Power System Model Research Articles

Investments in green hydrogen as a flexibility source for the European power system by 2050: Does it pay off?

The European Union aims to deploy a high share of renewable energy sources in Europe’s power system by 2050. Large-scale intermittent wind and solar power production requires flexibility to ensure an adequate supply–demand balance. Green hydrogen (GH) can increase power systems’ flexibility and decrease renewable energy production’s curtailment. However, investing in GH is costly and dependent on electricity prices, which are important for operational costs in electrolysis. Moreover, the use of GH for power system flexibility might not be economically viable if there is no hydrogen demand from the hydrogen market. If so, questions would arise as to, what would be the incentives to introduce GH as a source of flexibility in the power system, and how would electrolyzer costs, hydrogen demand, and other factors affect the economic viability of GH usage for power system flexibility. The paper implements a European power system model formulated as a stochastic program to address these questions. The authors use the model to compare various instances with hydrogen in the power system to a no-hydrogen instance. The results indicate that by 2050 deployment of approximately 140 GW of GH will pay off investments and make the technology economically viable. We find that the price of hydrogen is estimated to be around €30/MWh.

Transient behavior of pumped storage-wind hybrid power system under grid-connected operation condition

The large-scale grid connection of renewable energy represented by wind power threatens the safe and stable operation of electric system. The vigorous development pumped storage power station (PSPS) is a global consensus to support the grid-connected of renewable energy. This paper investigates the transient behavior of pumped storage-wind (PSW) hybrid power system under grid-connected operation condition (GCOC). Firstly, a model of PSW hybrid power system under GCOC is constructed. The stable domain is determined according to Hopf bifurcation theory. The influence of system parameters on the stability of PSW hybrid power system under GCOC is analyzed. A synergetic control strategy is designed to improve the dynamic performance of the system. Then, the mechanism of multi-time-scale dynamic response is revealed. Finally, the transient behavior of PSPS under different application scenarios and the interaction between PSPS and wind power station (WPS) are studied. The results show that the stability of PSW hybrid power system under GCOC can be judged by stable domain. The designed synergetic control strategy can improve the dynamic performance of the system. The dynamic response is composed of three oscillations with different frequencies, namely, mass oscillation at low frequency, water hammer oscillation at medium frequency, and electrical oscillation at high frequency. The principal oscillation is caused by water hammer. The interaction between PSPS and WPS has a significant effect on the transient behavior. By adjusting the interaction between PSPS and WPS, the system can absorb more wind power while ensuring safe and stable operation, which can increase profits and avoid unnecessary operation oscillations. The analytical methods and results presented in this paper are of great significance for improving the ability of power grid to accept renewable energy.

Dynamic Modeling of Distribution Power Systems with Renewable Generation for Stability Analysis

This paper presents a comprehensive study on the dynamic modeling of distribution power systems with a focus on the integration of renewable energy sources (RESs) for stability analysis. Our research delves into the static and dynamic behavior of distribution systems, emphasizing the need for enhanced load modeling to mitigate planning and operational uncertainties. Using MATLAB/Simulink®, we simulate four distinct study cases characterized by varying load types and levels of distributed generation (DG), particularly solar PV, under both balanced and unbalanced conditions. Our findings highlight the critical role of DG in influencing voltage stability, revealing that deviations in voltage and current during grid imbalances remain within acceptable limits. The study underscores the importance of DG-based inverters in maintaining grid stability through reactive power support and sets the stage for future research on microgrid simulations and battery storage integration to further enhance system stability and performance.

Complementary Analysis and Performance Improvement of a Hydro-Wind Hybrid Power System

Hydropower as a flexible regulation resource is a rare choice to suppress the ever-increasing penetration of wind power in electrical power systems. The complementary characteristics and performance improvement of a hydro–wind hybrid power system based on a mathematical model of the hybrid power system is studied in this paper. This established model takes into account the stochastic variation in wind speeds in the wind power subsystem and the hydraulic–mechanical–electrical coupling characteristics of the hydropower subsystem. The complementary analysis is conducted based on the evaluation variables outputted by the established model, such as the wind power, hydro-regulation power, hydraulic power, and frequency. To make full use of the regulation capability of the hydropower system, the optimization of parameter settings is also carried out to improve complementary performances of the hybrid power system. The results from the complementary analysis show the detailed characteristics of hydro–wind coordinated operation under different types of real wind speeds. Here, 95% of installed hydro-capacity is used to complement the power shortage of the intermittent wind energy under the low wind speed. Alternatively, only around 66% of the installed hydro-capacity can be utilized to cope with the fluctuation in wind power under the medium and high wind speeds before the optimization of parameter settings. The recommended values and change rules of the control, hydraulic, and electrical parameters for the hydropower system are subsequently revealed from the analysis of parameter settings to contribute to a stable and safe hybrid power system. The results show that the optimized parameter can increase the maximal regulating capacity of the hydropower system by nearly 9 MW, approximately a sixth of the total installed hydropower capacity. The method and results obtained in this paper provide theoretical and technical guidance for the safe and economical operation of power stations.

Rolling planning model for high proportion renewable energy generation power system considering frequency security constraints

In this paper, a rolling planning model for high proportion renewable energy generation power systems is proposed, considering frequency security constraints, to address the frequency stability challenges posed by increased integration of wind and solar energy into the power grid under the “double carbon” goal. First, this study establishes a frequency response model for a thermal generation unit (TGU) and analyzes the impact of the high proportion of renewable energy on system frequency stability. Subsequently, a dynamic frequency security constraint is formulated, which can be used in generation planning to address the frequency issues. Second, a bi-level rolling planning model for high proportion renewable energy generation power systems considering dynamic frequency security constraints is established. The upper level focuses on investment decisions. The lower level incorporates frequency security constraints into the operational simulation to guarantee the frequency stability of the power system when making decisions on the size of newly built TGUs annually. Finally, case studies are conducted to demonstrate the validity and effectiveness of the proposed rolling planning model.

Stability Studies of Grid-Forming and Grid-Following Inverter Penetrated Systems With Different External Power System Models

Stability Studies of Grid-Forming and Grid-Following Inverter Penetrated Systems With Different External Power System Models

A Bi-Level Peak Regulation Optimization Model for Power Systems Considering Ramping Capability and Demand Response

In the context of constructing new power systems, the intermittency and volatility of high-penetration renewable generation pose new challenges to the stability and secure operation of power systems. Enhancing the ramping capability of power systems has become a crucial measure for addressing these challenges. Therefore, this paper proposes a bi-level peak regulation optimization model for power systems considering ramping capability and demand response, aiming to mitigate the challenges that the uncertainty and volatility of renewable energy generation impose on power system operations. Firstly, the upper-level model focuses on minimizing the ramping demand caused by the uncertainty, taking into account concerned constraints such as the constraint of price-guided demand response, the constraint of satisfaction with electricity usage patterns, and the constraint of cost satisfaction. By solving the upper-level model, the ramping demand of the power system can be reduced. Secondly, the lower-level model aims to minimize the overall cost of the power system, considering constraints such as power balance constraints, power flow constraints, ramping capability constraints of thermal power units, stepwise ramp rate calculation constraints, and constraints of carbon capture units. Based on the ramping demand obtained by solving the upper-level model, the outputs of the generation units are optimized to reduce operation cost of power systems. Finally, the proposed peak regulation optimization model is verified through simulation based on the IEEE 39-bus system. The results indicate that the proposed model, which incorporates ramping capability and demand response, effectively reduces the comprehensive operational cost of the power system.

China's provincial power decarbonization transition in a carbon neutral vision

The power sector plays a crucial role in achieving the China's carbon neutrality target. However, there remain knowledge gaps regarding provincial emission reduction efforts toward carbon neutrality and the impact of carbon flows embodied in electricity transmissions. This study built a modeling framework, linking a bottom-up multi-regional power system model and Quasi-Input-Output approach, to investigate the provincial-level power system transition. Multiple combined scenarios based on shared socio-economic developments and different carbon mitigation policies were designed for a comprehensive assessment. Results indicates that the transition of the power system by 2060, under various scenarios, necessitates 7–7.8 TW of wind and solar photovoltaic power, 4810–6309 TWh of electricity transmissions, and 140–262 GW of coal power retrofits. Notably, carbon emission flows will accumulatively reach 12.7–18.7 Gt from 2020 to 2060. Inner Mongolia will bear a cumulative of more than 5 Gt of carbon flows from North China. When considering the indirect emissions, load centers such as Shandong will have higher peak emissions, and Shandong will replace Inner Mongolia as the largest emitter province. In addition, provincial emission factors under the influence of complex electricity transmissions and carbon flows are estimated.

Minimum Risk Quantification Method for Error Threshold of Wind Farm Equivalent Model Based on Bayes Discriminant Criterion

The error threshold is the cornerstone to balance the mathematical complexity and simulation speed of wind farm (WF) equivalent models, and can promote the standardization process of equivalent methodology. Due to differences in power system conditions and model evaluation standards in different countries, the form and indexes of error thresholds of WF equivalent models have not been unified yet. This paper proposes a theoretical method for quantifying the minimum risk of error threshold of WF equivalent models based on the Bayes discriminant criterion. Firstly, the Euclidean errors of WF equivalent models in different periods are quantified, and the probability density distributions of the errors are fitted by kernel density estimation. Secondly, the real-time weighted prior probability algorithm is used to obtain the prior probability of a valid WF equivalent model, and the different losses caused by the missed judgment and misjudgment of the model validity to power systems are taken into account. Thirdly, the minimum risk quantification model of error threshold is established based on the Bayes discriminant criterion, and the feasibility of the proposed method is verified by an actual WF with numerical examples. Compared with the existing error thresholds, the proposed error threshold can more quickly and accurately determine the validity of WF equivalent models.

Exploring a Dynamic Homotopy Technique to Enhance the Convergence of Classical Power Flow Iterative Solvers in Ill-Conditioned Power System Models

This paper presents a dynamic homotopy technique that can be used to calculate a preliminary result for a power flow problem (PFP). This result can then be used as an initial estimate to efficiently solve the PFP using either the classical Newton-Raphson (NR) method or its fast decoupled version (FDXB) while still maintaining high accuracy. The preliminary stage for the dynamic homotopy problem is formulated and solved by employing integration techniques, where implicit and explicit schemes are studied. The dynamic problem assumes an initial condition that coincides with the initial estimate for a traditional iterative method such as NR. In this sense, the initial guess for the FPF is adequately set as a flat start, which is a starting for the case when this initialization is of difficult assignment for convergence. The static homotopy method requires a complete solution of a PFP per homotopy pathway point, while the dynamic homotopy is based on numerical integration methods. This approach can require only one LU factorization at each point of the pathway. Allocating these points properly helps avoid several PFP resolutions to build the pathway. The hybrid technique was evaluated for large-scale systems with poor conditioning, such as a 109,272-bus model and other test systems under stressed conditions. A scheme based on the implicit backward Euler scheme demonstrated the best performance among other numerical solvers studied. It provided reliable partial results for the dynamic homotopy problem, which proved to be suitable for achieving fast and highly accurate solutions using both the NR and FDXB solvers.

Clustering of Electric Power Systems into Reliability Zones in Adequacy Assessment. Part 2

The article presents an analysis of clustering methods in relation to the problem of the formation of energy calculation models (ECM) of electric power systems (EPS). Classical clustering methods are considered, such as: the k-means method, the shortest path method, as well as methods for detecting communities in graphs according to given features, which are the most suitable for solving the problem. Based on the analysis, it was found that for graph clustering, the most adequate result can be obtained by applying the Leiden method. The experimental part of the article presents the results of applying the Leiden method for the formation of the ECM of the unified energy system of Siberia.

Inferring local social cost from renewable zoning decisions. Evidence from Lower Austria’s wind power zoning

Large infrastructures, such as wind turbines, may adversely affect their environment, so their deployment is often regulated. These regulations are frequently based on a dichotomy between areas considered feasible or infeasible areas for infrastructure deployment. To overcome the inability of such a binary distinction to adequately represent the involved economic trade-offs between, but also within feasible and infeasible areas, we establish a discrete choice framework to elicit social preferences implicit in Lower Austria’s wind power zoning and generate comprehensive estimates of local social costs in high spatial resolution. Our findings suggest that wind turbines were attributed significant local social costs in the political zoning process. These local social cost estimates can inform siting decisions, improve power system modelling and open a novel perspective on the assessment of potentials for renewable energies.

Load Frequency Optimal Active Disturbance Rejection Control of Hybrid Power System

The widespread adoption of the power grid has led to increased attention to load frequency control (LFC) in power systems. The LFC strategy of multi-source hybrid power systems, including hydroelectric generators, Wind Turbine Generators (WTGs), and Photovoltaic Generators (PVGs), with thermal generators is more challenging. Existing methods for LFC tasks pose challenges in achieving satisfactory outcomes in hybrid power systems. In this paper, a novel method for the multi-source hybrid power system LFC task by using an optimal active disturbance rejection control (ADRC) strategy is proposed, which is based on the combination of the improved linear quadratic regulator (LQR) and the ADRC controller. Firstly, an established model of a hybrid power system is presented, which incorporates multiple regions and multiple sources. Secondly, utilizing the state space representation, a novel control strategy is developed by integrating improved LQR and ARDC. Finally, a series of comparative simulation experiments has been conducted using the Simulink model. Compared with the LQR with ESO, the maximum relative error of the maximum peaks of frequency deviation and tie-line exchanged power of the hybrid power system is reduced by 96% and 83%, respectively, by using the proposed strategy. The experimental results demonstrate that the strategy proposed in this paper exhibits a substantial enhancement in control performance.

Optimal Battery Storage Configuration for High-Proportion Renewable Power Systems Considering Minimum Inertia Requirements

With the continuous development of renewable energy worldwide, the issue of frequency stability in power systems has become increasingly serious. Enhancing the inertia level of power systems by configuring battery storage to provide virtual inertia has garnered significant research attention in academia. However, addressing the non-linear characteristics of frequency stability constraints, which complicate model solving, and managing the uncertainties associated with renewable energy and load, are the main challenges in planning energy storage for high-proportion renewable power systems. In this context, this paper proposes a battery storage configuration model for high-proportion renewable power systems that considers minimum inertia requirements and the uncertainties of wind and solar power. First, frequency stability constraints are transformed into minimum inertia constraints, primarily considering the rate of change of frequency (ROCOF) and nadir frequency (NF) indicators during the transformation process. Second, using historical wind and solar data, a time-series probability scenario set is constructed through clustering methods to model the uncertainties of wind and solar power. A stochastic optimization method is then adopted to establish a mixed-integer linear programming (MILP) model for the battery storage configuration of high-proportion renewable power systems, considering minimum inertia requirements and wind-solar uncertainties. Finally, through a modified IEEE-39 bus system, it was verified that the proposed method is more economical in addressing frequency stability issues in power systems with a high proportion of renewable energy compared to traditional scheduling methods.

Fuzzy Modelling Algorithms and Parallel Distributed Compensation for Coupled Electromechanical Systems

Modelling and controlling an electrical Power Generation System (PGS), which consists of an Internal Combustion Engine (ICE) linked to an electric generator, poses a significant challenge due to various factors. These include the non-linear characteristics of the system’s components, thermal effects, mechanical vibrations, electrical noise, and the dynamic and transient impacts of electrical loads. In this study, we introduce a fuzzy modelling identification approach utilizing the Takagi–Sugeno (T–S) structure, wherein model and control parameters are optimized. This methodology circumvents the need for deriving a mathematical model through energy balance considerations involving thermodynamics and the non-linear representation of the electric generator. Initially, a non-linear mathematical model for the electrical power system is obtained through the fuzzy c-means algorithm, which handles both premises and consequents in state space, utilizing input–output experimental data. Subsequently, the Particle Swarm Algorithm (PSO) is employed for optimizing the fuzzy parameter m of the c-means algorithm during the modelling phase. Additionally, in the design of the Parallel Distributed Compensation Controller (PDC), the optimization of parameters pertaining to the poles of the closed-loop response is conducted also by using the PSO method. Ultimately, numerical simulations are conducted, adjusting the power consumption of an inductive load.

Research on a Chassis Stability Control Method for High-Ground-Clearance Self-Propelled Electric Sprayers

In response to the complex working conditions and poor driving stability of high-clearance self-propelled sprayers, a nonlinear model of the chassis power system was established based on the independently controllable torque of each wheel of the developed electric sprayer. A layered-architecture chassis drive control strategy was formulated, and a stability control framework comprising an instability judgment module, an upper controller, and a lower controller was constructed based on the analysis of the impact of the centroid slip angle, the yaw rate, and the wheel slip rate on driving stability. An ideal reference model was established based on the seven-degree-of-freedom model of the sprayer, and the current state of the sprayer body was determined using the instability judgment module. A drive anti-slip controller and a yaw moment controller based on fuzzy PID theory and sliding mode control theory were designed. Additionally, an optimal torque distribution algorithm was developed based on tire characteristics to rationally allocate drive torque to each wheel, ensuring the stability of the sprayer during operation. Simulation tests were conducted using MATLAB/Simulink to evaluate the sprayer under four different driving conditions during transport and field operations. The test results showed that the “SMC + optimal distribution” control method in the chassis stability control strategy reduced the maximum deviations of the yaw rate and centroid slip angle by an average of 89.5% and 13.6%, respectively, compared to no control. The wheel slip rate during straight driving was well maintained at around 15%, enhancing the driving stability of the sprayer.

Modeling and Stability Analysis of Fuel Cell-Based Marine Hybrid Power Systems

Modeling and Stability Analysis of Fuel Cell-Based Marine Hybrid Power Systems

A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch

This paper presents reduced-order modeling of thermal power dispatch (TPD) from a pressurized water reactor (PWR) for providing heat to nearby heat consuming industrial processes that seek to take advantage of nuclear heat to reduce carbon emissions. The reactor model includes the neutronics of the reactor core, thermal–hydraulics of the primary coolant cycle, and a three-lump model of the steam generator (SG). The secondary coolant cycle is represented with quasi-steady state mass and energy balance equations. The secondary cycle consists of a steam extraction system, high-pressure and low-pressure turbines, moisture separator and reheater, high-pressure and low-pressure feedwater heaters, deaerator, feedwater and condensate pumps, and a condenser. The steam produced by the SG is distributed between the turbines and the extraction steam line (XSL) that delivers steam to nearby industrial processes, such as production of clean hydrogen. The reduced-order simulator is verified by comparing predictions with results from separate validated steady-state and transient full-scope PWR simulators for TPD levels between 0% and 70% of the rated reactor power. All simulators indicate that the flow rate of steam in the main steam line and turbine systems decrease with increasing TPD, which causes a reduction in PWR electric power generation. The results are analyzed to assess the impact of TPD on system efficiency and feedwater flow control. Due to the simplicity of the proposed reduced-order model, it can be scaled to represent a PWR of any size with a few parametric changes. In the future, the proposed reduced-order model will be integrated into a power system model in a digital real-time simulator (DRTS) and physical hardware-in-the-loop simulations.

Short-term voltage stability analysis in power systems: A voltage solvability indicator

This paper presents an analytical study for short-term voltage stability based on a novel indicator. First, it is shown that the reduced Jacobian matrix of network equations can be transformed to obtain an approximately symmetric matrix which is usually positive definite when the system under study is stable. The minimum eigenvalue of the matrix is suggested as a short-term Voltage Solvability Indicator (VSI). Then, properties of the reduced conductive matrix and susceptance matrix which have significant impacts on VSI are examined. The focus of the study is power systems with multiple constant power injections, while VSI can also be applied to analyze the impact of generic power system models. It is shown that as the penetration level of constant power injections increases, VSI decreases and the system becomes more vulnerable to voltage collapse. Finally, the relationship between the eigenvalues of the reduced Jacobian matrix and the structure-preserving Jacobian matrix is established. As a result, the suggested VSI can be efficiently computed by exploring the sparsity of structure-preserving Jacobian matrix of network equations. Case studies of several test systems including a simplified 575-machine 8117-bus East China power system are reported, demonstrating the effectiveness and practicability of the proposed method.

Designing Retirement Strategies for Coal-Fired Power Plants To Mitigate Air Pollution and Health Impacts.

Retiring coal power plants can reduce air pollution and health damages. However, the spatial distribution of those impacts remains unclear due to complex power system operations and pollution chemistry and transport. Focusing on coal retirements in Pennsylvania (PA), we analyze six counterfactual scenarios for 2019 that differ in retirement targets (e.g., reducing 50% of coal-based installed capacity vs generation) and priorities (e.g., closing plants with higher cost, closer to Environmental Justice Areas, or with higher CO2 emissions). Using a power system model of the PJM Interconnection, we find that coal retirements in PA shift power generation across PA and Rest of PJM, leading to scenario-varying changes in the plant-level release of air pollutants. Considering pollution transport and the size of the exposed population, these emissions changes, in turn, give rise to a reduction of 6-136 PM2.5-attributable deaths in PJM across the six scenarios, with most reductions occurring in PA. Among our designed scenarios, those that reduce more coal power generation yield greater aggregate health benefits due to air quality improvements in PA and adjacent downwind regions. In addition, comparing across the six scenarios evaluated in this study, vulnerable populations─in both PA and Rest of PJM─benefit most in scenarios that prioritize plant closures near Environmental Justice Areas in PA. These results demonstrate the importance of considering cross-regional linkages and sociodemographics in designing equitable retirement strategies.