Capacitor Allocation Study Accounting For Load and Distributed

121 Pages·2015·2.14 MB·English

by  國立中山大學 電機電力工程國際碩士學程 林東

國立中山大學電機電力工程國際碩士學位學程
碩士論文
International Master's Program in Electric Power Engineering
National Sun Yat-Sen University
Master Thesis

應用 2PEM 機率電力潮流於考慮負載及分散式太陽能
發電不確定性之電容器配置研究
Capacitor Allocation Study Accounting For Load and Distributed
Solar Generation Uncertainty with the Use of 2PEM Probabilistic
Load Flow

硏究生: 林東
Natanael Acencio Rijo
指導教授: 林惠民 博士
Dr. Whei-Min Lin
中華民國 104 年 7 月
July 2015
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Acknowledments
“The present work is dedicated to my family, specially to my siblings and my parents
Juan Acencio and María Gisela Caraballo who always supported me through prayers and
caring, to my future wife Yuleisy F. Herrera for being patient and loving and also to those
friends that always offered their support when needed in midst of struggle”.
First of all, thanks to God who allowed me to live and become what I wanted to be. I
would like to express my thankfulness to the Taiwanese government that gave me the
opportunity to study in Taiwan through ICDF and to my lab-mates: Binarake Tebamuri,
Erita Ratreia Astrid, Walter Leguizamón, 蔡承佑, 許嘉維, 李承翰, 林暐翔,
蘇文賢, 王孟軒, 孫國峰, 呂凱弘, 吳鴻辰, 許祐瑄 who welcomed me
and offered their help until the last day. Thanks涂嘉勝 for your feedback that helped to
make this work better.
My appreciation also goes to the jury panel that evaluated this work: Dr. Jen Hao-Teng,
Dr. Tung-Sheng Zhang and Dr. Ting-Chia Ou.
Special thanks to my advisor Dr. Lin Whei-Min, who offered the support and guidance
necessary for the completion of this thesis.

Natanael Acencio Rijo
July, 2015
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Abstract
An implementation for probabilistic allocation of capacitors is introduced with the use of
Two Point Estimate Probabilistic Load Flow, this technique allows to consider
uncertainties that arise in the power system due to load variation and installed PV DG
solar irradiance dependent output. This uncertainty is accounted for by combining Pattern
Search optimization algorithm with Probabilistic Load Flow for the planning decision
evaluation of where is best to allocate capacitor banks to minimize the system losses; this
allows to obtain a solution that will result to be optimal in most of the cases that could
probably occur depending on the system load and PV DG’s historical and expected
behavior. The formulation is tested in a 34 bus power system with a defined probabilistic
load profile and the solution obtained compared against those obtained based on peak
load case studies. The robustness of each solution is tested with randomly generated cases
that follow the expected system behavior. The probabilistic allocation method produces
a solution that yields lower losses in the power system when uncertainty is present.

Keyword: Capacitor Allocation, Pattern Search Algorithm, Two Point Estimate
Probabilistic Load Flow, Uncertainty, Probability.

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摘要

本文以結合樣式搜尋最佳化演算法於機率負載潮流中，計算並
規劃最佳化的電容器配置以降低系統損失，在使用兩點機率估計法的
負載潮流於電容器的機率配置下，能將由於變動負載及太陽能發電的
不穩定電力輸出，所造成的電力系統中不確定因素加入考量；藉由負
載及太陽能發電機發電量的歷史資料及預測下，本方法能在大多數案
例下可得到最佳化的目標；本文使用34 bus 電力系統進行案例測試，
並以機率負載曲線所得的結果和一般尖峰負載的案例進行比較，同時
使用符合系統限制的隨機案例進行強韌性測試，結果證實本文所提出
的機率配置法可在電力系統有不確定的因素時得到更低的系統傳輸損
失。

關鍵詞：電容器配置、樣式搜尋演算法、兩點估計電力潮流、不確定
性、機率
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Table of Contents
Thesis/dissertation verification letter in Chinese................................................................i
Thesis/dissertation verification letter in English................................................................ii
Acknowledgement............................................................................................................iii
Abstract in English............................................................................................................iv
Abstract in Chinese............................................................................................................v
Chapter 1 Introduction
1.1 Introduction..................................................................................................................1
1.2 Motivation...................................................................................................................3
1.3 Literature review..........................................................................................................3
1.4 Content Organization...................................................................................................5
Chapter 2 Basic Concepts on Power Systems and Micro Grid
2.1 The power system elements..........................................................................................6
2.2 Load Flow Analysis....................................................................................................10
2.3 Complex power & Reactive Power Compensation.....................................................11
2.4 The smart grid............................................................................................................15
2.5 Distributed generation................................................................................................17
Chapter 3 Power System Planning and Probabilistic Load Flow
3.1 Power system planning...............................................................................................20
3.2 Planning in the presence of uncertainties....................................................................22
3.3 The capacitor allocation Problem in the planning process..........................................23
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3.4 The distributed generation allocation Problem in the planning process......................24
3.5 The Allocation with analytical and numerical optimization methods.........................25
3.6 Integrating uncertainty in the optimization of the allocation and planning problem...28
3.7 Uncertainty in statistics.............................................................................................28
3.8 Basic statistics concepts.............................................................................................29
3.9 The need for a probabilistic power flow explained.....................................................33
3.10 Monte Carlo probabilistic power flow......................................................................34
3.11 Two point estimate probabilistic power flow............................................................37
Chapter 4 Estimation of Uncertain Parameters
4.1 Uncertainty of Distributed Generation.......................................................................47
4.2 Solar irradiance uncertainty........................................................................................47
4.3 PV panels modeling....................................................................................................49
4.4 Solar PV penetration level..........................................................................................52
4.5 Modeling of solar PV in Load Flow study.................................................................52
4.6 Uncertainty of loads...................................................................................................53
4.7 Probabilistic forecast..................................................................................................54
Chapter 5 Probabilistic Planning Procedure and Optimization Method
5.1 Probabilistic planning: Definition..............................................................................55
5.2 Pattern search optimization as part of the probabilistic planning................................56
5.3 Probabilistic planning: Capacitor and PV distributed generation allocation...............62
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5.4 Probabilistic Load profile: definition and formulation...............................................63
5.5 Probabilistic objective function with weighted average: definition............................66
5.6 Integrating two point estimate load flow in probabilistic planning.............................67
5.7 Optimization Procedure considering uncertainty.......................................................68
5.8 Optimization procedure Flow Chart..........................................................................69
Chapter 6 Capacitor and DG allocation Study Cases
6.1 34 bus-study system for allocation study: data and schematics...................................71
6.2 Optimization procedure: Cases..................................................................................74
6.3 Case #1: Capacitor allocation under load uncertainty.................................................76
6.4 Case #2: PV-DG allocation under load uncertainty....................................................82
6.5 Case #3: Capacitor allocation under PV-DG and load uncertainty.............................87
6.6 Results discussion......................................................................................................92
Chapter 7 Conclusion
7.1 Conclusion.................................................................................................................93
7.2 Further Work..............................................................................................................95
References...................................................................................................................96
Appendix.....................................................................................................................99

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List of Figures and Tables
Figures
Figure 2.1 Basic Power System scheme..........................................................................10
Figure 2.2 Complex Power Triangle................................................................................13
Figure 2.3 Reactive Power Compensation........................................................................14
Figure 3.1 Skewness Concept Illustration........................................................................31
Figure 3.2 Normal probability distribution.......................................................................33
Figure 3.3 Flow chart: Monte Carlo simulation probabilistic load flow...........................36
Figure 3.4 Conceptual comparison: Deterministic load flow Vs. Prob. Load flow........43
Figure 4.1 Solar PV Model in Load Flow Study.............................................................53
Figure 5.1 Pattern Search Algorithm Flow Chart.............................................................61
Figure 5.2 Probabilistic allocation routine........................................................................69
Figure 5.3 Deterministic allocation routine.....................................................................70
Figure 6.1 34 Bus Distribution System.............................................................................72
Tables
Table 2.1 Today’s Grid vs. Smart Grid.............................................................................16
Table 2.2 Distributed Generation Classification..............................................................19
Table 3.1 Point Estimate Methods Comparison..............................................................37
Table 3.2 General Prob. Case: Bus voltages and angles....................................................44
Table 3.3 General Prob. Case: Line Flows and Losses.....................................................46
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