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íð Ö«²» îðïìAbstract
Traditional adequacy evaluation of power distribution systems does not consider the effect of momentary interruptions or voltage sags, assessing only sustained interruptions lasting longer than few minutes. This might lead to an overestimation of the performance of the distribution system, by neglecting failures/phenomena related with power quality concerns. Therefore, the main objective of this thesis is to integrate short-circuit analyzes with reliability adequacy assessment, providing a chronological perspective to the evaluation of the performance of power distribution systems. For this accomplishment, an algorithm based on sequential Monte Carlo simulation was developed to capture phenomena associated with short-circuit events. In this algorithm, resident time of components in temporary and permanent failures are sampled alongside fault impedance, fault section location, fault type, and phases involved. Furthermore, novel indices and test-functions for momentary and voltage sag events were designed to provide quantitative information regarding the service delivered.
The proposed approach was tested in a three-phase IEEE 34 node test feeder. Besides, the impact of distributed generation on the developed integrated assessment is also evaluated under the scope of the developed indices. The results obtained produced discussions regarding the necessity of combining short-circuit analyzes with reliability adequacy assessment. Additionally, they indicate that power quality concerns must not be underestimated in the performance assessment.
Resumo
A avalia¸c˜ao tradicional de adequa¸c˜ao dos sistemas de distribui¸c˜ao de energia n˜ao considera o efeito das interrup¸c˜oes momentˆaneas nem das cavas de tens˜ao, apenas avalia as interrup¸c˜oes que duram mais do que alguns minutos. Isso pode originar uma superestima¸c˜ao do desempenho do sistema de distribui¸c˜ao, ao negligenciar falhas/fen´omenos relacionados com preocupa¸c˜oes relativas `
a qualidade de energia. Desta forma, o principal objetivo desta tese ´e integrar as an´alises de curto-circuitos com a avalia¸c˜ao de adequa¸c˜ao de fiabilidade, ao mesmo tempo que fornece uma perspetiva cronol´ogica para a avalia¸c˜ao do desempenho de sistemas de distribui¸c˜ao de energia. Para alcan¸car este objetivo, foi desenvolvido um algoritmo baseado em simula¸c˜ao sequencial de Monte Carlo, que captura fen´omenos associados com eventos de curto-circuitos. Neste algoritmo, o tempo de residˆencia de componentes em falhas tempor´arias e permanentes ´e amostrado, bem como a impedˆancia da falha, localiza¸c˜ao da mesma na linha, tipo de falha, e as fases envolvidas. Al´em disso, foram projetados novos ´ındices e fun¸c˜oes de teste para eventos de cavas de tens˜ao e eventos momentˆaneos para fornecer informa¸c˜oes quantitativas em rela¸c˜ao ao servi¸co prestado.
A abordagem proposta foi testada na rede de teste trif´asica IEEE 34. Al´em disso, o impacto de gera¸c˜ao distribu´ıda na avalia¸c˜ao integrada desenvolvida tamb´em ´e avaliado no ˆambito dos ´ındices desenvolvidos. Os resultados obtidos produziram discuss˜oes sobre a necessidade de combinar a an´alise de curto-circuitos com a avalia¸c˜ao de adequa¸c˜ao de confiabilidade. Al´em disso, estes indicam que as preocupa¸c˜oes com a qualidade de energia n˜ao devem ser subestimadas na avalia¸c˜ao do desempenho.
Acknowledgements
First of all, I would like sincerely to express my gratitude to my supervisor, Dr. Vladimiro Miranda, who provided the opportunity of developing this thesis in Brazil and whose expertise and understanding added considerably to my graduate experience.
I would also like to thank my supervisors in Brazil, Mauro Rosa and Diego Issicaba, for their hospitality and warm reception. Furthermore, I would like to thank them for the time exempt and for their knowledge and experience, and several decisive contributions for this document.
Finally, a special thanks to my family and friends who always supported me unconditionally.
Sofia Leal
“O caos ´e uma ordem por decifrar.“
Livro dos contr´arios
Contents
Contents 13
List of Figures 15
List of Tables 17
1 Introduction 21
1.1 Motivation and Historical perspective . . . 21
1.1.1 Research Questions . . . 22
1.2 Objectives . . . 22
1.3 Document Structure . . . 22
2 State of the art 25 2.1 Reliability in Distribution Systems . . . 25
2.1.1 Adequacy and Security in Power Systems . . . 25
2.1.2 Functional Zones and Hierarchical Levels . . . 26
2.1.3 Adequacy and Security in Distribution Systems . . . 27
2.1.4 Distribution System Power Quality Indices . . . 28
2.2 Monte Carlo Simulation Methods to Power System Assessment . . . 34
2.2.1 System State Sampling or Non-Sequential Monte Carlo Simulation . . . 35
2.2.2 System State Transition Sampling or Sequential Monte Carlo Simulation . . 36
2.2.3 Pseudo-Sequential Monte Carlo Simulation . . . 37
2.3 Probabilistic Analysis of Short-circuits . . . 37
3 Proposed Approach 39 3.1 Proposed Computational Modeling . . . 39
3.2 Integrating Short-Circuit Analysis in Distribution System Adequacy Evaluation . . 44
3.2.1 Sampling Short-Circuit Events . . . 45
3.2.2 Test Functions and Performance Indices . . . 49
3.3 Proposed Algorithm . . . 51
4 Results and Discussions 55 4.1 Description of the test system . . . 55
4.2 Simulations and Result Analysis . . . 59
5 Final Considerations 71 5.1 Conclusions . . . 71
5.2 Future Works . . . 72
References 75
List of Figures
2.1 HL Evolution . . . 26 2.2 CBEMA Curve . . . 33 3.1 OpenDSS Structure . . . 40 3.2 OpenDSS Executive . . . 40 3.3 OpenDSS Iteration . . . 413.4 Object-oriented modeling of the combined discrete-continuous simulation approach 42 3.5 Object-oriented modeling of the proposed approach . . . 43
3.6 Markov Model . . . 45
3.7 Intervals that determine the type of fault in a line with three phases . . . 48
3.8 Intervals that determine the type of fault in a line with two phases . . . 48
3.9 Intervals for phase involved in single-phase faults . . . 48
3.10 Intervals for phases involved in line-to-line faults . . . 49
3.11 flowchart . . . 54
4.1 IEEE 34 node test feeder . . . 55
4.2 IEEE 34 Node Test Feeder with overcurrent protective devices . . . 59
4.3 Convergence of the SARFI index with DG . . . 61
4.4 Convergence of the MAIFI index with DG . . . 61
4.5 Current through fuse in node 834 for all short-circuit occurrences without DG . . . 62
4.6 Current through fuse in node 834 for all short-circuit occurrences with DG . . . . 62
4.7 Zoom for Figure 4.5 (without DG) . . . 63
4.8 Zoom for Figure 4.6 (with DG) . . . 63
4.9 Estimated probability distribution of voltage sags at node 848 without DG . . . . 64
4.10 Estimated probability distribution of voltage sags at node 848 with DG . . . 64
4.11 Estimated probability distribution of momentary interruptions without DG . . . . 65
4.12 Estimated probability distribution of momentary interruptions with DG . . . 65
4.13 Estimated probability distribution of momentary interruptions events without DG 66 4.14 Estimated probability distribution of momentary interruptions events with DG . . 66
4.15 Time over current without DG at node 834 . . . 67
4.16 Time over current with DG at node 834 . . . 67
4.17 Time over voltage without DG . . . 68
4.18 Time over voltage with DG . . . 68
4.19 Voltage during short-circuit in node 836 without DG . . . 69
4.20 Voltage during short-circuit in node 836 with DG . . . 69
List of Tables
2.1 Typical characteristics of short and long voltage duration variations . . . 30
3.1 Fault Type . . . 47
4.1 Line segment data . . . 56
4.2 Overhead line configuration data . . . 56
4.3 Transformer data . . . 57
4.4 Spot loads data . . . 57
4.5 Shunt capacitors data . . . 57
4.6 Distributed load data . . . 58
4.7 Voltage regulators data . . . 58
4.8 Performance indices and their respective units . . . 59
4.9 System-wide performance indices without and with DG . . . 60
List of Acronyms
CBEMA Computer Business Equipment Manufacture Association DG Distributed Generation
EPRI Electrical Power Research Institute HL Hierarchical Level
ITIC Information Technology Industry Council LV Low Voltage
MCS Monte Carlo Simulation MTTF Mean Time to Failure MTTR Mean Time to Repair
NSMCS Non Sequential Monte Carlo Simulation RMS Root Mean Square
SMCS Sequential Monte Carlo Simulation
Chapter 1
Introduction
This chapter introduces the context and motivation for this thesis. It also enumerates the established research questions and objectives. The challenges of the thesis topic are discussed and a revised structure of the document is outlined in the end of the chapter.
1.1
Motivation and Historical perspective
Over the last decades, society’s growing dependence on electrical energy and an increasing electricity consumption, combined with technological developments, originated the need of imple-menting increasingly larger and more complex systems. Consequently, technical, environmental and sustainability problems have emerged requiring new approaches and strategies.
Nowadays, environmental matters have a growing importance in decision making and affect several areas of knowledge, including power systems. These power systems hold an unquestionable importance in modern societies. Due to power systems huge impact in global economy, environment and society, it is crucial to promote energy efficiency. Electrical power systems are designed to provide electricity with a certain level of reliability, which has a significant relevance in this context. The increased demand for electricity also has some implications, such as concerns about secu-rity of supply and the environment, increasing the sustainability and growth of difficulties in the construction of transport infrastructure and distribution. This creates the need for diversification of energy sources, which can be achieved by increasing the use of renewable energy and improving energy efficiency.
Currently there is a new paradigm where renewable energies have an increasingly important role and it is patent a large-scale integration of Distributed Generation (DG). DG corresponds to small scale production of energy, usually located close to demand and/or connected to distribution systems.
This shift is strongly influenced by environmental concerns, particularly with greenhouse gas emissions and increase of the greenhouse effect. Furthermore, it is also subjective to the energy crisis, which is motivated by the strong dependence on oil exporting countries (not forgetting that these are often politically unstable areas).
Electric power systems are designed to serve loads in a safe and reliable manner. One of the 21
22 Introduction
major considerations in the design of a power system is adequate protection against short-circuits. During a short-circuit, very large currents can flow until a fuse, or a breaker or another interrupter breaks the circuit. During this time, the high short-circuit currents, can cause service outage, provoking production downtime and associated inconveniences, interruption of essential facilities or vital services, extensive equipment damage, personnel injury or deaths, and possible fire damage. Traditionally, adequacy assessment of power distribution systems does not consider the effect of short interruptions or power quality problems, but only assessed sustained interruptions lasting longer than a few minutes. However, this leads to ignoring some of the aforementioned consequences of short-circuits.
All of this enhances the necessity of incorporating short-circuit analysis in the distribution system adequacy evaluation.
1.1.1
Research Questions
The main research questions of this thesis are the following.
1. How to integrate short-circuit analysis in the distribution system adequacy evaluation? 2. How to evaluate the impact of the momentary interruptions and voltage sags in the
perfor-mance of power distribution systems?
So as to approach these questions, the objectives described in the next section were established.
1.2
Objectives
This dissertation has the objective of integrating short-circuit analysis in the distribution system adequacy evaluation in order to include issues related to momentary interruptions and voltage sag events in the adequacy evaluation.
1.3
Document Structure
Besides this introductory chapter, this document is structured as follows.
Chapter 2 introduces a background and state the art about the main topics approached in the
thesis. The chapter begins with a background and state the art on reliability assessment, focusing on concepts such as adequacy and security. Adequacy indices in distribution system evaluation are addressed and it is discussed the growing concern with power quality and the necessity of reliability indices that take into account power quality evaluation. The chapter proceeds discussing the state of the art about Monte Carlo Simulation (MCS). To conclude, is examined the emergent interest in the use of probabilistic methods in short-circuit analysis and methodologies proposed in the literature are reviewed.
Chapter 3 describes the proposed approach, exposing the advantages of applying simulation
1.3 Document Structure 23
evaluation. It also has some remarks regarding the architecture and computational imple-mentation outlined in the chapter.
Chapter 4 presents the system used for testing and for validating the results obtain with the
simulation and simulation results are presented and analyzed.
Chapter 5 completes the thesis by stating its conclusions, outlining its main contributions and
Chapter 2
State of the art
In this chapter it is performed an analysis of the state of the art with the aim of establish-ing a theoretical background required to comprehend the development of this proposed approach. First, in section 2.1, power system reliability assessment is reviewed, focusing on concepts such as adequacy and security. A breakdown of functional zones (generation, transmission and distri-bution) and hierarchical levels is also described in this section. Adequacy indices in distribution system evaluation are addressed and it is discussed the growing concern with power quality and the necessity of reliability indices that take into account a power quality evaluation. After that, in section 2.2, Monte Carlo simulation is reviewed and its main associated techniques are presented and detailed, comparing advantages and disadvantages, as well as the simulation process for each one. Lastly, in section 2.3, it is examined the emergent interest in the use of probabilistic methods in short-circuit analysis and reviewed methodologies proposed in the literature.
2.1
Reliability in Distribution Systems
Reliability intents to establish models to evaluate the power system behavior, being that the primary function of an electrical power system is to provide electrical energy to its customers as economically as possible and with an acceptable degree of continuity and quality. The occurrence of random failures of equipment and systems have a significant impact in the cost of electricity and a high correlation with customer satisfaction. The failures are generally outside of the control of the power systems operators, but investments can be made to improve reliability.
2.1.1
Adequacy and Security in Power Systems
Power system reliability assessment can be divided into two basic aspects: system adequacy and security [1]. The first one relates to the existence of enough facilities within the system to satisfy the load demand or system operational constraints. These include the facilities needed to generate satisfactory energy and the associated transmission and distribution facilities required to transport the energy to the actual consumer load points. Adequacy is, therefore, related with static conditions which don’t include system dynamic and transient disturbances. Security is related to the ability
26 State of the art
of the system to respond to dynamic or transient disturbances emerging within the system. It is, consequently, associated with the response of the system to whatever perturbations it is subject to. These include the conditions associated with both local and widespread disturbances and the abrupt loss of major generation or/and transmission facilities which can lead to dynamic, transient or voltage instability of the system.
2.1.2
Functional Zones and Hierarchical Levels
Adequacy studies are conducted in each one of the three distinct segments of power systems: generation, transmission and distribution system [1]. These functional zones, usually called hierar-chical levels (HLs), are represented in Figure 2.1, where their evolution is illustrated. Hierarhierar-chical level 1 (HL 1) is concerned with only the generation facilities. HL 2 includes both generation and transmission facilities while HL 3 includes all three functional zones in an assessment of consumer load point adequacy.
Due to the large scale of the problem in a practical system, it is usually unfeasible to perform HL 3 adequacy assessment involving the consideration of all the three functional zones. Instead of the complete aggregation, distribution reliability studies are only performed within the distri-bution system functional zone. In general, this is satisfactory since distridistri-bution networks often interface with the transmission system through one supply point, and this link (substation) with generation and transmission systems is assumed to be unlimited in capacity and 100% reliable. In addition to this, distribution systems account for up to 90% of all customer reliability problems and, consequently, dictate the overall reliability indices [2].
Generation Transmission Distribution HL 1 HL 2 HL 3 Energy Generation Transmission HL 0 HL 1 HL 2 Distribution HL 3 Energy Generation Transmission Distribution (a) (b) (c) Figure 2.1: HL Evolution [2]
2.1 Reliability in Distribution Systems 27
concepts [2]. In the functional zones presented in Figure 2.1(a), the traditional HL were proposed under a centralized paradigm where the utilities were organized with the three segments (gener-ation, transmission and distribution) aggregated in a single company. Due to the restructuring and privatization process of the power sector, many countries in the world adopted a decentralized power industry where generation, transmission and distribution are managed separately. There-fore, generation company strategies have incorporated primary resources as an important factor to be held under consideration in the new scenario of the power industry. Figure 2.1(b) shows the first evolution in the traditional functional zones of the power networks considering HL 0 - energetic resources. Figure 2.1(c) introduces the most recent evolution where the large-scale integration of DG is regarded in the HL structure.
2.1.3
Adequacy and Security in Distribution Systems
In the past, when the presence of generators in distribution systems was limited, the assump-tions applied to adequacy studies were generally considered sufficient to provide satisfactory input to the decision-making processes. Nonetheless, when a substantial number of generators of dif-ferent technologies are connected to distribution networks, aspects related with system dynamics could be of great importance to evaluate the distribution system operation.
A power system is considered adequate taking into account its ability to meet the demand regarding operation constraints, and considering planned and unplanned component outages. On the other hand, a power system is considered secure according with its ability to withstand distur-bances.
Unfortunately, the definitions commonly used to bulk generation and transmission system eval-uation cannot be directly applied to distribution system assessment. Due to the meshed structure and radial operation of distribution systems, feeders without alternative supply (either from other feeders or DGs) are always predisposed to service unavailability caused by a permanent fault. Thus, some common bulk power systems deterministic criteria (such as the loss of the largest generating unit) lose their meaning on distribution systems analysis. Therefore, distribution systems are usu-ally assessed from a customer service point of view, rather than operation state classifications [3]. Also, the distribution system adequacy evaluation evolved from assessing the ability of the system
to provide a continuous service in terms of interruptions in its points of consumption, to assessing the ability of the system to provide an adequate service in terms of voltage waveform in its points
of consumption, taking into account planned and unplanned component outages.
Generating stations are individually very capital intensive and generation inadequacy can have widespread catastrophic consequences for both society and its environment. Because of this, over the past few decades, distribution systems have received considerably less of the attention devoted to reliability modeling and evaluation than have generating systems. A distribution system is relatively cheap and outages have a strongly localized effect. Consequently less effort has been devoted to quantitative assessment of the adequacy of various alternative designs and reinforce-ments. On the other hand, analysis of the customer failure statistics of most utilities shows that the distribution system makes the greatest individual contribution to the unavailability of supply to a customer.
28 State of the art
The need to evaluate the reliability of distribution systems requires the consideration of other aspects. Firstly, even though a given reinforcement scheme may be relatively inexpensive, big sums of money are expended collectively on such systems. Secondly, it is required to ensure a reasonable balance in the reliability of the various parts of a power system, i.e. generation, transmission, distribution. Thirdly, a number of alternatives are available to the distribution engineer in order to achieve acceptable customer reliability, including alternative reinforcement schemes, allocation of spares, improvements in maintenance policy and alternative operating policies [4].
2.1.4
Distribution System Power Quality Indices
Perfect power quality is regarded as having a sinusoidal voltage source without waveform dis-tortion, variation in amplitude or in frequency. Since reliability is primarily dedicated to customer interruptions, and these are power quality concerns, reliability is a subset of power quality. How-ever, the boundary separating the two is not well defined [5]. Sustained interruptions have always been categorized as a reliability issue, however, in the past, momentary interruptions have been classified as power quality concerns. Nowadays, they are an important customer issue and are regarded as a reliability matter. Power quality problems can be divided into many categories such as: interruptions, sags, swells, noise, flicker, harmonic distortion and frequency variation [5]. This
thesis scope is focused on interruptions and sags.
It is important to understand the difference between an interruption and a voltage sag or a swell. Interruptions imply a complete loss of voltage, which occurs when a protective device interrupts a circuit serving a particular customer. This will generally only happen if there is a fault on that circuit. Voltage sags are temporary root-mean-square (RMS) reductions in voltage to a customer, typically lasting from half a cycle to several seconds. Voltage swells, on the other hand, are temporary RMS increases in voltage, usually lasting from half a cycle to several seconds [5].
The magnitude of a sag is described by either the resulting per unit voltage, or the per unit voltage decrease below a nominal value. Both sags and swells magnitude and duration are often compared against voltage tolerance envelopes [5]. Voltage sags and swells take place during the period of a fault over a wide part of the power system. Faults on parallel feeder circuits or on the transmission system will cause voltage sags but will not result in actual interruptions [6]. For that reason, voltage sags and swells are considerably more common than interruptions. If equipment is sensitive, the frequency of problems will be much greater than if the equipment was only responsive to interruptions.
A fault on a single feeder will most likely cause an outage to loads on that feeder, as well as a sag on the parallel feeders. The closer the fault is to the substation bus, more effect it will have on the parallel feeders. When a breaker opens or a fuse blows, clearing a fault, the system current and bus voltage will return to normal function. The recloser will open, and then reclose into the fault after about 1-10 seconds (depending on the type of recloser scheme). Afterwards, the breaker is either locked out, or the fault has been cleared. Depending on the number of reclosing operations before lock-out, parallel feeders can experience as many as four voltage sags in succession. When the fault occurs on a fused branch of a distribution feeder, the fuse blows and the customer located on that branch will experience an outage, which will last until the fuse is replaced. If the breaker/reclose
2.1 Reliability in Distribution Systems 29
operates during the fault, all the customers on that feeder experience an interruption of a duration that depends on the recloser setting [7].
A common underlying cause of sags and swells is a sudden change of current flow through the source impedance. In the case of a sag, the sudden, large increase in the current required from a source will cause a larger voltage to be developed across the source impedance. This will result in a reduction in the voltage, as seen by the load. Likewise with a surge, a sudden reduction in the current flow will cause an increase in voltage in inductive/capacitive impedances, which the load may experience [7].
Sags result from high currents, typically due to faults or starting motors, interacting with system impedances [5]. Preliminary results from an Electric Power Research Institute (EPRI) study indicate that the most important cause of momentary voltage sags is lightning strikes [7]. Swells are ordinarily triggered by the sudden load reduction or asymmetrical faults, for instances, a single line to ground fault will cause a cause a temporary voltage rise on the unfaulted phases. This is particularly evident in ungrounded or floating ground delta systems, where the abrupt change in ground reference results in a voltage rise on the ungrounded phases. Close to the substation on a grounded system, there will be no voltage rise on unfaulted phases because the substation transformer is usually connected delta-wye, providing a low impedance path for the fault current [7]. The consequences of sags are frequently more perceptible than those of swells. Yet, the reper-cussions of a swell can often be more destructive than those of a sag. This happens because sags impacts in equipment are often not distinguishable from momentary outages [7]. Sensitive equipment may experience intermittent lockups or garbled data. Even relays and contactors in motor starters can be sensitive to voltage sags, resulting in shutdown of a process when the drop out occurs. A swell, on the other hand, due to the overvoltage condition, may cause insulation breakdown in sensitive electronic equipment if voltage rise is large enough for a long enough period of time.
IEEE Standard 1159-1995, Recommended Practice on Monitoring Electric Power Quality, de-livers a common terminology that can be used to discuss and assess RMS voltage variations. This standard defines magnitude ranges for sags, swells and interruptions. Also, IEEE Standard 1159-1995 proposes that the terms sag, swell, and interruption be preceded by a modifier describing the duration of the event, i.e. instantaneous, momentary, temporary, or sustained [8], as described in Table 2.1.
Most reliability indices are average values of a particular reliability characteristic for an entire system, operating region, substation service territory or feeder [5]. The most broadly used relia-bility indices are averages that weight each customer equally. Customer-based indices are popular with regulatory authorities since a small residential customer has just as much importance as a larger industrial customer [5].
The three basic load-point sustained interruption indices in distribution system adequacy as-sessment are the failure rate λ [interruptions/year], the unavailability or annual outage time U [h/year] and the mean time to repair r =U/λ [h/interruptions] at the customer point of
connec-tion [1, 10].
30 State of the art
Table 2.1: Typical characteristics of short and long voltage duration variations [9]
Category Duration Voltage Magnitude
Sag 0.5 to 30 cycles 0.1 to 0.9 pu Instantaneous
Swell 0.5 to 30 cycles 1.1 to 1.8 pu Interruption 0.5 to 3 s <0.1 pu
Short
Momentary Sag 30 cycles to 3 s 0.1 pu to 0.9 pu Duration
Swell 30 cycles to 3 s 1.1 to 1.8 pu Variation
Interruption 3 s to 1 min <0.1 pu
Temporary Sag 3 s to 1 min 0.1 pu to 0.9 pu Swell 3 s to 1 min 1.1 to 1.8 pu
Long Interruption >1 min 0 pu
Duration Sustained Undervoltage >1 min 0.8 to 0.9 pu
Variations Overvoltage >1 min 1.1 to 1.2 pu
System Average Interruption Frequency Index. This index measures how many sustained
interruptions an average customer will experience over the course of a year. For a fixed number of customers, the only way to improve SAIFI is to reduce the number of sustained interruptions experienced by customers.
SAIFI = Average n ◦ of customer interruptions N◦of system customers = ∑ iλiNi ∑ iNi [ interruptions year ] (2.1)
where λi is the failure rate and Ni is the number of customers at the point of connection i.
System Average Interruption Duration Index. This index measures how many interruption
hours an average customer will experience over the course of a year. For a fixed number of customers, SAIDI can be improved by reducing the number of interruptions or by reducing the duration of this interruptions.
SAIDI = Total average customer interruption durations N◦ of system customers = ∑ iUiNi ∑ iNi [ h year ] (2.2)
where Ui is annual outage time at point of connection i.
Customer Average Interruption Duration Index. This index measures how long an average
interruption lasts.
CAIDI = Total average customer interruption durations Average n◦ of customer interruptions =
∑ iUiNi ∑ iλiNi [ h interruption ] (2.3)
Average Service Availability Index. This index measures the customer weighted availability
of the system. CAIDI can be improved by reducing the length of interruptions, but it can also be decreased by an increasing the number of short interruptions. Thus, a reduction in CAIDI does not necessarily reflect an improvement in reliability.
ASAI = Total average customer service durations Total customer year durations =
∑ i8760Ni− ∑ iUiNi ∑ i8760Ni (2.4)
2.1 Reliability in Distribution Systems 31
where 8760 is the number of hours in a calendar year.
Average Service Unavailability Index. This index measures the customer weighted
unavail-ability of the system and provides the same information as SAIDI.
ASUI = Total average customer interruption durations Total customer year durations =
∑
iUiNi
∑
i8760Ni
= 1− ASAI (2.5)
Energy Not Supplied. This index measures the total energy not supplied by the system.
ENS = Energy not supplied by the system =∑
i PiUi [ MWh year ] (2.6)
where Pi is the load connected to the point of connection i.
Average Energy Not Supplied. This index measures the average customer total energy not
supplied.
AENS =Energy not supplied by the system N◦ of system customers = ∑ iPiUi ∑ iNi =∑ENS iNi [ MWh customer.year ] (2.7) For several years, electricity distribution companies have used the before mentioned indices as indicators of the reliability of their systems. However, the development and proliferation of power electronic devices and other sensitive equipment have altered the reality of what is actually a reliable service [8].
The increasing sensitivity of customer load to brief disturbances has generated a need for indices related to momentary interruptions. In the future, the number of sensitive loads will only increase more and hence, its becoming more and more important for utilities to understand how momentary outages impact their systems. Two momentary indices have become standard. One is based on the frequency of momentary interruptions and the other is based on the frequency of momentary events [5].
A momentary event interruption is an interruption of duration limited to the period required to restore service by an interrupting device. This switching operations must be completed in a specified time inferior to 5 min. The aforementioned definition comprises all reclosing operations that occur within 5 min of the first interruption. For example, if a recloser or breaker operates two, three, or four times and then holds, the event shall be considered one momentary interruption event. On the other hand, a momentary interruption is a single operation of an interrupting device that results in a zero voltage. For instance, two breaker or recloser operations equals two momentary interruptions [11].
The traditional reliability indices do not consider the effect of momentary interruptions or voltage sags, but assess only sustained interruptions lasting longer than a few minutes, with the minimum time varying by location [12]. Nevertheless, more than 70% of faults on overhead distri-bution systems are temporary [13]. Hence, reclosers are normally used to de-energize the system
32 State of the art
for a short period of time to allow each fault a chance to clear itself.
When a fault occurs on the system a recloser opens, interrupting all customers downstream of the recloser. After a short time delay, the recloser closes. If the fault is cleared, the recloser remains closed. If not, the recloser may operate one or more times until the fault clears itself. As previously explained, this situation consists in a single momentary interruption event, even if multiple reclosing operations are necessary.
When a permanent fault (i.e., a non-self-clearing fault) happens on a distribution system a re-closer opens, interrupting all customers downstream of the rere-closer. The rere-closer operates several times. After the maximum set number of operations is reached, the recloser remains closed to allow time-overcurrent devices to operate. A time-overcurrent device (such as a fuse or circuit breaker) operates, which interrupts all customers downstream of the device. Automated switching, if avail-able, quickly restores power to certain customers. Therefore, certain customers will experience a sustained interruption, while others will experience momentary interruptions.
The system-wide power distribution momentary interruption indices are the following [11]:
Momentary Average Interruption Frequency Index. This index measures the average
num-ber of momentary interruptions that a customer experiences during a given time period.
MAIFI = Average n
◦ of customers momentary interruptions
N◦ of customers served [ occ. year ] (2.8)
Momentary Event Average Interruption Frequency Index. This index measures the
aver-age frequency of momentary interruption events.
MAIFIE=
Average n◦ of customers momentary events N◦ of customers served [ occ. year ] (2.9)
Note that SAIFI and MAIFI are interrelated. In fact, automated restoration techniques will reduce SAIFI at the expense of increasing MAIFI [12]. MAIFIE is a better measure of customer
satisfaction since multiple closely spaced interruptions have much less impact than the same number of interruptions spaced days or weeks apart [5].
Many sensitive loads cannot tell the difference between voltage sags and momentary interrup-tions. Because of this, interruption-based reliability indices are not able to reflect all customer concerns and voltage sag indices are becoming necessary [5].
Nowadays, it is regarded as sensitive equipment, industrial and commercial loads such as: adjustable speed drive units and other power electronic devices that use 3-phase power that will be connected directly to the low voltage (LV) node, or through an isolation transformer; control devices such as computers, contactors, and programmable logic controllers that are often supplied through a single phase control transformer; computed tomography device; motors, heating elements, and other 3-phase loads that can be connected directly to the LV node; a complete line of industrial production and lamp of gaseous discharge [6, 14].
Different categories of equipment, and even distinct brands of equipment within a category, have unrelated sensitivities to voltage sags [6]. The ability of the sensitive equipment to with-stand voltage sags without dropout is function of the magnitude of the voltage reduction and
2.1 Reliability in Distribution Systems 33
of the perturbation duration. Many typical ride-through capability curves have been proposed as guidelines, be that as it may, the most widely used curve is the one proposed by the North American association of makers of computers for commercial use, CBEMA (Computer Business Equipment Manufacturer Association), which applies primarily to data processing equipment [15]. Later on, this curve has been modified, receiving the names of ITIC (Information Technology In-dustry Council) and SEMI F47, nevertheless the original curve is the one that continues being widely accepted [14].
These curves are normally provided in graphical form, having two well bounded parts that correspond to the overvoltage and undervoltage withstand values [15]. The present work is confined to the lower part, related to the voltage sag ride-through capability, since the scope of this work focus on voltage sags, as previously mentioned in the beginning of this subsection.
The paper in [15] gives the fitting equation of CBEMA curve as: {
U2t = 4400
U = 87 − 100UM UN
(2.10)
where U is the duration of voltage deficit below the minimum specified voltage defined in the CBEMA curve (87%), t is the duration of the voltage sag in cycles,UM is the magnitude of node
residual phase voltage andUN is the rated node phase voltage.
0.0001 0.001 0.01 0.1 1 10 100 1000 -100 -50 0 50 100 150 200 250 TIME IN SECONDS OVERVOLTAGE CONDITIONS UNDERVOLTAGE CONDITIONS RATED VOLTAGE ACCEPTABLE POWER
Figure 2.2: CBEMA Curve [16]
As it has been shown previously, reliability is no longer specified only by the frequency and duration of sustained interruptions occurring on the distribution system. For instance, to a textile manufacturer whose main process is driven by an adjustable speed drive units, a six-cycle voltage sag to 80% of the nominal voltage may be just as costly in terms of lost productivity as a two-hour interruption of service. Using the traditional reliability indices to assess quality of service provided to this textile manufacturer, this costly disturbance would be neglected [8].
34 State of the art
Therefore, System Average RMS Variation Index (SARFI) represents the average number of specified voltage RMS variation events that occurred over the assessment period per customer served, where the events are featured by a magnitude less than x for sags or a magnitude greater than x for swells [8]. In view of the fact that the severity of voltage sags depends upon duration as well as magnitude, to ensure that enough information is contained by the index so it can be useful in all cases, this index should be based on a curve that corresponds to a number of voltage sags (or swells) outside of equipment compatibility curve over the assessment period. Another approach would be to decompose SARFI into instantaneous, momentary and temporary index based on the duration of the sag [5, 17]. A formal definition of this index is given in the followings.
System Average RMS Variation Index. This index measures how many voltage sag
occur-rences an average customer will experience over the course of a year.
SARFI = Average n
◦ of customers sags below CBEMA
N◦ of system customers [ occ. year ] (2.11)
The complexity of modeling the aspects of interest of the power distribution system operation leads to the necessity of the use of simulations methods to estimate performance indices. For this purpose, Monte Carlo Simulation is applied in this work.
2.2
Monte Carlo Simulation Methods to Power System
As-sessment
The techniques used in power system adequacy assessment can be frequently divided into two basic categories: analytical and simulation [2]. Analytical methods attempt to evaluate all the system states contained in state space, or approximations of such through mathematical models and equations. Simulation procedures, on the other hand, rely on a set of simulations representing the actual system behavior in order to attain the reliability indices, thus requiring some type of stopping criteria. Therefore, simulation methods tend to obtain an approximation of the indices values obtained by the analytical methods [18].
Methodologies based on probability concepts can be extremely useful to assess the performance of power systems [4]. MCS base-tools have proven to be extremely useful when regarding reliability evaluation problems. Also, they provide a wide-ranging reliability assessment, especially for large and complex power systems [19].
One advantage of the Monte Carlo procedure is that it can provide information related to the probability distributions of the reliability indices in addition to the mean, or average, values [1]. MCS-based tools are extremely robust to solve power system reliability problems, particularly for large and complex power systems. Still, due to their sampling strategy based on probability of occurrence, they may face some difficulties when dealing with very reliable system configurations. In other words, the performance of MCS-based methods could be jeopardized if the encountering of a failure state can be classified as a rare event, i.e., with probabilities of occurrence smaller than 10−5 [19].
2.2 Monte Carlo Simulation Methods to Power System Assessment 35
In the literature several mechanisms can be found to improve the computational performance for the Monte Carlo methods to reliability assessment, such as, heuristic tools to estimate relia-bility indices, artificial intelligence techniques or variance reduction techniques to improve Monte Carlo Simulation, Hybrid approaches, and others [2]. There can be found three types of basic MCS approaches, which will be presented in the next subsections. Those are the System State Sampling or Non-Sequential Monte Carlo Simulation (NSMCS), System State Transition Sampling or Sequential Monte Carlo Simulation (SMCS) and Pseudo-Sequential Monte Carlo Simulation.
2.2.1
System State Sampling or Non-Sequential Monte Carlo Simulation
Since a system depends on the combination of all component states and each component state can be determined by sampling the probability that the component appears in that state, the main concept of this method is to sample randomly a sufficient amount of system states, through the use of their respective probability distribution [1].The sampling procedure is processed N times, with the reliability indices being estimated using the mean values of the suitable test functions:
¯ E[F ] = 1 N N ∑ k=1 F (xk) (2.12)
where F (xk) is the random variable value of a given test function, which is dependent of the
respective sampled system state xk. Since it is a mean value it can be perceived as a random
variable with the following variance:
¯
V [E(F )] =
¯
V (F )
N (2.13)
From (2.13), it is possible to verify that the estimated variance depends on the variance of the test function and the number of samples N . In other words, the larger is the number of samples the more accurate is the method [1].
The uncertainty of the Monte Carlo estimate is usually characterized by the coefficient of variation β, β = √ ¯ V [ ¯E(F )] ¯ E(F ) 100% (2.14)
where√V [ ¯¯ E(F )] is the standard deviation of the estimated expectation and ¯E(F ) is the estimated
expectation of the index.
The Monte Carlo approach can be implemented in the following steps [1]:
Step 1 Initialize the number of samples N = 0;
Step 2 Sample all the system states from their respective probability distribution; update N ; Step 3 Calculate function F to each sample system state;
36 State of the art
Step 5 Calculate β using equation (2.14). If the confidence degree is acceptable then stop, if not,
then go back to step 2.
In general, the NSMCS does not allow the estimation of frequency indices and the representation of time dependent features.
2.2.2
System State Transition Sampling or Sequential Monte Carlo
Sim-ulation
The sequential approach is based on sampling by the probability distribution of the component state duration [1]. A single component model is a component that has two states, operating state and repair state. These are associated with mean-time-to-failure (MTTF) and mean-time-to-repair (MTTR). Bearing in mind the two-state Markov Model, these are the operating and repair state duration distribution functions that are usually assumed to be exponential [2].
For the SMCS approach, the estimation of reliability indices is obtained as follows:
¯ E[F ] = 1 N Y N Y ∑ n=1 F (yn) (2.15)
where N Y is the number of simulated years and yk is the sequence of system states in year k.
The sequential approach can be summarized in the following steps [20]:
Step 1 Initiate all the component states. Generally it is assumed that all the components are in
the success or up state;
Step 2 Sample the duration of each component residing in its actual state. If using an exponential
distribution for the state duration, then the duration of the state is calculated as
Ti =−
1
λi
ln(Ui) (2.16)
where Ui is a uniformly distributed random number between [0, 1] and i stands for the
component number. If λ is a failure rate, Ti denotes the sampled time in the up state.
Otherwise, if λ is the repair rate, Ti stands for the sampled time in the down state.
Step 3 Repeat the step 2 each time span, in this case yearly, and record the results of each
duration sampled for all components;
Step 4 In order to obtain yearly reliability indices, calculate the test function F (yn) over the
accumulated values;
Step 5 Estimate the expected mean values of the yearly indices as the average over the yearly
results for each simulated sequence yn;
Step 6 The stop criterion is also based on the relative uncertainty of the estimates. Therefore,
calculate β (coefficient of variation) using (2.14);
Step 7 End the methodological procedure if the desired degree of confidence is achieved. If not
2.3 Probabilistic Analysis of Short-circuits 37
The advantages of SMCS are that it can easily be used to calculate the actual frequency index, any state duration index can be easily considered and the statistical probability distributions of the reliability indices can be calculated in addition to their expected values. The disadvantages are the computing time necessary, which is greater since it is necessary to generate a random variate following a given distribution for each component and store information on chronological component state transition processes of all components in a long time span. Another disadvantage is that this method requires parameters associated with all component state duration distributions [1].
2.2.3
Pseudo-Sequential Monte Carlo Simulation
In this method the main distinction from the preceding approaches is how the states are visited. Pseudo-Sequential Monte Carlo follows the time span of each transition state while the previous methods focused on the duration sampling. So, the Pseudo-Sequential Monte Carlo simulation retains the computational efficiency of the NSMCS and the accuracy from SMCS [1].
The pseudo-sequential approach can be summarized in the following steps:
Step 1 Sample the state of each component;
Step 2 Evaluate the sampled system state for a time span, e.g. a year. If the system state was
up then go back to the Step 1. If the system state was down estimate the test function for the reliability indices and go to the Step 3;
Step 3 Obtain the interruption sequence based on the forward/backward simulation.
Step 4 The stop criterion is also based on the relative uncertainty of the estimates. Therefore,
calculate β (coefficient of variation) using the (2.14). If convergence is achieved then stop if not return to the Step 1;
The objective of this approach is to use the non-sequential method to select the failures states of the system and to only use the sequential approach when there is a complete interruption of the system. The pseudo-sequential Monte Carlo simulation is described in detail in [21].
2.3
Probabilistic Analysis of Short-circuits
The estimation of power distribution performance indices, either analytically or by MCS ap-proaches, is based on the idea that disturbances may cause short or long voltage variations, thereby causing service interruptions or other types of power quality problems. For instance, in power distribution reliability analyzes, failures are assumed to cause protective device operations and customer service interruptions. Under the scope of problems such as interruptions and voltage sags, in between failures and interruptions, there is the inherent concept of a short-circuit.
In a power system the magnitude of the currents provoked by short-circuits is the most signifi-cant factor, influencing many aspects of power system design like bus systems, grounding systems, substation apparatus, among others. Besides this, the increase of the fault current levels has en-forced the reduction of safety margins in the operation of the power system. These modifications
38 State of the art
of the operating conditions often impose new requirements. If the short-circuit currents calculated exceed the original designed ones, a engineer is called to take crucial decisions regarding replace-ment or uprating of existing substation equipreplace-ment, installation of series reactors and/or current limiting devices and the adoption of special operating procedures [22].
Short circuit currents are influenced by several factors, such as structural system characteristics, for instance, the impedance and length of the lines; operational system characteristics, which, in turn, are functions of the network topology during the fault occurrence (generators, transformers, live lines) and fault conditions, for example, location and type of fault [23]. Structural quantities are usually fixed, however operational ones may vary statistically. Moreover, fault conditions are random in nature.
The fault currents are typically based on a deterministic modeling, i.e. they are calculated using the worst-case conditions. This approach leads to conservative designs with a subsequent larger monetary investment [22]. Hence, an emergent interest has been perceived in the use of probabilistic methods as a power engineering tool in areas such as reliability evaluation, insulation coordination and short-circuit analysis [24]. Since, the main factors influencing the magnitude of fault currents are random, probabilistic approaches appear to be the most promising [25]. Furthermore, the latter can lead to more accurate designs and allows using design criteria given in terms of fault current histograms rather than in terms of worst-case situations [24–26].
A probabilistic approach that has been used in short-circuit evaluation is the Monte Carlo method, the technique described in Section 2.2.2. Monte Carlo is based on the process of gener-ating random numbers from assigned probability density functions of the input random variables. These random numbers can be used to sample other random quantities of interest, such as fault locations, fault type, phases faulted, fault impedance and so on, from their respective probability distributions. In probabilistic short-circuit analyzes, this sampling needs to be done taking into account suitable statistical information about these quantities [23], as well as the fault type and component faulted might be considered to be discrete random variables (independent) [25]. In ad-dition, some alternatives to the Monte Carlo methods can also be found. In [27], the probabilistic short-circuit analysis is based on a particular case of the point estimated method, which is known as three-point estimate method. This technique has chosen instead of Monte Carlo due to its low computational effort and similar convergence.
In subsection 2.1.4 we discussed the increasing concern with power quality due to the growing usage of sensitive equipment and the necessity to study power quality problems associated with voltage sags. In [28], a probabilistic short-circuit approach is developed to generate the proba-bilistic distribution frequency associated with the SARFI index.The methodology is based on the combination of the NSMCS with the admittance summation method in phase coordinates.
Conversely, this work focuses on estimating sustained interruption, momentary interruptions and voltage sag indices in an integrated way, using a SMCS based approach, considering the integration of DG.
Chapter 3
Proposed Approach
In this chapter, it will be presented a methodology with the purpose of integrating short-circuit analysis in distribution system adequacy evaluation using a SMCS approach. Firstly, in section, 3.1 the proposed computational implementation is described. Then, in section 3.2, it is exposed the advantages of applying simulation procedures and it is explained how the short-circuit analysis can be integrated in the adequacy evaluation. Lastly, the proposed approach algorithm is illustrated in section 3.3, covering every step of it and illustrating that with a flowchart.
3.1
Proposed Computational Modeling
This section briefly describes the various software simulation packages used in this thesis. OpenDSS was used for simulating short-circuits in the test system. JAVA programming was used to further develop the existing software, JDistribution. And finally, Matlab was used for commu-nicating between JAVA and OpenDSS and for analyzing results. The short-circuit is simulated through the OpenDSS, that is called by Matlab, that in its turn is called by the JDistribution. All the results (current and voltage in all nodes) and the short-circuit characteristics (fault location, fault resistance, phases involved, duration) are saved for posterior analysis.
The Open Distribution System Simulator, or simply OpenDSS, is a broad-gauge electrical system simulation tool for electric utility distribution systems. In 2008, EPRI released the software under an open source license to promote and instigate the development of modernization efforts active in the Smart Grid area [29].
OpenDSS is implemented in two ways: as a standalone executable program and as an in-process COM server DLL. The executable version has a basic text-based user interface on the solution engine to assist users in developing scripts and viewing solutions. The COM interface is designed to be driven from a variety of existing software platforms, such as MATLAB, VBA, C#, Python, etc.
The program is a script-driven simulation engine that is nominally configured as shown in Figure 3.1. In order to better support other operating systems and service oriented simulations the main simulation engine was subdivided into several modules.
40 Proposed Approach
Figure 3.1: OpenDSS Structure [30]
Figure 3.2: OpenDSS Executive [30]
The OpenDSS Executive and Circuit element models are currently written in the Delphi pro-gramming language, which successfully combines object-oriented Pascal with rapid application development for the Windows platform. The ease with which COM interfaces could be imple-mented was one motivation for choosing Delphi. The system Y matrix and associated arrays of the Solution object are maintained by a sparse solver implemented in a DLL. The solvers used have been written in C++ [30].
The COM interface allows the user to design and execute custom solution modes and features from an external program and carry out the functions of the simulator, comprehending the defini-tion of the model data [29, 31]. It also provides direct access to the text-based command interface and to numerous methods and properties for obtaining many of the characteristics of the simula-tor’s models. Several of the results can be retrieved through the COM interface as well as from various output files. A wide variety of the outputs or export files are written in Comma-Separated Value (CSV) format that can be imported easily into other tools such as Microsoft Excel or Matlab
3.1 Proposed Computational Modeling 41
for post-processing [29]. But on the other hand in this thesis we are running a large number of short-circuits, so importing CSV files for each one would be very time consuming. Therefore, it is necessary to get direct access to the results in Matlab instead of having to import a CSV file for each time we simulate a short-circuit. It is possible to get all the node voltages in one statement (DSSCircuit.AllNodeVmagPUByPhase()). However, currents and powers are different. So the so-lution is to get them one circuit element (cktelement) at a time. So we grab the device index for the element of interest then extract the voltage and current (in magnitude and phase) from the active element device [32].
The majority of electrical engineers learned how to write nodal admittance equations in their early University courses, and this is how OpenDSS represents circuits. Each element of the system is represented by a primitive nodal admittance (Y) matrix, and each primitive Y is then combined into one large system Y matrix. The system of equations representing the distribution system is then solved using sparse matrix solvers [29].
Figure 3.3: OpenDSS Iteration [30]
An initial guess at the voltages is attained by doing a zero load power flow. That is, all shunt elements are disconnected and only the series power delivery elements are considered [29]. The iteration cycle is started by obtaining the current injections from all the elements, such as load devices and generators, and introducing them in the line vector [31]. An equation is formed by populating the current vector with the compensation current, which consists in the difference between the current drawn by the nonlinear power conversion element and the linear portion of the element, if any, that is implanted in the system Y matrix [30]. This means that the current predicted from the linear portion of the model that resides in the system Y matrix is compensated by an external injection to iteratively obtain the correct current [29]. The sparse set of matrices is solved until the voltages converge to the specified tolerance.
The simulation engine OpenDSS requires a plain text file that describes the topology of the distribution system to be simulated [33]. In this thesis it was used the IEEE 34 node test feeder, as previously mentioned. Many of the IEEE Test Feeders have been implemented in OpenDSS, and the one used is no exception. A summary description of the IEEE 34 node test feeder can be found in section 4.1.
42 Proposed Approach
the system at a selected location, defining the type of fault, and the value of the fault resistance. A fault is a circuit element (a resistor network) just like any other element and can be manipulated the same way and configured in a variety of ways. It is nominally designed with the same philoso-phy as the Capacitor. That is, it is a two-terminal device in which the second terminal defaults to ground. Nonetheless, the OpenDSS fault object may be configured to do much more and can be configured to represent any type of fault. [29] An more elaborate explanation of how to simulate each type of fault can be found here [34].
The program used, JDistribution, is implemented using JAVA language and is described in [10]. The main classes of this software are exhibited in Figure 3.4, where a class named CDCSapproach is highlighted at the top of a diagram. This class abstracts the simulation model as an aggregation of a state composer, a state evaluator and an index composer. In a nut shell, the state composer is responsible for sampling, transiting and constituting operation states using as information the stochastic and deterministic models of the power distribution system elements. The state evaluator is responsible to evaluate operation states. The resultant state evaluations are then transmitted to the index composer which must keep track of the estimation of performance indices. Assuredly, all these classes depend upon a series of additional developments. These developments are outlined in the right-hand side of the figure, where several supplementary classes are illustrated. For instance, a topology processor and protection rule engine classes were developed with the aim of assigning electrical islands to a power distribution system object. Power flow and dynamic behavior analysis were encoded in separated classes using subclasses to specify control blocks and models [10].
Figure 3.4: Object-oriented modeling of the combined discrete-continuous simulation approach. [10]
In order to integrate the short-circuit analysis in JDistribution some new classes were created and some new methods and variables were added to others. All of these modifications can be seen in the UML diagram presented in 3.5.
3.1 Proposed Computational Modeling 43 tools .handler OpenDSSHandler - sopenDSSHandlerID : String - myMatlabHandle r: MatlaHandler -out : double [][] + setOpenDSSHandlerID (sopenDSSHandlerID : String ): void + getOpenDSSHandler ID (): sopenDSSHandlerID + setMatl aHandler (myMatlaHandle r: String ): void + getMatl aHandler (): myMatlaHandle r + shortCir cuit (bus 1 , bus 2 , phases , distance , r): double [][] tools .shortci rcui t ShortCir cuit Sampler - myRandom : Random - shortCir cuit SamplerID : String - myOpenDSSHandler : OpenDSSHandler - iSeed : static int - phases : int - faultBus 1 :String - faultBus 2 : String - resistanc e : double - distance : double - Rdeviation : static int - Rmean : static int - timeDe viation : static int - timeM ean : static int - faultType : String - previousLoc : String - phaseAfect : String - faultTi me : double - sPhases : String + getInit ialSeed (): int + setInit ialSeed (iSeed : int ): void + getShort Circ uitSampler ID (): String + setShortCi rcui tSampler ID (shortCir cuit Sampler : String ): void + setMyOpenDSSHandler (myOpenDSSHandler : openDSSHandler ): void + getMyOpe nDSSHandler (): openDSSHandler + getFaultB us 2 (): String + setFaultB us 2 (faultBus 2 : String ): void + getFaultB us 2 (): String + setFaultB us 1 (faultBus 1 : String ): void + getFaultB us 1 (): String + getPhases (): int + setPhases (phases : int ): void + sampleShortCi rcui t( myStateOfOper ation : StateOfOperat ion ): double [][] + sampleDistance (): double + sampleFaultTy pe (): void + samplePhaseSeq (): void + samplePhaseInv (): void + sampleResistance (): double + getFaultDat a (): String [] + getFaultT ype (): String + setFaultT ype (faultType :String ): void tools .monteCarl o StateEvaluator +....:.. .. - myShortCi rcui tSampler : ShortCir cuit Sampler - bFlagSC : boolean +....:.. .. +....:.. .. + evaluateState OfOperation (): StateEvaluati on +....:.. .. tools .monteCarl o StateEvaluati on +....:.. .. - aShortCir cuit Results : double [][] - faulData : String [] +....:.. .. +....:.. .. + setAShortCi rcui tResult s( aShortCir cuit Results : double [][]): void + getAShortCi rcui tResult s(): double [][] + setFaultData (faultData : String []): void + getFaultDat a (): String [] +....:.. .. << Stereot ype >> IndexCompositor +....:.. .. - vYearSCRes : Vect or < double [][] > - vAnnualYearSCRes : Vect or < Vect or < double [][] >> - vFaultData : Vect or < String [] > - vAnnualFaultData : Vect or < Vect or < String [] >> +....:.. .. +....:.. .. + export ShortCir cuit Res (): void + export ShortCir cuit Data (): void +....:.. .. StateOfOperat ion +....:.. .. - sPreviousStat eChangerID : String +....:.. .. +....:.. .. + set sPreviousStat eChangerID (sPreviousSt ateChangerID : String ): void + get sPr eviousStateChanger ID (): String +....:.. .. << Stereot ype >> TwoTer minalEl ement +...:... - sphases : String +...:... +...:... tools .monteCarl o MonteCarl oSetti ngs ...+... + bShortCir cuit : boolean + dPtempor aryFaults : static double ...+... ...+... << Stereot ype >> Stochastic Component ...+... - bTemporar y: boolean - myFault : Random ...+... ...+... tools .handler MatlabHandler - proxy : MatlabPr oxy + setPr oxy ( proxy : MatlabPr oxy ): void + getPr oxy ( ): MatlabPr oxy + init iateHandle r(): void + termi nateHandler (): void + creat eStruc t( year : String , occ String , res : double [][] , data : String []): void tools .shortci rcui t ShortCir cuit Results - result s: Vect or < Vect or < double >> - myMatlabHandle r: MatlabHandler - faultData : Vect or < Vect or < String [] >> + setFaulData (faultData : Vect or < Vect or < String [] >> ): void + getFaultDat a (): Vect or < Vect or < String [] >> + import ShortCir cuit Res (proxy : MatlabPr oxy ): void + import ShortCir cuit Data (): void + setResult s (result s: Vect or < Vect or < double [][] >> ): void + getResult s ( ): Vect or < Vect or < double [][] >> + sendToMatl ab (): void matlabContr ol MatlabPr oxy ...+... ...+... Figure 3.5: Ob ject-orien ted mo deling of the prop osed approac h
44 Proposed Approach
On of the new classes is ShortCircuitSampler, in which all the data required for calculating short-circuits is sampled. In this class the next component to fail and the duration of the fault are known, the other necessary variables (section of the line, fault impedance, fault type and phases involved) are sampled using the techniques detailed in subsection 3.2.1. Once the sampling is done, another new class, OpenDSSHandler, calls a Matlab function that creates the test feeder system and inserts a fault there and retrieves the short-circuit results. In order for Matlab to be able to start OpenDSS, yet another new class is used. This is MatlabHandler, which is used to start, terminate and communicate between Matlab and OpenDSS. Finally, in the end of the simulation, all the serialized1short-circuit results are deserialized and sent to another Matlab function, which
is used for calculating indices and plotting histograms, that present some results.
3.2
Integrating Short-Circuit Analysis in Distribution
Sys-tem Adequacy Evaluation
Simulation is an important mechanism that allows to study a wide variety of topics related to the behavior of real-life systems. The combination of some factors such as, recent advances in simulation methodologies, software availability, sensitivity analysis, and stochastic optimization, has made simulation one of the most widely accepted, and used, tool in systems analysis and operations research. The continued growth in size and complexity of emerging real-world systems will undoubtedly ensure that the popularity of computer simulation continues to increase [36].
Simulation presents some very important advantages, for instance, it can be used to experiment with new scenarios so as to gain insight into system behavior under new circumstances. Also, even in systems whose behaviour might be captured by mathematical models, it may not be possible to obtain a solution to the problem embodied in the model by straightforward analytical techniques. Another advantage of simulation is that it allows to study dynamic systems in either real, compressed, or expanded time horizons [36].
Probabilistic fault analysis using Monte Carlo simulations comprises the stochastic determina-tion of short-circuit currents. For this, it is necessary to simulate the system state under fault conditions, recurring to different input data for each simulation. This data is modelled by random variables which represent the faulted component, the fault type, the fault impedance, the location and phases involved.
The random variables used in Monte Carlo are generated by a pseudo-random number gener-ator. This simulates randomness without actually being random and should be created methods setSeed() and getSeed(), these retrieve or set out the attribute seed2, respectively [36]. In Java, if two instances of Random are created with the same seed, and the same sequence of method calls is made for each, they will generate and return identical sequences of numbers [37]. This is helpful in debugging and reproducing results across platforms [36].
A basic sampling is a procedure that originates independent sampled values of random variables each time it is called. In subsection 3.2.1, it is explained how short-circuit events are sampled within
1Serializing is the process of translating data structures or object state into a format that can be stored [35].