IEEE 30-bus Power System Research Articles

Vulnerability assessment for voltage stability based on solvability regions of decoupled power flow equations

This paper proposes a novel method of identifying buses vulnerable to power system voltage instability. Unlike traditional sensitivity and modal analysis methods, the proposed method can preserve the nonlinearity of power flow equations, and visually pinpoint the vulnerable buses in advance for any possible load increasing scenarios. Based on the power flow equations on decomposed two-bus equivalent channels from the power network, a vulnerability index is introduced and visualized for each channel in the solvability region of its decoupled power flow equations bounded by a parabola. It is found that the arrival at the parabolic boundary indicates a potentially vulnerable bus but not necessarily results in voltage collapse. Thus, a criterion on the gradient of vulnerability index trajectory is proposed to discover and differentiate two types of potentially vulnerable buses: one type has trajectories that are tangent to the boundary but stay inside the solvability region; the other type has trajectories crossing the boundary to result in unsolvable power flow equations, which are identified as the vulnerable buses. The proposed method is validated on the IEEE 14-bus, IEEE 118-bus, and New England power systems with comparison to the traditional methods, and the test results show that the proposed method performs better than the traditional methods with satisfactory robustness under voltage fluctuation. In particular, the proposed method is 33.3% and 66.7% more accurate than the voltage sensitivity method in prospective operating conditions on the IEEE 14-bus and 118-bus systems, respectively.

Steady state stability in electrical power systems considering operation limits in generators, transformers and transmission lines

Electrical power systems are exposed to several events that can cause unstable operation scenarios. This is due to improper operation of certain components. If an event occurs, the system must be designed to overcome that contingency, thus remaining in a permanent condition that must be evaluated in order to monitor and prevent a possible collapse of the system. An evaluation of steady state stability is proposed at this work based on the capacity curves of generators, transformers and transmission lines. These remarked curves provide information on the operation point of these elements, thus allowing the application of remedial actions. PowerFactory and Matlab are used to carry out the tool for monitoring the operation points after a contingency. The effectiveness of the developed tool is validated at the IEEE 39-bus power system model, where results shows that the functionalaty for different contingencies based on the operating conditions when the components of the power system are varied, cosnquently, the tool identifies cases that require actions at the operational level.

Low-Carbon Economic Bi-Level Optimal Dispatching of an Integrated Power and Natural Gas Energy System Considering Carbon Trading

The integrated power and natural gas energy system (IPGES) is of great significance to promote the coordination and complementarity of multi-energy flow, and it is an important carrier to increase the proportion of wind power accommodation and achieve the goal of carbon emission reduction. In this paper, firstly, the reward and punishment ladder-type carbon trading model is constructed, and the impact of the carbon trading mechanisms on the carbon emission sources in the power system is comparatively analyzed. Secondly, in order to achieve a reasonable allocation of carbon resources in IPGES, a bi-level optimization model is established while taking into account the economics of dispatching and the requirements of carbon emission reduction. Among them, the outer layer is the optimal carbon price solution model considering carbon trading; in the inner layer, considering the power system constraints, natural gas system constraints, and coupling element operation constraints, a stochastic optimal dispatching model of IPGES based on scenario analysis is established. Scenario generation and reduction methods are used to deal with the uncertainty of wind power, and the inner model is processed as a mixed integer linear programming problem. In the MATLAB environment, program the dichotomy and call the Gurobi optimization solver to complete the interactive solution of the inner and outer models. Finally, case studies that use an integrated IEEE 39-bus power system and Belgian 20-node gas system demonstrate the effectiveness and scalability of the proposed model and optimization method.

An adaptive multi-step Levenberg-Marquardt continuation power flow method for voltage stability assessment in the Ill-conditioned power systems

Continuation power flow (CPF) is a well-known way for determining voltage instability point in electrical power systems. In an ill-conditioned power system, solving traditional CPF using the Newton’s method encounters divergence or very slow convergence, because the Jacobian matrix is singular or near singular. This paper presents the application of the adaptive multi-step Levenberg-Marquardt (AMSLM) method to solve the power flow problem in an ill-conditioned power system. In the next step and based on the new proposed AMSLM power flow (AMSLM-PF) method, an AMSLM continuation power flow (AMSLM-CPF) method for voltage stability assessment of the ill-conditioned power systems is presented. Moreover, a fuzzy inference system (FIS) is proposed to optimize the parameters of the new AMSLM-PF method. To demonstrate the effectiveness of the proposed AMSLM-PF and AMSLM-CPF methods, detailed simulation results are presented and analyzedfor IEEE 14-bus, IEEE 43-bus, IEEE 118-bus and 2383-bus power systems.

An optimisation model based approach for power systems voltage stability and harmonic analysis

This paper presents a novel optimisation problem formulation for power systems voltage stability and harmonic analysis. The purpose is to evaluate the maximum loadability of an electrical power system considering voltage magnitudes, active/reactive powers, total and individual harmonic distortion limits as inequality constraints. The impact of power quality on the maximum loadability margin is evaluated based on the results of the optimisation problem solved by interior-point method and the proposed indices in which Lagrange multipliers are used to identify sensitive buses of electrical systems due to power quality degradation and voltage instability. Simulations are carried out using IEEE 30-bus power system assuming the insertion of non-linear loads to validate the use of the proposed method and show the applicability of the indices based on Lagrange multipliers for the assessment of both voltage stability and harmonic distortion. Results are compared with the traditional modal analysis to validate the ability of the proposed method for identifying the most critical buses of the system.

A Voltage Stability-Based Approach to Determining the Maximum Size of Wind Farms in Power Systems

Current methods to determine the wind farms maximum size do not consider the effect of new wind generation on the Voltage Stability Margins (VSMs). Installing wind power in one area may affect VSMs in other areas of the power system. Buses with high VSMs before wind power injection may be converted into weak buses after wind power injections in other parts of power systems, which may lead to limited future wind farms expansion in other areas. In this paper, two methods are proposed to determine two new wind farms maximum size in order to maximize wind power penetration level. In both methods, the size of any new wind farm is determined using an iterative process which is increased by a constant value. Proposed methods were used in the IEEE 14-bus power system. The results of applying these new methods indicate that the second method results in higher maximum sizes than the first method.

Peer-to-peer market with network constraints, user preferences and network charges

With an increase of distributed generation growing attention is paid to the possibilities of its utilization in the network. The peer-to-peer market represents one of the possible ways to address this question. Largely driven by distributed ledger technologies, the peer-to-peer market architectures ignored network constraints for a long time, paying more attention to the organization of the financial transactions. In this paper we propose a peer-to-peer market design, incorporating network constraints, user preferences, and trade-independent network fees. In this way, we ensure a meeting of three requirements critical to the practical implementation of the peer-to-peer market as secure operation, consumer-centric nature of the market, and the provision of benefits for the grid. We develop a distributed procedure and demonstrate the applicability of the proposed algorithm using the IEEE 39-bus power system, and compare it with the correction-based algorithm.

An Alternative Learning-Based Approach for Economic Dispatch in Smart Grid

This article tries to provide a new alternative approach to solve the economic dispatch (ED) problem in a smart grid system. Such a problem has been widely studied recently with several advanced numerical optimization algorithms being proposed. However, most of these numerical algorithms may suffer from high computational cost for on-line optimization. In this article, we aim to address this problem by proposing a learning-based optimization strategy. The key idea is to regard the optimization strategy of the ED problem as an unknown mapping relationship. With the help of traditional ED optimization algorithms to obtain the ground truth, we employ a deep neural network (DNN) to learn the ED optimization strategy and use it for online ED. In particular, our main contribution in this article is to theoretically show that one popular ED algorithm, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> -iteration algorithm, can be accurately approximated by a well-constructed DNN with finite network size. Moreover, dynamic units status of dispatchable generators is also considered and can be well solved by our proposed approach. Furthermore, several simulation case studies implemented on a 3-unit power system and an IEEE-30 bus power system validate the effectiveness of our proposed method.

An Accelerated Distributed Gradient-Based Algorithm for Constrained Optimization With Application to Economic Dispatch in a Large-Scale Power System

In this article, we consider a convex optimization problem which minimizes the sum of local agents' cost functions subject to certain local constraints. Besides, both the local cost function and local constraints are only known by the local agent itself. To solve this problem, a new accelerated distributed gradient-based algorithm is proposed, which is inspired by the “momentum” phenomena in nature and aims to accelerate the convergence speed of conventional distributed gradient algorithms. Sufficient conditions for the stepsizes and the acceleration gains are derived to ensure the convergence of the proposed algorithm. Furthermore, based on this proposed fast distributed algorithm, a new decentralized approach is proposed to solve economic dispatch problem, especially for a large-scale power system. Based on the idea of virtual agent, it is proved that this decentralized algorithm is equivalent to the original fast distributed gradient method. Several case studies implemented on IEEE 30-bus, IEEE 118-bus power systems, and a large-scale power system consisting of 1000 generators are conducted to validate the proposed method.

A Dynamic Bayesian Network Control Strategy for Modeling Grid-Connected Inverter Stability

The dynamic performance of a grid-connected inverter in a distributed generation system brings new challenges by affecting the power quality and dynamic stability. The traditional linear control method for the inverter requires complex processes including decoupling and control parameter tuning and relies on a pulsewidth modulation module. The nonlinear control method, e.g., the model predictive control (MPC), can address some of the aforementioned challenges but is incapable of dealing with system parameter changes. A data-driven method using the dynamic Bayesian network-based model predictive control (DBN-MPC) is proposed, which takes advantage of the predictive ability of the DBNs to implement the MPC strategy. A predictive model is built, and the prediction signals are generated based on the DBNs. Then, by constructing the cost function and optimization criteria, the controller generates the optimal switching state combination. Using the proposed DBN-MPC method, the predictive model implements parameter learning online, providing more accurate prediction signals for further optimization and the feedback correction. In addition, the control law of the proposed controller can update over time, which enables the grid-connected inverter system to achieve the optimal control. The case studies using the grid-connected inverter system and IEEE 39-bus benchmark power system integrated with the battery energy storage system demonstrate and verify the superiority of the proposed DBN-MPC method.

Static Stability Analysis Based on Probabilistic Power Flow Calculation considering P2G Technology

At present, integrated energy systems have received extensive attention, but there is no basic framework for stability analysis of coupled systems. The injection of a large amount of renewable energy also has a great impact on the stability of the system. This paper focuses on how to analyze the static stability of the coupling system with uncertainty, which mainly considers the uncertainty of wind power generation and photovoltaic power generation and also considers the influence of P2G technology on the whole system. Firstly, this paper analyzes the principles of wind power generation and photovoltaic power generation and constructs the probability model of renewable energy power generation power. Then, the three-point estimation method is used to process the data, and the probability distribution of the unknown quantity is obtained by probabilistic power flow analysis. Finally, the probability distribution of each eigenvalue is obtained by analyzing the sensitivity of the characteristic roots to the voltage. Thus, the static stability of the system is judged. The applicability of proposed methodology is demonstrated by analyzing an integrated IEEE 14-bus power system and a Belgian 20-node gas system in this paper.

Scalable design methods for online data‐driven wide‐area control of power systems

A novel online system-identification-based control design for damping inter-area oscillations in power systems using supplementary wide-area excitation control is presented. The identification is based on a partly reduced-order and a partly full-order model of the grid. Assuming the grid to be divided into coherent areas with phasor measurement units located across the grid, the coherent states of the generators are averaged while the non-coherent states, such as the internal states of each power system stabilizer, are not. A hybrid state vector consisting of these averaged and non-averaged states is computed, and used for identifying a hybrid linear time-invariant state-space model. A linear quadratic regulator based on this hybrid model is, thereafter, designed. The reduced-order part of the model is found to save significant amount of online time for both learning and control, while the full-order part serves to enhance closed-loop stability. N4SID with randomized singular value decomposition (rSVD) is used for making the identification loop fast. The reduced-dimensional controller is finally implemented using a broadcast control strategy. The design is extended to non-linear models of power systems using Carleman bilinearization. Results for linear and bilinear control designs are validated using the IEEE 68-bus power system model.

Multi-model power system state estimation based on linear transition models

Power system state estimation is one of the most important functions of power system control centers. In recent years, the complexity of power system state estimation has significantly increased due to the growing number of distributed, including renewable energy sources, electric vehicles, the demand response technologies, and the increased risk of cyber-attacks. Under these conditions, state estimation methods, which consider information about the time-correlation of the power system states have a great potential. The correlation is described by a transition model. The well-known state estimation methods usually use one single model. However, in case of stochastic behavior of the load and generation, it is impossible to assert the adequacy of the chosen model over the entire observation interval. Therefore, the paper proposes a multi-model forecasting power system state estimation method, which has lower errors in comparison with a single-model assessment at the moments of the lowest accuracy of the latter. Multi-model parameter estimation is used based on three procedures of the single-model Kalman filtering estimation and various transition models based on autoregressive and vector autoregressive analyzes, as well as Holt's exponential smoothing. Uniting the single-model estimation has been carried out according to the criterion of the minimum of variance of the resulting estimate. An algorithm of multi-model power system state estimation has been developed. Its version has been analyzed using a three-model forecasting-aided estimation using linear transition models. The state of the IEEE 30-bus test power system has been assessed by the means of simulation modeling. The maximum accuracy increase of the multi-model estimation in comparison with the single model is set up. 26,1 % is for autoregressive analysis; 16,9 % is for vector regression analysis and 37,7 % is for Holt’s exponential smoothing. The proposed method of multi-model state estimation has higher robustness and accuracy at the moments of the lowest accuracy of single-model estimation. It is advisable to use the method to solve control tasks of power systems with rapidly changing dynamic modes.

Sensorless real-time reduced order model-based adaptive maximum power tracking pitch controller for grid connected wind turbines

To overcome the mechanical stress and damage caused by the high wind speed and grid transient on the wind turbine (WT) and to ensure the smooth operation of WT, a sensorless maximum power tracking (MPT) pitch controller for grid integrated WT is proposed in this paper. The advantages of the proposed controller are: a) reduced rotor speed oscillations, b) reduced transients in Point of Common Coupling (PCC) voltage, and c) controlled output power of WT without exceeding its thermal limits. The controller is validated on the WT integrated into the frequency-dependent reduced order model (FDROM) of the power grid. Another advantage is that, as the reference speed for the controller is estimated using FDROM, actual wind speed measurements are not required in this approach. To ensure smooth operation, and to limit the aerodynamic power and speed within the normal operating range, the difference between the actual and reference speed of the generator is used as the input to the controller. The architecture is validated using a real-time digital simulator (RTDS) on WT integrated two-area and IEEE-39 bus power system models. The simulation results show that the proposed controller is more effective than the conventional methods during changing system operating conditions.

Profit‐based evaluation of optimal FACTS devices planning for the large consumers and TRANSCO considering uncertainty

This paper seeks to address the impact of optimal FACTS devices planning on the obtained profit of Transmission Company (TRANSCO) and large consumers. An economic investigation is done to verify how the investment cost of FACTS devices can be compensated using the obtained benefits of TRANSCO and large consumers. It is shown that the gained benefit by the consumers might be considered as an effective policy for the participation of the demand side in the FACTS devices' investment costs. Additionally, in this paper, a new hybrid approach, consisting of both mathematical and heuristic methods for solving the problem, is presented. The mentioned algorithm is a combination of the hunting search (HuS) algorithm as a heuristic algorithm and non-linear programming (NLP) as a mathematical approach. Also, the stochastic natures of renewable energy sources and load variations have been considered. For modeling the stochastic parameters, two points estimation method has been employed. Also, the spatial correlation among uncertain parameters has been considered. Finally, the proposed approach has been tested on a modified IEEE 57-bus and IEEE 118-bus power systems to confirm its efficiency and capability. The results indicate that by this methodology and procedure for the planning of FACTS, there is a reduction of 4.6474 × 105$ in payment of large consumers in 57-bus system and 3.8089 × 108$ in 118-bus system. Also, the respected values of power loss reduction cost of 57-bus and 118-bus test systems are 2.6246 × 105$ and 2.8250 × 107$.

A model‐based method for rotor speed estimation of synchronous generators using wide area measurement system

In this paper a novel method is proposed to estimate the rotor speed of synchronous generators in steady state and dynamic conditions using phasor measurement unit's data. This method uses the synchronous generator model to find the relationship between generator rotor speed and frequencies at different buses of the power system. The principles of the proposed method are first presented through a simple network consisting a generator connected to a transmission line. Afterward the general formulation is developed. To demonstrate the effectiveness of our method, IEEE 9-bus and IEEE 39-bus power systems are used as the benchmark systems. Different tests are carried out under three conditions including, normal condition, presence of measurement errors and uncertainty of the power system parameters. As well, the estimation results are compared with the results of other estimation methods. The results show the high accuracy of the proposed method in different conditions.

A Hybrid Particle Swarm Optimization Algorithm for the Wide-Area Damping Control Design

The presence of low-frequency and low-dampened oscillation modes can compromise the operating stability of power systems. Recent research has shown that the use of phasor measurement units data to compose a wide-area damping controller (WADC) has been shown to be effective in mitigating such oscillation modes but the possibility of loss of communication channels due to cyber-attacks or failures can compromise the proper operation of this controller. Besides, traditional control design methods present difficulties for the WADC control design. This article proposes a method based on hybrid particle swarm optimization in order to design a WADC that ensures robustness to power system-operating uncertainties, time delays variations on the WADC channels, and the permanent failure of the WADC communication channels. Modal analysis and nonlinear time-domain simulations were conducted in the IEEE 68-bus power system considering a set of scenarios.

Robust load frequency control for networked power system with renewable energy via fractional‐order global sliding mode control

Owing to random load changes and transmission time delays in interconnected power systems with renewable energy, the load frequency control scheme has become one of the main methods to keep stability and security of power systems. To relieve communication burden and increase network utilisation, an adaptive event-triggered scheme is explored. Then, a new fractional-order global sliding mode control scheme comprising the fractional-order term in the sliding surface is adopted to improve robustness of load frequency control. The fractional-order term generates a new degree of freedom and more adjustable parameters to improve control performance. Furthermore, the Markov theory is applied in the modelling process to better describe the uncertainty of parameters and external disturbances. The stability and stabilisation criteria for multi-area power systems load frequency control are put forward by employing the improved Lyapunov function and integral inequalities with auxiliary functions. Finally, two simulation examples containing a two-area power system and modified IEEE 39-bus New England test power system with three wind farms are presented to investigate the effectiveness of the proposed method.

Scalable Designs for Reinforcement Learning-Based Wide-Area Damping Control

This article discusses how techniques from reinforcement learning (RL) can be exploited to transition to a model-free and scalable wide-area oscillation damping control of power grids. We present two control architectures with distinct features. Performing full-dimensional RL control designs for any practical grid would require an unacceptably long learning time and result in a dense communication architecture. Our designs avoid the curse of dimensionality by employing ideas from model reduction. The first design exploits time-scale separation in the generator electro-mechanical dynamics arising from coherent clustering, and learns a controller using both electro-mechanical and non-electro-mechanical states while compensating for the error in incorporating the latter through the RL loop. The second design presents an output-feedback approach enabled by a neuro-adaptive observer using measurements of only the generator frequencies. The controller exhibits an adaptive behavior that updates the control gains whenever there is a notable change in the loads. Theoretical guarantees for closed-loop stability and performance are provided for both designs. Numerical simulations are shown for the IEEE 68-bus power system model.

Effect of P2G on Flexibility in Integrated Power-Natural Gas-Heating Energy Systems with Gas Storage

The low carbon transition requires the high growth of renewable generation penetration in energy systems to ultimately achieve net-zero carbon target. To ensure the reliable operation of energy systems with high intermittent renewable output, it is critical to have sufficient flexible resources to avoid curtailment. Therefore, the integrated power-natural gas-heating energy systems with power to gas (P2G) and gas storage has attracted great research interest especially on the combined operation method to enhance the flexibility provision between each other. In this paper, taking heating demand, P2G and gas storage into consideration, a multi-objective optimal operation strategy of integrated power-natural gas-heating energy systems is presented to obtain the maximum economic and environmental benefits. Furthermore, a novel model of flexibility metric is proposed based on redundant linepack and gas storage. Case studies without P2G and with P2G are carried out on integrated IEEE 39-bus power and Belgian 20-node gas system. Simulation results demonstrate that P2G not only can be beneficial for operation of the integrated energy systems in terms of total operational cost decline from M$2.510 to M$2.503, CO2 emission reduction from 62,860 ton to 62,240 ton and wind curtailment decrease from 25.58% to 4.22% but also has significant effect on flexibility improvement of a 71.72% increase.