrolyser sizing methodology is developed. The new approach accounts for uncertainties in electricity prices as well as local renewable generation and demand through an original hybrid stochastic-robust model. The developed uncertainty modelling is integrated into a novel four-level optimization framework, whose main result is the optimal electrolyser rated power. To efficiently attain the solution, an original hybridization of the Benders' decomposition and the Column and Constraint Generation Algorithm is proposed. The developed methodology results efficient in an illustrative three-industry park, showing that installing local hydrogen generation may reduce the amount of hydrogen purchased externally (by 38%) and project costs by 2.5%. Furthermore, increasing the robustness level leads to increase the project cost by 8%, while assuming unfavourable realization of uncertainties. Moreover, the developed tool is further validated in larger parks, involving an increasing number of industries, showing that the proposed methodology scales well with the size of the park.

Low-carbon Economic Dispatching Strategy Based on Feasible Region of Cooperative Interaction between Wind-storage System and Carbon Capture Power Plant

The high penetration of new energy into the grid is an effective method for reducing carbon emissions. However, the randomness and uncertainty of large-scale wind power (WP) output pose challenges to the grid dispatch operation and increase the requirements for carbon emission control. This paper proposes a low-carbon economic dispatching strategy based on the feasible region (FR) of cooperative interaction between WP and flexible resources to promote the consumption of WP and reduce carbon emissions. In particular, energy storage (ES) and carbon capture power plant (CCPP) are used as a set of adjustable flexible resources, and the power FR of WP, ES and CCPP is constructed to provide a visualization reference for grid scheduling. Then, a two-stage robust optimization (RO) dispatching FR-based model considering WP consumption capacity is proposed to cope with the operational risk of WP output stochasticity for power grid. Finally, the column constraint generation algorithm (C&CG) is used to solve the problem and evaluate low carbon level in the system according to the carbon flow theory. The simulation results verified the effectiveness of the suggested approach demonstrated by the modified IEEE 39-bus and IEEE 118-bus test cases.

Optimal Scheduling of Integrated Energy System Considering Electric Vehicle Battery Swapping Station and Multiple Uncertainties

In recent years, there has been rapid advancement in new energy technologies aimed at mitigating greenhouse gas emissions stemming from fossil fuels. Nonetheless, uncertainties persist in both the power output of new energy sources and load. To effectively harness the economic and operational potential of an Integrated Energy System (IES), this paper introduces an enhanced uncertainty set. This set incorporates N-1 contingency considerations and the nuances of source–load distribution. This framework is applied to a robust optimization model for an Electric Vehicle Integrated Energy System (EV-IES), which includes Electric Vehicle Battery Swapping Station (EVBSS). Firstly, this paper establishes an IES model of the EVBSS, and then proceeds to classifies and schedules the large-scale battery groups within these stations. Secondly, this paper proposes an enhanced uncertainty set to account for the operational status of multiple units in the system. It also considers the output characteristics of both new energy sources and loads. Additionally, it takes into consideration the N-1 contingency state and multi-interval distribution characteristics. Subsequently, a multi-time-scale optimal scheduling model is established with the objective of minimizing the total cost of the IES. The day-ahead robust optimization fully considers the multivariate uncertainty of the IES. The solution employs the Nested Column and Constraint Generation (C&CG) algorithm, based on the distribution characteristics of multiple discrete variables in the model. The intraday optimal scheduling reallocates the power of each unit based on the robust optimization results from the day-ahead scheduling. Finally, the simulation results demonstrate that the proposed method effectively reduces the conservatism of the uncertainty set, ensuring economic and stable operation of the EV-IES while meeting the demands of electric vehicle users.

Communication network robust routing optimization in an integrated energy cyber–physical system based on a random denial-of-service attack

The integration of power grids and communication networks in smart grids enhances system safety and reliability but also exposes vulnerabilities to network attacks, such as Denial-of-Service (DoS) attacks targeting communication networks. A multi-index evaluation approach is proposed to optimize routing modes in integrated energy cyber-physical systems (IECPS) considering potential failures from attacks. Security and economic service evaluation indexes are incorporated to quantify the significance of information flow routing. An optimization model for electric, heat, and gas routing in worst-case scenarios is formulated and solved using a column and constraint generation algorithm. The optimized routing method effectively circumvents specified attack areas, reducing the correlation degree of communication links within the attack area. Comparison with single-service optimization methods demonstrates the superiority of the proposed approach in mitigating the impact of network attacks on IECPS. The study highlights the importance of considering security and economic factors in optimizing routing modes to enhance the resilience of integrated energy cyber-physical systems against network attacks, particularly DoS attacks on communication networks. The evaluation index approach presented in this study provides a comprehensive method for assessing the importance of communication links in IECPS and optimizing routing modes to improve system robustness and reliability in the face of network attacks.

A two-stage robust configuration optimization model and solution algorithm for new flexibility resources considering uncertainty response characterization

As the proportion of new energy continues to increase, the safety and stability of the new power system are challenged, urgently requiring the allocation of new flexible resources. This paper proposes a two-stage robust capacity optimization model considering flexibility demand constraints. Firstly, the uncertain characteristics of new energy are described, and a model of flexible resource adjustment capacity is established. Then, uncertain parameters are introduced to construct a robust capacity optimization model considering supply-demand balance, solved by column constraint generation algorithm and KKT theorem. Finally, a power system in a certain region of China is selected as the simulation object for empirical analysis to verify the effectiveness of the constructed model. The results show that the two-stage robust configuration optimization model constructed in this paper can address the uncertainty of power system and the flexibility demand brought by new energy, and the planning results can achieve a balance between the safety and economy of the new power system.

Equalizing multi-temporal scale adequacy for low carbon power systems by co-planning short-term and seasonal energy storage

Power supply faces seasonal security risks due to the large seasonal volatility of renewable energy sources (RES) generation. Power systems with high shares of RES generation are more difficult to keep seasonal and daily/hourly supply adequacy at the same level. Therefore, this paper first addresses multi-temporal adequacy detail accounting for differences in RES output and timing of production, and demand. Then a planning approach is proposed for sizing short-term and seasonal energy storage accompanying with RES to achieve multi-temporal adequacy equilibrium. Unlike existing methods based on linking typical days or 8760-h simulations, the seasonal electricity adequacy constraints are captured by orderly clustering yearly net power curves, then the energy balance constraints are decoupled into long-term (i.e., seasonal) and short-term (i.e., hourly) energy balances. At the short-term scale, the robust optimization is used to address the uncertainty and randomness of wind and solar generation, in the same time realizing the coordination of short-term and seasonal energy storage. A modified column and constraint generation algorithm is used to solve the min-max-min model with binary variables. Finally, case studies are carried out on the Garver-6 system and the Northwest China Power Grid. The results demonstrate that the proposed planning method ensures multi-temporal scale adequacy equilibrium for high-RES power systems, and improving the planned system's economic performance.

Evaluating the reliability of microgrids consisting of renewable energy sources using stochastic scheduling based on the data-driven uncertainty set

The paper addresses challenges arising from the unpredictable and probabilistic nature of wind speed and solar irradiance, leading to variable power production in renewable sources. Power imbalance issues in grids result from the difficulty in accurately estimating these variables. The study introduces an improved data-driven uncertainty set, utilizing a neural network trained with extensive historical data from a multi-microgrid system. This set efficiently identifies strong coupling and extracts characteristic scenarios, ensuring high reliability with a minimal number of scenes. The proposed probabilistic model, implemented in the coordination of pumped storage, wind, and solar power plants, incorporates energy limits and storage characteristics. A four-mode IEEE model for storage units allows quick response to system needs. Simulating storage unit states every hour, considering system load, output power, and energy limitations, optimizes power dispatch based on battery capacity. Additionally, the paper addresses the uncertainty in electric power demand in microgrids, proposing an improved data-driven uncertainty set obtained from a neural network. By eliminating unrealistic worst-case scenarios, the approach accurately captures system characteristics, maintaining high reliability while significantly reducing convergence time. The proposed uncertainty set is applied in a novel two-stage robust optimization dispatch model, transforming the optimization problem into a mixed-integer linear programming problem, and solving it using a column and constraint generation algorithm. Numerical case studies verify the feasibility and superiority of the proposed approach in terms of economy and convergence performance compared to existing robust optimization methods.

Research on distributionally robust energy storage capacity allocation for output fluctuations in high permeability wind and solar distribution networks.

This paper presents a novel approach to addressing the challenges associated with energy storage capacity allocation in high-permeability wind and solar distribution networks. The proposed method is a two-phase distributed robust energy storage capacity allocation method, which aims to regulate the stochasticity and volatility of net energy output. Firstly, an energy storage capacity allocation model is established, which considers energy storage's investment and operation costs to minimize the total cost. Then, a two-stage distributed robust energy storage capacity allocation model is established with the confidence set of uncertainty probability distribution constrained by 1-norm and ∞-norm. Finally, a Column and Constraint Generation (C&CG) algorithm is used to solve the problem. The validity of the proposed energy storage capacity allocation model is confirmed by examining different wind and solar penetration levels. Furthermore, the model's superiority is demonstrated by comparing it with deterministic and robust models.

Robust fault recovery strategy for multi-source flexibly interconnected distribution networks in extreme disaster scenarios

To enhance the resilience of power distribution networks against extreme natural disasters, this article introduces a robust fault recovery strategy for multi-source, flexible interconnected power distribution networks, particularly under scenarios of extreme disasters. Initially, the comprehensive risk of system failure due to ice load on distribution lines and poles is fully considered, and a model for the overall failure rate of lines is constructed. This model addresses the diverse failure scenarios triggered by various meteorological conditions. Through the use of information entropy, typical extreme disaster failure scenarios are identified, and lines with high failure rates under these scenarios are determined. Subsequently, a box-type interval model is developed to represent the uncertainty in the output of distributed generation (DG), and on this basis, a robust fault recovery model for multi-source power distribution networks interconnected through soft open points (SOPs) is established, and use the Column and Constraint Generation (C&CG) algorithm to solve the problem. Finally, the fault recovery model and strategy proposed are validated through an illustrative example based on a modified IEEE 33-node interconnected system.

A Distributionally Robust Optimization Strategy for a Wind–Photovoltaic Thermal Storage Power System Considering Deep Peak Load Balancing of Thermal Power Units

With the continuous expansion of grid-connected wind, photovoltaic, and other renewable energy sources, their volatility and uncertainty pose significant challenges to system peak regulation. To enhance the system’s peak-load management and the integration of wind (WD) and photovoltaic (PV) power, this paper introduces a distributionally robust optimization scheduling strategy for a WD–PV thermal storage power system incorporating deep peak shaving. Firstly, a detailed peak shaving process model is developed for thermal power units, alongside a multi-energy coupling model for WD–PV thermal storage that accounts for carbon emissions. Secondly, to address the variability and uncertainty of WD–PV outputs, a data-driven, distributionally robust optimization scheduling model is formulated utilizing 1-norm and ∞-norm constrained scenario probability distribution fuzzy sets. Lastly, the model is solved iteratively through the column and constraint generation algorithm (C&CG). The outcomes demonstrate that the proposed strategy not only enhances the system’s peak-load handling and WD–PV integration but also boosts its economic efficiency and reduces the carbon emissions of the system, achieving a balance between model economy and system robustness.

A network search space reduction method for robust coordinated energy storage and transmission expansion planning

AbstractThe development of renewable energy will increase the demand for flexible resources in power systems due to the strong uncertainties. To allocate resources and cope with these uncertainties, it is beneficial to apply robust coordinated energy storage and transmission expansion planning (ES&TEP). The large candidate line set can significantly increase the computational complexity of robust optimization models. However, there is currently no suitable network search space reduction (NSSR) method to address this problem. This paper designs a NSSR method based on redundancy constraint identification that only requires information on component power ranges rather than fixed power curves, which can be well adapted to robust optimization. Additionally, this method requires only basic numerical calculations and ensures convergence within a finite number of iterations. The classical stochastic robust ES&TEP model and the column and constraint generation (C&CG) algorithm are used to validate the effectiveness of the NSSR method. In the case studies, the numerical results confirm the rationality and effectiveness of the approach proposed in this paper. By selecting appropriate parameters, the candidate line set can be reduced by over 70% and the computational efficiency can be improved by an order of magnitude.

Energy management of multi-microgrid system with renewable energy using data-driven distributionally robust optimization

ABSTRACT By clustering multiple microgrids (MGs), a multi-microgrid (MMG) system plays a significant role in integrating a large amount of renewable generation. However, the large-scale utilization of renewable energy also brings uncertainties to MMG energy management. In this work, a novel comprehensive bi-level MMG energy management model considering uncertainties of renewable energy is first developed which includes unit commitment (UC) problem and other models in the lower MG level. Then considering the non-convexity of the bi-level problem, a decomposition method called analytical target cascading (ATC) is employed to deal with it by decentralization. With regard to the energy management of each individual MG, a two-stage distributionally robust model is developed which describes the uncertainties from probability distribution of renewable generation with a metric-based ambiguity set. Moreover, an efficient solution scheme based on column and constraint generation (CCG) algorithm and a decomposition method without duality is designed to handle the MG energy management problem. Finally, we implement extensive experiments to corroborate the effectiveness of the proposed approach. Particularly, the optimal solution from the proposed method can attain 2.98% less cost compared with that from robust optimization (RO) method and achieve 86.17% less energy trading amount than that in independent mode.

Robust optimal operation scheduling method for integrated energy system considering flexible energy storage and mixed hydrogen natural gas

ABSTRACT At present, the number of electric vehicles is increasing day by day. The full integration of electric vehicles and multi-energy coupled integrated energy systems is the future development trend. This paper introduces a novel form of flexible energy storage in the integrated energy system ;(IES): electric vehicle (EV). And It proposes that mixed natural gas hydrogen be used as the primary energy source for IES, which replaces traditional natural gas. Combined with the above, the IES is scheduled to meet the system’s multi-load for heating, cooling, and electricity demands. Based on the integrated energy system’s structure and energy conversion principles, a robust two-stage optimization model for the IES is proposed to minimize the daily operation scheduling costs. The proposed model considers the uncertainty of distributed renewable generation and flexible energy storage. Uncertain adjustment parameters are introduced into the model, which can flexibly adjust the conservatism of the scheme. Using the column and constraint generation algorithm (C&CG) and the strong duality theory, the model presented in this paper is solved and the optimal scheduling scheme is obtained. The final simulation results validate the effectiveness of the model and algorithm. The addition of flexible energy storage and mixed natural gas hydrogen effectively improves the economy and flexibility of the system while reducing carbon emissions costs. Consideration of uncertainty improves system robustness and safety. In addition, sensitivity analyses of the influence of the proportion of hydrogen mixed with natural gas, the setting of uncertain adjustment parameters, electricity prices, weather, and load fluctuations on system operation. The results show that compared to existing research, electric vehicles as a flexible energy storage device and mixed natural gas hydrogen supply, increase the economic benefits of IES by 19.8% and 23%, respectively.

Robust stochastic optimal dispatching of integrated electricity-gas-heat system considering generation-network-load uncertainties

Integrated energy systems with the deep coupling of electric power, natural gas, and heat have attracted much interest lately. In the modeling of such an integrated electric-gas-heat system (IEGHS), there is the problem of generation–load uncertainty. The literature has not yet addressed the uncertainties related to pipeline parameters and buried temperature in a natural gas network. To fill this gap, a robust stochastic optimal dispatching model has been proposed in this paper, which can effectively solve the IEGHS dispatching problem under multiple uncertainties. A robust adjustable uncertain set is adopted to deal with the uncertainties of wind power generation and pipeline parameters. The Wasserstein generative adversarial network based on gradient normalization is proposed to generate load-side demand scenarios. Then, a column and constraint generation algorithm is adopted to solve the proposed model. The simulation analysis successfully demonstrates the efficacy of the proposed model and algorithm. By utilizing this approach, the system can obtain a scheduling scheme with the lowest operating cost even under worst-case scenarios.

Data-driven-based distributionally robust optimization approach for a virtual power plant considering the responsiveness of electric vehicles and Ladder-type carbon trading

To encourage the utilization of decentralized renewable energy systems, a data-driven-based distributionally robust optimization (DRO) model is proposed for a virtual power plant (VPP) considering the responsiveness of electric vehicles (EVs) and a ladder-type carbon trading mechanism (LT-CTM). An EV virtual energy storage (EV-VES) calculation model for dispatchable power is formulated to facilitate the centralized scheduling of EVs, considering responsiveness and spatial–temporal distribution characteristics. Additionally, multiple kinds of energy storage systems and flexible loads are considered in the VPP. Furthermore, to handle multiple uncertainties for both the renewable energy and load, Latin hypercube sampling is applied to generate the renewable energy scenarios, and K-means clustering is used to obtain typical scenes. Then the DRO model is used to solve the dispatch problem. An LT-CTM is leveraged to reduce carbon emissions. The column and constraint generation algorithm is then employed to identify an optimal operational benefit solution. Finally, a multi-parameter coupling analysis of ladder-type carbon trading is used for the environmental protection and economy of the VPP. The results confirm the efficacy of the proposed day-ahead scheduling model, offering a theoretical reference for operators when making scheduling decisions.

Robust resilience enhancement strategy for gas‐electricity integrated energy system considering multiple reinforcement levels

AbstractNatural disasters are extreme events with low probability but strong destructive ability, which have a serious impact on the power system. The gas‐electricity integrated energy system is more likely to be affected by natural disasters due to its complex multi‐energy coupling characteristic. In order to improve the resilience of the gas‐electricity integrated energy system under natural disasters, this paper proposes a three‐layer defence‐attack‐defence robust resilience improvement model with the objective of minimizing the load loss in the gas‐electricity integrated energy system. Firstly, in order to cope with various levels of disaster and improve the economy of line/pipeline reinforcement in the gas‐electricity integrated energy system, a multi‐level line/pipeline reinforcement model is proposed on the basis of load weight in the upper layer. Then, information entropy is introduced to represent the impact of natural disasters in the middle layer. Based on the operation constraints of the gas‐electricity integrated energy system, the optimal allocation of the mobile electricity storage and liquefied gas storage is established in the lower layer. The three‐layer resilience improvement model is solved by the nested column and constraint generation algorithm. Finally, the case study proves the feasibility of the model and the effectiveness of the solution method.

Data-Driven Distributionally Robust Optimization-Based Coordinated Dispatching for Cascaded Hydro-PV-PSH Combined System

The increasing penetration of photovoltaic (PV) and hydroelectric power generation and their coupling uncertainties have brought great challenges to multi-energy’s coordinated dispatch. Traditional methods such as stochastic optimization (SO) and robust optimization (RO) are not feasible due to the unavailability of accurate probability density function (PDF) and over-conservative decisions. This limits the operational efficiency of the clean energies in cascaded hydropower and PV-enriched areas. Based on data-driven distributionally robust optimization (DRO) theory, this paper tailors a joint optimization dispatching method for a cascaded hydro-PV-pumped storage combined system. Firstly, a two-step model for a Distributed Renewable Optimization (DRO) dispatch is developed to create the daily dispatch plan, taking into account the system’s complementary economic dispatch cost. Furthermore, the inclusion of a complementary norm constraint is implemented to restrict the confidence set of the probability distribution. This aims to identify the optimal adjustment scheme for the day-ahead dispatch schedule, considering the adjustment cost associated with real-time operations under the most unfavorable distribution conditions. Utilizing the MPSP framework, the Column and Constraint Generation (CCG) algorithm is employed to resolve the two-stage dispatch model. The optimal dispatch schedule is then produced by integrating the daily dispatch plan with the adjustive dispatch scheme. Finally, the numerical dispatch results obtained from an actual demonstration area substantiate the effectiveness and efficiency of the proposed methodology.

Planning model for rural distribution networks with integrated energy stations via robust optimization method

With the modernization and intelligent development of agriculture, the energy demand in rural areas continues to increase, which leads to an increased operational burden on the existing rural distribution network. Integrated energy stations (IESs), in rural areas, use renewable energy sources such as biogas, wind power, and photovoltaic as energy inputs, which can fully improve energy efficiency and help reduce the operating load and peak valley difference of rural distribution networks. In this paper, a multistage planning model is proposed for rural distribution networks with IESs based on the robust optimization method. Firstly, a rural distribution network operation framework with IESs is proposed, and a mathematical model of rural IESs is built based on the energy hub (EH). Then, the multistage robust planning model of rural distribution net-works with IESs is developed and typical scenarios of stochastic source and load are generated based on improved k-means. An iterative solution method for a two-stage robust optimization method is proposed based on the nested column constraint generation (NC&CG) algorithm. Finally, the effectiveness of the presented model and solution approach is assessed through case studies on a modified IEEE 33-node distribution network and a real 152-node distribution network.

Robust Optimization of Large-Scale Wind–Solar Storage Renewable Energy Systems Considering Hybrid Storage Multi-Energy Synergy

With the rapid integration of renewable energy sources, such as wind and solar, multiple types of energy storage technologies have been widely used to improve renewable energy generation and promote the development of sustainable energy systems. Energy storage can provide fast response and regulation capabilities, but multiple types of energy storage involve different energy conversion relationships. How to fully utilize the advantages of multiple energy storage and coordinate the multi-energy complementarity of multiple energy storage is the key to maintaining a stable operation of the power system. To this end, this paper proposes a robust optimization method for large-scale wind–solar storage systems considering hybrid storage multi-energy synergy. Firstly, the robust operation model of large-scale wind–solar storage systems considering hybrid energy storage is built. Secondly, the column constraint generation (CCG) algorithm is adopted to transform the original problem into a two-stage master problem and sub-problem for solving to obtain the optimal strategy of system operation with robustness. Finally, the validity of the proposed method is verified through case tests. The results show that the proposed method can effectively coordinate the multi-energy complementary and coordinated operation of multiple hybrid energy storage, and the obtained operation strategy of large-scale wind–solar storage systems can well balance the economy and robustness of the system.

A distributionally robust optimization approach for optimal load dispatch of energy hub considering multiple energy storage units and demand response programs

The coupling relationship among various energy sources has been consistently reinforced by the advancement of the energy Internet. In the context of modeling multi-energy systems, the energy hub (EH) represents a significant and valuable approach. To attain optimal operation of the EH, this study proposes an optimal load dispatch model for a system that incorporates a combined heat and power (CHP) unit, gas boiler (GB), electric chiller (EC), absorption chiller (AC), heat energy storage (HES) unit, and electrical energy storage (EES) unit. A two-stage distributionally robust optimization (DRO) method that is driven by data is employed to address the uncertainties of electricity prices. Additionally, the proposed two-stage DRO model is effectively solved through the utilization of the column and constraint generation (C&CG) algorithm. Three cases are discussed in the paper with various energy storage units and demand response (DR) settings. The simulation results show that by deploying energy storage units and participating in DR projects, the EH system can reduce the total costs by 2.56 % and 10 %, respectively. Meanwhile, simulation results reveal that the proposed data-driven DRO model can achieve a compromise between the economy and robustness of the scheduling model compared with stochastic optimization (SO) and robust optimization (RO) methods. The simulation results illustrate the effectiveness of the proposed model for ensuring the economical and efficient operation of the system in the face of electricity price uncertainties.