Loading Margin Research Articles

Neural network based on a genetic algorithm for power system loading margin estimation

In this study, a new methodology based on the predictor-corrector method is introduced to trace the total system equilibrium of the power system model. This methodology considers the automatic voltage regulator voltage limit of all generation units and computes the loading margin associated with both saddle node bifurcation and saddle limit induced bifurcation points. Furthermore, a neural network based on the genetic algorithm approach is presented for fast voltage stability analysis. The neural network can establish a mapping between the operating conditions and the power system loading margin obtained by the above simultaneous equilibrium tracing technique. In order to improve the neural network efficiency, the genetic algorithm is used to generate the optimal feature subset and the neural network parameters at the same time. The method is examined on the New England 39-bus system and a mean absolute estimation error of 0.57% and a response time ≤0.1 s are obtained. By comparing the results obtained through different methods, it is concluded that the genetic algorithm-neural network approach provides a compromise between accuracy and speed of calculation. Hence, for operational purposes, for which having a fast response is vital, using the genetic algorithm-neural network approach is recommended.

Determination and enhancement of probabilistic stability margin with load uncertainties

Load margin is a reasonable measure to quantify the bifurcation-related instability, defined as the amount of additional load on a specified pattern of load increase that would cause system instability. If the initial operating point and load increase pattern are specific, the stability margin is specific and can be obtained easily. If the initial operating point is random, the stability margin is also a random variable. This paper adopts a probabilistic eigenvalue method to determine the stability margin under load uncertainty. With the assumption of load being of normal distribution, the computed eigenvalues distribution is also close to normal distribution, but the stability margin distribution is irregular. An effective and systematic probabilistic approach to assess the probabilistic margin is proposed. Monte Carlo simulations consisting of 10,000 samples are used as a reference solution for evaluation of the accuracy of the proposed method. In addition, power system voltage stabilizer is adopted to improve the probabilistic stability margin by a proposed optimization technique. The proposed methods are investigated on two test systems.

Available transfer capability and least square method

In deregulated power industries, accurate and fast calculation of Available Transfer Capability (ATC) for seller in the electricity market is required. In this paper, deterministic ATC will be calculated using algebraic equation and linear optimization by Least Square (LSQR). Probabilistic ATC is also calculated by considering time varying load and load margin. The proposed method will be tested on IEEE 30 bus system. Deterministic ATC results will be compared with Benders, OPF and HCACO and probabilistic ATC results also will be compared with GA and HCACO.

Multi-Objective Optimal SVC Installation for Power System Loading Margin Improvement

Proper installation of flexible ac transmission systems (FACTS) in existing transmission networks can improve transmission system loading margin (LM) to a certain degree and reduce network expansion cost. In the paper, under each contingency with high risk index (RI) value, the modal analysis (MA) technique is used to determine which buses need static var compensator (SVC) installation, and with maximum LM and minimum SVC installation cost composed into the multi-objective function the optimal LM enhancement problem is formulated as a multi-objective optimization problem (MOP) and solved by using the fitness sharing multi-objective particle swarm optimization (MOPSO) algorithm for a Pareto front set. In the Pareto front set for each considered contingency, the solution with the biggest performance index value is determined for SVC installation. Finally, an SVC installation scheme derived from the union of the SVC installations for all considered contingencies is recommended for LM enhancement. The proposed method is validated on the IEEE 24-bus reliability test system (RTS) and a practical power system.

Optimal Generation Direction Method with SVC Installation for Loading Margin Improvement

In order for transmission systems to accommodate more power transfer with less network expansion by building new transmission lines, it can be a good measure to operate under optimal generation direction (GD) under existing networks. In this paper, the problem considering static voltage stability to determine the optimal GD is solved by a PSO algorithm, in which the continuation power flow (CPF) process is used to calculate the loading margin (LM) for each particle. Three objective functions are suggested for different purposes, including maximum loading margin (LM), minimum generation cost, and minimum generation cost and maximum LM as well. In the tests, to validate the effectiveness of the proposed method, the results derived with the respective objectives and from the cost participating factor (Cost PF) approach are made com- parison. And, under each GD, with an SVC installation on the specified critical bus, how much the LM that can be increased is also investigated.

A novel approach for optimal allocation of distributed generations based on static voltage stability margin

This paper presents a newly developed approach to find the optimal location of distributed generations (DGs) to improve power system voltage stability margin and reduce losses incorporating the constraints. The loadability limit index is used to assess the static voltage stability security margin, which is associated with the point of voltage collapse limit. Based on this, a toolbox is developed to recognize the loadability margin in power networks. Finally, the mentioned problem is modeled as a nonlinear and multiobjective optimization problem. The proposed method establishes a tradeoff between the security index and power losses in DG placement using the hybrid particle swarm optimization (HPSO) algorithm method to reach the best performance and acceptable operation. The simulations are performed on IEEE 14- and IEEE 30-bus test systems to find the optimal location of the DGs. The results are compared with the particle swarm optimization (PSO) algorithm to ascertain the effectiveness.

Reactive Power Loss Sensitivity Approach in Placing FACTS Devices and UPFC

In this paper, a simple placement technique of Flexible AC Transmission System (FACTS) devices and Unified Power Flow Controller (UPFC) is proposed for loading margin enhancement. Reactive-power loss sensitivity approach is proposed to identify the weakest line of the system and to narrow down the appropriate site of FACTS device. The combination of Reactive-power loss sensitivity and Tangent Vector is proposed to find the appropriate location of UPFC. Proper modeling of FACTS devices, including DC side, is used to accurately capture their behaviors when they are operating at limits. The proposed placement approach may be useful for utilities who wish to find appropriate location of FACTS devices and UPFC regarding to loading margin enhancement.

Identification of maximum loadability limit and weak buses using security constraint genetic algorithm

Maximum loadability limit (MLL) is a realistic index to evaluate the steady state voltage stability because it provides system operator a better practical sense of security margin in the aspects of engineering parameter like system loading. If MLL is identified, load margin, voltage stability, security margin can be determined and precaution can be taken. Conventional power flow methods like Newton–Raphson, Gauss–Siedel, fast decoupled power flow methods suffer to provide proper MLL under security constraints as Jacobian matrix becomes singular when system loading approaches its loadability limit. Hence evolutionary techniques such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) are now-a-days applied to solve the non-linear complex MLL problem. Phase angles, active power, voltage magnitudes of load buses, reactive power of PV buses are considered as security constraints for MLL problem. New simple real coded Security Constraint GA (SCGA) is developed to solve the problem. MLL problem is formulated as maximization problem. As handling of real coded power flow variables are easier than binary coding, real coding of SCGA parameters is applied. Novel formulas are developed to update power flow parameters considering corresponding power mismatches. Utilizing decoupling properties of power system, mutation is implemented. To provide diversity, new parent selection in crossover section is adopted. Weak buses are also identified for the application of FACTS devices. The developed method is compared with general PSO (GPSO) technique for test systems of IEEE 14, 30, 57 and 118 bus. Showing characteristics and results, the effectiveness and efficiency of the proposed method is established.

Adaptive Interference Management of OFDMA Femtocells for Co-Channel Deployment

Femtocell technology has been drawing considerable attention as a cost-effective means of extending cellular coverage and enhancing capacity as well as realizing its potential, when combined with orthogonal frequency-division multiple access (OFDMA), for improved indoor broadband wireless services. However, under the expected co-channel deployment of femto- and macro-cells, femtocells may incur high uplink interference to macrocells, and vice versa. To mitigate this interference, we propose a distributed and self-organizing femtocell management architecture, called the Complementary TRi-control Loops (CTRL), that consists of three control loops to determine (1) maximum transmit power of femtocell users based on the fed-back macrocell load margin for protection of the macrocell uplink communications; (2) target signal to interference plus noise ratios (SINRs) of femtocell users to reach a Nash equilibrium; and (3) instantaneous transmit power of femtocell users to achieve the target SINRs against bursty interference from other nearby users. CTRL requires neither special hardware nor change to the radio resource management (RRM) of existing macrocells, thus facilitating non-disruptive (hence seamless) penetration of femtocells. Also, CTRL guarantees convergence in the presence of environmental changes and delayed feedback. Our evaluation has shown CTRL to successfully preserve the macrocell users' service quality under highly dynamic user transmission conditions and be able to make a tradeoff between macrocell and femtocell capacities.

Stability Constrained Optimal Power Flow in Deregulated Power Systems

The dynamic security-constrained dispatch of an electric power network is a difficult task facing an independent system operator mandated to provide equitable and fair transmission services in an open-market environment. In this article, a novel technique based on iterative stability-constrained optimum power flow is proposed. The particle swarm optimization methodology is employed to maximize the social welfare with consideration of static and dynamic functional operating constraints and dynamic loading margin requirements with respect to normal condition and contingencies. Furthermore, since the pattern of load increase is difficult to predict in the new market environment, a new method for determining the sensitive loading direction associated with a dynamic loading margin is proposed. An IEEE 14-bus test system with both supply and demand bidding is used to illustrate and test the proposed technique.

Using PV and QV curves with the meaning of static contingency screening and planning

This paper investigates the use of the QV and PV curves in the planning scenario, when some system reinforcements and contingency screening are analyzed. The idea is to employ the continuation method to obtain the system load margin and the QV curve to calculate the reactive power reserve associated with each bus. Combining these approaches enables one to identify the system critical area, the actual operating conditions, the most severe contingencies and the most important reinforcements. The methodology proposed may provide important signals to system planners, since the planning is focused under the voltage security point of view. The ideas are tested with the help of some academic systems and two real (a Brazilians and a Paraguayan) systems with all the system limits considered.

A new technique for computation of closest saddle-node bifurcation point of power system using real coded genetic algorithm

Estimation of voltage stability margin is essential for operation of the system with an adequate security margin. In this paper, a new technique to determine the worst case loading margin, i.e., shortest distance to voltage instability is developed. The problem of determining the closest saddle-node bifurcation point (CSNBP) is formulated as an optimization problem and solved using Real Coded Genetic Algorithm (RCGA). The method is capable of handling various operational constraints and can determine the CSNBP accurately even if the transfer limit surface is not smooth. The proposed approach has been applied on a simple radial system, IEEE 14-bus and IEEE 57-bus systems. The developed method has been compared with the method based on Particle Swarm Optimization. Simulation results show the validity and feasibility of the proposed method.

Application of bifurcation theory in dynamic security constrained optimal dispatch in deregulated power system

In a deregulated environment of power systems, the transmission networks are often operated close to their maximum capacity. Besides, the independent system operator must operate the system to satisfy its dynamic stability constraints under credible contingencies. In this paper, a novel technique based on iterative stability constrained Optimum Power Flow is proposed. Particle Swarm Optimization methodology is employed to maximize the social welfare with consideration of static and dynamic functional operating constraints and Dynamic Loading Margin (DLM) requirements with respect to normal condition and contingencies. New linear Hopf bifurcation (HB) index is used for fast detection of the DLM. Furthermore, since the pattern of load increase is difficult to be predicted in the new market environment, a method for determining sensitive loading direction associated with DLM is proposed. IEEE14 bus test system with both supply and demand bidding are used to illustrate and test the proposed technique.

Maximum Load-Carrying During Takeoff of Leach's Storm-PetrelOceanodroma leucorhoaand Cassin's AukletPtychoramphus aleuticus

Abstract. Birds at-sea increase body mass as a consequence of food consumption and plumage wettability. However, little is known about the effect of maximum extra load on takeoff of aquatic birds. Experimental evaluation of maximum load-lift during takeoff was performed on a wing-propelled diver with high wing loading, Cassin's Auklet Ptychoramphus aleuticus, and on a surface feeder with low wing loading, Leach's Storm-Petrel Oceanodroma leucorhoa. Leach's Storm-Petrel supported a maximum extra load of 45% of its body mass, and that of Cassin's Auklet was 25%. The relation of maximal load to food transport and plumage wettability indicates that the storm-petrel and the alcid maintain safety load margins of 31% and 8% of the maximum supported extra load during takeoff, respectively. Load margin showed by storm-petrels suggests an enhanced flight performance, increasing specific lift during foraging; meanwhile that of auklets allows for reduction of specific buoyancy during diving.

The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities

The loading margin to a saddle-node or fold bifurcation measures the proximity to voltage collapse blackouts of electric power transmission systems. Sensitivities of the loading margin can be used to select controls to avoid voltage collapse. We analytically justify the use of static models to compute loading margins and their sensitivities and explain how the results apply to underlying dynamic models. The relation between fold bifurcations of the static models and saddle-node bifurcations of the underlying dynamic models is clarified.

New technique for computation of closest Hopf bifurcation point using real-coded genetic algorithm

Hopf bifurcation in power systems leads to oscillatory instability, and it is desirable to operate the system with sufficiently large loading margin to Hopf bifurcation. A new technique to determine the shortest distance to Hopf bifurcation is developed. The problem of determining the closest Hopf bifurcation point is formulated as an optimisation problem and solved using real-coded genetic algorithm. The advantage of this method is that it is capable of handling various operational constraints and can determine the closest Hopf bifurcation point accurately even if the hypersurface is not smooth. The proposed approach has been applied on two-area and IEEE 14-bus test systems. The details of implementation and simulation results are presented. The effect of load modelling on closest Hopf bifurcation point is also investigated for various loading patterns.

Effective method for optimal allocation of distributed generation units in meshed electric power systems

Improper placement of distributed generation (DG) units in power systems would not only lead to an increased power loss, but could also jeopardise the system operation. To avert these scenarios and tackle this optimisation problem, this study proposes an effective method to guide electric utility distribution companies (DISCOs) in determining the optimal size and best locations of DG sources on their power systems. The approach, taking into account the system constraints, maximises the system loading margin as well as the profit of the DISCO over the planning period. These objective functions are fuzzified into a single multi-objective function, and subsequently solved using genetic algorithm (GA). In the GA, a fuzzy controller is used to dynamically adjust the crossover and mutation rates to maintain the proper population diversity (PD) during GA's operation. This effectively overcomes the premature convergence problem of the simple genetic algorithm (SGA). The results obtained on IEEE 6-bus and 30-bus test systems with the proposed method are evaluated with the simulation results of the classical grid search algorithm, which confirm its robustness and accuracy. This study also demonstrates DG's economic viability relative to upgrading substation and feeder facilities, when the incremental cost of serving additional load is considered.

Formulation, computation and improvement of steady state security margins in power systems. Part II: Results

A steady state security margin for a particular operating point can be defined as the distance from this initial point to the secure operating limits of the system. Four of the most used steady state security margins are the power flow feasibility margin, the contingency feasibility margin, the load margin to voltage collapse, and the total transfer capability between system areas. This is the second part of a two part paper. Part I has proposed a novel framework of a general model able to formulate, compute and improve any steady state security margin. In Part II the performance of the general model is validated by solving a variety of practical situations in modern real power systems. Actual examples of the Spanish power system will be used for this purpose. The same computation and improvement algorithms outlined in Part I have been applied for the four security margins considered in the study, outlining the convenience of defining a general framework valid for the four of them. The general model is used here in Part II to compute and improve: (a) the power flow feasibility margin (assessing the influence of the reactive power generation limits in the Spanish power system), (b) the contingency feasibility margin (assessing the influence of transmission and generation capacity in maintaining a correct voltage profile), (c) the load margin to voltage collapse (assessing the location and quantity of loads that must be shed in order to be far away from voltage collapse) and (d) the total transfer capability (assessing the export import pattern of electric power between different areas of the Spanish system).

Formulation, computation and improvement of steady state security margins in power systems. Part I: Theoretical framework

A steady state security margin for a particular operational point can be defined as the distance from this initial point to the secure operational limits of the system. Four of the most used steady state security margins are the power flow feasibility margin, the contingency feasibility margin, the load margin to voltage collapse, and the total transfer capability between system areas. A comprehensive literature survey has shown that these security margins have been studied separately. This fact has suggested to the authors the possibility of researching a common analysis framework valid for all of them. This is the first part of a two-part paper. In part I, a novel mathematical formulation valid to address the study of any steady state security margin is proposed. The developed general approach is presented in three steps: (a) formulation, (b) computation, and (c) improvement of security margins. In part II, the performance of the proposed approach when used to compute and improve the aforementioned steady security margins is illustrated through its application to the Spanish power system. Results denote that this approach can be a useful tool to solve a variety of practical situations in modern real power systems.

Investigation on Limit Surfaces in Space Spanned by Generation Parameter

In a space spanned by generation parameter, the different properties of loading margin surface and generation limit surface are investigated at first in this paper. Then, the shortage of taking the generation limit surface as limit boundary for generation rescheduling (GR) is elaborated and a developed GR model is presented. Additionally, in order to take the uncertainty of load pattern into consideration, a bilevel programming model with the opposite structure to each other is proposed. In this model, the upper level is used to optimize generation pattern (GP) for maximizing the loading margin while the lower level is used to determine the worst load pattern for checking the adaptability of the GP to the variation of the load pattern. A Step-by-step Approximation based Primal Dual Interior Point method (SAPDIP method) and Successive Linear Programming method (SLP method) are used to solve the two sub-models, respectively. The GP optimized by the proposed model reflects the balance between the “variation” and “adaption”, and is less sensitive to the changes in load pattern. Finally, the proposed method is tested on multiple standard IEEE test systems as well as a real power system in China.