Minimum Operating Research Articles

Notes on peculiarities of the Schwinger-DeWitt technique: One-loop double poles, total-derivative terms, and determinant anomalies

We discuss peculiarities of the Schwinger-DeWitt technique for quantum effective action, associated with the origin of dimensionally regularized double-pole divergences of the one-loop functional determinant for massive Proca model in a curved spacetime. These divergences have the form of the total-derivative term generated by integration by parts in the functional trace of the heat kernel for the Proca vector field operator. Because of the nonminimal structure of second-order derivatives in this operator, its vector field heat kernel has a nontrivial form, involving the convolution of the scalar d’Alembertian Green’s function with its heat kernel. Moreover, its asymptotic expansion is very different from the universal predictions of Gilkey-Seeley heat kernel theory because the Proca operator violates one of the basic assumptions of this theory—the nondegeneracy of the principal symbol of an elliptic operator. This modification of the asymptotic expansion explains the origin of double-pole total-derivative terms. Another hypostasis of such terms is in the problem of multiplicative determinant anomalies—lack of factorization of the functional determinant of a product of differential operators into the product of their individual determinants. We demonstrate that this anomaly should have the form of total-derivative terms and check this statement by calculating divergent parts of functional determinants for products of minimal and nonminimal second-order differential operators in curved spacetime. Published by the American Physical Society 2024

An innovative design and development of Up-flow Compact Constructed Wetland for sewage treatment

The growing demand for sustainable sewage treatment requires technologies that overcome the limitations of energy-intensive and chemical-dependent systems. This study presents an innovative solution addressing both environmental and operational challenges with the design and development of an Up-flow Compact Constructed Wetland (UCCW) based Sewage Treatment Plant (STP). This system integrates preliminary, primary, secondary, and tertiary treatment units into a single setup. The performance of UCCW based STP was evaluated over 720 days under different Hydraulic Retention Times (HRTs), considering seasonal variations in both rectangular and circular configurations. The system achieved significant pollutant removal as Total Suspended Solids (96%), Chemical Oxygen Demand (86%), Biochemical Oxygen Demand (90%), Total Nitrogen (70%), Total Phosphorus (65%), and Fecal Coliforms (99%) at a 36-hour HRT. These parameters meet discharge standards, except FC, which requires disinfection for safe reuse and recycling. Further, Response Surface Methodology (RSM) and Monte Carle Simulation of UCCW based STP confirmed optimal and reliable performance at a 36-hour HRT. Compared to conventional treatment technologies, the UCCW based STP demonstrated higher efficiency, a smaller footprint (1m2/KLD), better operational flexibility, cost-effectiveness, and minimal operation & maintenance to make it sustainable for decentralised treatment.

Commutator technique for the heat kernel of minimal higher derivative operators

We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic 2Mth order, F(∇)=(−□)M+⋯, in the background field formalism of gauge theories and quantum gravity. This technique represents the conversion of the recently suggested Fourier integral method of generalized exponential functions [A. O. Barvinsky and W. Wachowski, Heat kernel expansion for higher order minimal and nonminimal operators, ] into the commutator algebra of special differential operators, which allows one to express expansion coefficients for F(∇) in terms of the Schwinger-DeWitt coefficients of a minimal second-order operator H(∇). This procedure is based on special functorial properties of the formalism including the Mellin-Barnes representation of the complex operator power HM(∇) and naturally leads to the origin of generalized exponential functions without directly appealing to the Fourier integral method. The algorithm is essentially more straightforward than the Fourier method and consists of three steps ready for a computer codification by symbolic manipulation programs. They begin with the decomposition of the operator into a power of some minimal second-order operator H(∇) and its lower derivative perturbation part W(∇), F(∇)=HM(∇)+W(∇), followed by considering their multiple nested commutators. The second step is the construction of special local differential operators—the perturbation theory in powers of the lower derivative part W(∇). The final step is the so-called procedure of their “Syngification,” consisting of a special modification of the covariant derivative monomials in these operators by the Synge world function σ(x,x′) with their subsequent action on the Hadamard-Minakshisundaram-DeWitt coefficients of H(∇). Published by the American Physical Society 2024

A novel machine-learning aided platform for rapid detection of urine ESBLs and carbapenemases: URECA-LAMP.

Pathogenic gram-negative bacteria frequently carry genes encoding extended-spectrum beta-lactamases (ESBL) and/or carbapenemases. Of great concern are carbapenem resistant Escherichia coli, Klebsiella pneumoniae, Pseudomonas aeruginosa, and Acinetobacter baumannii. Despite the need for rapid AMR diagnostics globally, current molecular detection methods often require expensive equipment and trained personnel. Here, we present a novel machine-learning-aided platform for the rapid detection of ESBLs and carbapenemases using Loop-mediated isothermal Amplification (LAMP). The platform consists of (i) an affordable device for sample lysis, LAMP amplification, and visual fluorometric detection; (ii) a LAMP screening panel to detect the most common ESBL and carbapenemase genes; and (iii) a smartphone application for automated interpretation of results. Validation studies on clinical isolates and urine samples demonstrated percent positive and negative agreements above 95% for all targets. Accuracy, precision, and recall values of the machine learning model deployed in the smartphone application were all above 92%. Providing a simplified workflow, minimal operation training, and results in less than an hour, this study demonstrated the platform's feasibility for near-patient testing in resource-limited settings.IMPORTANCEExtended-spectrum beta-lactamases (ESBL) and carbapenemases confer resistance to third-generation cephalosporins and carbapenems in pathogenic Gram-negative bacteria such as Escherichia coli, Klebsiella pneumoniae, Pseudomonas aeruginosa, and Acinetobacter baumannii. Conventional antimicrobial susceptibility testing is based on phenotypic methods, and results can take several days to be obtained. Current genotypic detection methods can be rapid but require expensive equipment and trained personnel. In this study, we present a novel machine learning-aided platform for the rapid detection of ESBLs and carbapenemases using Loop-mediated isothermal Amplification (LAMP). The validation of the platform demonstrated percent positive and negative agreements above 95% for all targets. The newly developed platform provided a simplified workflow, minimal technical training, and results in less than an hour. This study demonstrated the platform's feasibility for rapid testing of ESBL and carbapenemases in bacteria and urine specimens.

Explore the expression of mitochondria-related genes to construct prognostic risk model for ovarian cancer and validate it, so as to provide optimized treatment for ovarian cancer.

The use of gene development data from public database has become a new starting point to explore mitochondrial related gene expression and construct a prognostic prediction model of ovarian cancer. Data were obtained from the TCGA and ICGC databases, and the intersection with mitochondrial genes was used to obtain the differentially expressed genes. q-PCR, Cox proportional risk regression, minimal absolute contraction and selection operator regression analysis were performed to construct the prognostic risk model, and ROC curve was used to evaluate the model for centralized verification. The association between risk scores and clinical features, tumor mutation load, immune cell infiltration, macrophage activation analysis, immunotherapy, and chemosensitivity was further evaluated. A prognostic risk score model for ovarian cancer patients was constructed based on 12 differentially expressed genes. The score was highly correlated with ovarian cancer macrophage infiltration and was a good predictor of the response to immunotherapy. M1 and M2 macrophages in the ovarian tissue in the OV group were significantly activated, providing a reference for the study of the polarity change of tumor-related macrophages for the prognosis and treatment of ovarian cancer. In terms of drug sensitivity, the high-risk group was more sensitive to vinblastine, Acetalax, VX-11e, and PD-0325901, while the low-risk group was more sensitive to Sabutoclax, SB-505124, cisplatin, and erlotinib. The prognostic risk model of ovarian cancer associated to mitochondrial genes built on the basis of public database better evaluated the prognosis of ovarian cancer patients and guided individual treatment.

Discovery of a novel binary azeotrope with positive synergistic insulation strength as eco-friendly SF6-alternative

Abstract Sulfur hexafluoride (SF6), as the arc extinguishing and insulating medium, is broadly applied in power equipment. While it is very essential to find an environmentally friendly substitute gas for SF6 due to its strong greenhouse effect. Although there are many potential alternatives, most have relatively high boiling points that cannot meet the minimum operating temperature of the power equipment. In the past, the liquefaction temperature of the mixture was reduced by mixing with buffer gases, such as CO2, N2, or dry air. But this method cannot take the insulation performance requirements of eco-friendly insulating gas into account. Therefore, given the current problems and challenges, a novel approach is presented to exploring new eco-friendly gases by incorporating the azeotropic theory. The liquefaction temperature of the gas mixture can be reduced simultaneously while the insulation strength is increased. In this approach, a theoretical prediction model E-PPR78 was introduced to predict the vapor-liquid equilibrium data and RC318 was found to exhibit azeotrope behavior with HFO-1336mzz(E) at 17%. Furthermore, the predicted vapor-liquid equilibrium data obtained were validated against cyclic-analytical experimental results, affirming the efficacy of the proposed model. Subsequently, to assess its insulation performance, breakdown tests were conducted under both AC and lightning impulse voltages, revealing significant positive synergistic effects in the gas mixture. The possible mechanisms of this positive synergistic effect were also discussed. This study offers an innovative way of tackling high boiling point issues plaguing eco-friendly gases. The findings may also enlighten the design of eco-friendly switchgear that utilizes HFO-1336mzz(E) mixtures to replace traditional SF6 gases.

A hybrid Improved Salp Swarm Algorithm and Harris Hawk Optimizer for energy planning in microgrids with minimum operating cost

ABSTRACT Achieving optimal energy planning in Microgrids (MGs) is pivotal for addressing complex challenges associated with cost-effective and reliable energy supplies. This paper proposes a novel hybrid metaheuristic algorithm for optimal energy planning in microgrids using an Improved Salp Swarm Algorithm with Harris Hawk Foraging (ISSAHF). This technique is based on an improved multi-leader Salp Swarm Algorithm with an elite leader following strategy combined with Harris Hawks foraging. A simulation study is conducted on a low-voltage microgrid in off-grid and grid-connected modes. The optimization algorithm resulted in a daily average cost of 28.3370€ in off-grid mode compared to 19.2676€ in grid-connected one. Furthermore, the statistical study shows that the proposed algorithm outperforms well-established metaheuristic techniques regarding search capability and robustness. It yields mean optimal cost of 623.5248€ in off-grid and 404.7475€ for the grid-connected one, compared to other optimization techniques that vary from 667.2141€ to 959.5747€ in off-grid mode, and from 424.5841€ to 813.932€ in grid-connected mode. For robustness, the proposed technique performs well with a standard deviation of 20.765€ compared to the best (17.024€) and the worst (47.2423€) cases in off-grid mode, while in grid-connected mode, it is 28.8771€ compared to the best (21.6316€) and the worst (45.3774€) values.

Detection of Chemical Contaminants in Water for Irrigation Systems: A Systematic Review

Water pollution is a detrimental issue that occurs when there are bad changes in water quality parameters. It directly disrupts water usage and poses a danger to society, environment, economy, and agriculture. Water quality should be monitored to alert authorities on water pollution, so that action can be taken quickly. Improper water management pollutes rivers and lakes in Malaysia such as Klang River, Semenyih River, Kim Kim River, Slim River, and others. Various techniques are introduced to detect contaminants in water such as electronic sensors, biosensor approaches, laboratory analysis, and optical techniques. The functionality tool varies depending on the specific contaminants or parameters that are targeted, and the resources allocated. Several common contaminant types are found in polluted water including heavy metals, organic and inorganic chemicals, industrial pollutants, suspended solids, and others. The objective of the review is to study various non-optical and optical contaminant detection methods in water to identify the strengths and weaknesses of the methods. In this review, water pollution problems mainly due to the agricultural sector in several countries are discussed. Besides, conventional, and modern methods are compared in terms of parameters, complexity, and reliability. We believe that conventional methods are costly and complex, whereas modern methods are also expensive but simpler with real-time detection. Recent contaminant detection methods in water are also reviewed to study any loopholes in the latest methods. We found that the spectroscopy method based on light propagation theory is suitable and one of the promising methods for chemical contaminants detection for water quality analysis. This method offers fast analysis time, high sensitivity detection, non-invasive analysis, provides reliable data, and others. Undoubtedly, some contaminants in water can be challenging to be identified rapidly and confidently even though there are numerous tools and techniques available for water quality analysis. Thus, the review is important to compare previous methods and to improve current chemical contaminants detection analysis in terms of reliability with a minimum operating system and cost effectiveness.

Erratum: Heat kernel expansion for higher order minimal and nonminimal operators [Phys. Rev. D 105 , 065013 (2022)

Erratum: Heat kernel expansion for higher order minimal and nonminimal operators [Phys. Rev. D <b>105</b> , 065013 (2022)

Research on distributed optimal scheduling method based on consensus

Abstract With access to large-scale distributed power sources, the physical structure of the power grid system tends to be distributed. The application of traditional centralized optimal scheduling methods will lead to a surge in communication overhead and computational complexity, which will affect the performance and efficiency of the solution. In this paper, the minimum operating cost of the system is taken as the goal, and the distributed direct current optimal power flow (DC-OPF) optimization calculation of the photovoltaic-storage power generation system is considered to approximately solve the economic dispatch problem. The DC optimal power flow model with energy storage charging penalty is constructed. Then, the distributed optimization method based on the consensus alternating direction multiplier method (ADMM) is adopted. By decoupling the objective function and constraints of the whole system problem, the fully distributed DC-OPF calculation is realized by introducing the global consensus variable to deal with the boundary buses. Finally, the improved IEEE 30-bus example is used to test the method, and the simulation results verify the convergence and accuracy of the method.

A Game Theory Based Scheduling Approach for Charging Coordination of Multiple Electric Vehicles Aggregators in Smart Cities

In this paper, a game theory-based coordination approach is presented to find the minimum operation cost of multiple electric vehicle (EV) aggregators that are connected to the upstream network. In order to provide a comprehensive study various EVs aggregators including residential, commercial, official, university, and industry parking lots have been considered and the proposed game theory is utilized to coordinate the charging power from/to different microgrids and/or upstream network. In addition of operation cost, a reliability index, service charge and power loss are included in the objective function. The proposed approach is applied on an electricity network with 7 connected microgrids and different scenarios have been investigated. The simulation results show the overall operation cost in the coalition operation mode is globally minimized in comparison with the non-coalition operation mode. In addition, the reliability index, service charge and power loss force the aggregators to buy their necessary power from the nearby microgrids. The average network loss in the coalition and non-coalition modes are 2.88% and 4.28%, respectively. Moreover, the average reliability cost in coalition and non-coalition modes are $2.65 and $4.25, respectively.

Motif Graph Neural Network.

Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional graph representations. Graph neural networks (GNNs) are currently the most popular model in graph embedding approaches. However, standard GNNs in the neighborhood aggregation paradigm suffer from limited discriminative power in distinguishing high-order graph structures as opposed to low-order structures. To capture high-order structures, researchers have resorted to motifs and developed motif-based GNNs. However, the existing motif-based GNNs still often suffer from less discriminative power on high-order structures. To overcome the above limitations, we propose motif GNN (MGNN), a novel framework to better capture high-order structures, hinging on our proposed motif redundancy minimization operator and injective motif combination. First, MGNN produces a set of node representations with respect to each motif. The next phase is our proposed redundancy minimization among motifs which compares the motifs with each other and distills the features unique to each motif. Finally, MGNN performs the updating of node representations by combining multiple representations from different motifs. In particular, to enhance the discriminative power, MGNN uses an injective function to combine the representations with respect to different motifs. We further show that our proposed architecture increases the expressive power of GNNs with a theoretical analysis. We demonstrate that MGNN outperforms state-of-the-art methods on seven public benchmarks on both the node classification and graph classification tasks.

High-Sensitivity and Fast-Response Photomultiplication Type Photodetectors Based on Quasi-2D Perovskite Films for Weak-Light Detection.

Photovoltaic photodiodes often face challenges in effectively harvesting electrical signals, especially when detecting faint light. In contrast, photomultiplication type photodetectors (PM-PDs) are renowned for their exceptional sensitivity to weak signals. Here, an advanced PM-PD is introduced based on quasi 2D Ruddlesden-Popper (Q-2D RP) perovskites, optimized for weak light detection at minimal operating voltages. The abundant traps at the Q-2D RP surface capture charge carriers, inducing a trap-assisted tunneling mechanism that leads to the photomultiplication (PM) effect. Deep-lying trap states within the Q-2D RP bulk accelerate charge carrier recombination, resulting in an outstanding rise/fall time of 1.14/1.72 µs for the PM-PDs. The PM-PD achieves a remarkable response level of up to 45.89 AW-1 and an extraordinary external quantum efficiency of 14400% at -1V under an illumination of 1 µWcm- 2. The intrinsic high resistance of the Q-2D perovskite results in a low dark current, enabling an impressive detectivity of 4.23 × 1012 Jones based on noise current at -1V. Furthermore, the practical application of PM-PDs has been demonstrated in weak-light, high-rate communication systems. These findings confirm the significant potential of PM-PDs based on Q-2D perovskites for weak light detection and suggest new directions for developing low-power, high-performance PM-PDs for future applications.

Metoda pomiaru parametrów kamer termowizyjnych za pomocą zautomatyzowanego stanowiska pomiarowego

To achieve precise and repeatable measurements of thermal camera’s parameters, it is essential to eliminate human error. For this purpose, an automated test bench has been developed that allows fully automatic, semi-automatic and manual control of the measurement process. The designed stand supports remote control via Ethernet interface or USB connection. The developed software enables control, data recording and parameter determination of thermal cameras. The test bench ensures high quality and reliability of thermal measurements, enabling controlled examination of camera characteristics with minimal operator involvement.

The overdetermined Cauchy problem for the hyperbolic Gellerstedt equation

Abstract Overdetermined boundary value problems and the minimal operators generated by them are extremely important in the description of regular boundary value problems for differential equations, and are also widely used in the study of local properties of solutions. In addition, for inverse problems of mathematical physics arising from applications, when determining unknown data, it is necessary to study problems with overdetermined boundary conditions, which is reflected in the study of problems, including for hyperbolic equations and systems, arising in physics, geophysics, seismic tomography, geoelectrics, electrodynamics, medicine, ecology, economics and many other practical areas. Thus, the study of overdetermined boundary value problems is of both theoretical and applied interest. In this paper, a criterion for the regular solvability of the overdetermined Cauchy problem for the Gellerstedt equation and the minimal differential operator generated by it in a hyperbolic domain is established, as which both the case of a characteristic triangle and the case of a more general domain with fairly general assumptions about the boundary of the domain are considered. Due to overdetermined boundary conditions, the problem under consideration will be ill-posed in the general case, therefore, for its regular solvability, additional conditions must be imposed on the initial data. In other words, we have considered the inverse problem: to determine what requirements the initial data of the problem, in particular the right part of the Gellerstedt equation, should meet, in question, so that the overdetermined Cauchy problem is regularly solvable. The proof is based on the Gellerstedt potential, the properties of solutions of the Goursat problem in the characteristic triangle, and the properties of special functions.

Spike load smoothing strategy considering behavioral decision under vehicle-road-network convergence

To reduce the impact of large-scale electric vehicles on traffic and electric load peaks, we propose a "vehicle-road-network" integration strategy that takes into account behavioral decisions. To reduce the impact of large-scale electric vehicles on traffic and electric load, we propose a peak load suppression strategy that takes into account behavioral decisions under "vehicle-road-network" integration. Firstly, a "vehicle-road-network" fusion model is constructed based on the large-scale access of EVs; then, a load model is built considering the large-scale access of EVs; finally, based on the third-generation foreground theory, the behavioral decision of EV users is analyzed based on the operation state of the fusion system, and a decision model is built by the foreground value to minimize the operation cost. The spike load smoothing strategy scheme is established with minimum operation cost. By using the fusion of Sioux Falls urban road network system and IEEE33 node grid system as the simulation example, the simulation results show that the proposed peak load smoothing strategy can coordinate the distribution of charging load and relieve traffic pressure during peak load hours, and reduce the travel and charging costs of EV users.

Exploring resveratrol against Alzheimer's disease and Parkinson's disease through integrating network pharmacology, bioinformatics, and experimental validation strategy in vitro

BackgroundThe study aims to investigate the pharmacological basis and molecular mechanisms of resveratrol in the treatment of Alzheimer's disease (AD) and Parkinson's disease (PD) through the approach of treating different diseases with the same method, guided by traditional Chinese medicine theory. Utilizing network pharmacology and bioinformatics methods, this research aims to provide modern medical evidence for the theory of treating different diseases with the same method in traditional Chinese medicine. MethodsOmnibus from Swiss Target Prediction, TCMSP, SuperPred, SEA, HIT, CTD, TCMIP and Gene Expression Disease datasets for resveratrol related genes, Alzheimer's disease, and Parkinson's disease were obtained from the GEO database. Core targets were identified by weighted gene coexpression network analysis (WGCNA) and minimum absolute contraction and selection operator (LASSO). The expression of core targets was verified in AD and PD cell models. The immune characteristics of AD and PD were analyzed by CIBERSORT algorithm. Finally, the potential mechanism of resveratrol intervention on the core target was studied by molecular docking technique. ResultsThe results of network pharmacological analysis showed that resveratrol acted on 85 common targets such as STAT3 and CASP3, affected AGE-RAGE signaling pathway and PI3K-Akt signaling pathway, and showed the effect of "same disease and different treatment" for AD and PD. Three core targets associated with AD and PD (PLK4, FCGRT, and PRKAR2A) were finally identified through comprehensive transcriptome analysis, and experimentally verified in cell models of AD and PD. At the same time, the analysis of immune cell infiltration suggested that AD and PD had dysregulation of inflammation, and the core target was significantly related to M2 macrophages. ConclusionResveratrol may play a potential mechanism of "treating the same disease with different diseases" and target three core targets (PLK4, FCGRT and PRKAR2A) to improve the disease process of AD and PD by participating in the regulation of immune and inflammatory pathways. These findings have potential implications for clinical practice and future research.

Conjunctive optimal design of water and power networks

Water distribution systems (WDS) and power grids (PG) are critical infrastructure systems that are vital to all human activity. As such, their quality of service is of great importance for economic, environmental, and human welfare reasons. Although traditionally being analyzed separately, the two systems are interconnected and can mutually affect one another. In order to utilize the potential benefits that the two systems can produce for each other, their design and operation should be analyzed conjunctively. In this paper, a conjunctive optimal design approach for water and power networks is presented, with the objective of finding the dimensions of the systems’ facilities that will result in minimal overall costs, for both design and operation. The model is formulated and implemented on two example applications using an off-the-shelf nonlinear solver by MATLAB and compared to the optimal design of the independent WDS. A sensitivity analysis is performed to provide validity to the obtained results. The conjunctive design is compared to the design of an independent WDS to emphasize the effect of including the PG in the optimization problem. Results show a clear link between the availability of renewable energy and sizing of WDS components. The design of the independent WDS leads to the violation of PG constraints, which are satisfied when including both systems under a single optimization model, demonstrating the importance of a holistic design approach.

Design of a multilayer absorber for ultra‐wideband radar cross section reduction

AbstractThis study proposes an ultra‐wideband multilayer absorber by combining frequency selective surface (FSS) and absorbing material. The structure is composed by three layers which are FSS loaded with resistors, absorbing material at the bottom and each layer is separated by air. The FSS in bottom has good absorption performance at high frequency while the upper layer is used to achieve low‐band absorption. To extend the absorption band to the low frequency, it further add a layer of absorbing material at the bottom. Equivalent circuit is employed to analyze the principle of the designed absorber. The simulation results show that an ultra‐wide absorption band from 0.61 to 12.33 GHz with a fractional bandwidth of 181% is realized for both TE and TM waves under the normal incidence. Furthermore, the thickness of the structure is only 0.07λL, where λL represents the wavelength of the minimum operating frequency. The designed absorber is fabricated and measured, and the measurement is in good agreement with the simulation.

Flexible resource allocation optimization model considering global K-means load clustering and renewable-energy consumption

Abstract Vigorously developing flexible resources in power systems will be the key to building a new power system and realizing energy transformation. The investment construction cost and operation cost of various flexible resources are different, and the adjustment ability is different in different timescales. Therefore, the optimization of complementary allocation of various resources needs to take into account the economy and adjustment ability of different resources. In this paper, the global K-means load clustering model is proposed and the 365-day net load is reduced to eight typical daily net loads by clustering. Secondly, a two-level optimization model of flexible resource complementary allocation considering wind power and photovoltaic consumption is constructed. The flexible resources involved include the flexible transformation of thermal power, hydropower, pumped storage, energy storage, and demand response. The upper-layer model optimizes the capacity allocation of various flexible resources with the minimum investment and construction cost as the goal and the lower layer optimizes the operating output of various units with the minimum operating cost as the goal. The results of the example analysis show that the flexible capacity of thermal power units has nothing to do with the abandonment rate of renewable energy. As the abandonment rate of renewable energy decreases, the optimal capacity of pumped storage, electrochemical energy storage, and hydropower units increases. When the power-abandonment rate of renewable energy is 5%, the optimal allocation capacity of thermal power flexibility transformation, pumped storage, electrochemical energy storage, hydropower unit, and adjustable load in Province A is 5313, 17 090, 5830, 72 113, and 4250 MW, respectively. Under the condition that the renewable-energy abandonment rate is 0, 5%, and 10% respectively, the configured capacity of pumped storage is 20 000, 17 090, and 14 847 MW, respectively.