Static Voltage Stability Limit Research Articles

An Extended Continuation Power Flow Method for Static Voltage Stability Assessment of Renewable Power Generation-Penetrated Power Systems

The continuation power flow method (CPF) has been extensively used for obtaining the static voltage stability limit of power systems, which provides important guidance for the stable operation. However, the conventional CPF cannot account for the dynamic characteristics of renewable power generation, thus resulting in prominent errors for renewable power generation-penetrated power systems. In this paper, we investigate the static voltage stability assessment (SVSA) of power systems with high penetration of rgb0,0,0renewable power generation (RPG). An extended Jacobian matrix is firstly established by considering the dynamic characteristics of synchronous generators (SG) and renewable power generation in constant AC voltage control mode (CVRPG). Based on the extended Jacobian matrix, an extended CPF method is proposed for SVSA of the power system and a reactive power sensitivity index is proposed to indicate the voltage support capability of nodes. Simulation results show that the proposed extended CPF method has higher accuracy than conventional CPF in assessing the static voltage stability of power systems with high penetration of RPG. It is also revealed that that the voltage support capability of each node rises as the proportion coefficient is increases.

Calculation of static voltage stability margin under N-1 contingency based on holomorphic embedding and Pade approximation methods

A calculation technique for the static voltage stability margin (SVSM) under N-1 contingency based on the fast and flexible holomorphic embedding (FFHE) and Pade approximation (PA) methods is proposed. The technique can also obtain the approximate analytic function between the post N-1 contingency SVSM and the pre-contingency SVSM. Using the contingency parameter as an embedded variable, the relationship between the post N-1 contingency SVSM and the pre-contingency SVSM is approximately described in the form of power series. By constructing the FFHE matrix equation, the values of state variables at the pre-contingency static voltage stability limit point are taken as the 0th order coefficients. The FFHE matrix equation is solved to obtain the higher order coefficients from the lower order coefficients step by step. Thereby the power series expression of post N-1 contingency SVSM is obtained. In addition, by using the PA method, the approximate rational fraction expression of the post-contingency SVSM which can improve the convergence and accuracy of the power series can be obtained. Test results for the IEEE 39-bus system and an actual 1559-bus power grid demonstrate that the proposed method to calculate the post-contingency SVSM has high accuracy and strong robustness compared with the optimal power flow and continuation power flow methods. The average relative errors of the proposed method in the two cases are 0.58155% and 1.0862%. The strong robustness is reflected in the fact that there is no need to repeatedly select the initial value for calculation under different contingencies.

Impacts of Large-Scale Offshore Wind Power Plants Integration on Turkish Power System

In this paper, the impacts of large-scale OWPPs penetration on the Turkish power system is addressed. The grid compliance analyses for the large-scale OWPP integration are carried out by using the grid connection criteria defined in the Turkish grid code. PV and QV curves are obtained to assess the effect of OWPP on the static voltage stability limit. Eight scenarios are conducted to analyze the effect of the OWPP on the static and dynamic characteristics of the power grid. To observe the large-scale OWPP impact on the voltage and frequency stability, transient events such as the outage of conventional power plants and three-phase to ground faults are applied. The results of the voltage and frequency stability analysis reveal that the Turkish grid remains stable after the integration of an 1800 MW OWPP. Furthermore, the Turkish system remains stable even in the event of the outage of the international transmission lines to Bulgaria and Greece.

Static Voltage Stability Analysis of Distribution Systems Based on Network-Load Admittance Ratio

It is well known that a single (constant power) load infinite-bus system reaches a static voltage stability limit point, or equivalently, a singularity point of the power flow Jacobian, at the unity line-load admittance ratio, i.e., the equivalent admittance of the load has the same modulus as the transmission line admittance. In this paper, we rigorously extend this result to generic distribution systems with distributed generators (DGs). We introduce a new concept called the network-load admittance ratio that is in terms of the parameters of power network, loads, and DGs. This concept is a generalization of the line-load admittance ratio that characterizes the loading status of a distribution system with the effects of DGs included. We prove that the power flow Jacobian is singular if and only if the network-load admittance ratio is unity, which provides new insights into the mechanism of voltage stability. In addition, we establish a new voltage stability index by using the network-load admittance ratio. Numerical simulations on several IEEE test systems show that the index has good linearity with load increase and estimates voltage stability margin with high precision. The index also reflects the impact of DG penetration level and control mode on voltage stability. The obtained results can be extended to ZIP load models, unbalanced three-phase networks, and mesh networks with slight modifications.

Study on Fast Evaluation Method of the Power Receiving Capability of the Multiple-Section Receiving-End System Considering Voltage Stability Constraint

With the rapid growth of the end-system load, the power system lacks sufficient power supply, and the transient voltage stability after the large disturbance become worse. Considering the lack of quantitative evaluation method of the power receiving capability, a fast evaluation method of the power receiving capability of the multiple-Section receiving-end system considering voltage stability constraint is proposed in this paper. Firstly, an evaluation method of the power receiving capability of the single-section is proposed, which is combined with static voltage stability limit, the amplitude of transient power fluctuations, load power factor, reactive power of receiving-end system, transient voltage stability effect of HVDC. Based on the research of the single-section system, an evaluation method of the power receiving capability of the multiple-Section receiving-end system is proposed, which is utilized the interrelated relations between the average value and standard deviation of the multiple sections. This method can more fully and quickly evaluate the power receiving capability. The results are verified in the Hunan power system. The results show that the proposed method has better engineering applicability and it can be adopted to evaluation method of the power receiving capability of the multiple-section receiving-end system considering voltage stability constraint.

Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability

This paper presents a new algorithm for voltage stability security assessment accounting uncertainties in the line parameters and control variables. Security index has been evaluated using Monte-Carlo simulation with & without consideration of unavailability of transmission lines, which is used to perform contingency selection. Further, probabilistic insecurity index at various loading conditions considering voltage stability limit has been obtained using cut-set method for single & double line outages. Static voltage stability limit for various sampled values of system parameters and control variables have been obtained using continuation power flow methodology. Few cases have been used to train back propagation algorithm (BPA). Obtained results for contingency selection based on security index have been compared with well-established methods.

Reconstruction of security region with high information content using effective attributes extraction

Summary Security region-based power system operation guides operators in a fast and relevant decision-making process as to what conditions require operators' actions. The key to this approach is the manner in which effective attributes are extracted among the network's operating variables. This paper reconstructs the security region of power system with high information content. The security region of power system is constructed by means of the static security boundaries such as static voltage stability limit, generator output power limit, and transformer and transmission line thermal limits by increasing loading factor along various directions until these limits are violated. Then, the security region is described by means of effective features set that contain maximum information content. In this paper, nonlinear feature extraction techniques have been proposed to dimensionality reduction and relevant extraction of power system operating variables. Convex and nonconvex techniques of feature extraction are analyzed based on a mutual information index and generalization error. The simulation results on the IEEE 9-bus and the IEEE 118-bus test systems demonstrate the effectiveness of the proposed method for describing the security region by considering high information content.

Evaluation Method of Voltage Stability Based on Minimum Singular Value

When the system reaches the static voltage stability limit point, Jacobian matrix is singular. By checking if minimum singular value is zero, its very easy to determine whether or not Jacobian matrix is singular. So the minimum singular value of Jacobian matrix can reflects the degree of system voltage stability effectively. Firstly this paper introduces singular value decomposition, analyses load characteristic and excitation limits involved in this method and examples on PSD-FDS are demonstrated. At last, suggestion on voltage stability monitoring by minimum singular value is proposed.

The Static Voltage Stability Limit Calculation of AC/DC Hybrid Power System Based on Improved Continuation Power Flow Algorithm

With the HVDC system interconnected to power grid, the voltage stability problem of power grid has become increasingly prominent. This paper establishes the mathematical model of AC/DC hybrid power system and proposed an improved Continuation Power Flow (CPF) algorithm to calculate the static voltage stability limit of AC/DC hybrid system, the characteristics of this algorithm are as following: PQ decoupled power flow algorithm is used; Lagrange quadric interpolation is used in the process of predictor and step control; local parameter method is used in the correction. The iterations of AC/DC calculation alternate to solve power flow equations and select the step control near the critical power limit points to ensure the convergence of power flow solution. In order to verify the correctness of the proposed algorithm, this paper compares the calculation results by the improved algorithm and Matpower on the IEEE 14 bus-system. This paper calculates the static voltage stability limit of AC/DC hybrid power system under different DC control patterns of modified IEEE 14 bus-system and analyzes the impacts of different DC control pattern to the system voltage stability.

Research on Impacts of FACTS on Static Voltage Stability Characteristics of AC/DC Power System

Based on the improved Continuation Power Flow algorithm, this paper investigates the impacts of FACTS on static voltage stability characteristics of AC/DC hybrid power system. This paper introduces the steady-state model of different FACTS devices, and the power flow mathematical model is established about AC/DC power system with FACTS devices. The impacts of FACTS devices with various capacities in different locations on static voltage stability are compared and analyzed. The calculation results of a four-machine two regions AC/DC power system show that FACTS are able to improve the voltage stability and the installation of SVC shunt compensation can possess a better effect to improve the system static voltage stability limit than TCSC series compensation.

Probabilistic assessment and preventive control of voltage security margins using artificial neural network

This paper describes a new technique for probabilistic assessment and preventive control of voltage security margins using artificial neural network. The probabilistic insecurity index (PISI) has been obtained for various operating conditions considering single and double line outages and accounting static voltage stability limit. Evaluated PISI has been obtained for various settings of reactive power control variables and loading conditions using cut-set method. These results have been used to train a multi layer feed forward network so as to assess the security on line. Further sensitivities of PISI have been evaluated based on trained network and have been used to control power system security. The algorithm has been implemented on a 6-bus, 7-line IEEE standard test system.

Determination of probabilistic risk of voltage collapse using radial basis function (RBF) network

This paper describes a viewpoint for voltage stability assessment accounting uncertainties in line parameters and settings of reactive power control variables. A probabilistic risk of voltage collapse, however small it may be, is always present if system parameters and control variables are treated as random variables. Such uncertainties become important if operating point of system is near to voltage collapse point. Monte-Carlo simulation has been used to evaluate probabilities of voltage collapse for various operating conditions. Static voltage stability limit for various sampled values of system parameters and control variables have been obtained using continuation power flow methodology. Monte-Carlo simulation is a time-consuming process. Hence, a radial basis function (RBF) network has been used to get probabilistic risk of voltage collapse. Training and testing instances have been generated using Monte-Carlo simulation. The algorithm developed has been implemented on two standard test systems.

Use of V–I characteristic as a tool to assess the static voltage stability limit of a power system

P-V or Q-V curves are very commonly used to determine the maximum permissible load or static voltage stability limit of a power system. Voltage versus current curve or V-I characteristic is presented as a tool to assess the voltage stability limit. It requires only bus voltage and current data at present and some immediate past operating points. The above data are processed through the least squares method to establish the V-I characteristic. The extrapolated part of the characteristic is then used to estimate the critical load at the verge of voltage collapse. The proposed method does not require the knowledge of other system parameters or system-wide information. Any change in system condition usually modifies the V-I characteristic and thus the effect of the change is indirectly incorporated in finding the critical load through the V-I characteristic. The effectiveness of the proposed method is vigorously tested on the IEEE 30-bus system. Some of the results obtained by the proposed method are also compared with the corresponding actual values found through repetitive power flow simulations and are observed to be in excellent agreement.

Look-ahead approach to power system loadability enhancement

The paper presents a new look-ahead approach to loadability (static voltage stability limit) enhancement of power systems. Most researchers have used approaches that optimise the reactive losses/reactive reserves based on present operating condition. Although reactive power optimisation based on such strategies may result in an increase in distance to collapse, such an increase may not be sufficient. This is because a key factor in loadability enhancement is the reflection of load increase scenario in the optimisation problem. The proposed approach achieves this objective without making the problem too complex. The objective is to minimise reactive power losses near critical loading such that constraints at both loadings are satisfied. Results for two sample test systems, IEEE 30 bus and IEEE 14 bus have been obtained with local as well as look-ahead optimisation strategies to demonstrate the superiority of the latter over the former.

Voltage dependent reactive power limits for voltage stability studies

This paper presents and studies a static model for synchronous generators with voltage dependent reactive power limits due to maximum stator current, maximum and minimum rotor (field) current as well as maximum rotor angle (underexcitation) limiters. The proposed generator model for static voltage stability studies can be included in an ordinary power flow program, and results from studies on a test system with twenty generators are presented. The influence of voltage dependent reactive power limits is compared with fixed (conventional) limits, by use of the minimum singular value of the power flow Jacobian matrix and related submatrices as indicators of the static voltage stability limit. >

Identifying electrically weak and strong segments of a power system from a voltage stability viewpoint

Voltage instability leading to collapse appears to be due to the inability of networks to meet a demand for reactive power at certain critical (or weak) buses. Practical control algorithms to prevent voltage collapse should identify the critical buses in the network and maintain control on voltages at these buses in particular. Two methods are proposed for identifying the weak buses and segments in power transmission networks. Both methods employ a technique presented earlier for determining the static voltage stability limit in multimachine power systems. The first method is based on the relative change in the bus voltages going from an initial operating state to the voltage stability limit. The second method is based on the sensitivity parameters computed at the voltage stability limit.