Two-stage Robust Optimization Model Research Articles

Decomposition algorithms for the robust unidirectional quay crane scheduling problems

Our study focuses on a two-stage robust optimization model for the unidirectional quay crane scheduling problem with uncertain handling times at container terminals. We first implement two classical algorithms adopted in Li and Zhang (2021), the Benders decomposition algorithm and the column-and-constraint generation algorithm, to solve the robust model. Based on analytical and numerical comparisons of them, we design an exact hybrid algorithm to leverage capabilities of both algorithms by alternatively adding cuts of both kinds. Extensive experiments validate the effectiveness of this mechanism. Numerical experiments also reveal that the benefit and the cost of robustness fade away as the uncertainty budget increases and highlight the advantage of our robust approach to deal with uncertainty over a two-stage stochastic program under extreme situations.

Dynamic aggregation strategy for a virtual power plant to improve flexible regulation ability

The virtual power plant (VPP) provides an effective way for the coordinated and optimized operation of distributed energy resources (DERs). To solve the aggregation problem of a VPP containing scattered layouts and heterogeneous performance DERs, this study proposes a dynamic aggregation strategy to improve the flexible regulation ability of the VPP. A VPP aggregation model considering network constraints and temporal coupling constraints of DERs is constructed, while some VPP performance parameters are proposed to characterize and quantify the regulation ability. An uncertainty set considering time-series coupling properties of variables is constructed, and an aggregation method under uncertainty scenarios is proposed based on a two-stage robust optimization model. In addition, a dynamic aggregation strategy is proposed for the application of VPPs in electricity markets. Finally, case studies demonstrates that the proposed method provides a more extensive feasible region compared to other methods, and the deviation power remains within a reasonable range. The dynamic aggregation strategy facilitates the synergistic and correlative operation of DERs, exploits the regulation ability of the VPP in frequency regulation and spinning reserve, and improves the feasibility of practical applications. Simultaneously, the income of the VPP increased by 29.5 %.

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.

Uncertain parameters adjustable two-stage robust optimization of a rural housing integrated energy system considering biomass on-site utilization

Rural areas will be an important component to achieve carbon neutrality. However, there are currently issues such as an unreasonable energy consumption structure and low efficiency in renewable energy utilization. It is urgent to propose an energy optimization solution to address these problems. Therefore, considering the advantages of renewable energy in rural areas and the diversified and decentralized energy consumption patterns of rural households, a rural housing integrated energy system (RHIES) is proposed, which includes photovoltaics and a biomass utilization chain through self-production and local consumption. Subsequently, considering the economic and low-carbon aspects of the system's operational process, an uncertain parameters adjustable two-stage robust optimization model (UPATSRO) is developed to achieve a balance between robustness and economic efficiency during the scheduling optimization process. The results of case study indicate that the proposed RHIES reduces costs and carbon emissions by 28.15% and 93.83%, respectively, compared to conventional approaches. The biomass utilization mode satisfies 52.31% of the gas load and 39.71% of the thermal load for households. Additionally, it is shown that the proposed UPATSRO optimization model can achieve a flexible adjustment of scheduling schemes during the scheduling optimization process.

Two-stage robust transaction optimization model and benefit allocation strategy for new energy power stations with shared energy storage considering green certificate and virtual energy storage mode

In the context of the large-scale participation of renewable energy in market trading, this paper designs a cooperation mode of new energy power stations (NEPSs) and shared energy storage (SES) to participate in the power-green certificate market, which divides SES into physical energy storage and virtual energy storage. Secondly, combining the advantages of scenario generation and robust optimization (RO), a two-stage RO model with improved uncertainty interval is proposed to determine the optimal trading strategy. Then, to better align the distribution results of cooperative benefits with the actual contributions of NEPSs and SES, an entropy weight modified Shapley value benefit allocation strategy is constructed. Finally, the new energy base in Qinghai Province, China is chosen for simulation. The results show: (1) Adding energy storage and using two-stage RO are able to effectively improve the ability of NEPSs to resist uncertainty, which increases the revenue of the alliance by 22.8%. (2) The application of SES has better economic benefits than each member equipped with energy storage separately. Compared with the latter, the deviation penalty cost of the former is reduced by 66.4%, and the revenue is increased by 3.4%. (3) The proposed entropy weight modified Shapley value method embodies the important auxiliary role of SES more obviously. Based on this method, the overall satisfaction of the alliance increases by 12.6%. Generally speaking, the optimization model and benefit allocation strategy proposed in this paper can provide guidance for NEPSs and SES participating in power trading, and promote the low-carbon transformation of the power sector.

Gate appointment design in a container terminal: A robust optimization approach

Gate congestion is a main challenge faced by container terminals worldwide. In the scenario of gate congestion, the long waiting line of container trucks can block the traffic into the terminal, leading to disrupted terminal operations and unsatisfactory operating efficiency. In this paper, we study a gate appointment design problem that aims to manage the number of trucks allowed to a container terminal over time, so as to minimize the length of the truck waiting line and alleviate gate congestion. To optimize the gate appointment strategy, the truck service plans need also be devised, which involve the decisions for assigning trucks to yard blocks for container transhipment. We develop a two-stage robust optimization model for the problem by taking into account the uncertain service capacities of the yard blocks. Our model considers two decision stages, where the first-stage decision allocates slot capacities for the appointment slots, whereas the second-stage decision designs truck service plans with observed yard service capacity. We solve the two-stage robust model using an adapted column-and-row generation algorithm. In each iteration of the adapted column-and-row generation algorithm, the second-stage decision is generated by means of a pseudo-polynomial-time dynamic programming algorithm, while the first-stage decision is generated by a tailored scenario decomposition method. We test the computational performance of the proposed solution method on instances generated from real terminal operation data, and reveal managerial insights that would inspire terminal operators in the management of truck appointment for gate congestion mitigation.

Two-stage robust optimization of unified power quality conditioner (UPQC) siting and sizing in active distribution networks considering uncertainty of loads and renewable generators

This paper proposes a robust optimization siting and sizing strategy for the unified power quality conditioner (UPQC) in the active distribution network (ADN) integrated with renewable energy generators. The optimization objectives including investment cost, line loss, and voltage deviation are integrated into an overall cost for both the planning and operating stages. A novel UPQC equivalent power injection model is proposed based on the auxiliary branch method. A set of linear and second-order conic (SOC) constraints are employed to accurately describe the steady-state operation of UPQC. An improved branch current flow model is developed to incorporate radial distribution networks with UPQCs. The UPQC siting and sizing planning is formulated as a mixed integer second-order conic programming (MISOCP) problem. Accounting for the uncertainty in loads and distributed generators, a two-stage robust optimization model is established to address worst-case operational scenarios. A solving strategy is developed based on the strong duality theory and the column-and-constraint generation (C&CG) algorithm, and then commercial solvers can solve the problem accurately and efficiently. Case studies on an IEEE 33-node distribution network demonstrate this strategy's robustness in dealing with loads and renewable energy uncertainties, making it applicable across different UPQC topologies and operation modes. The proposed method has superior performance over the representative meta-heuristic approaches in terms of global optimality as well as an over 7.5 times faster computation speed. This work has significance in enhancing the quality and efficiency of modern power systems highly integrated with renewable energy.

Robust optimal dispatch strategy of integrated energy system considering CHP-P2G-CCS

Integrated energy systems (IESs) can improve energy efficiency and reduce carbon emissions, essential for achieving peak carbon emissions and carbon neutrality. This study investigated the characteristics of the CHP model considering P2G and carbon capture systems, and a two-stage robust optimization model of the electricity-heat-gas- cold integrated energy system was developed. First, a CHP model considering the P2G and carbon capture system was established, and the electric-thermal coupling characteristics and P2G capacity constraints of the model were derived, which proved that the model could weaken the electric-thermal coupling characteristics, increase the electric power regulation range, and reduce carbon emissions. Subsequently, a two-stage robust optimal scheduling model of an IES was constructed, in which the objective function in the day-ahead scheduling stage was to minimize the start-up and shutdown costs. The objective function in the real-time scheduling stage was to minimize the equipment operating costs, carbon emission costs, wind curtailment, and solar curtailment costs, considering multiple uncertainties. Finally, after the objective function is linearized with a ψ-piecewise method, the model is solved based on the C&CG algorithm. Simulation results show that the proposed model can effectively absorb renewable energy and reduce the total cost of the system.

Robust energy management through aggregation of flexible resources in multi-home micro energy hub

This study introduces a novel approach to home energy management systems (HEMS) through the development of a micro energy hub. The hub proficiently aggregates flexible resources across multiple homes, underpinned by a detailed modeling of appliance characteristics for enhanced energy management accuracy. The integration of Distributed Energy Systems (DES) further enriches the micro energy hub's capabilities, while a multi-objective two-stage robust optimization (M-TSRO) model is developed to address the inherent uncertainty of DES, aiming to concurrently realize energy savings, carbon emission reduction, and load smoothing. The effectiveness of the proposed micro energy hub is evaluated using real-world REFIT data set, demonstrating improved load scheduling, smoother load profiles, and enhanced energy flexibility. The results indicate significant improvements in grid control levels, reaching 68.75% in the basic scenario and 56.25% in the prosumer scenario. The prosumer scenario exhibits a significant reduction of 13.34% in the integrated objective compared to the basic scenario. This reduction is primarily driven by a notable decrease of 31.44% in the operational cost and an 8.06% decline in carbon emissions of the micro energy hub. These findings highlight the potential of micro energy hubs in optimizing energy consumption and increasing power flexibility through collaborative load scheduling strategies.

A two-stage robust configuration optimization framework for integrated energy system considering multiple uncertainties

The optimal configuration of integrated energy system (IES) is the cornerstone of efficient investment and low-carbon operation, which is of high importance for realizing energy system sustainable transformation. Yet, the intermittency of renewable energy and uncertainty of multiple energy demands pose severe challenges to IES configuration and operation. To address the issue, this research presents a two-stage robust configuration optimization model incorporating the multiple uncertainties of supply and demand. The model takes economic benefits, environmental benefits and energy utilization efficiency as objective functions, and is executed by column and constraint generation algorithm. A case study justifies the proposed model. The findings indicate the uncertainty from renewable energy and demand raises the equipment capacity and results in an increase of investment cost. Contrasted with the deterministic scenario, the total costs in the uncertainty scenario increase from 7043795.8CNY to 7785296CNY, but the performance shows more robust and the loss of load penalty is saved up to 296888CNY. Sensitivity analysis reveals energy price fluctuations primarily impair the operating costs, whereas they cause moderate effects on the configuration results. Load fluctuations cause greater consequences on both configuration and operating costs. The research provides references for IES configuration under multiple uncertainties with renewable energy penetration.

Distribution network restoration supply method considers 5G base station energy storage participation

This paper proposes a distribution network fault emergency power supply recovery strategy based on 5G base station energy storage. This strategy introduces Theil's entropy and modified Gini coefficient to quantify the impact of power supply reliability in different regions on base station backup time, thereby establishing a more accurate base station's backup energy storage capacity model that can fully utilize the base station's energy storage resources to participate in the emergency power supply of distribution network faults. First, the optimal Copula function in each cycle is determined through the Akaike information criterion and squared Euclidean distance to establish a wind power-photovoltaic output scenario. Secondly, the traditional Gini coefficient is modified using the weighted average node degree and influence rate indicators. A comprehensive vulnerability model is established through the modified Gini coefficient and Theil's entropy indicators. Based on the comprehensive vulnerability model, a backup energy storage time model and a modified backup energy storage capacity model of the base station affected by power supply reliability are established. Thus, the callable energy storage capacity of base stations in different areas is obtained. Finally, a two-stage robust optimization model is introduced to minimize system operating costs to solve the volatility of 5G base station communications and wind-solar output, thereby establishing an emergency power supply recovery model for base station energy storage and wind-solar output. Simulated with the improved IEEE-33 node model, the results show that the proposed base station's energy storage model improves the utilization of the base station energy storage resources and, at the same time, effectively reduces the loss of load during the fault phase of the distribution network and improves the absorption of the PV output.

A robust optimization model for demand response management with source-grid-load collaboration to consume wind-power

To accommodate wind power as safely as possible and deal with the uncertainties of the output power of wind- driven generators, a min-max-min two-stage robust optimization model is presented, considering the unit commitment, source-network load collaboration, and control of the load demand response. After the constraint functions are linearized, the original problem is decomposed into the main problem and subproblem as a matrix using the strong dual method. The minimum-maximum of the original problem was continuously maximized using the iterative method, and the optimal solution was finally obtained. The constraint conditions expressed by the matrix may reduce the calculation time, and the upper and lower boundaries of the original problem may rapidly converge. The results of the example show that the injected nodes of the wind farms in the power grid should be selected appropriately; otherwise, it is easy to cause excessive accommodation of wind power at some nodes, leading to a surge in reserve costs and the load demand response is continuously optimized to reduce the inverse peak regulation characteristics of wind power. Thus, the most economical optimization scheme for the worst scenario of the output power of the generators is obtained, which proves the economy and reliability of the two-stage robust optimization method.

Multi-Timescale Trading Strategy for Renewable Power to Ammonia Virtual Power Plant in the Electricity, Hydrogen, and Ammonia Markets

Renewable power to ammonia (RePtA) is a prominent zero-carbon pathway for decarbonization. Due to the imbalance between renewables and production energy demand, the RePtA system relies on electricity exchange with the power grid. Participating in the electricity market as a virtual power plant (VPP) may help to reduce energy costs. However, the power profile of local photovoltaics and wind turbines is similar to those in the market, resulting in rising energy costs under the conventional strategy. Hence, we develop a multi-timescale trading strategy for the RePtA VPP in the electricity, hydrogen, and ammonia markets. By utilizing the hydrogen and ammonia buffer systems, the RePtA VPP can optimally coordinate production planning. Moreover, we find it possible to describe the trading of electricity, ammonia, and hydrogen in a unified timeframe. The two-stage robust optimization model of the electricity market is extended to multiple markets and solved by the column and constraint generation (CC&G) algorithm. The case is derived from an actual project in the Inner Mongolia Autonomous Region. Sensitivity analysis demonstrates the economic advantages of the RePtA VPP joining multiple markets over the conventional strategy and reveals the necessity of the hydrogen and ammonia buffer and reactor flexibility.

Capacity Value Assessment for a Combined Power Plant System of New Energy and Energy Storage Based on Robust Scheduling Rules

With the rapid increase in new energy penetration, the uncertainty of the power system increases sharply. We can smooth out fluctuations and promote the more grid-friendly integration of new energy by combining it with energy storage. This paper proposes an evaluation method for assessing the value of a combined power plant system of new energy and energy storage using robust scheduling rules. Firstly, the k-means clustering algorithm is improved by using the elbow method in order to generate typical scenarios that can be used for the operation optimization of the combined power plant system of new energy and energy storage. Then, a two-stage robust optimization model of the combined power plant system of new energy and energy storage with a min–max–min structure is constructed according to the uncertainty of new energy. In this model, the operation constraints and coordinated control of wind–solar–thermal–storage units are considered. By constructing the uncertainty set of the new energy output, the overall operating cost of the system is minimized and uncertainty adjustment parameters are introduced to flexibly adjust the conservatism of the scheduling rules. Furthermore, based on the column and constraint generation algorithm and strong duality theory, the original problem can be decomposed into a master problem and subproblems with mixed integer linear characteristics for an alternating solution, so as to obtain the optimal solution of the original problem, and finally obtain the robust scheduling rule with the lowest operating cost under the worst scenario. Finally, based on the wind and solar power output curves and the output of each unit under the robust scheduling rules, combined with the value estimation method of the combined power plant system of new energy and energy storage, the value of the combined power plant system of new energy and energy storage is evaluated. Through the establishment of models and example analysis, it is proven that raising the quantity of the grid-connected power generated with new energy will cause an increase in the volatility of the power system; it will also bring considerable benefits to new energy plants, and the energy storage can improve the stability of the system. The above can provide references for the subsequent energy storage configuration in the planning of a combined power plant system of new energy and energy storage.

Two-stage robust optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage hybrid energy system

The hybrid energy system of hydro-powers, pumped storages and renewable energies has become a new topic direction in modern power system developments. Consequently, it is essential to realize a rational and efficient allocation of different energy source capacities. Nevertheless, there is still a gap between the available studies and the requirement for further hybrid energy system development. This paper focuses on the optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage power system. In this direction, a bi-level programming model for the optimal capacity configuration of wind, photovoltaic, hydropower, pumped storage power system is derived. To model the operating mode of a pumped storage power station, two 0-1 variables are introduced. To handle the nonlinear and nonconvex lower level programing problem caused by the two 0-1 variables, it is proposed that the 0-1 variables are treated as some uncertain parameters. Also, by treating the 0-1 variables as some uncertain parameters, a two-stage robust optimization problem to decompose the original bi-level programing one into a master problem and a subproblem is finally introduced. The Karush-Kuhn-Tucker (KKT) conditions are then applied to simplify and linearize the min-max problem and nonlinear terms in the master problem. This results in both the master problem and the subproblem being formulated as mixed integer linear programming (MILP) problems. By utilizing the powerful Column-and-Constraint Generation (C&CG) algorithm, the two-stage robust optimization model is decomposed into an iterative procedure of solving the master problem and the subproblem sequentially. This approach eliminates the need for intricate optimization algorithms as commonly used in existing bi-level planning problems in hybrid energy systems. Finally, the effectiveness and advantages of the proposed model is verified by the numerical results on a case study.

A Two-Stage Robust Optimization Microgrid Model Considering Carbon Trading and Demand Response

To enhance the low-carbon level and economic performance of microgrid systems while considering the impact of renewable energy output uncertainty on system operation stability, this paper presents a robust optimization microgrid model based on carbon-trading mechanisms and demand–response mechanisms. Regarding the carbon-trading mechanism, the baseline allocation method is utilized to provide carbon emission quotas to the system at no cost, and a ladder carbon price model is implemented to construct a carbon transaction cost model. Regarding uncertainty set construction, the correlation of distributed generation in time and space is considered, and a new uncertainty set is constructed based on historical data to reduce the conservative type of robust optimization. Based on the column constraint generation algorithm, the model is solved. The findings indicate that upon considering the carbon-trading mechanism, the microgrid tends to increase the output of low-carbon units and renewable energy units, and the carbon emissions of the microgrid can be effectively reduced. However, due to the increase in power purchase from the distribution network and the increase in carbon transaction costs, the operating costs of the microgrid increase. Secondly, through the utilization of demand–response mechanisms, the microgrid can achieve load transfer between peaks and troughs. It is imperative to establish appropriate compensation costs for demand and response that balances both economic efficiency and system stability. At the same time, due to the time-of-use electricity price, the energy storage equipment can also play a load transfer effect and improve the system’s economy. Finally, sensitivity analysis was conducted on the adjustment parameters of distributed power sources and loads that have uncertain values. A comparison was made between the deterministic scheduling model and the two-stage robust optimization model proposed in this study. It was proved that this model has great advantages in coordinating the economy, stability and low carbon level of microgrid operations.

Cyber-Physical Interdependent Restoration Scheduling for Active Distribution Network via Ad Hoc Wireless Communication

This paper proposes a post-disaster cyber-physical interdependent restoration scheduling (CPIRS) framework for active distribution networks (ADN) where the simultaneous damages on cyber and physical networks are considered. The ad hoc wireless device-to-device (D2D) communication is leveraged, for the first time, to establish cyber networks instantly after the disaster to support ADN restoration. The repair and operation crew dispatching, the remote-controlled network reconfiguration and the system operation with DERs can be effectively coordinated under the cyber-physical interactions. The uncertain outputs of renewable energy resources (RESs) are represented by budget-constrained polyhedral uncertainty sets. Through implementing linearization techniques on disjunctive expressions, a monolithic mixed-integer linear programming (MILP) based two-stage robust optimization model is formulated and subsequently solved by a customized column-and-constraint generation (C&CG) algorithm. Numerical results on the IEEE 123-node distribution system demonstrate the effectiveness and superiorities of the proposed CPIRS method for ADN.

Plant-wide byproduct gas distribution under uncertainty in iron and steel industry via quantile forecasting and robust optimization

In the modern iron and steel industry, the efficient distribution of byproduct gases faces significant challenges due to quantity- and quality-related uncertainties of gases. This study presents an optimal approach to gas distribution that addresses this issue by incorporating the energy flow network and the uncertain surplus gases from the manufacturing system. The uncertain optimization problem is formulated as a two-stage robust optimization (TSRO) model, including “here-and-now” decisions aimed at minimizing the start-stop cost of energy conversion units, as well as “wait-and-see” decisions aimed at minimizing the operating cost of gasholders and the penalties resulting from energy excess or shortage. To facilitate practical implementation, we propose a “first quantify, then optimize” approach: (1) quantifying the uncertainty of surplus gases via a conditional quantile regression (CDQ)-based T-step time series model, and (2) finding the optimal solution through a column-and-constraint generation algorithm. Furthermore, a case study is conducted on an industrial energy system to validate the proposed methodology. Computational results, using evaluation indicators, such as MAPE, RMSE, PICP, and PINAW, confirm the effectiveness of the data-driven time series model in accurately quantifying uncertainties in each period. Sensitivity analysis demonstrates that the proposed TSRO model achieves a favorable balance between robustness and flexibility by selecting the combination of “budget and quantile” and the parameters of storage and conversion units. Comparative results reveal: (1) the optimal objective of the TSRO closely aligns with that of stochastic programming (SP) and is 2.717 times higher than that of deterministic optimization (DO); and (2) the computation time of TSRO is 2.388 times longer than that of DO, yet significantly smaller than that of SP, being only 0.07 times longer. Consequently, TSRO can efficiently find a robust gas distribution solution with the desired level of conservativeness for integrated iron and steel plants.

The robust cyclic job shop problem

This paper deals with the cyclic job shop problem where the task durations are uncertain and belong to a polyhedral uncertainty set. We formulate the cyclic job shop problem as a two-stage robust optimization model. The cycle time and the execution order of tasks executed on the same machines correspond to the here-and-now decisions and have to be decided before the realization of the uncertainty. The starting times of tasks corresponding to the wait-and-see decisions are delayed and can be adjusted after the uncertain parameters are known. In the last decades, different solution approaches have been developed for two-stage robust optimization problems. Among them, the use of affine policies, row and row-and-column generation algorithms are the most common. In this paper, we propose a branch-and-bound algorithm to tackle the robust cyclic job shop problem with cycle time minimization. The algorithm uses, at each node of the search tree, a robust version of the Howard’s algorithm to derive a lower bound on the optimal cycle time. Moreover, we design a row generation algorithm and a column-and-row generation algorithm and compare it to the branch-and-bound method. Finally, encouraging preliminary results on numerical experiments performed on randomly generated instances are presented.

Unit Combination Scheduling Method Considering System Frequency Dynamic Constraints under High Wind Power Share

Power systems with a high wind power share are characterized by low rotational inertia and weak frequency regulation, which can easily lead to frequency safety problems. Providing virtual inertia for large-scale wind turbines to participate in frequency regulation is a solution, but virtual inertia is related to wind power output prediction. Due to wind power prediction errors, the system inertia is reduced and there is even a risk of instability. In this regard, this article proposes a unit commitment model that takes into account the constraints of sharp changes in frequency caused by wind power prediction errors. First, the expressions of the equivalent inertia, adjustment coefficient, and other frequency influence parameters of the frequency aggregation model for a high proportion wind power system are derived, revealing the mechanism of the influence of wind power prediction power and synchronous machine start stop status on the frequency modulation characteristics of the system. Second, the time domain expression of the system frequency after the disturbance is calculated by the segment linearization method, and the linear expressions of “frequency drop speed and frequency nadir” constraints are derived to meet the demand of frequency regulation in each stage of the system. Finally, a two-stage robust optimization model based on a wind power fuzzy set is constructed by combining the effects of wind power errors on power fluctuation and frequency regulation capability. The proposed model is solved through affine decision rules to reduce its complexity. The simulation results show that the proposed model and method can effectively improve the frequency response characteristics and increase the operational reliability of high-share wind power systems.