Steady-state Security Region Research Articles

Model, Characterization, and Analysis of Steady-State Security Region in AC/DC Power System with a Large Amount of Renewable Energy

A conventional steady-state power flow security check only implements point-by-point assessment, which cannot provide a security margin for system operation. The concept of a steady-state security region is proposed to effectively tackle this problem. Considering that the commissioning of the increasing number of HVDC (High Voltage Direct Current) and the fluctuation of renewable energy have significantly affected the operation and control of a conventional AC system, the definition of the steady-state security region of the AC/DC power system is proposed in this paper based on the AC/DC power flow calculation model including LCC/VSC (Line Commutated Converter/Voltage Sourced Converter)-HVDC transmission and various AC/DC constraints, and hence the application of the security region is extended. In order to ensure that the proposed security region can accurately provide global security information of the power system under the fluctuations of renewable energy, this paper presents four methods (i.e., a screening method of effective boundary surfaces, a fitting method of boundary surfaces, a safety judging method, and a calculation method of distances and corrected distance between the steady-state operating point and the effective boundary surfaces) based on the relation analysis between the steady-state security region geometry and constraints. Also, the physical meaning and probability analysis of the corrected distance are presented. Finally, a case study is demonstrated to test the feasibility of the proposed methods.

Transmission capacity margin in market clearing

To ensure the secure operation of a power market, transmission networks must maintain an appropriate margin to account for various uncertainties. The uncertainties have increased significantly by the increasing penetration of renewable energy generation. A steady-state security distance (SSD) is an effective security margin that describes the distance of an operation point (OP) from steady-state security region boundaries. It captures both the available capacity and topological location of each transmission line that are important considerations for the ability of each line to withstand uncertainties. The proposed SSD-based transmission capacity margin is integrated into the market clearing model. The proposed SSD-constrained market clearing (SSDC-MC) model ensures that the SSD between the scheduled OP and security boundaries does not fall below a specified threshold. The SSDC-MC is formulated as a bi-level optimization problem. A novel algorithm is developed by dynamically identifying the binding constraints in the lower-level model. The SSDs are expressed as piecewise analytic functions of the scheduled OP. As a result, the bi-level problem is transformed into a single-level one. Two test cases are used to compare the SSDC-MC method with a different transmission margin determination method, which imposes constraints on loading of all transmission lines.

N− 1 security assessment approach based on the steady‐state security distance

The traditional N - 1 security assessment approaches give a limited perspective on the degree of power system security. This study proposes a novel security assessment approach using the index of post-contingency steady-state security distance (PCSSD). Two PCSSD models are established for contingencies causing or not causing system overloads, respectively. If the system is secure following a contingency, the PCSSD provides the shortest distance of the operating point (OP) to the post-contingency steady-state security region (PCSSR) boundaries, to indicate the OP's remaining security margin. If an overload condition arises after a contingency, the PCSSD provides the shortest distance of the OP to the PCSSR, to show the difficulty in eliminating power grid violations. With the index of the PCSSD, one can continuously quantify post-contingency OPs whether they are secure or insecure and rank all possible contingencies according to their severity. The PCSSD model is a large-scale non-linear optimisation model which has to be calculated numerous times. A novel algorithm is proposed to improve the computational efficiency. It identifies the active boundaries of the PCSSR, and then approximates most of the PCSSDs by the corresponding ante-contingency ones, reducing the number of optimisation problems to be solved. Case studies are performed to demonstrate the effectiveness of the proposed approach.

Probabilistic available transfer capability calculation considering static security constraints and uncertainties of electricity–gas integrated energy systems

The increasing share of natural gas-fired power plants (NGFPPs) has strengthened the linkage between electric power systems (EPSs) and natural gas systems (NGSs). It is imperative to analyze both systems jointly. In this paper, a probabilistic available transfer capability (PATC) model considering the static security constraints and uncertainties of electricity–gas integrated energy systems (IESs) is proposed. The concept of IES steady-state security regions is developed, and the mathematical model of ATC within IES security regions is formulated. The active constraint limiting the ATC is identified by the linear prediction and calculation (LPC) method, and then it is augmented into IES energy flow equations to determine the value of ATC. The uncertainties of correlated electricity/gas loads and wind power generations are also taken into account and are addressed by a combination of Latin hypercube sampling (LHS) and the Nataf transformation. Moreover, the corrective adjustment in NGSs can be adopted to ensure the fuel availability of NGFPPs. Finally, test results on the modified IEEE 118-bus system and a 20-node NGS are presented to verify the applicability of the proposed methodology.

Eliminating Redundant Line Flow Constraints in Composite System Reliability Evaluation

Reliability evaluation of composite systems involves extensive calculations. Current solutions to this computational burden have mainly focused on extracting failure states from the state space. Instead, the evaluation of failure states is accelerated by methods presented in this paper. The scale of optimizations required for generation redispatching and/or load shedding in failure states is reduced by eliminating redundant line flow constraints. First, a sufficient and necessary condition for a line flow constraint to be redundant is established in the form of a linear programming problem, based on the concept of steady-state security region (SSR). Then, two redundancy elimination methods are proposed-a conservative one based on a heuristic, and a radical one based on an analytical condition. Numerical tests are conducted on IEEE-RTS79 and a real-life system. More than half of the line flow constraints are eliminated by the conservative method and nearly 90% by the radical method. The proposed methods can be used in conjunction with most of the existing acceleration techniques to further improve efficiency.

Steady‐state security assessment method based on distance to security region boundaries

Steady-state security region (SSR) provides a region-wise approach to assess the steady-state security of power systems. Based on the SSR model, we introduce the concept of `steady-state security distance' (SSD) to provide exact `quantitative analysis' on the scale of security margins for system operators. Then, mathematical models of SSD are formulated. On this basis, implementation of SSD is discussed towards various uncertainties within the power system operation. As the calculation of SSD is in essence a large-scale non-linear optimisation process, it requires very long computation time, and thus could not be utilised in practical application. In order to enhance the efficiency of computation, a novel algorithm is proposed, which decomposes the complex optimisation process into two steps: active SSR boundary identification and partial constrained solution. The proposed algorithm remarkably cuts the scale of the optimisation model as well as the number of calculations, thus significantly reduces the computation time to meet requirements of assessment towards day ahead and hours ahead generation schedules. In the end, an IEEE-30 bus case and a practical case on a provincial power system are both studied to testify the effectiveness of the proposed model and algorithm.

Applications of Lagrange-Quasi-Newton Method in Power System Steady-State Security Region

With the proportion of the installed capacity of wind farm in the grid increasing, the impact of wind farm on the power system security becomes obvious. The steady-state security analysis is one of the important measures to improve the power system security. Based on DC flow, considering the available transmission capability limit, the paper chooses the biggest security region volume as objective function with the upper and lower limits of security region multi-dimensional cuboid being as control variables, which transforms the maximum steady-state security region into nonlinear programming problem with linear constraints. This not only includes the biggest points for the safe operation, but also the order expansion problem doesn’t exist. Then Lagrange-Quasi-Newton is used to solve the equation, and the analysis of the example proves the feasibility of the proposed model and algorithm. Then we assume that wind speed distribution is weibull distribution, so we can assess the safe operation probability of wind power.

Self-adaptive evolutionary programming and its application to multi-objective optimal operation of power systems

Abstract This paper proposes a new algorithm to solve multi-objective optimal operation of power systems problem. The algorithm is based on combination of general evolutionary programming and random search technique. The algorithm includes two important procedures. First, a new pattern of mutation is developed in this paper. Secondly, the developed mutation operator is self-adaptive during optimization. Furthermore, in a multi-objective optimal operation study four objectives (cost of generation with valve point loading, transmission losses, environmental pollution and steady-state security regions) are considered for optimization, and an ideal point method is used to solve the problem. The proposed algorithm is tested on the IEEE six-bus and 30-bus systems. Numerical results and comparison demonstrate that the new method not only can deal agilely with constraints, but also can reduce the CPU time and prevent the search from being in local optima.

98/02983 Construction of maximal steady-state security regions of power systems using optimization method

98/02983 Construction of maximal steady-state security regions of power systems using optimization method

Construction of maximal steady-state security regions of power systems using optimization method

Abstract This paper proposes a new approach to construct the maximal steady-state security regions of power systems using optimization. The method is based on DC load flow. For the first time, the maximal steady-state security region—hyperbox is directly computed through a linear programming (LP) model, in which the upper and lower limits of each component forming hyperbox are taken as unknown variables, and the objective is to maximise the sum of each generator's power adjustment range. The proposed approach is tested on the IEEE six-bus and 30-bus systems. The calculation results and comparison show that the new method is superior to the extending method which is the conventional means for constructing maximal steady-state security regions.

A STUDY ON REACTIVE POWER STEADY-STATE SECURITY REGIONS

ABSTRACT A geometric description of reactive power steady-state security regions(RPSSR) is explored using the properties of affine mapping and tested using real power system models. Based on this geometric description an approximate RPSSR is given.To improve the conservative property of the approximate RPSSR two methods are recommended. One is the method of eliminating “ Passing Buses”, the other is the reactive power steady—state response security region(RPSSR-R).

A New Method for the Construction of Maximal Steady-State Security Regions of Power Systems

A New Method for the Construction of Maximal Steady-State Security Regions of Power Systems

Characterization of power system small disturbance stability with models incorporating voltage variation

The small disturbance (SD) stability of a power system is studied with the model including generator swing equations, the real and reactive power flow equations. The effects of voltage variation and reactive power constraints are thus explicitly represented in the model. It is shown that the necessary and sufficient condition for an operating point to be SD stable is that the reduced matrix from the power flow Jacobian is positive definite. A sufficient condition is that the power flow Jacobian itself is positive definite. The result is compared to the one obtained from the constant voltage model and the latter is shown to be more optimistic. Also derived are conditions for steady-state security regions to be SD stable.

A New Method for the Construction of Maximal Steady-State Security Regions of Power Systems

This paper presents a method to compute maximal steady-state security regions based on the DC load flow model. The proposed method consists of three steps. First, an initial region (hyperbox) is obtained explicitly using an analytic method. A developed algorithem is then utilized to expand the upper and lower bounds of the initial region in as many dimensions as possible. The algorithm is based on a necessary and sufficient condition for a region to be secure. Due to the proposed condition, the algorithm is computationally very efficient. Finally, the expanded security region is used to initiate a set of optimization problems, which can be solved to yield maximal regions. Applications of security regions to power system planning and operation are discussed. Numerical testing indicates that the algorithms proposed to expand the initial region produces nearly maximal security regions. The results of the paper provide a systematic way to deal with practical issues such as the size of security regions and computational efficiency.

Steady-State Security Regions of Power Systems

A steady-state security region is a set of real and reactive power injections (load demands and power generations) for which the power flow equations and the security constraints imposed by equipment operating limits are satisfied. The problem of determining steady-state security regions is formulated as one of finding sufficient conditions for the existence of solutions to the power flow map within the security constraint set. Explicit limits on real and reactive power injections at each bus are obtained, such that if each injection lies within the corresponding limits, the system is guaranteed to operate with security constraints satisfied.

Power System Security Corridors Concept and Computation

This paper introduces a novel scheme for the region-wise predictive security assessment. The proposed scheme is based on the concept of the security corridor, which assumes that the normal range of operating points can be restricted to the neighborhood of the system's predicted (or nominal) trajectory. Our scheme tries to characterize this neighborhood by a number of ellipsoids overlapping along the system's predicted trajectory. The intersection of these ellipsoids with the system's steady-state security region defines a security corridor which is characterizable by a relatively small number of constraints. Each ellipsoid covers a specific operating time interval, so the time of operation serves as a localizing parameter in this scheme. The small number of constraints needed to describe the secure part of an ellipsoid allows the efficient use of the security corridors in a variety of power system operation and planning applications. For on-line security monitoring, for instance, as long as the actual trajectory stays within the width of the security corridor - which can be verified rather trivially - the system security is guaranteed. The effort involved in constructing a security corridor is explained through a discussion on some computational aspects of the scheme, and by presenting the results of some numerical studies performed on a sample system.