Francesco Torelli

A neural network-based method for voltage security monitoring

In this paper, a neural network-based method is proposed for monitoring the online voltage security of electric power systems. Using a dynamic model of the system, voltage stability is measured totally, considering a suitable stability index for the whole system, and locally, by defining appropriate voltage-margins for detecting the area of the system where the instability phenomenon arises. A three-layer feedforward neural network is trained to give, as outputs to a pre-defined set of input variables, the expected values of the above defined indices. The neural network is designed by using a fast learning strategy that allows the optimal number of hidden neurons to be easily determined. Moreover, it is shown that, in the operation mode, the system power-margin and the bus power-margins can be easily evaluated using the value of the voltage stability index given by the designed NN. The effectiveness of the proposed approach has been demonstrated on the IEEE 118-bus test system.

A Gauss-Jacobi-Block-Newton method for parallel transient stability analysis (of power systems)

A parallel method for the transient stability simulation of power systems is presented. The trapezoidal rule is used to discretize the set of algebraic-differential equations which describes the transient stability problem. A parallel Block-Newton relaxation technique is used to solve the overall set of algebraic equations concurrently on all the time steps. The parallelism in space of the problem is also exploited. Furthermore, the parallel-in-time formulation is used to change the time steps between iterations by a nested iteration multigrid technique, in order to enhance the convergence of the algorithm. The method has the same reliability and model-handling characteristics of typical dishonest Newton-like procedures. Test results on realistic power systems are presented to show the capability and usefulness of the suggested technique. >

A pipelined-in-time parallel algorithm for transient stability analysis (power systems)

A new parallel algorithm for transient stability analysis is presented. An implicit trapezoidal rule is used to discretize the set of algebraic-differential equations which describe the transient stability problem. A parallel-in-time formulation has been adopted. A Newton procedure is used to solve the equations which describe the system at each time step, whereas a Gauss-Seidel algorithm relaxes the solution across the time steps. A Gauss-Seidel-like procedure can be usefully exploited in the parallel processing mode by pipelining the computation through time steps. The parallelism in space of the problem is also exploited. Furthermore, the parallel-in-time formulation is used to change the time steps between iterations by a nested iteration multigrid technique in order to enhance the convergence of the algorithm. The method has the same reliability and model-handling characteristics of typical dishonest Newton-like procedures. Test results on realistic power systems are presented to show the capability and usefulness of the suggested technique. >

A generalized approach to the analysis of voltage stability in electric power systems

Abstract In this paper a new method for analysing the voltage stability problem in electric power systems is presented. The approach starts with a linearized model in state space form of a multi-machine power system, then rigorous voltage stability conditions are derived on the basis of a suitable aggregated model of the original system capable of retaining the dynamics of voltages at generator and load nodes. The approach allows a systematic individualization of all the dynamic factors which affect voltage instability phenomena and suggests the appropriate representation which has to be adopted for each dynamic component of the system. The validity and usefulness of the suggested method are illustrated by carrying out simulation studies on a sample power system.

Quadratic probabilistic load flow with linearly modelled dispatch

Abstract A second-order probabilistic load flow technique is presented, which takes into account the effects of nonlinearities in the system equations and of different dispatching strategies. This approach uses as input a normal probability distribution for the loads. The probability distribution for the generated powers is computed by linearly modelling the dispatching activity. The technique of moments is then applied to second-order approximations for the load flow and current equations, allowing the noniterative computation of the means and standard deviations for the various output quantities. Generation outages are separately treated, with the possibility of embedding different postoutage dispatching strategies. The cumulative results are finally obtained by combining the pertinent probabilistic load flows with the occurrence probabilities of the various conditions. Results on two sample systems are given.

State space representation of interconnected power systems for dynamic interaction studies

Abstract In this paper a linearized model of an interconnected power system in state space form is presented in order to analyse the dynamic interactions of its components across the interconnection network. The model, modularly structured, proves flexible and includes detailed descriptions of generators with their control devices, static and dynamic loads. The mathematical representation of the system is formulated such that the effect of interconnection on system characteristic polynomial and system dynamic stability can be systematically investigated. Additionally, a suitable index is defined to measure the degree of dynamic interaction which may occur between the machines of the interconnected power system. A numerical example is included using a four-generator ten-bus system to illustrate the capability of the developed model and the usefulness of the proposed technique.

Load Following Control Schemes for Deregulated Energy Markets

Load following can be carried out in a centralized way by the independent system operator from scheduling coordinators in the day-ahead market, hour-ahead market and in real-time or by longer term contracts, or can be competitively procured through bilateral contracts between supplier and customer. In this paper, a new method has been developed for correlating system imbalances with unbalanced transactions in a bilateral transaction-based market. Depending on the assumed-even coexisting-market structure for load following service, two different control schemes are required to excite reset controllers to vary generator outputs until power imbalances vanish. The suggested procedure has been implemented on the IEEE 30-bus test system under a variety of operating conditions and power system disturbances, which confirm the effectiveness of the proposed methodology to selectively assign the load following burden to unbalanced transactions

Relaxation-Newton methods for transient stability analysis on a vector/parallel computer

In this paper, the implementation of transient stability analysis programs on a vector/parallel computer is considered. The windowing technique is adopted. The parallelism-in-time is exploited by using the Gauss-Jacobi or the Gauss-Seidel methods to relax the dependency between time steps within a time window; the Newton method is employed to solve the discretized equations corresponding to each time step exploiting the parallelism-in-space. The computation of the bus voltage and state variables pertaining to different time steps is carried out in parallel by the processors available. A reordering of the operations relative to the synchronous machine equations is introduced to obtain an efficient use of the vector hardware of the computer. The W-matrix method is employed to solve the network equations. Test case simulations are performed for the IEEE 118 bus system and two US networks with 662 and 904 buses using a 4-processor CRAY Y-MP8/464 computer. The proposed vector/parallel programs achieve substantial speed-ups over a scalar reference program based on the Very Dishonest Newton method. The synergy between vector and parallel processing allows speed-ups in excess of 22 to be attained for the US 904 bus network; run times are always shorter than the simulation interval. Best results are obtained by implementing the proposed travelling window approach. Thanks to a suitable task partitioning, the apparently sequential Gauss-Seidel approach is demonstrated to be an effective alternative to the Gauss-Jacobi relaxation scheme. >

Nondiscrinilnatory System Losses Dispatching Policy in a Bilateral Transaction-Based Market

A new method to allocate transmission losses for simultaneous bilateral transactions is proposed. The methodology utilizes a circuit approach of the system in conjunction with a classical power flow. For a given operating point, it is possible to derive system loss expression as a sum of partial terms due to each transaction. These transaction loss components, supplied by slack buses, can turn into costs associated to the respective transactions. Alternatively, in this paper, it is proposed that each transaction provides for its own loss, thus eliminating the need for a balancing mechanism. In this case, the developed methodology evaluates the increase of active power at each transaction generator through loss contributions not arbitrarily assumed but calculated from a developed loss allocation formula. The main advantage of the developed method lies in its simplicity and capability of treating multiple transactions simultaneously.

A tracking time domain simulator for real-time transient stability analysis

Real-time power system transient stability analysis requires the analysis of hundreds of contingencies in terms of minutes using online data from state estimation. The final objective is to present timely information about transfer limits and stability margins and eventually implement corrective actions. In this paper, the authors assume that the dynamic contingency analysis (DCA) has to be repeated every 15 minutes. During this period of time, the loading and configuration conditions of the system change significantly but not drastically. They verify that the set of the relevant contingencies remains almost the same in the time interval comprised between two cycles of the functions associated to dynamic security analysis (DSA). Parallel-in-time formulated algorithms can be used in tracking the load conditions in real-time adopting as initial guess for the simulation of each contingency, the trajectories obtained for the same contingency at the previous cycle of DSA functions (that is the ones calculated in the previous 15 minutes). In this way, the information obtained in a previous cycle of DCA is not lost completely as in step-by-step algorithms. The feasibility of the approach has been tested on the Italian 380-220kV transmission system operated by ENEL. A parallel implementation of the approach on a nCUBE multiprocessor is reported.