Static Voltage Stability Region Research Articles

Characterization of static voltage stability region of offshore wind farms considering submarine cable capacitance parameters and converter saturation

Accurately characterizing the static voltage stability region (SVSR) is the key to ensure the safe and stable operation of offshore wind farms (OWFs). However, the traditional SVSR evaluation methods ignore the influence of capacitance parameters, and the stability criteria fail after d-axis current saturation, leading to a large deviation in the evaluation results. Therefore, this paper proposes an improved method to characterize the SVSR of OWFs, which takes the cable capacitance parameters and the saturation effect of the converter into account. Firstly, based on the equivalent circuit method, the power common connection (PCC) voltage charact- erization model considering cable capacitance parameters was derived. Then, the DC voltage stability was defined to describe the static voltage instability caused by the current limiting of the converter. The SVSR constraints are summarized into three categories: power flow stability, DC voltage stability and dq-axis stability, and stability criteria are designed according to different stability. Based on the method of intersection of multiple stability regions and Z-plane projection, the SVSR is characterized. Finally, the influence of different parameter settings on the SVSR is analyzed, and the accuracy of the proposed method is verified by RT-Lab experimental platform.

Parametric Problems in Power System Analysis: Recent Applications of Polynomial Approximation Based on Galerkin Method

In power systems, there are many uncertainty factors such as power outputs of distributed generations and fluctuations of loads. It is very beneficial to power system analysis to acquire an explicit function describing the relationship between these factors (namely parameters) and power system states (or performances). This problem, termed as parametric problem (PP) in this paper, can be solved by Galerkin method, which is a powerful and mathematically rigorous method aiming to seek an accurate explicit approximate function by projection techniques. This paper provides a review of the applications of polynomial approximation based on Galerkin method in power system PPs as well as stochastic problems. First, the fundamentals of polynomial approximation and Galerkin method are introduced. Then, the process of solving three types of typical PPs by polynomial approximation based on Galerkin method is elaborated. Finally, some application examples as well as several potential applications of power system PPs solved by Galerkin method are presented, namely the probabilistic power flow, approximation of static voltage stability region boundary, and parametric time-domain dynamic simulation.

Relaxed decoupled direct calculation of voltage collapse points and its application in static voltage stability region boundary formation

Static voltage stability is critical for the operation of power grids. With the penetration of renewable energies, region-based method become a choice to present the stability of a power grid. Static voltage stability region is hence a useful and intuitive tool to determine the safety margin of a power grid. The formation of static voltage stability region is however time consuming. To overcome such issue, this work proposes a relaxed decoupled direct calculation (RDDC) method to find voltage collapse points (VCPs). The direct calculation of VCPs is a Newton-Raphson type method and faces the sensitivity issue of the initial values. Boundary tracking method provides a framework to utilize the information from neighbor VCPs and hence is integrated with the proposed RDDC method. The results show that the RDDC method is able to calculating VCPs as precise as continuation power flow with less computational time. When RDDC is integrated with boundary tracking, results show that the static voltage stability region boundary can be generated with high precision, and computational performance improvement can be observed for all the test systems from nine buses to ten thousand of buses. This demonstrates the applicability and scalability of the proposed method to power systems with different scales.

Global Approximation of Static Voltage Stability Region Boundaries Considering Generator Reactive Power Limits

Power system static voltage stability region boundary (SVSRB) is a complicated hypersurface in parameter space. Due to inequality constraints such as generator reactive power limits, different critical points on the SVSRB may be related to different groups of active constraints and can be associated with different types of loadability limit, which makes it difficult to approximate the whole SVSRB at once or assemble many local approximations of the SVSRB. To overcome the difficulty, this paper proposes an approach for globally approximating the whole SVSRB considering generator reactive power limits at one go. First, a parametric optimization model incorporating all inequality constraints is formulated to describe the SVSRB, where the optimal solutions are the critical points on the SVSRB. The optimality condition, i.e., parametric Karush–Kuhn–Tucker conditions (KKT conditions), is also derived. Then, by applying the Galerkin method to the parametric KKT conditions in an interior-point-method-like manner, the whole SVSRB is approximated and represented using a single polynomial expression. Case studies in a 10-bus system and IEEE 300-bus system verify the effectiveness and accuracy of the proposed method.

Global Parametric Polynomial Approximation of Static Voltage Stability Region Boundaries

A novel method for globally approximating the static voltage stability region boundaries (SVSRBs) of power systems is proposed by applying parametric polynomial approximation to the criterion equation which defines the SVSRB. Known as the Galerkin method, the implicit function portraying the SVSRB is described as a linear combination of basis polynomial functions, and the coefficients of the basis functions are obtained by projecting the SVSRB criterion onto each basis function. The approximation guarantees high precision globally in the whole domain of the parameter of interest rather than only in the neighborhood of a point, and the error can be controlled by the degree of polynomial basis functions. In the meantime, analytical expression of the left or right eigenvector of the system's Jacobian matrix corresponding to the zero eigenvalue is obtained in the form of polynomial, which provides valuable information for online voltage stability control or monitoring. Case studies in a 10-bus test system and IEEE 118-bus test system verifies the validity, accuracy, and flexibility of the proposed method.

Probabilistic total transfer capability analysis based on static voltage stability region integrated with a modified distributed-level nodal-loading model

In this paper, a new evaluation method of probabilistic TTC based on SVSR calculation is developed through a hierarchical simulation. A smooth technology based on the non-parametric kernel estimator is adapted to obtain the time-dependent probabilistic density function of the feeder-head load data. In order to describe possible operating change directions of the operating point, the original hyper-cone-like (HCL) model is constructed to consider the probabilistic distribution function (PDF) extracted from feeder-head load data to replace the simple Normal Distribution model and the uncertain generator outputs. To realize the fast TTC calculation of the current operating point in random conditions, a sub-hyper-cone-like (SHCL) model in full power injections space is proposed, which is a similarity transformation of the original one.

A New Method for Monitoring Local Voltage Stability using the Saddle Node Bifurcation Set in Two Dimensional Power Parameter Space

This paper proposes a new method for monitoring local voltage stability using the saddle node bifurcation set or loadability boundary in two dimensional power parameter space. The method includes three main steps. First step is to determine the critical buses and the second step is building the static voltage stability boundary or the saddle node bifurcation set. Final step is monitoring the voltage stability through the distance from current operating point to the boundary. Critical buses are defined through the right eigenvector by direct method. The boundary of the static voltage stability region is a quadratic curve that can be obtained by the proposed method that is combining a variation of standard direct method and Thevenin equivalent model of electric power system. And finally the distance is computed through the Euclid norm of normal vector of the boundary at the closest saddle node bifurcation point. The advantage of the proposed method is that it gets the advantages of both methods, the accuracy of the direct method and simple of Thevenin Equivalent model. Thus, the proposed method holds some promises in terms of performing the real-time voltage stability monitoring of power system. Test results of New England 39 bus system are presented to show the effectiveness of the proposed method.

The Mechanism of Voltage Instability Analysis Considering Load Characteristic

Load characteristics are the main factor to affect voltage stability. In addition, load modeling reflecting the actual load characteristics has been a well—known difficult problem and unsolved so far, It is mainly due to the fact that the load composition, amount and characteristics are always changing. This paper introduces the slip into the equivalent impedance load model to analyze load characteristic, the varying slip is employed to indicate time-varying load characteristic precisely, and considering the dissimilar load behaviors, discusses node voltage, power during the changes of load characteristic, obtains voltage inflexion and power inflexion, and then analyzes the mechanism of power system voltage instability based on static voltage stability region. An example indicates the feasibility of the method.

Security region based real and reactive power pricing of power system

This paper develops a novel model and an algorithm of security region based real and reactive power pricing of power systems. In the proposed model, the reactive power production cost is represented as the opportunity cost. The static voltage stability region in the cut set power space (CVSR) and the practical dynamic security region (PDSR) in the injection power space are used to represent the constraints of voltage stability and transient stability, so that the consideration of this kind of constraints in the optimization becomes very easy. In the proposed algorithm, a decoupled optimization and iteration method of active power production cost and reactive power production cost is suggested. According to the K-T optimality conditions, the prices of active power and reactive power, and the different components corresponding to the concerned security constraints are derived. The components of spot prices can reflect the influence of different node power injections on each kind of security constraints, so that through the node price all of the participants in power market can be stimulated to take an active part in maintaining the system security. An illustrative example on the New England 10-genetator 39-bus System is used to demonstrate the proposed method.

Security constrained distributed optimal power flow of interconnected power systems

The security constrained distributed optimal power flow (DOPF) of interconnected power systems is presented. The centralized OPF problem of the multi-area power systems is decomposed into independent DOPF subproblems, one for each area. The dynamic security region (DSR) to guarantee the transient stability constraints and static voltage stability region (SVSR) constraints, and line current limits are included as constraints. The solutions to the DOPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the centralized OPF solution. The nonlinear DOPF subproblem is solved by predictor-corrector interior point method (PCIPM). The IEEE three-area RTS-96 system is worked out in order to demonstrate the effectiveness of the proposed method.