Computing the Load Margin of Power Systems Using Particle Swarm Optimization

The power system load margin is an important index used in power system operation centers. Traditional load margin calculation involves solving a set of differential-algebraic equations where not all information is always available. Data-driven methods such as Neural Networks (NNs) have been proposed but present poor performance and lack of generalization, especially in cases other than the operating history of power systems. In this article, we propose a Physics-Guided Neural Network (PGNN) to calculate the load margin of power systems. The PGNN is regularized by an auxiliary process that aims to reconstruct the power flow equations at the stability threshold that defines the load margin. In the PGNN training stage, there are two error functions that must be minimized, one related to the empirical knowledge of the system and the other related to the physical knowledge of the system associated with the guarantee of power flow. Case studies are presented for two test power systems, IEEE 68-bus system and Brazilian interconnected power system, considering a set of operating conditions, signal noise and outliers. The results show the superior performance of PGNN over traditional NNs.

The load margin due to voltage instability and small-signal instability can be a valuable measure for the operator of the power system to ensure a continuous and safe supply of electricity. However, if this load margin was calculated without considering system operating requirements, then this margin may not be adequate. This article proposes an algorithm capable of providing the power system load margin considering the requirements of voltage stability, small-signal stability, and operational requirements, as limits of reactive power generation of synchronous generators in dynamic security assessment. Case studies were conducted in the 107-bus reduced order Brazilian system considering a list of contingencies and directions of load growth.

The identification of voltage collapse (VC) is crucial to prevent a possible collapse of the preventive control actions and voltage security evaluation. Selecting the critical buses in the network can assist in determining the locations where voltage collapses may occur. VC initially manifests at the weakest bus in a serious emergency case. So, for operational and planning purposes, it is essential to detect critical buses in an electric power system. The analysis of the power system in view of voltage stability (VS) was performed under different loading conditions using voltage stability indices (VSIs). The line voltage stability indices in terms of the fast voltage stability index (FVSI) and line stability index (LMN) are utilized in this paper to identify the weakest bus in the network. The suggested procedure is tested on a standard network (IEEE 14-bus system) at different overloading conditions (25 – 100 % overload) utilizing power system analysis toolbox (PSAT) software. The results proved that this index has a higher standard for predicting the point of voltage collapse and identification the weakest bus in the network, so consider more reliable and accurate relative to other indices.

With the rapid development of the Chinese power grid, its dynamic behavior becomes increasingly complex. How to prevent voltage instability and voltage collapse at the receiving-end system has become an urgent problem at present. To prevent voltage collapse, the key is to determine the stability margin at the operating point of the power system, and the load margin is the most basic and widely accepted voltage stability margin indicator. Considering the role of medium and long-term slow-acting elements in the actual system that affect the system voltage stability, this paper combines the static voltage stability analysis with the transient, medium, and long-term dynamic voltage stability analysis based on whole process simulation, and uses time-domain simulation methods to evaluate the voltage stability of the actual system. By analyzing the various dynamic characteristics of generator overexcitation limits and transformer on-load regulation on the development process of voltage-collapsing accidents, this paper proposes an evaluation index for the whole process dynamic stability margin of the receiving-end system. On this basis, the whole process dynamic defense system of the power grid is also constructed. The proposed method is validated by using a provincial power grid in China as an example.

In recent years, voltage instability has become a major threat for the operation of many power systems. This paper proposes a scheme for on-line assessment of voltage stability of a power system for multiple contingencies using an Extreme Learning Machine (ELM) technique. Extreme learning machines are single-hidden layer feed- forward neural networks, where the training is restricted to the output weights in order to achieve fast learning with good performance. ELMs are competing with Neural Networks as tools for solving pattern recognition and regression problem. A single ELM model is developed for credible contingencies for accurate and fast estimation of the voltage stability level at different loading conditions. Loading margin is taken as the indicator of voltage instability. Precontingency voltage magnitudes and phase angles at the load buses are taken as the input variables. The training data are obtained by running Continuation Power Flow (CPF) routine. The effectiveness of the method has been demonstrated through voltage stability assessment in IEEE 30-bus system. To verify the effectiveness of the proposed ELM method, its performance is compared with the Multi Layer Perceptron Neural Network (MLPNN). Simulation results show that the ELM gives faster and more accurate results for on-line voltage stability assessment compared with the MLPNN.

Many technological advancements in the modern era have made actual use of electrical power and the constrained operating of power systems within stability limits. Some expeditious load variations and rising power demands initiate complications in voltage stability and can put stress on performance, leading to voltage instability. Voltage Stability Indices can be used to perform voltage stability assessment. This review evaluates various VSIs based on mathematical derivations, assumptions, critical values, and methodology. VSIs determine the maximum loadability, voltage collapse proximity, stability margin, weak areas, and contingency ranking. Stability indices can also specify the optimal placing and sizing of Distributed Generators. Thus, VSIs play a vital role in power system voltage stability. This review is a comprehensive survey of various indices and analyses their accuracy in determining the instability of power systems. Voltage stability is a crucial concern in operating a reliable power system, and the systematic evaluation of voltage stability is essential in a power system. This review considered and analyzed 34 indices from 138 articles from the literature for their significant performance in various power system stability problems. Of 33 indices, were 22 derived from transmission line parameters, referred to as line indices, and 12 from bus and line parameters, referred to as bus indices.

Voltage instability and voltage collapse have been considered as a major threat to present power system networks due to their stressed operation. It is very important to do the power system analysis with respect to voltage stability. Flexible AC Transmission System (FACTS) is an alternating current transmission system incorporating power electronic-based and other static controllers to enhance controllability and increase power transfer capability. A FACTS device in a power system improves the voltage stability, reduces the power loss and also improves the load ability of the system. FACTS have made the power systems operation more flexible and secure. Amongst the several FACTS controllers, the Unified Power Flow Controller (UPFC) is most effective to improve the enhancement of voltage stability and reduces the power loss. This study investigates the application of Particle Swarm Optimization (PSO) to find sizing of Unified Power Flow Controller (UPFC) device to minimize the voltage stability index, total power loss, load voltage deviation, and cost of FACTS devices to improve voltage stability in the power system. A new model is proposed in this thesis to improve existing power-based model by using the Norton Equivalent Theorem. The proposed model can be integrated with the Equivalent Current Injection (ECI) power flow model easily. By ECI algorithm, it is much quickly and precisely to implement power flow calculations. Finally It is observed from the results that the voltage stability margin is improved, the voltage profile of the power system is increased and real power losses also reduced by optimally sizing UPFC device in the power system. Index Terms: Voltage stability, Unified Power Flow Controller (UPFC), Equivalent -Current Injection (ECI), Modified particle swarm optimization (MPSO)

In recent decades, voltage instability has become an important contributor to large-scale power outages globally. Periodic voltage security assessments are key for the secure operation of power systems. There are various indicators which have been implemented in different types and complexity of systems to provide a measure of closeness to voltage collapse, but some of these algorithms may require advanced computational resources or may not perform well, depending on the prevailing conditions. Expanding interconnected power systems is needed like never before due to the increasing world demand for electricity, and voltage stability is therefore a worth consideration. The growing demand penetration of solar photovoltaic (PV) systems has some potential stability challenges due to their intermittent characteristics. Existing research evaluates the test systems of voltage stability and does not optimize using Intelligent models, which have variable power generation from Solar PV and Wind, as well as uncertainties in load demand and the initial step considering the evaluation of the model have to cover either inputs. A feed–forward back propagation artificial neural network (ANN) for voltage stability assessment to classify the operating scenario of a power system into one of two states, i.e. safe or unsafe. Neural network input data is generated from load flow analysis using Newton-Raphson (NR), and stability indices are computed over different scenarios. Line Stability Index (Lmn), counts the stability of a transmission line in power systems and provides an indication of its potential voltage collapse. The Fast Voltage Stability Index (FVSI), which also estimates line stability through reactive power and impedance characteristics. Voltage Collapse Proximity Index (VCPI) assesses system proximity to voltage collapse and identifies weak transmission lines. Values approaching 1 suggest voltage collapse conditions. The FVSI, VCPI, and Lmn are compared to a baseline NR stability index. Moreover, self-organizing map (SOM) neural network is used for stability results classification. Multi-objective grasshopper optimization algorithm (MOGOA) has been employed as an optimization network on the dual axis solar PV and wind turbine-based hybrid power generation system to analyze technical, economic, as well as environmental relations of energy conversion. The findings reveal that the adapted grid-tied solar-wind composite power system substantially mitigates the power deficiencies, reduces the real-power outages, diminishes the motion voltage small amendments, maximizes voltage prosperity, and improves power system resilience. The main findings show a significant reduction in real power loss, which went from 289,391.30 kW to only 5.43 kW, and a remarkable decrease in voltage deviation, which reduced from 0.56 p.u to 0.0493 p.u. Ensures Improved Service Quality and Enhanced Equipment Protection While gas generation costs increased by a small amount, it is important to note that this is an acceptable trade-off for a more robust and sustainable system, with costs per kWh of $0.142 vs $0.2881 per kWh, respectively. In addition, stability index was substantially decreased from 0.7666 to 0.0768, indicating better grid and resilience to disturbances. Findings emphasize the contribution of embedding MOGOA in conjunction with machine learning models including ANN and Self Organizing Maps (SOM) to fulfill the primal requisites of stability, efficiency and sustainability in modernized power systems, illustrating a coupled advancement in the realm of power systems engineering and optimization.

Voltage deviation and stability constrained VAr planning or reactive power planning (RPP) is an important challenging issue in power systems. This paper presents a new hybrid technique for modeling and solving RPP problem taking into account the static voltage stability constraint. First, the uncertain fuzzy clustering theory is employed to select new candidate VAr source locations. Then, modified gray code is applied and used to represent a series of non-uniform VAr capacity intervals at different candidate buses. Based on the new ordering of the VAr capacity intervals, a simplified piecewise linear function between the total transfer capability and new VAr capacity is derived and applied as static voltage stability constraint in RPP problem. Last, the RPP optimization problem is solved by a self adaptive fuzzy chaotic interactive honey bee mating optimization (FCIHBMO) technique taking advantage of the modified gray code. In the FCIHBMO algorithm, a modified definition of the updating factors on generation solution is proposed. In the case study, uncertain fuzzy clustering mechanism, the modified gray code, and the modified HBMO are applied to the IEEE 118-bus and IEEE 300-bus systems. Test results conclude that the proposed hybrid technique is a simplified and effective approach for voltage stability constrained VAr planning with contingency considered.

Stress on the generation and transmission capability of the power system increased as the energy demand increases. Distributed generation (DG), which is usually placed near the load centre has the capability to meet these energy increment in demands. Hence, for making the power system highly durable and reliable, Distributed generations are interconnected with the existing power system. Based on the nature of the primary source of generation and the energy conversion technology these types of generation have important impacts on power system voltage stability. One of the most significant threats considered for a secure operation of the power system is voltage instability problem. Voltage collapse might occur in an interconnected power system due to voltage instability and thus lead to power blackouts. Hence in an interconnected power system it is essential to know the strength of the buses to monitor and improve the stability of the system. This paper focuses on voltage stability analysis of an interconnected distributed photovoltaic system with IEEE 30 bus system. The voltage stability of the system assessed by evaluating voltage stability indicators at each bus of interconnected power systems. Fast Voltage Stability Index value of each bus is evaluated under normal and critical load conditions. The index value helps to identify the weakest or the bus which is likely to get voltage collapse due to voltage instability problem in the interconnected system.

Nowadays the modern power systems are large complex systems and widely distributed geographically. The increase in demand, generator reaching reactive power limits and line/generator outages may operate the power system in stressed conditions leads to voltage instability or voltage collapse. Voltage stability has become of major concern among the power utilities, because of several events of voltage collapse occurred in the past decade. Thus the real time voltage stability assessment is essential by estimating the loadability margin of the power system. Voltage stability analysis was studied on IEEE 30 and IEEE 118 bus systems using many voltage stability indices based on line/nodal and the results are compared with the proposed new index based on SVM and ELM.

This paper investigates on-load tap changer OLTC effect on voltage stability. Chaos theory used in this analysis is via the calculation of the maximum power transmission. Resulted chaotic behavior is exhibited by singular induced bifurcation which clearly shows the voltage stability of the power system with OLTC from a singular induced bifurcation point of view. The paper is organized as follows: 1) increasing in the maximum reactive power via increasing the ratio of OLTC and the possibility of voltage collapse decrease under the same load command. 2) Noting that the voltage instability is directly affected by the load characteristics, shown via the effect of OLTC on the voltage instability under different static load models. 3) Studying voltage stability in state space and the effects of the generator excitation current limit, the OLTC and load dynamics on voltage collapse. In addition, a small-disturbance voltage stability region of a power system is constructed. The voltage stability of the system is determined by the dynamic characteristics of both the OLTC and the load.

Due to rising energy consumption, electrical power system networks are frequently exposed to severe stress and operate close to their maximum stability limits. Consequently, these systems are becoming less secure, and voltage instability is becoming a constant concern. The operators must have a precise understanding of how the current system is operating. Voltage stability indices are one of the most powerful tools for evaluating power system stability. In order to avoid voltage instability and collapse, PMU-based real-time voltage stability assessment is one of the novel concepts. The line stability index (Lmn), fast voltage stability index (FVSI), line stability factor (LQP), line index (L-index), voltage collapse proximity index (VCPI-P and VCPI-Q), line voltage stability index (LVSI), and critical voltage (Vcr) were all taken into account in this study. This paper is unique in that it computes and compares these standard line voltage stability indices on a static load model with the help of PMU recordings to identify the weak areas. Under steady-state operating conditions, these indices are computed on the classic WSCC 3-machine 9-bus system. These findings could be extremely useful to system operators to improve the static voltage stability margin, grid planning, and protection to prevent future blackouts.

This paper discusses voltage stability analysis of power systems using two static voltage stability analyses: voltage sensitivity, modal analysis including participation factor. These methods determine how far the power system is from its break point providing relative measure of voltage instability proximately. Results show all method indices share voltage stability margins having a precise voltage collapse point when a power system is subjected to sudden load increase. The application has been demonstrated on the IEEE 14-bus System.

Using demand response to improve power system small-signal stability