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However, this method does not take into account uncertainties in the power system, thus the power flow calculation tool integrated with probability method has been proposed and become a

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THE UNIVERSITY OF DANANG

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THE UNIVERSITY OF DANANG

Advisors:

1 Assoc Prof Dr Ngo Van Duong

2 Assoc Prof Dr Le Dinh Duong

Reviewer 1:

Reviewer 2:

Reviewer 3:

The dissertation is presented to the Assessment Committee at

The University of Danang (UD)

Time:

Date:

The dissertation can be found at:

- National Library of Vietnam;

- Learning Resources and Communications Center, UD

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INTRODUCTION

1 The urgency of the research

Nowadays, renewable energy resources such as wind and solar energies are increasingly gained interests because of practical benefits from these sources, especially environmental factors However, besides the benefits, these energy resources contain many uncertainties due to their random nature together with uncertainties inherited from electric power systems They could be accidental incidents of elements

in power systems, load variations and so on which cause many difficulties for calculating and analyzing power systems Therefore, it

is necessary to propose an appropriate calculation and analysis taking into account uncertainties to analyze current power systems

To ensure the operation of power systems safely, it is necessary

to calculate and check the system parameters against the allowable values corresponding to different operating states during operation process, and thus assessing the system safety level and find solutions

to enhance the safety operation for power systems The Raphson or Gauss-Seidel algorithms are often used to calculate the system with input data including operating parameters (load capacity, generated power ), system parameters (line impedance, transformer impedance .) and grid structure (working status of devices and associated lines .) These data are fixed values, so the calculation results are a set of parameters The characteristics of the power system such as node voltages, current and transmission capacities on the lines, phase angles are also fixed values, so the uncertainties in the system is not considered

Newton-In order to integrate uncertainty factors in the power system, based on data collected during the system operation, it is possible to determine the variation rules of operating parameters and system structure by statistical probability methods This is the input

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information of the network analysis problem and calculation results will expose the variation rules of the mode parameters Based on the changing rules of the regime parameters, corresponding to the actual operating modes, it is allowed to assess the safety of the power system taking into account the uncertainties of the power sources, loads and grid structures The calculation method allows to determine the existence probability of dangerous modes (voltage, current and transmission power parameters exceed the permissible values) based

on the characteristics of the power grid and the load requirements As

a result, solutions are calculated and proposed to enhance the safety of the power system

Based on aforementioned analyses, the research entitled

"Evaluating Impact of Uncertainties on the Security of Vietnam Power System" is significantly essential and meets practical current

requirements

2 Literature reviews

To evaluate the safe operation levels of the power system, it is necessary to firstly calculate the system parameters and then compare with the allowable limits Then, the safety evaluation is considered and solutions are proposed to ensure the system safety if unsafe risks are exposed The traditional method of calculating the power flows (calculation of the steady states of the power system) in [1, 2] has been used to determine the regime parameters in Vietnam However, this method does not take into account uncertainties in the power system, thus the power flow calculation tool integrated with probability method has been proposed and become a very effective tool in which all uncertainty factors in the system are described by probabilistic rules [8] and integrated into the calculation process This method was first proposed by Borkowska in 1974 [14] and since then many studies on

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this field have been published around the globe On the contrary, this field has not been studied to put into application to solve issues in Vietnam Power System so far, especially to analyze and assess the risks of unsafe conditions during the operation process

In general, calculating the power flows using probability method can be categorized into three main groups: analytical method [10, 11,

38, 47, 62, 70, 76, 79, 80, 83, 85], approximation method [5, 12, 17,

31, 33, 46, 50, 53, 68, 73, 84] and numerical method [15, 22, 23, 25,

35, 39, 48, 54, 63, 64, 67, 78] An important thing with the power flow calculation method that takes into account the uncertainties of

input variables is that there is a correlation between input variables

[17, 19, 39, 46, 47, 48, 54, 59, 74, 75, 84], especially this correlation

is relatively close for renewable energy resources like wind and solar energies for the actual power systems Therefore, correlations among the input variables (if any) must be considered in order to represent the input uncertainties in accordance with their inherent nature

In general, each method has its own characteristics and advantages and drawbacks, the most appropriate calculation method is selected depending on actual applications and requirements Analytical and approximation methods have fast computation time, but the accuracy is not high and it is difficult to integrate the correlation

of the input variables and distribution functions types, especially those that do not follow the standard distribution laws In contrast, Monte-Carlo simulation method gives very accurate and reliable results Probability distribution rules of input variables are generally easier to implement than analytical and approximation methods However, the biggest disadvantage of Monte-Carlo simulation is the heavy calculation volume, the calculation time is relatively long so it is difficult to do the calculation of power systems, especially large power grids in reality

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Within the scope of this study, in order to achieve highly accurate calculation results and to be able to represent uncertainty factors with the nature, the simulation method is chosen in this research However,

to overcome the limitations of the simulation method, multiple approriate treatment techniques are applied so that the simulation method can be proposed and developed as a tool for power system calculation and analysis

3 Purposes of the research

This research aims to develop a calculation tool for analyzing and evaluating the power system taking into account uncertainties This tool is then tested and applied to analyze the security of Vietnam power dystem

4 Objects and scopes of the research

 Research objects: Models representing uncertainty factors;

data mining techniques; calculation methods of power systems taking into account uncertainty factors

 Research scopes: Developing algorithms and calculation

programs, analyzing the power system with consideration of uncertainty factors, then using the results from the program to assess the safety level of the power system, determining the violation extent

of the regime parameters of the power system, if any, thereby proposing solutions to ensure safety for the system The proposed program is used to calculate power flow of 500 kV Vietnam Power Transmission System until 2025

5 Research approach and methodology

 Research approach: From theoretical basis to method

development and building calculation tools; testing and practical application

 Research methodology: To achieve the objectives of the

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thesis, the following methods are used in the research: methods of synthesizing and analyzing documents; methods of field survey and investigation; methods of theoretical research combined with practical testing

6 Research structure

This dissertation is structured as follows:

Introduction

Chapter 1: Methods of developing data sets for calculating and

analyzing the operation modes of the power system taking into account uncertainty factors

Chapter 2: Data processing techniques applied in calculation and

analysis of electricity systems taking into account uncertainty factors

Chapter 3: Methods of analysis and assessment of the safety

operation level of the power system incorporating with uncertainty factors

Chapter 4: Assessing the results of the proposed method on

sample power systems and applying the calculation of safety operation capacity of Vietnam Power System

Conclusions and recommendations

7 Scientific and practical contributions of the research

 Scientific contributions:

Scientific contributions of this dissertation are as follows:

- Proposing advanced data processing techniques, especially processing techniques, processing techniques to reduce data size by using Principal Component Analysis (PCA) technology With data clustering techniques such as K-means, Differential Evolution (DE)

pre-is applied not only in effectively solving the research problems but also can be extended to apply for other fields These techniques are

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important when dealing with large database issues

- Proposing a new CMC (Clustering based Monte-Carlo) method to process the input data sets for the calculation and analysis of the power system taking into account uncertainties The proposed method helps to minimize the data set whilst still fully reflects the actual operating parameters of power system accurately As a result, the calculation time is fast and the results are highly accurate This is one of the important contributions of the dissertation in terms of scientific methodology

- Based on data processing and analysis method of power systems, a monitoring program for the operation of the power system taken into account uncertainties has been developed The program allows monitoring of power system parameters for actual operating state, comparing with the level of parameter variabilities according to the input uncertainties and the allowable limits to assess the level of safety operation of power systems Based on those criteria, it is possible to identify dangerous nodes and areas on the power system, which should be regularly monitored and have appropriate solutions

to ensure safe and reliable operation

 Practical contributions:

The results of the dissertation will bring about the following practical contributions: The program of calculating and analyzing the power system using data processing techniques for the uncertainties of input parameters has been developed and the proposed monitoring operation program can be applied to planning and operation problems with various time domain in practice

CHAPTER 1 METHODS OF BUILDING DATA SETS FOR ANALYSIS OF THE OPERATION REGULATIONS IN

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POWER SYSTEMS WITH CONSIDERATION OF UNCERTAINTY FACTORS

1.1 Introduction

1.2 Concepts in statistical probability [21, 34]

1.2.1 Probability of random events

1.2.2 Random variables, distribution functions and characteristics

of random variables

1.3 Common probability distribution functions are used to represent random elements in power system [8, 21, 34]

1.3.1 Uniform distribution function

1.3.2 Standard distribution function (Gaussian / normal distribution)

1.3.3 Distribution function 0-1 and binomial distribution function 1.3.4 Weibull distribution function

1.3.5 Beta distribution function

1.3.6 Gamma distribution function

1.3.7 Multimodal distribution function

1.4 Developing distribution functions and generating random data sets of uncertainty elements in the power system

Figure 1.15 The process of developing the distribution function

and generating a random dataset

Figure 1.15 gives an overview of the developing process a

distribution function and generating a random dataset

1.5 Chapter conclusions

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There are many random factors in the power system and during the operation of the power system, it is possible to collect randomly occurring data on the operating parameters (load capacity, transmitter power, etc.) and number of incidents of system elements (transformers, lines, generators, etc.) Based on the random data set of each parameter, it is possible to formulate the rule of parameter variations according to certain forms of distribution function For power consumption at load nodes, there is usually a standard distribution function form; generation capacity of renewable energy sources such

as wind and solar energy is usually in the form of Weibull, Gamma or Beta distribution; incident probabilities of power elements are with a binomial distribution

Based on distribution functions of operating parameters and incident probability of elements, it is possible to create a random dataset of operating parameters and grid structure for the power system This data set is the fundemental information for providing input to the calculation program, and then to analyze the operation modes of the power system in which taken into account uncertainties

CHAPTER 2 DATA HANDLING TECHNIQUES APPLICABLE TO THE CALCULATION PROBLEMS AND ANALYSIS OF THE POWER SYSTEM WITH CONSIDERATION OF UNCERTAINTY FACTORS

2.1 Introduction

In order to integrate the uncertain factors in the calculation and analysis of the operating conditions of the power system, it is necessary to develop random distribution functions of parameters and the probability of elements’ failure in accordance with reality The random distribution function is built on actual operational data collected in the past However, the collected data usually contain some

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errors, data loss, data heterogeneity and other issues that make the process of data mining as well as building a random distribution function for those parameters encountered many difficulties, giving inaccurate results Advanced data processing techniques applied to processing collected data from random elements in the power system are the basis for creating a standard dataset of operating parameters and elements’ state in the system to apply for the problem of pratical power flow analysis

2.2 Data processing techniques in statistical probability

Data processing techniques include [37, 56, 77]: Data cleaning, data integration, data transformation, data reduction

2.2.1 Handling missing data

2.2.2 Eliminating foreign elements (outliers)

2.2.5 Data grouping techniques

One of the commonly used methods is the K-means method which is considered in this research In addition, clustering can be addressed as an optimization problem Therefore, optimization algorithms such as GA [66], PSO [44, 52, 82], etc., can be applied to clustering methods In recent years, a promising approach is the DE algorithm [18, 24, 43, 60] with advantages in proposed applications Unlike K-means, all GA, PSO, DE algorithms give more accurate

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results and global optimization However, all of the above mentioned clustering methods (except K-means) require a long processing time

so it is difficult to perform for large data which are the input database

of the power system calculation problem To overcome this difficulty, this research proposes a suggestion by applying data size reduction using PCA prior to using DE algorithm to form combined PCA + DE algorithm

2.3 Applying data processing techniques to build random data sets for the analysis of power system taking into account uncertainty factors

Figure 2.19 Data processing steps for calculating and analyzing the electricity

system take into account the random factors

The steps for applying data processing techniques are shown in Figure 2.19 Blocks in dashed rectangular frames are applied when the input data set is very large (large power system)

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2.4 Chapter conclusion

By using data processing techniques efficiently, it is possible to build random distribution functions of operating parameters and working status of elements in the power system to ensure accurate and practical reflection Resizing techniques by PCA technology combined with data clustering techniques such as K-means and DE are proposed

to be applied not only in effectively solving the research problem of the thesis but also it is possible to extend to other areas related to large

databases

CHAPTER 3 ANALYSIS AND EVALUATION OF THE SAFETY OPERATION LEVELS OF POWER SYSTEM WITH INTEGRATION OF UNCEERTAINTY FACTORS

3.1 Introduction

Based on the MCS method combined with the data processing techniques in Chapter 2, the dissertation proposed a new calculation method The proposed method allows to significantly shorten the time and volume of calculations but still ensure high accuracy, so it can be applied to large power systems

3.2 Developing the calculation module of the steady states for power system

The proposed algorithm of CMC and MCS is run in Matlab environment which uses iterative calculations to calculate the steady state of power system, so that one of the contents in the thesis is to build a calculation module This module is called PFC (Power Flow

Computation) The nrpfc.m and gspfc.m modules are built on the

Newton-Raphson and Gauss-Seidel algorithms and are integrated into the PFC module

In addition, to properly reflect the actual operation of a power system, the multi-node slack model (Distributed Slack Bus - DSB) was

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investigated and the dsbpfc.m module was also built and integrated in

the PFC module Different from the one-node slack model, the power deviation in the system is shared by multiple transmitters with frequency modulation function in the DSB model and each transmitter participates in the process of sharing the power deviation by the parameter respectively [49]

3.3 Algorithms and programs to analyze and assess the safe operation level of the power system taking into account uncertainty factors

3.3.1 Introduction

The traditional MCS algorithm has been applied and studied with high accuracy, but the implementation time is very long To both significantly reduce the time and ensure accuracy, a method called CMC is proposed

3.3.2 Analytical algorithm evaluating the safe operation level of the power system taking into account uncertainties

Algorithm for calculating, analyzing, evaluating the safe operation level of the power system according to the uncertainty elements of the operating parameters according to MCS method is illustrated in Figure 3.1

MCS must perform for very large number of samples and long computation time To solve this problem, data processing techniques, especially the size reduction and clustering of data in Chapter 2 are proposed to be applied and combined with MCS to form a new algorithm called CMC Algorithm diagram as in Figure 3.2 In figure 3.2, the data collection and reduction blocks are placed in dashed rectangular frames to clarify the differences from the traditional MCS method Thanks to a reduction in the number of input samples, the

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CMC algorithm is implemented with very short time but still ensures high accuracy results

Figure 3.1 MCS algorithm diagram Figure 3.2 CMC algorithm diagram

3.3.3 The program to analyze and assess the safe operation level of the power system taking into account uncertainties

Based on the algorithm diagrams in Section 3.3.2, the calculation, analysis and evaluation programs of the safe operation level of the power system taking into account the uncertainties are developed in Matlab software

First and foremost, algorithms and analysis programs to evaluate the safety of the power system taking into account uncertainties are applied to the 14-button IEEE sample power system [61] This is a

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