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Number of pages: 129 File Format: word File Code: 32189
Year: 2013 University Degree: Master's degree Category: Electrical Engineering
Tags/Keywords: Closed variables - discrete parameters - Distribution networks - load spread - Modeling - Power grid - restructuring - Time series
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  • Summary of Time series loading

    Master's thesis

    In the field of electrical-power engineering

    Abstract

    Time series loading

    Next, the time series load distribution introduced in this thesis is used in the problem of restructuring distribution networks and to find the best network structure with the aim of minimizing losses in the power system.

    Finally, the time series models introduced in recent years have been used to simulate discrete parameters in the power system. Conventional ARMA time series are used to model continuous data. Variables such as the output power of CHP distributed generation units and the state of capacitor banks in the power system are discrete in nature. These models can consider some discrete distribution functions for different variables.

     

    Key words: load spreading, time series, closed variables, restructuring of distribution networks, discrete parameter modeling

     

    1- Introduction

    1-1- Importance of the problem

    The first and most important step in the operation, planning and design of power systems is to have sufficient information about the conditions of the power network, including the power passing through Bus lines and voltage are in permanent mode. Having such information requires load distribution in the power network. The need to carry out load distribution studies has been the attention of researchers for a long time, so that every year new methods and models are presented to improve the existing methods of load distribution. Different methods of load distribution are widely used for planning and operation studies in the power network.

    The load distribution tool calculates the output by responding to the injected power inputs of the generator, the load and network topology, the variables of the network state and the power passing through the lines. In deterministic load distribution [1] of the power system, the values ??of the generators' production powers and system load consumption, as well as the network topology are considered in a very specific way. Therefore, this method cannot model the uncertainty in the system load, the exit rate of generators from the circuit, as well as the network topology changes. While system state variables have a variable nature due to the possibility of loads, load prediction error and inaccurate estimation of system parameters. The probabilistic load distribution method [2] is an effective solution for non-deterministic inputs by knowing their statistical characteristics.

    With the evolution of power systems due to the penetration of scattered energy sources and the lack of control over natural stimuli in some of these sources, such as wind turbines and photovoltaic systems [3], a normal load distribution determines the system state variables in a limited time frame. With the expansion of distributed generation in the power network, the use of production and consumption time series in load distribution analysis can be useful, because production and consumption data are obtained in a period of time and can be written as a time series [1].

    In a power system, loads change frequently and the statistical distribution and relationship between them must be modeled. Unlike probabilistic load distribution analysis, whose input data is obtained from statistical distributions, here, production and consumption time series are used directly.In this research, an attempt is made to introduce time series load spreading as well as the use of time series modeling for some parameters with a discrete nature, such as tap trans, the state of capacitor banks and the output power of distributed generation units [4] CHP in the power system. rtl;"> 

    In order to consider cases of uncertainty in power systems, as it was said before, various methods based on statistical mathematics have been proposed to analyze these random phenomena, which are in the following three general forms:

    probabilistic methods[5]

    fuzzy method[6]

    open analysis[7]

    probabilistic methods among them have mathematical foundations and are also used in other aspects of the power system.

    probabilistic load distribution was first proposed in 1974 by Allen[8] and Berkoska[9], and then it was used in the operation of power systems and for short-term and long-term planning. [2[.

    In probabilistic load distribution and in the general case, the inputs of the problem are random variables in the form of density distribution function [10] or cumulative distribution function [11], and the system state variables and power passing through the lines will be in the form of PDF or CDF in the output, so uncertainty can be considered in this case.

    The probabilistic load distribution problem can be solved in one of three general ways To be solved below:

    Numerical methods[12], the most obvious example of which is the Monte Carlo method[13].

    Analytical methods[14], for example, the convolution technique[15] is used. 

    Approximate methods[16], among which we can mention the estimation of points[17]. This method was based on the assumption of the normality of the system variables and the power passing through the lines, which makes the calculations easier, but the answers of this method were not cited by the researchers. Considering the momentary uncertainty of production and consumption, the SLF algorithm models uncertainty in the short term and is more suitable for exploitation purposes. rtl;">In numerical methods such as Monte Carlo, at each stage by replacing numerical values ??for system variables and parameters and carrying out deterministic load distribution for each iteration, the output will also be in the form of numerical values.

    Two important features in Monte Carlo simulation are generating random numbers and sampling them. Software such as MATLAB [19] have created algorithms to generate random numbers. But the random sampling technique is more complex and various methods such as simple sampling and stratified sampling are used [4]. Because in the Monte Carlo method, different combinations of inputs are selected in each iteration and non-linear equations are used in solving the problem, therefore the results of the Monte Carlo method are usually used to check the correctness of other methods that consider simplifications in the equations. The most important problems of the Monte Carlo method are time-consuming and the need to perform a large number of simulations.

  • Contents & References of Time series loading

    List:

    Chapter One: Introduction

    1-1- Importance of the problem. 2

    1-2- Possible load distribution. 3

    1-3- An overview of the work done 12

    1-4- Objectives of the thesis. 24

    1-5- Structure of thesis. 25

    Chapter Two: Time Series

    2-1- Introduction. 27

    2-2- ARMA models. 27

    2-2-1- Stationary and unstable processes 27

    2-2-2- Moving average processes (MA) 29

    2-2-3- Autoreversion processes (AR) 29

    2-2-4- ARMA processes. 30

    2-2-5- ARIMA processes. 30

    2-2-6- SARIMA processes. 31

    2-2-7- Multivariate ARMA processes. 31

    2-3- Characteristics of time series model. 32

    2-3-1- autocorrelation and partial autocorrelation functions. 32

    2-3-2- Determining the stationarity and nonstationarity of time series using the ACF function. 35

    2-3-3- Pattern identification using ACF and PACF functions. 36

    2-3-4- The condition of stationarity and invertibility according to the coefficients of the model. 37

    2-3-5- pattern recognition tests. 38

    Chapter three: Time series load distribution

    3-1- Introduction. 40

    3-2- Possible load distribution. 41

    3-3- Introduction of formulation load spreading method 4. 43

    3-4- Formulation of the proposed method. 47

    3-5- Simulation of the studied network. 51

    3-5-1- Time series modeling of wind turbine output power. 52

    3-5-2- Injection active and reactive power modeling. 55

    3-5-3- Simulation results. 56

    Chapter Four: Using time series load distribution to change the network structure with the aim of minimizing losses

    4-1- Introduction. 67

    4-2- The problem of network rearrangement in power systems. 68

    4-3- Introduction of BPSO algorithm. 70

    4-4- Using time series models in network reorganization. 71

    4-5- Simulation results. 73

    4-5-1- The studied network. 73

    4-5-2- Results. 74

    4-5-3- checking the correctness of the proposed method. 77

    Chapter Five: Using DAR time series to model discrete parameters in the power system

    5-1- Introduction. 83

    5-2- Discrete variables in the power system. 84

    5-2-1- Tap trans modeling. 84

    5-2-2- Modeling of distributed CHP production units. 85

    5-3- Discrete autoregressive processes (DAR) 87

    5-3-1- Model introduction. 87

    5-3-2- Selection of model grade. 88

    5-3-3- checking the correctness of the selected model 90

    5-3-4- estimation of unknown parameters in the model. 92

    5-4- Simulation results. 93

    Chapter Six: Conclusion and Suggestions

    6-1- Conclusion. 99

    6-2- Suggestions. 100

    Appendix

    7-1- IEEE 14-bus network information. 102

    7-2- 69 bus network information. 104

    Sources and References 108

    Source:

     

    [1] T. Boehme, A. R. Wallace, and G. P. Harrison, “Applying Time Series to Power Flow Analysis in Networks With High Wind Penetration,” IEEE Transactions on Power Systems, vol. 22, no. 3, pp. 951–957, 2007.

     

    [2] P. Chen, Z. Chen, and B. Bak-Jensen, “Probabilistic load flow: A review,” in Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, 2008. DRPT 2008, 2008, pp. 1586–1591.

     

    [3] G. J. Anders, “Probability Concepts in Electric Power Systems”, New York: Wiley, 1990.

     

    [4] P. Chen, Stochastic Modeling and Analysis of Power System with Renewable Generation. Department of Energy Technology, Aalborg University, 2010.

    [5] E. Rosenblueth, "Point estimates for probability moments", Proc. Nat. Acad. Sci., Vol. 72, pp. 3812–3814, Oct. 1975. [6] E. Rosenblueth, "Two-point estimates in probability", Appl. Math. Model. Vol. 5, pp. 329-335, Oct. 1981.

    [7] K. S. Li, "Point-estimate method for calculating statistical moments", J. Eng. Mech.-ASCE, Vol. 118, No. 7, pp. 1506-1511, Jul. 1992. [8] M. E. Harr, "Probabilistic estimates for multivariate analysis", Appl. Math. Model., Vol. 13, No. 5, pp. 313-318, May. 1989.

    [9] H. P. Hong, "An efficient point estimate method for probabilisticHong, "An efficient point estimate method for probabilistic analysis", Reliab. Eng. Syst. Saf., Vol. 59, No. 3, pp. 261-267, Mar. 1998.

    [10] B. Borkowska, “Probabilistic load flow”, IEEE Trans. Power Apparatus and Systems, Vol. PAS-93, No. 3, pp. 752-755, May-Jun. 1974.

     

    [11] R. N. Allan and M. R. G. Al-Shakarchi, “Probabilistic a.c. load flow", Proceedings of the Institution of Electrical Engineers, Vol. 123, No. 6, pp. 531-536, Jun. 1976.

     

    [12] R. N. Allan and M. R. G. Al-Shakarchi, “Probabilistic techniques in AC load flow analysis”, Proc. IEEE PAS-124, pp. 154–160, Feb. 1976.

     

    [13] R. N. Allan and A. M. Leite da Silva, “Probabilistic load flow using multilinearisations”, IEE Proc., Part C: Generation, Transmission and Distribution, Vol. 128, No. 5, pp. 280-287, Sep. 1981.

     

    [14] A. P. S. Meliopoulos, G. J. Cokkinides and X. Y. Chao, “A new probabilistic power flow analysis method”, IEEE Trans. Power Systems, Vol. 5, No. 1, pp. 182-190, Feb. 1990. [15] A. M. Leite da Silva and V.L. Arienti, "Probabilistic load flow by a multilinear simulation algorithm", IEE Proc. Part C: Generation, Transmission and Distribution, Vol. 137, No. 4, pp. 276-282, Jul. 1990. [16] M. Brucoli, F. Torelli and R. Napoli, "Quadratic probabilistic load flow with linearly modeled dispatch", Electrical Power & Energy Systems, Vol. 7, No. 3, pp. 138-146, Jul. 1985.

     

    [17] A. M. Leite da Silva, R. N. Allan, S. M. Soares, “Probabilistic load flow considering network outages”, IEE Proc., Part C: Generation, Transmission and Distribution, Vol. 132, No. 3, pp. 139-145, May. 1985.

     

    [18] L. A. Sanabria and T. S. Dillon, “Stochastic power flow using cumulants and Von Mises functions,” International Journal of Electrical Power & Energy Systems, vol. 8, no. 1, pp. 47–60, Jan. 1986. [19] N. S. Rau and C. Necsulescu, “Solution of probabilistic load flow equations using combinatorics,” International Journal of Electrical Power & Energy Systems, vol. 12, no. 3, pp. 156–164, Jul. 1990. [20] P. Zhang and S.T. Lee, "Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion", IEEE Trans. Power Systems, Vol. 19, No. 1, pp. 676-682, Feb. 2004. [21] C.-L. Su, “Distribution probabilistic load flow solution considering network reconfiguration and voltage control devices,” in 15th Power Systems Computation Conference, Liege, 2005.

     

    [22] N. D. Hatziargyriou, T. S. Karakatsanis, and M. I. Lorentzou, “Voltage control settings to increase wind power based on probabilistic load flow,” International Journal of Electrical Power & Energy Systems, vol. 27, no. 9–10, pp. 656–661, Nov. 2005.

     

    [23] C. L. Su, “Probabilistic load-flow computation using point estimate method”, IEEE Trans. Power Systems, Vol. 20, No. 4, pp. 1843-1851, Nov. 2005.

     

    [24] Z. Hu and X. Wang, “A probabilistic load flow method considering branch outages”, IEEE Trans. Power Systems, Vol. 21, No. 2, pp. 507-514, May. 2006. [25] J.M. Morales, J. Perez-Ruiz, "Point estimate schemes to solve the probabilistic power flow", IEEE Transaction on Power Systems, Vol. 22, No. 4, pp. 1594-1601, Nov. 2007.

     

    [26] H. Liao, “Fast Deterministic Sampling for Mean and Covariance Estimation in Stochastic Load Flow”, IEEE Conference Power Engineering Society General Meeting, Tampa, FL, pp. 1-6, 24-28 June 2007.

     

    [27] J. Schwippe, O. Krause, C. Rehtanz, "Extension of a Probabilistic Load Flow Calculation Based on an Enhanced Convolution Technique", IEEE Conference on Sustainable Alternative Energy, Valencia, pp. 1-6, 28-30 Sept 2009. [28] J.

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