CEATI - MANAGING ELECTRICAL POWER QUALITY CHALLENGES

The existence of modern society and its efficient functioning are more than anything else dependent on one single product - electricity. All electricity users - industry, commercial organizations, telecommunications, hospitals, educational institutions, and millions of private citizens - fully expect that electric power will always be available at a simple flick of a switch, in whatever quantity is required, and with the all the quality attributes that are required for safe, efficient and continuous operation of the devices it powers. In our society, electricity is a product where availability and quality is taken for granted. Yet in contrast to other products, electricity cannot be effectively stockpiled and carefully inspected for quality before it is delivered. Electrical supply must continuously match load demand every second of the day, each and every day, month and year, making it difficult to control and maintain power quality. Slight disturbances such as momentary voltage sags and spikes, power harmonics and voltage unbalances are intrinsic characteristics of electricity that directly impact the efficiency and performance of the electric equipment. Very often these problems will go undetected until after more serious disturbances occur interrupting the manufacturing process, damaging equipment or spoiling products. Unless the sources of these power quality disturbances are quickly identified and the underlying causes diagnosed and corrected, the cost to the user can be very high. As electricity permeates virtually every aspect of contemporary society, poor power quality will affect a large number of users. A number of studies have estimated the annual cost of power quality problems to the American economy at 12 billion dollars annually.

Determining the sources of poor power quality can prove to be a complex task. There are hundreds of possible factors. Some disturbances may originate within the electricity supply network while others may be located within the users' systems. In addition, many of the sources of power quality disturbances are interactive, making it difficult to accurately trace them and to diagnose the root cause of the problem.

Power quality also involves a large number of stakeholders, from electrical utilities, electrical equipment manufacturers and suppliers, regulators, consultants, educational institutions, right to the multitude of electricity users. To properly resolve power quality issues, it is important that the stakeholders not only have a common understanding of those issues, but also work in coordinated and cooperative ways to find solutions.

To remain competitive in today's global market, developed nations must expand the "knowledge economy" which is based on skills, cutting-edge technologies and high productivity. Such efforts cannot be achieved without an affordable, reliable and high quality electrical power base. It has long been recognized that power quality will continue to play an increasingly important role in defining the competitive capability of national economies and infrastructure systems. The increasing role of power quality will be further accelerated by the proliferation of non-linear loads - such as switched power supplies which are found in most of today's electronic equipment. Also to be considered is an increasing penetration of small distributed generators with electronic interfaces between the device and the power system, such as photovoltaic cells, fuel cells, wind turbine generators, etc. Additionally, the commercial aspects of open electricity markets are increasingly stretching power systems' operation closer to their technical limits and narrowing the operational safety margins needed to cope with larger power quality disturbances. Real or perceived decrease of power quality levels will also influence public opinion and, indirectly, government regulators who in turn will develop and assert the policy framework in which the electricity industry will be regulated.

To deal with power quality concerns, many leading utilities around the world are examining the economic impacts of the problem and revising their planning and operation practices. Many are also heavily involved in the establishment of equipment protection standards and regulatory guidelines, in the ultimate goal of minimizing the combined cost of supply and use of electricity by achieving a high degree of electromagnetic compatibility between the electrical service providers and the electricity end users.

To facilitate and coordinate these efforts, CEA Technologies Inc. (CEATI) has organized a Power Quality Interest Group, composed of electric utilities that pool their financial resources to sponsor power quality technology developments.

The Power Quality interest group is currently financing several key projects:
• Power Quality impact assessment of distributed wind generation
• Techniques for locating voltage sag disturbances
• Utility incentives and penalties for power quality under performance based Government regulation
• Assessing power quality disturbances using power quality monitoring features of distribution network equipment

Power Quality Impact Assessment of Distributed Wind Generation
With wind generation receiving increasing political and environmental attention, it is expected that the number and capacity of wind generation installations will grow substantially across North America. Many of these installations will be significant in size and will be connected directly to the distribution system. In these distributed applications it is quite common for turbines to be connected to rural distribution feeders that also serve load customers, and that may exhibit significant differences between the maximum and minimum loads. In such cases, turbines may noticeably influence the distribution feeder voltage, both in magnitude and in waveform shape, for either the benefit or detriment of the customers served by the same feeder. The impact on voltage regulation, voltage flicker, and voltage unbalance is one of the most common limiting factors for distributed generation and especially distributed wind turbine generators. Under some circumstances there may also be a possibility of formation of isolated electrical islands, where the local feeder load would be supplied by the local distributed generators, but disconnected from the grid and its voltage and frequency-regulating influence. In such cases there is a danger of damage to the end user equipment due to possible overvoltages and frequency variations.
The above issues can be addressed quantitatively by using advanced simulation tools. Detailed computer simulation of representative commercial wind turbine technologies on typical distribution feeders would provide insight into the impact wind generation would have on rural distribution systems. Time- and frequency-domain system models could be used to quantitatively characterize wind turbine impacts on system voltage, with parametric evaluation of various feeder characteristics, wind regimes, and turbine technologies.

Because of the growing interest and penetration of wind generation, the CEATI’s Power Quality Interest Group has initiated research that would identify the potential problems associated with wind generation and allow utilities to model and assess the potential impact of wind turbine generators on feeder voltage regulation, reliably predicting voltage flicker problems, voltage unbalance and harmonic emissions to ensure sustainment of high quality electrical supply to their customers.

The model will also allow sensitivity analysis of system impact on various types of wind turbine generators to ensure acceptable and reliable connections for the generators.
Techniques for Locating Sources of Voltage Sag Disturbances Utility operating experience indicates that momentary voltage sags are one of the most disruptive short duration power quality disturbances on customer operations. A significant amount of work has been done in developing protocols for measuring and indexing power quality disturbances, including voltage sags.

However, relatively little work has been reported on the development of techniques for reliably identifying and locating the origins of voltage sags. In order to maintain an appropriate level of electrical service quality, utilities are increasingly interested in quantifying the individual contributions to the "aggregate" power quality problems and determining the level of responsibilities for such problems. In this context, the ability to locate the sources of voltage sags has become very important.

The existing technical literature describes several voltage sag source locating techniques. However, these have not been sufficiently tested and evaluated in the field to determine their respective advantages, disadvantages and limitations, and above all, their dependability in accurately locating the origins of voltage sags. For this reason CEATI’s Power Quality Interest Group has initiated a project, aimed at evaluating various voltage sag source locating techniques and developing a practical, step-by-step implementation guide which will provide sound technical measurement tools and a methodology that could be readily used by utility staff to quickly identify and locate sources of voltage sags on theirs systems.

Utility Incentives and Penalties for Power Quality under Performance-based Government Regulation
In a regulated environment, the goal of public utilities is to provide safe, reliable, and least-cost service to consumers. To achieve this goal, regulatory commissions have traditionally relied on a cost-of-service/rate-of-return basis to determine appropriate utility rates thus permitting utilities to recover reasonable operating expenses and to earn a fair return on investment. In the deregulated market, however, utilities no longer have incentives to provide additional power quality or reliability service improvements. To remedy the situation there has been in recent years a considerable interest from utility regulators to entertain the well-known theory of performance-based rates. The expectation is that price-based incentive mechanisms will allow utilities to proactively invest in reliability and quality improvement initiatives. In several countries the price and penalty-based incentives for reliability improvement are already in effect, with regulators now looking more closely at measures for power quality improvement incentives as well. To prepare the participating utilities for the upcoming regulatory environment, CEATI's Power Quality Interest Group has initiated a study that would acquaint them with various power quality and reliability metrics and methodologies used in price-based incentive schemes. The main objective of this project is to provide sponsors with a detailed overview of how power quality and reliability performance-based rates are being implemented in other parts of the world. The final report will describe several options for measuring and predicting the value of power quality investments. It will also outline a framework for responding to price-based incentive mechanisms and creating the appropriate power quality and reliability metrics.

Based on an extensive analysis of the existing and proposed schemes that are currently being implemented in different parts of the world, the project will also outline the future role for utility power quality engineers.

Assessing Power Quality Disturbances using Power Quality Monitoring features of Distribution Network Equipment
Power quality disturbances are a real concern for both utilities and consumers. Detecting, recording and processing power quality data is crucial for monitoring network performance, and identifying and resolving power quality problems. In the past, such effort required installation of dedicated power quality monitors and communication channels for downloading the collected data for further analysis and archiving. Today's monitoring systems involve distribution network equipment already in place such as reclosers, voltage regulators and revenue meters, equipped with controls featuring a PQ option allowing for the recording and analysis of voltage and current signals to detect disturbances and to perform the statistical analysis of measurements. This approach to power quality monitoring will be much more cost-effective and allow for greater coverage of the distribution network. On the other hand, such a monitoring network will generate huge volumes of data, often in different formats, that will have to be processed, archived and displayed in order to provide useful information to the end users.

The CEATI Power Quality Interest Group has initiated a study that will provide utilities with a list of distribution equipment suitable for power quality monitoring, including a description of the methods used for assessing power quality disturbances. The report will include recommended monitoring equipment configuration suitable for recording and processing power quality information, including planning and operating requirements, and the methods for assessing and displaying the network power quality performance.

Joining Together To Fund Power Quality Research
The Power Quality Interest Group (PQIG) was established as one of the many "interest groups" of CEA Technologies Inc. (CEATI). The PQIG participants jointly sponsor studies and research projects in the area of power quality that will benefit them, the electrical utility industry and customers at large.

Participation in the group is open to all electrical utilities, power producers and government organizations that have interest in power quality related issues. The group identifies areas of common concern or specific problems, defines research objectives to solve those concerns. The individual group participants can then select to co-fund the projects of interest or benefit to their organizations. This flexible and collaborative approach provides substantial cost-benefit advantage to the participants. The products of the research are made available to the sponsors of the projects.

About the Author
Mr. Jerry Lepka heads CEA Technologies' Power Quality Interest Group. Mr. Lepka, a graduate from the University of Manitoba, has worked both abroad and in Canada managing complex technical operations and implementing new technologies. His most recent project was with the Gestore Rete Transmissione Nazionale in Italy, where he was a member of the Advisory Committee analyzing the causes of the September Italian system blackout and recommending preventive measures. At Ontario Power Generation, Jerry was involved in development of the performance-based Protection and Control Technical Training Program as well as Maintenance Strategies for their high voltage equipment. He also led Ontario Hydro's province-wide power quality monitoring program aimed at reducing system disturbances and their impact on electrical supply to major customers. For more information please visit www.ceatech.ca.

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• M.P.Donsión, & J.M. Rodríguez, Department of Electrical Engineering, University of Vigo, Campus of Lagoas Marcosende, Vigo (Spain), :
• J.A. Güemes2, Department of Electrical Engineering, University of Basque Country (Spain)

Abstract. Flexible AC transmission systems or FACTS are devices which allow the flexible and dynamic control of power systems. This paper is aimed toward the benefits of utilizing FACTS devices with the purpose of improving the operation of an electrical power system.

Introduction

Power quality is an issue that is becoming increasingly important to electricity consumers at all levels of usage. Sensitive equipment and non-linear loads are commonplace in both the industrial and the domestic environment, because of this a hightened awareness of power quality is developing. The sources of problems that can disturb the power quality are: power electronic devices, arcing devices, load switching, large motor starting, embedded generation, sensitive equipment, storm and environment related damage, network equipment and design.

The solution to improve the energy quality (PQ-Power Quality) at the load side is of great important when the production processes get more complicated and require a bigger liability level, which includes aims like to provide energy without interruption, without harmonic distortion and with tension regulation between very narrow margins. The devices that can fulfil these requirements are the Custom Power; a concept that we could include among the FACTS, but that is different to them because of their final use. In fact the topologies that they employ are identical to the ones in the FACTS devices with little modifications and adaptations to tension levels, therefore they are most oriented to be used in distribution networks of low and medium tension, sometimes replacing the active filters.

Recent developments in electrical power systems such as deregulation, open access, and cogeneration are creating scenarios of transmission congestion and forced outages. Addition of new transmission lines is an almost impossible solution due to environmental and other considerations, and developing new approaches to Power System Operation and Control is the need of the hour for overload relief and efficient and reliable operation. Flexible AC Transmission Systems (FACTS), with the underlying concept of independent control of active and reactive power flows, offer an attractive alternative for achieving the objectives.

The use of static power converters in electricity networks has the potential of increasing the capacity of transmission of the electric lines and improving the supply quality of the electric energy. The devices used to achieve this, are the FACTS (Flexible Alternating Current Transmission Systems). The FACTS technology has a collection of controllers, that can be used individually or co-ordinated with other controls installed in the network, thus permitting to profit better of the network’s characteristics of control.

The FACTS controllers offer a great opportunity to regulate the transmission of alternating current (AC), increasing or diminishing the power flow in specific lines and responding almost instantaneously to the stability problems. The potential of this technology is based on the possibility of controlling the route of the power flow and the ability of connecting networks that are not adequately interconnected, giving the possibility of trading energy between distant agents.

Flexible Alternating Current Transmission System (FACTS) is a static equipment used for the AC transmission of electrical energy. It is meant to enhance controllability and increase power transfer capability. It is generally a power electronics based device.

FACTS is defined by the IEEE as “a power electronic based system and other static equipment that provide control of one or more AC transmission system and increase the capacity of power transfer.”

The FACTS devices can be divided in three groups, dependent on their switching technology: mechanically switched (such as phase shifting transformers), thyristor switched or fast switched, using IGBTs [4]. While some types of FACTS, such as the phase shifting transformer (PST) and the static var compensator (SVC) are already well known and used in power systems, new developments in power electronics and control have extended the application range of FACTS. Furthermore, intermittent renewable energy sources and increasing international power flows provide new applications for FACTS. The additional flexibility and controllability of FACTS allow to mitigate the problems associated with the unreliable of supply issues of renewable. SVCs and STATCOM devices are well suited to provide ancillary services (such as voltage control) to the grid and fault ride through capabilities which standard wind farms cannot provide ¡Error! No se encuentra el origen de la referencia.. Furthermore, FACTS reduce oscillations in the grid, which is especially interesting when dealing with the stochastic behavior of renewable.

In a liberalized market, the added value of FACTS, and especially power flow controlling devices, is the ability to control flow paths and therefore the ability to resolve congestions and optimally utilizing available grid infrastructure ¡Error! No se encuentra el origen de la referencia., ¡Error! No se encuentra el origen de la referencia.. Although FACTS devices are currently quite expensive, it is expected that with a growing utilization and experience, prices will drop considerably.

Benefits of utilizing FACTS devices

The benefits of utilizing FACTS devices in electrical transmission systems can be summarized as follows [1]:

• Better utilization of existing transmission system assets
• Increased transmission system reliability and availability
• Increased dynamic and transient grid stability and reduction of loop flows
• Increased quality of supply for sensitive industries
• Environmental benefits Better utilization of existing transmission system assets

In many countries, increasing the energy transfer capacity and controlling the load flow of transmission lines are of vital importance, especially in de-regulated markets, where the locations of generation and the bulk load centers can change rapidly. Frequently, adding new transmission lines to meet increasing electricity demand is limited by economical and environmental constraints. FACTS devices help to meet these requirements with the existing transmission systems.

Classification

There are different classifications for the FACTS devices:

Depending on the type of connection to the network FACTS devices can differentiate four categories

• serial controllers
• derivation controllers
• serial to serial controllers
• serial-derivation controllers

Depending on technological features, the FACTS devices can divided into two generations

• first generation: used thyristors with ignition controlled by gate(SCR).
• second generation: semiconductors with ignition and extinction controlled by gate (GTO´s , MCTS , IGBTS , IGCTS , etc).

These two classifications are independent, existing for example, devices of a group of the first classification that can belong to various groups of the second classification.

The main difference between first and second generation devices is the capacity to generate reactive power and to interchange active power.

The first generation FACTS devices work like passive elements using impedance or tap changer transformers controlled by thyristors. The second generation FACTS devices work like angle and module controlled voltage sources and without inertia, based in converters, employing electronic tension sources(three-phase inverters, auto-switched voltage sources, synchronous voltage sources, voltage source control) fast proportioned and controllable and static synchronous voltage and current sources.

Table 1. Two generations of the FACTS devices [2]

First Generation

Second Generation

FACTS in Electrical Power Systems

The concept of FACTS devices was presented in , but the practical implementation and development of new analytical procedures are still in evolution. One of the objectives of the paper is to present the state-of-the-art technology and analysis of FACTS devices. Since the field demonstration of the world’s first UPFC in , another FACTS controller, namely Sent Transformer (ST), has been proposed. In contrast to the UPFC, which uses a large number of solid-state switching devices, the ST uses time-tested components, such as transformer and load tap changers, but provides the same independent active and reactive power flow control as the UPFC at a much lower cost.

The FACTS devices are installed on electric power (high voltage AC) transmission lines to stabilize and regulate power flow for the dynamic control of voltage impedance and phase angle. Power lines protected by FACTS devices can support greater current because anomalies—frequency excursions, voltage drop, phase mismatch, malformed wave shape, power spikes, etc.—that would otherwise cause breakers to trip are removed or greatly reduced by FACTS conditioning.

A FACTS device can also limit the amount of current that flows on a line by effectively increasing the line’s impedance. This enables a much greater degree of flow control than provided by a switch or breaker. In particular, when current applied to a FACTS-protected line is greater than the device will allow, the power merely flows elsewhere rather than tripping a breaker, and power continues to flow on the protected line.

Essentially, lines can be run closer to their theoretical capacities when they are protected by FACTS devices. For a large line, that can mean substantial additional power. High voltage, high-power FACTS devices are building-sized and expensive, but they are lower cost and have less impact per added unit of electric power than new transmission lines. This is the essential benefit of operating standalone FACTS devices on individual lines.

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FACTS devices offer an additional benefit: consider an interconnected network where two identical lines are carrying power, one at 50% of its capacity (for this example assume that capacity refers to the line’s operational limit under local conditions), the other at 99%. Assume that any additional load will be supplied equally through the two lines and that there is sufficient generating capacity to support the additional load being considered. Under these conditions additional load can be supplied only up to the limit of either line, and since one is at 99%, the system can support only about twice the remaining 1% (half of the additional power would go to each line). Additional power would cause the 99% line’s protective breakers to trip, at which point all power would attempt to pass through the remaining line, which would then also trip; the generators, being disconnected from their loads, would shut down, and the system would go dark.

However, if the line at 99% were held there by a FACTS device, any added power would go through the 50% line while power continued to flow in the 99% line at its original level. The capacity of this network considered as a whole would be increased by 25%, over and above the stabilizing and regulating benefits provided by the FACTS device. Note that this benefit cannot be recognized by analyzing just the FACTS device and its assigned branch, but only by considering the entire network. For a system that often operates in this sort of unbalanced state, FACTS devices can provide substantial additional capacity simply by forcing more of the network to carry the level of power it was designed to carry.

This idea leads to a new mode of operation: FACTS Devices can also direct power to less utilized parts of the transmission network, effectively increasing the capacity of the network, in addition to their customary standalone roles. Because optimum flow for the network as a whole cannot be achieved by considering only single branches, FACTS devices can perform this function only in cooperation with one another, so in this report such devices are referred to as Cooperating FACTS devices, or CFDs.

In practice, however, the additional communication required of CFDs opens the potential for subverting the operation of a cooperative system. This report considers both the operational and security aspects of CFDs operating in an electric power system network.

Installing FACTS devices factors

There are three factors to be considered before installing a FACTS devices:

1. The type of device
2. The capacity required
3. The location that optimize the functioning ofthe device

Of these three factors, the last one is of great importance, because the desired effect and the proper features of the system depend of the location of FACTS.

Steps for the identification of FACTS Projects:

1. The first step should always be to conduct a detailed network study to investigate the critical conditions of a grid or grids’ connections. These conditions could include: risks of voltage problems or even voltage collapse, undesired power flows, as well as the potential for power swings or subsynchronous resonances;
2. For a stable grid, the optimized utilization of the transmission lines– e.g. increasing the energy transfer capability – could be investigated;
3. If there is a potential for improving the transmission system, either through enhanced stability or energy transfer capability, the appropriate FACTS device and its required rating can be determined;
4. Based on this technical information, an economical study can be performed to compare costs of FACTS devices or conventional solutions with the achievable benefits.

Types of network connection

1.Serial controllers Can consist of a variable impedance as a condenser, coil, etc or a variable electronics based source at a fundamental frequency. The principle of operation of all serial controllers is to inject a serial tension to the line. A variable impedance multiplied by the current that flows through it represents the serial tension. While the tension is in quadrature with the line current the serial controller only consumes reactive power; any other phase angle represents management of active power. A typical controller is Serial Synchronous Static Compensator (SSSC).

2.Controllers in derivation. As it happens with the serial controller, the controller in derivation can consist of a variable impedance, variable source or a combination of both. The operation principle of all controllers in derivation is to inject current to the system in the point of connection. Available impedance connected to the line tension causes variable current flow, representing an injection of current to the line. While the injected current is in quadrature with the line tension, the controller in derivation only consumes reactive power; any other phase angle represents management of active power. A typical controller is Synchronous Static Compensator (STATCOM).

3.Serial-serial Controllers. This type of controllers can be a combination of coordinated serial controllers in a multiline transmission system. Or can also be an unified controller in which the serial controllers provide serial reactive compensation for each line also transferring active power between lines through the link of power. The active power transmission capacity that present a unified serial. controller or line feed power controller (also called BtB), makes possible the active and reactive power flow balance and makes the use of transmission bigger. In this case the term “unified” means that the DC terminals of the converters of all the controllers are connected to achieve a transfer of active power between each other. A typical controller is the Interline Power Flow Compensator (IPFC).

4.Serial-derivation Controllers. This device can be a combination of serial and derivations controllers separated, coordinately controlled or a unified power flow controller with serial and derivation elements. The principle of operation of the serial-derivation controllers is to inject current to the system through the component in derivation of the controller, and serial tension with the line utilizing the serial component. When the serial and derivation controllers are unified, they can have an exchange of active power between them through their link. A typical controller is Unified Power Flow Controller (UPFC), witch incorporating function of a filtering and conditioning, becomes a Universal Power Line Conditioner (UPLC).

Applications and technical benefits of FACTS

Table 2 describe the technical benefits of the principal FACTS devices. For each problem the conventional solution (e.g. shunt reactor or shunt capacitor) also can be used. For dynamic applications of FACTS in addressing problems in transient stability, dampening, post contingency voltage control and voltage stability. FACTS devices are required when there is a need to respond to dynamic (fast-changing) network conditions. The conventional solutions are normally less expensive than FACTS devices – but limited in their dynamic behavior. It is the task of the planners to identify the most economic solution.

Table2. Technical benefits of the main FACTS devices

The Unified Power Flow Controller (UPFC)

The UPFC may be seen to consist of two VSCs sharing a common capacitor on their DC side and a unified control system.

On Figure 1 we can see two back-to-back voltage source converters (VSCs), with one VSC connected to the AC network using a shunt transformer and the second connected to the AC network using a series transformer.

While operating both inverters as a UPFC, the exchanged power at the terminals of each inverter can be imaginary as well as real.

The mathematical UPFC model has been derived with the aim of being able to study the relations between the electrical transmission system and UPFC in steady and transient conditions.

The active power demanded by the series converter is drawn by the shunt converter from the AC network and supplied to bus m through the DC link. The output voltage of the series converter is added to the nodal voltage, at say bus k, to boost the nodal voltage at bus m. The voltage magnitude of the output voltage VcR provides voltage regulation, and the phase angle δcR determine the mode of power flow control.

In addition to providing a supporting role in the active power exchange that takes place between the series converter and the AC system, the shunt converter may also generate or absorb reactive power in order to provide independent voltage magnitude regulation at its point of connection with the AC system.

The UPFC equivalent circuit shown in Figure 3 consists of a shunt-connected voltage source, a series-connected voltage source, and an active power constraint equation, which links the two voltage sources. The two voltage sources are connected to the AC system through inductive reactances representing the VSC transformers. In a three-phase UPFC, suitable expressions for the two voltage sources and constraint equation would be:

Where ρ indicates phase quantities, a, b, and c.

Based on the equivalent circuit shown in the Figure 2, and assuming three-phase parameters, the following transfer admittance equation can be written:

Conclusion

Flexible Alternating-Current Transmission Systems (FACTS) is a recent technological development in electrical power systems. It builds on the great many advances achieved in high-current, high-power semiconductor device technology, digital control and signals gained with the commissioning and operation of high-voltage direct-current (HVDC) links and static VAR compensator (SVC) systems, over many decades, may have provided the driving force for searching deeper into the use of emerging power electronic equipment and techniques [5]. Due to the, every time higher requirements of the liability and quality of the electricity the implantation of devices capable of guaranteeing these requirements will keep increasing.

FACTS devices are improving the operation of an electric power system. The influences of such devices on steady state variables (voltage levels, transmission losses, and generating costs) are very remarkable. The benefit for each type of FACTS can be associated with its particularities and properties. They control the interrelated parameters that rule the operation of the transmission systems, including the serial impedance, the derivation impedance, the current, the voltage, the phase angle and the muffling of oscillations to different frequencies under the nominal frequency.

References

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