PROBABILISTIC ANALYSIS OF POWER SYSTEM WITH WIND GENRATORS

Abstract

Owing to the great proliferation of intermittent generation (wind, solar) in power grid, open access system, deregulation and competitive power markets, the power system operation has become uncertain. Generally, the deterministic load flow (DLF) method using Newton Raphson technique is widely used for the planning and operation of a power system on a daily basis. DLF uses the crisp values of power generations and load demands corresponding to a particular network configuration to calculate the output variables of interest and as a result, it discounts the uncertainties in the power systems, e.g. load demand variation, generator outages and the change of network configurations. Further, DLF also does not take into account the fluctuating and uncertain power generated by the renewable energy sources such as wind, photovoltaic systems etc. For addressing various issues of power system operation and planning, while taking into account uncertainties, probabilistic load flow (PLF) was proposed in 1970s and has been widely used since then. PLF is used to find the probability that the various parameters of the system such as bus voltage magnitudes, line power flows and reactive power injection from the generators are within their respective specified limits. If the calculated probabilities of various limit violations are found to be unacceptable, suitable remedial measures are adopted to alleviate the problem. Additionally, by performing PLF studies in an open access system, the system planning engineers gain more confidence in making proper judgments concerning investments in an uncertain environment. In the recent years, the power system industry has undergone a radical change i.e. transition to the horizontally operated system from a vertically operated power system. One of the major changes brought by this new structure is the incorporation of higher levels of non-dispatchable, stochastic generation in the system. The high penetration of intermittent generation in power grid has increased the uncertainty in power systems, which affects the medium and long term planning and day-ahead operation of the system. Now, among all the non-dispatchable intermittent distributed generation (DG) resources, wind energy has achieved substantial penetration level in the power grid. Therefore, for a system with large amount of wind power penetration, the probabilistic load flow analysis tool becomes even more important. However, the non-Gaussian probability density function (Weibull or Rayleigh) of wind speed and the correlation among the wind farms pose a major challenge for carrying out PLF for a system with high level of embedded wind power generation. To address the above issues, different methods of PLF have been proposed in the literature. Among these methods, point estimate method (PEM) is an efficient method for estimating the moi ments of output variables of interest for a given set of input random variables. The point estimate method uses discrete locations on the probability density function (PDF) and the corresponding weights of the input random variables to calculate the statistical moments of the output variables using non-linear load flow (LF) equations. By this approximation, the contribution of each input random variable to the output variables is taken into account. The method can be applied to problems involving either continuous or discrete random variables. PEM has many variants, which use either 2, 3, 5 or 7 points to approximate a given PDF in the increasing order of their accuracies. As PEM requires less amount of statistical information about the random input data and is also computationally efficient with sufficient degree of accuracy, in this thesis, PLF using PEM has been carried out. To obtain the PDF and the cumulative distribution function (CDF) of the output variables from the moments calculated by the PEM based PLF, Gram-Charlier (GC) and Cornish-Fisher (CF) series have been used in the literature. Now, GC and CF series are quite accurate for approximating a unimodal PDF with CF being marginally better than GC. However, with the inclusion of generator reactive power limits and multimodal PDF of the loads, the resulting PDFs of the output variables also become multimodal which cannot be approximated satisfactorily by both GC and CF series, as both are based on Gaussian distribution. Hence, for constructing a multimodal PDF satisfactorily, spline based reconstruction technique has been adopted in this thesis along with 7PEM based PLF (because of its highest level of accuracy as compared to the other versions of PEM). Further, this method has also been augmented to consider the correlation among the loads of a power system. Now, in the standard procedure of load flow, the real power outputs of all the generators except the slack bus are kept fixed. As a result, the slack bus absorbs (generates) all uncertainties in the total load of the system and thus, it has the widest possible variations of real power among all the generators. If the rating of the slack bus generator is adequately high to cover this wide variation, then the solution obtained by the probabilistic load flow is feasible. On the other hand, if the rating of the slack bus is not sufficient to cover the entire variation, then sometimes the slack bus generator would hit its maximum real power generation limit. Hence, it becomes necessary to consider the slack bus real power generation limit in PLF and towards this goal, necessary modifications in the basic PLF have been made. All the results obtained using the adopted methods have also been compared with those obtained by detailed Monte Carlo simulation (MCS) studies on two IEEE test systems and have been found to be reasonably satisfactory. The PLF method, developed so far, has been suitably modified further to include the uncertain wind generation. In the literature, uncertain wind generation is usually modeled as random real and ii reactive power injection (due to random variations of wind speed). However, to accurately estimate the reactive power consumption of wind turbine generator (WTG), detailed models of four types of WTGs have been included in the PLF. Further, as the generations from wind turbine generators are strongly correlated among adjacent wind farms due to the similar wind speed at that area, it is important to model the interdependence among the power generations from wind farms. Towards this goal, the correlation among the wind speeds experienced by WTGs has also been included in PLF. Due to the operation of the WTGs, the reactive power consumed by the system increases which leads to the variations in the bus voltages and line flows. For the successful operation of the power system, it is mandatory to keep the bus voltages and line power flows of the system within the desired limits under various operating conditions. For this purpose, the power system operators use a number of reactive power control devices such as shunt capacitors and transformer taps. The optimal adjustment of these control devices has a significant influence on the security and economic operation of power system. Hence, proper reactive power planning is needed for ensuring the secure and economic operation of the system. Traditionally, classical optimization techniques have been widely used for determining the optimal settings of the reactive power control devices. However, in modern power system problems, the objective functions and constraints are complex, non-smooth and non-differentiable and therefore, classical approaches often do not perform satisfactorily in these situations. To overcome the drawback of classical techniques, evolutionary algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO), gravitational search algorithm (GSA), a combination of PSO and GSA (PSOGSA) etc. have been applied to reactive power planning problem. However, all these methods suffer from the problem of reproducibility of the results, i.e. if these techniques are run repeatedly, they tend to produce different results on each run. To overcome this limitation, in this thesis, a new modified PSOGSA (MPSOGSA) optimization method has been proposed and its performance has been compared with the other optimization methods such as GA, GSA and PSOGSA. In all the above studies, network configuration of the power system has been assumed to be fixed and, consequently, the probability of the basic configuration of the system has been assumed to be unity. Thus, the probability of outage of any network element, such as transmission line, transformer, generator etc., is neglected. However, changes do occur in the network configuration because of generator and line outages owing to faults, overloads or scheduled maintenance. Therefore, the assumption of constant network configuration is unrealistic, particularly when the power generation iii and load uncertainties are significant. Now, any change in the power systems configuration will alter the set of functions relating the input and output variables and consequently, PDF of output variables may change substantially, which in turn, may affect the techno-economic decisions regarding the secure and optimal operation of power system. The outages of any power system element can be modeled as a random variable with an associated PDF. Subsequently, every network state caused by the outage of a power system component (generator/transmission line) has an associated probability of occurrence. In this thesis, the basic PEM based PLF procedure has also been modified to take into account the probability of occurrence of different network states. The effect of wind power injection with generator and line outages has also been studied.