<a href='https://top10electrical.blogspot.com/' itemprop='url' title='ENGINEERING ARTICLES'> ENGINEERING ARTICLES

A metal oxide varistor (MOV) is built from zinc oxide disks in series and parallel arrangement to achieve the required protective level and energy requirement. One to four columns of zinc oxide disks are installed in each sealed porcelain container, similar to a high-voltage surge arrester. A typical MOV protection system contains several porcelain containers, all connected in parallel. The number of parallel zinc oxide disk columns required depends on the amount of energy to be discharged through the MOV during the worst-case design scenario. Typical MOV protection system specifications are as follows.

The MOV protection system for the series capacitor bank is usually rated to withstand energy discharged for all faults in the system external to the line section in which the series capacitor bank is located. Faults include single-phase, phase-to-phase, and three-phase faults. The user should also specify the fault duration. Most of the faults in EHV systems will be cleared by the primary protection system in three to four cycles. Backup fault clearing can be from 12 to 16 cycles duration. The user should specify whether the MOV should be designed to withstand energy for backup fault clearing times. Sometimes it is specified that the MOV be rated for all faults with primary protection clearing time, but for only single-phase faults for backup fault clearing time. Statistically, most of the faults are single-phase faults.

The energy discharged through the MOV is continuously monitored and if it exceeds the rated value, the MOV will be protected by the firing of a triggered air gap, which will bypass the MOV.

SHUNT REACTIVE POWER COMPENSATION

Since most loads are inductive and consume lagging reactive power, the compensation required is usually supplied by leading reactive power. Shunt compensation of reactive power can be employed either at load level, substation level, or at transmission level. It can be capacitive (leading) or inductive (lagging) reactive power, although in most cases as explained before, compensation is capacitive. The most common form of leading reactive power compensation is by connecting shunt capacitors to the line.

SHUNT CAPACITORS:

Shunt capacitors are employed at substation level for the following reasons:

1. VOLTAGE REGULATION: The main reason that shunt capacitors are installed at substations is to control the voltage within required levels. Load varies over the day, with very low load from midnight to early morning and peak values occurring in the evening between 4 and 7 pm. Shape of the load curve also varies from weekday to weekend, with weekend load typically low. As the load varies, voltage at the substation bus and at the load bus varies. Since the load power factor is always lagging, a shunt-connected capacitor bank at the substation can raise voltage when the load is high.

The shunt capacitor banks can be permanently connected to the bus (fixed capacitor bank) or can be switched as needed. Switching can be based on time, if load variation is predictable, or can be based on voltage, power factor, or line current.

2. REDUCING POWER LOSSES: Compensating the load lagging power factor with the bus-connected shunt capacitor bank improves the power factor and reduces current flow through the transmission lines, transformers, generators, etc. This will reduce power losses (I2R losses) in this equipment.

3. INCREASED UTILIZATION OF EQUIPMENT: Shunt compensation with capacitor banks reduces kVA loading of lines, transformers, and generators, which means with compensation they can be used for delivering more power without overloading the equipment.

Reactive power compensation in a power system is of two types, shunt and series. Shunt compensation can be installed near the load, in a distribution substation, along the distribution feeder, or in a transmission substation. Each application has different purposes. Shunt reactive compensation can be inductive or capacitive. At load level, at the distribution substation, and along the distribution feeder, compensation is usually capacitive. In a transmission substation, both inductive and capacitive reactive compensations are installed.

NEED FOR REACTIVE POWER COMPENSATION

Except in a very few special situations, electrical energy is generated, transmitted, distributed, and utilized as alternating current (AC). However, AC has several distinct disadvantages. One of these is the necessity of reactive power that needs to be supplied along with active power. Reactive power can be leading or lagging. While it is the active power that contributes to the energy consumed, or transmitted, reactive power does not contribute to the energy. Reactive power is an inherent part of the “total power.”

Reactive power is either generated or consumed in almost every component of the system, generation, transmission, and distribution and eventually by the loads. The impedance of a branch of a circuit in an AC system consists of two components, resistance and reactance. Reactance can be either inductive or capacitive, which contributes to reactive power in the circuit. Most of the loads are inductive, and must be supplied with lagging reactive power. It is economical to supply this reactive power closer to the load in the distribution system.

TECHNICAL COMPLEXITIES AND RISKS OF GRID INTERCONNECTIONS

The fact that interconnections between power systems are increasingly common does not imply that they are as simple as connecting a few wires. Interconnections obviously entail the expense of constructing and operating transmission lines and substations, or in the case of HVDC, converter stations. Interconnections also entail other costs, technical complexities, and risks. For AC interconnections especially, a power system interconnection is a kind of marriage, because two systems become one in an important way when they operate in synchronism. To do this requires a high degree of technical compatibility and operational coordination, which grows in cost and complexity with the scale and inherent differences of the systems involved. To give just one example, when systems are interconnected, even if they are otherwise fully compatible, fault currents (the current that flows during a short circuit) generally increase, requiring the installation of higher capacity circuit breakers to maintain safety and reliability. To properly specify these and many other technical changes required by interconnection requires extensive planning studies, computer modeling, and exchange of data between the interconnected systems.

The difficulties of joint planning and operation of interconnected systems vary widely. As with marriages, from the institutional and administrative standpoint, coupled systems may become a single entity, or they may keep entirely separate accounts. Within the North American interconnections, for example, there are hundreds of electric utility companies that are entirely separate commercial entities. Customers receive power from, and pay bills to, the utility that serves their area, for example Consolidated Edison.

They may do so without even knowing of the existence of the Eastern interconnection. Yet all the utilities in the Eastern interconnection are in a technical marriage that dictates or constrains key aspects of their technology choices and operating procedures.

Within countries, there are typically common technical standards for all utilities, which reduce the complexity of interconnecting separate systems. In different countries, on the other hand, power systems may have evolved quite separately, with very different standards and technologies, which adds an extra layer of technical complexity to interconnections. Institutional and administrative features of power systems in different countries are also likely to differ in many ways, and these differences invariably affect the technical and operational dimensions of an interconnection. Issues ranging from power trading agreements to reliability standards, while expressed in technical terms, often must be resolved within the realm of policy and political economy. As one expert on international interconnections has remarked “many technical, organizational, commercial and political problems have had to be solved to get large networks linked by international interconnections to operate”.

The greatest benefits of interconnection are usually derived from synchronous AC operation, but this can also entail greater reliability risks. In any synchronous network, disturbances in one location are quickly felt in other locations. After interconnecting, a system that used to be isolated from disturbances in a neighboring system is now vulnerable to those disturbances. As major blackouts in North America and Europe in 2003 demonstrated, large-scale disturbances can propagate through interconnections and result in cascading outages, bringing down systems that had previously been functioning normally. In addition, long-distance interconnections with long transmission lines have potentially greater stability problems than is the case for shorter lines. Finally, many systems that have undergone electricity liberalization in recent years have experienced large increases in transmission capacity utilization, reducing reserve margins. Minimizing the likelihood that an interconnection will lead to such problems as voltage collapse, dynamic and transient instability, or cascading outages due to propagated disturbances requires careful planning and well-coordinated operation.

GENERAL POTENTIAL BENEFITS OF GRID INTERCONNECTIONS

There are number of technical rationales for grid interconnections, many of which have economic components as well. Technical rationales for grid interconnection include:

• Improving reliability and pooling reserves: The amount of reserve capacity that must be built by individual networks to ensure reliable operation when supplies are short can be reduced by sharing reserves within an interconnected network.

• Reduced investment in generating capacity: Individual systems can reduce their generating capacity requirement, or postpone the need to add new capacity, if they are able to share the generating resources of an interconnected system.

• Improving load factor and increasing load diversity: Systems operate most economically when the level of power demand is steady over time, as opposed to having high peaks. Poor load factors (the ratio of average to peak power demand) mean that utilities must construct generation capacity to meet peak requirements, but that this capacity sits idle much of the time. Systems can improve poor load factors by interconnecting to other systems with different types of loads, or loads with different daily or seasonal patterns that complement their own.

• Economies of scale in new construction: Unit costs of new generation and transmission capacity generally decline with increasing scale, up to a point. Sharing resources in an interconnected system can allow the construction of larger facilities with lower unit costs.

• Diversity of generation mix and supply security: Interconnections between systems that use different technologies and/or fuels to generate electricity provide greater security in the event that one kind of generation becomes limited (e.g., hydroelectricity in a year with little rainfall). Historically, this complementary has been a strong incentive for interconnection between hydro-dominated systems and thermal-dominated systems. A larger and more diverse generation mix also implies more diversity in the types of forced outages that occur, improving reliability.

• Economic exchange: Interconnection allows the dispatch of the least costly generating units within the interconnected area, providing an overall cost savings that can be divided among the component systems. Alternatively, it allows inexpensive power from one system to be sold to systems with more expensive power.

• Environmental dispatch and new plant sitting: Interconnections can allow generating units with lower environmental impacts to be used more, and units with higher impacts to be used less. In areas where environmental and land use constraints limit the sitting of power plants, interconnections can allow new plant construction in less sensitive areas.

• Coordination of maintenance schedules: Interconnections permit planned outages of generating and transmission facilities for maintenance to be coordinated so that overall cost and reliability for the interconnected network is optimized.

Some costs and benefits of interconnections are difficult to quantify, but as a rough figure of merit it has been estimated that interconnections in North America have resulted in an overall annual cost savings of $20 billion in the 1990s, and that the Western European interconnection has resulted in reduced capacity requirements of 7-10 percent.

REACTIVE POWER AND ITS SOURCES

REACTIVE POWER:

Reactive power is a concept used by engineers to describe the background energy movement in an Alternating Current (AC) system arising from the production of electric and magnetic fields. These fields store energy which changes through each AC cycle. Devices which store energy by virtue of a magnetic field produced by a flow of current are said to absorb reactive power; those which store energy by virtue of electric fields are said to generate reactive power.

Power flows, both actual and potential, must be carefully controlled for a power system to operate within acceptable voltage limits. Reactive power flows can give rise to substantial voltage changes across the system, which means that it is necessary to maintain reactive power balances between sources of generation and points of demand on a 'zonal basis'. Unlike system frequency, which is consistent throughout an interconnected system, voltages experienced at points across the system form a "voltage profile" which is uniquely related to local generation and demand at that instant, and is also affected by the prevailing system network arrangements. National Grid is obliged to secure the transmission network to closely defined voltage and stability criteria. This is predominantly achieved through circuit arrangements, transformers and shunt or static compensation.

SOURCES OF REACTIVE POWER:

Most equipment connected to the electricity system will generate or absorb reactive power, but not all can be used economically to control voltage. Principally synchronous generators and specialised compensation equipment are used to set the voltage at particular points in the system, which elsewhere is determined by the reactive power flows.

1) SYNCHRONOUS GENERATORS:

Synchronous machines can be made to generate or absorb reactive power depending upon the excitation (a form of generator control) applied. The output of synchronous machines is continuously variable over the operating range and automatic voltage regulators can be used to control the output so as to maintain a constant system voltage.

2) SYNCHRONOUS COMPENSATORS:

Certain smaller generators, once run up to speed and synchronised to the system, can be declutched from their turbine and provide reactive power without producing real power. This mode of operation is called Synchronous Compensation.

3) CAPACITIVE AND INDUCTIVE COMPENSATORS:

These are devices that can be connected to the system to adjust voltage levels. A capacitive compensator produces an electric field thereby generating reactive power whilst an inductive compensator produces a magnetic field to absorb reactive power. Compensation devices are available as either capacitive or inductive alone or as a hybrid to provide both generation and absorption of reactive power.

4) OVERHEAD LINES AND UNDERGROUND CABLES:

Overhead lines and underground cables, when operating at the normal system voltage, both produce strong electric fields and so generate reactive power. When current flows through a line or cable it produces a magnetic field which absorbs reactive power. A lightly loaded overhead line is a net generator of reactive power whilst a heavily loaded line is a net absorber of reactive power. In the case of cables designed for use at 275 or 400kV the reactive power generated by the electric field is always greater than the reactive power absorbed by the magnetic field and so cables are always net generators of reactive power.

5) TRANSFORMERS:

Transformers produce magnetic fields and therefore absorb reactive power. The heavier the current loading the higher the absorption.

6) CONSUMER LOADS:

Some loads such as motors produce a magnetic field and therefore absorb reactive power but other customer loads, such as fluorescent lighting, generate reactive power. In addition reactive power may be generated or absorbed by the lines and cables of distribution systems.

BEHAVIOUR OF SHUNT REACTOR DURING EXTERNAL AND INTERNAL FAULTS

Shunt reactors are connected in parallel with the rest of the power network. Shunt reactor can be treated as a device with the fixed impedance value. Therefore the individual phase current is directly proportional to the applied phase voltage (i.e. I=U/Z).

Thus during external fault condition, when the faulty phase voltage is lower than the rated voltage , the current in the faulty phase will actually reduce its value from the rated value.

Depending on the point on the voltage wave when external fault happens the reduce current might have superimposed dc component. Such behavior is verified by an ATP simulation and it is shown in Figure 17.

Figure 17: External Phase A to Ground Fault, Reactor Phase Currents

As a result, shunt reactor unbalance current will appear in the neutral point as shown in Figure 18. However, this neutral point current will typically be less than 1 pu irrespective of the location and fault resistance of the external fault.

Figure 18: External Phase A to Ground Fault, Reactor Zero-sequence Currents

Similarly during an internal fault the value of the individual phase currents and neutral point current will depend very much on the position of the internal fault. Assuming that due to the construction details, internal shunt reactor phase-to-phase faults are not very likely, only two extreme cases of internal phase to ground fault scenarios will be presented here.

In the first case the Phase A winding to ground fault, 1% from the neutral point has been simulated in ATP. As a result the phase currents on the HV side (i.e. in reactor bushings) will be practically the same as before the fault as shown in Figure 19.

Figure 19: Internal Phase A Winding to Ground Fault, Phase Currents

However phase A current at the shunt reactor star point and common neutral point current will have very big value due to so-called transformer effect. These currents can be so high to even cause CT saturation as shown in Figure 20 for the common neutral point current.

Figure 20: Internal Phase A Winding to Ground Fault, Zero-sequence Currents

This type of the internal fault shall be easily detected and cleared by the differential, restricted ground fault or neutral point ground overcurrent protection, but not by reactor HV side overcurrent or HV residual ground fault protections.

In the second case the Phase A to ground fault, just between the HV CTs and shunt reactor winding (i.e. shunt reactor bushing failure) has been investigated. In this case the currents have opposite properties. The phase A current on the HV side is very big (limited only by the power system source impedance and fault resistance), while the phase A current in reactor star point will have very small value due to a fact that phase A winding is practically short-circuited.

As a result, shunt reactor unbalance current will appear in the neutral point. However, this neutral point current will typically have a value around 1 pu (i.e. similar value as during external ground fault).

That type of the internal fault (i.e. shunt reactor bushing failure) shall be easily detected and cleared by the differential, restricted ground fault or HV side overcurrent or residual ground fault protections. Neutral point ground overcurrent protection can operate with the time delay.

For internal ground fault in some other location in-between these two positions the shunt reactor currents will have values somewhere in the range limited by this two extreme cases.

TYPICAL CONTROL SCHEMES OF SHUNT REACTOR

The shunt reactors are generally designed for natural cooling with the radiators mounted directly on the tank. However sometimes it is required to have some control action in the cooling circuit depending on the status of the shunt reactor circuit breaker. The control action can be initiated by the circuit breaker auxiliary contact or by operation of an overcurrent relay set to 50% of the reactor rated current. By using overcurrent relay secure control action is obtained when reactor is energized regardless the circuit breaker auxiliary contact status.

In order to improve power system performance, lately it is often required by the electrical utilities to perform automatic shunt reactor in and out switching, by monitoring the busbar voltage level. This functionality is quite easy to integrate into multifunctional, numerical relay.

However user must carefully check relay performance regarding the following points:

• over/under voltage relay with reset ratio or 1% or better is required for such application.

• typically more than one over/under voltage level with independently settable time delays are required within the relay.

• over/under voltage relay shall be capable to operate only when all three voltages are above/below set operate level or relay must be capable to measure and operate on the value of the positive sequence voltage.

MECHANICAL FAULT DETECTION OF SHUNT REACTOR

Similarly to the power transformers, HV oil immersed shunt reactors typically have build-in mechanical devices for internal fault or abnormal operating condition detection. Typically the following built-in mechanical fault detection devices can be encountered within shunt reactor:

• gas detection relay (i.e. Buchholz relay) with alarm and trip stage

• sudden pressure relay

• winding temperature contact thermometer with alarm and trip stage

• oil temperature contact thermometer with alarm and trip stage

• low oil level relay

These mechanical relays are excellent compliment to the electrical measuring relays previously explained. Typically it is recommended to arrange that these mechanical relays trip reactor circuit breaker independently from electrical relays. However signals from mechanical devices shall be connected to binary inputs of numerical relays in order to get time tagging information, disturbance recording and event reporting in case of their operation.

TURN TO TURN PROTECTION SCHEMES OF SHUNT REACTOR

Turn-to-turn faults in shunt reactor present a formidable challenge to the protection engineer. The current and the voltage changes encountered during such fault are very small and therefore sensitive and reliable protection against turn-to-turn faults is difficult to achieve. At the same time the longitudinal differential protection offers no protection at all for such faults. Hence special protection schemes shall be employed.

One such scheme, often used in certain countries, utilizes a fact that the HV shunt reactor winding is often made of two half-windings connected in parallel (i.e. the HV lead is brought out at the mid point of the winding, and the two neutral leads at the bottom and the top of the winding). This gives the opportunity to install two CTs in the winding star point (i.e. one in each winding part). Then so-called split phase differential protection can be utilized to detect turn-to-turn faults. However this protection scheme have the following drawbacks:

• this special CT arrangement typically causes reactor manufacturing problems

• typically low CT ratio is required, which can cause longitudinal differential protection problems during reactor switching in, if the same CTs are used for both differential protections

• this scheme can be only used if the shunt reactor is specifically ordered with these CTs

Second turn-to-turn protection scheme for shunt reactors, successfully used in some other counties, utilize the following facts:

• HV power system voltages are well balanced during normal load conditions

• Modern HV, oil immersed shunt reactors have very small manufacturing asymmetry between individual phases

• Shunt reactor winding impedance is approximately proportional to the square of the number of active turns

• Short circuit between some number of turns will cause the decrease of the winding impedance only in the faulty phase and corresponding small raise of the shunt reactor neutral point current

• Currents during turn-to-turn fault are of the small magnitude and they will not produce any sufficient unbalance voltage

• Any external cause of neutral point current (i.e. external phase to ground fault) will cause appearance of unbalance voltage which can be used to block the operation of turn-to-turn protection scheme

• In case of a bigger winding turn-to-turn fault which might cause the sufficient voltage unbalance, sensitive directional zero sequence relay connected on the shunt reactor HV side and set to look into the reactor shall be capable to detect such fault This protection scheme was developed even before multifunctional numerical relays were available. To implement such shunt reactor turn-to-turn protection scheme within multi-functional numerical relay utilizing its graphical configuration facilities, and readily available logical gates, timers etc. shall not be a big problem for a protection engineer.

In order to verify above statements, shunt reactor behavior, for phase A winding 1% turn-to-turn faults, is verified by an ATP simulation and it is shown in Figures 21 & 22. From these figures is obvious that the above-described scheme can be successfully implemented if the power system itself is well balanced.

Figure 21: Internal Phase A Winding turn-to-turn fault, Phase Currents

Figure 22: Internal Phase A Winding turn-to-turn fault, Zero-sequence Quantities

OPERATING CHARACTERISTICS OF SHUNT REACTOR

1) LINEARITY:

For normal operating voltages there is a linear relationship between applied voltage and reactor current (i.e. a small increase in voltage will result in a proportional increase in current). Magnetic fluxes and flux densities are also proportional to the time integral of the applied voltage. With a voltage of sinusoidal shape the fluxes and flux densities are also proportional to the voltage. The deviation from a true sinusoidal shape in line voltage is in general negligible for normal operating voltages.

As the magnetic flux to a great extent has its path in magnetic core steel the core steel will get saturated for flux densities above a certain level, the saturation point. Below and up to the saturation point only a small current is needed to magnetize the core steel and the extra current needed to reach a marginal increase flux density is small. Once above the saturation point the extra current needed to further increase the flux density will be large.

2) HARMONIC CONTENT:

Steady state harmonics in reactor current arise from partial saturation in the magnetic circuit. These effects are in fact very small, and without practical importance for relaying and communication interference. Of all harmonics the third harmonic will be dominant. In the reactor neutral the third harmonics in the three phases add together and act like a zero sequence current.

3) ASYMMETRY BETWEEN PHASES:

The tolerances on asymmetry between phases of a three-phase reactor or between single-phase units forming a three-phase bank can be judged by the amount of residual harmonics. The result is a zero sequence current in the neutral connection. Standards are realistic, but better tolerances are possible to achieve. A usual figure is 0.5 %.

FOSSIL FUEL POWER PLANTS

Steam turbine power plants can use coal, oil, natural gas, or just about any combustible material as the fuel resource. However, each fuel type requires a unique set of accessory equipment to inject fuel into the boiler, control the burning process, vent and exhaust gases, capture unwanted byproducts, and so on.

Some fossil fuel power plants can switch fuels. For example, it is common for an oil plant to convert to natural gas when gas is less expensive than oil. Most of the time, it is not practical to convert a coal burning power plant to oil or gas unless it has been designed for conversion. The processes are usually different enough so that switching will not be cost effective.

Coal is burned in two different ways in coal fired plants. First, in traditional coal fired plants, the coal is placed on metal conveyor belts inside the boiler chamber. The coal is burned while on the belt as the belt slowly traverses the bottom of the boiler. Ash falls through the chain conveyor belt and is collected below where it is sometimes sold as a useful by-product for other industries.

In pulverized coal power plants, the coal is crushed into a fine powder and injected into the furnace where it is burned similar to a gas. Pulverized coal is mixed with air and ignited in the furnace. Combustion by-products include solid residue (ash) that is collected at the bottom of the furnace and gases that include fine ash, NO2, CO, and SO2, which are emitted into the atmosphere through the stack. Depending on local environmental regulations, scrubber and Baghouse equipment may be required and installed to collect most of these by-products before they reach the atmosphere.

Scrubbers are used to collect the undesirable gases to improve the quality of the stack output emissions. Baghouses are commonly used to help collect fly ash.

Some of the drawbacks that could be encountered with coal fired steam generating power plants are:

Environmental concerns from burning coal (i.e., acid rain).
Transportation issues regarding rail systems for coal delivery.
Length of transmission lines to remote power plant locations.

Figure 2-10 shows the layout of a typical steam power plant. Notice the steam line used to transfer super heated steam from the boiler to the turbine and then through the condenser where it is returned to a water state and recycled.

Notice the steam turbine connected to the generator. The turbine speed is controlled by the amount of steam applied in order to control frequency. When load picks up on the electrical system, the turbine shaft speed slows down and more steam is then placed on the turbine blades to maintain frequency. Notice how coal is delivered to the boiler and burned. Exhaust is vented through the stack. Scrubbers and bags remove the by-products before they enter the atmosphere. Water from a nearby reservoir is pumped to the condenser where it is used to convert steam back into water and recycled.

Figure 2-10. Steam power plant.

Figure 2-11 shows a coal fired steam turbine power plant. The ramp in front lifts the coal to the pulverizer where it is crushed before being injected into the boiler and burned. Plant operators must be careful to not allow the spontaneous combustion of coal while it is stored in the yard.

Figure 2-11. Coal power plant.

STEAM TURBINE POWER PLANTS

High pressure and high temperature steam is created in a boiler, furnace, or heat exchanger and moved through a steam turbine generator (STG) that converts the steam’s energy into rotational energy that turns the generator shaft. The steam turbine’s rotating shaft is directly coupled to the generator rotor. The STG shaft speed is tightly controlled for it is directly related to the frequency of the electrical power being produced.

High temperature, high pressure steam is used to turn steam turbines that ultimately turn the generator rotors. Temperatures on the order of 1,000°F and pressures on the order of 2,000 pounds per square inch (psi) are commonly used in large steam power plants. Steam at this pressure and temperature is called super heated steam, sometimes referred to as dry steam.

The steam’s pressure and temperature drop significantly after it is applied across the first stage turbine blades. Turbine blades make up the fan shaped rotor to which steam is directed, thus turning the shaft. The super heated steam is reduced in pressure and temperature after it passes through the turbine.

The reduced steam can be routed through a second stage set of turbine blades where additional steam energy is transferred to the turbine shaft. This second stage equipment is significantly larger than the first stage to allow for additional expansion and energy transformation. In some power plants, the steam following the first stage is redirected back to the boiler where it is reheated and then sent back to the second turbine stage for a more efficient energy transformation.

Once the energy of the steam has been transferred to the turbine shaft, the low temperature and low-pressure steam has basically exhausted its energy and must be fully condensed back to water before it can be recycled. The condensing process of steam back to water is accomplished by a condenser and cooling tower(s). Once the used steam is condensed back to warm water, the boiler feed pump (BFP) pumps the warm water back to the boiler where it is recycled. This is a closed-loop processes. Some water has to be added in the process due to small leaks and evaporation.

The condenser takes cold water from nearby lakes, ponds, rivers, oceans, deep wells, cooling towers, and other water sources and pumps it through pipes in the condenser. The used steam passes through the relatively cold water pipes and causes dripping to occur. The droplets are collected at the base of the condenser (the well) and pumped back to the boiler by the BFP.

The overall steam generation plant efficiency in converting fuel heat energy into mechanical rotation energy and then into electrical energy ranges from 25 to 35%. Although it is a relatively low efficiency system, steam turbine generation is very reliable and is commonly used as base load generation units in large electric power systems. Most of the inefficiency in steam turbine generation plants comes from the loss of heat into the atmosphere in the boiler process.

REAL TIME ELECTRICAL POWER GENERATION

Power plants produce electrical energy on a real-time basis. Electric power systems do not store energy such as most gas or water systems do. For example, when a toaster is switched on and drawing electrical energy from the system, the associated generating plants immediately see this as new load and slightly slow down. As more and more load (i.e., toasters, lights, motors, etc.) are switched on, generation output and prime mover rotational shaft energy must be increased to balance the load demand on the system.

Unlike water utility systems that store water in tanks located up high on hills or tall structures to serve real-time demand, electric power systems must control generation to balance load on demand. Water is pumped into the tank when the water level in the tank is low, allowing the pumps to turn off during low and high demand periods. Electrical generation always produces electricity on an “as needed” basis. Note: some generation units can be taken off-line during light load conditions, but there must always be enough generation online to maintain frequency during light and heavy load conditions.

There are electrical energy storage systems such as batteries, but electricity found in interconnected ac power systems is in a real-time energy supply system, not an energy storage system.

TYPES OF ELECTRIC LOADS

Devices that are connected to the power system are referred to as electrical loads. Toasters, refrigerators, bug zappers, and so on are considered electrical loads. There are three types of electrical loads. They vary according to their leading or lagging time relationship between voltage and current.

The three load types are resistive, inductive, and capacitive. Each type has specific characteristics that make them unique. Understanding the differences between these load types will help explain how power systems can operate efficiently. Power system engineers, system operators, maintenance personnel, and others try to maximize system efficiency on a continuous basis by having a good understanding of the three types of loads. They understand how having them work together can minimize system losses, provide additional equipment capacity, and maximize system reliability.

The three different types of load are summarized below.

1) RESISTIVE LOAD:

The resistance in a wire (i.e., conductor) causes friction and reduces the amount of current flow if the voltage remains constant. Byproducts of this electrical friction are heat and light. The units (measurement) of resistance are referred to as ohms. The units of electrical power associated with resistive load are watts. Lightbulbs, toasters, electric hot water heaters, and so on are resistive loads.

Resistive loads.

2) INDUCTIVE LOAD:

Inductive loads require a magnetic field to operate. All electrical loads that have a coil of wire to produce the magnetic field are called inductive loads. Examples of inductive loads are hair dryers, fans, blenders, vacuum cleaners, and many other motorized devices. In essence, all motors are inductive loads.

The unique difference between inductive loads and other load types is that the current in an inductive load lags the applied voltage. Inductive loads take time to develop their magnetic field when the voltage is applied, so the current is delayed. The units (measurement) of inductance are called Henrys.

Regarding electrical motors, a load placed on a spinning shaft to perform a work function draws what is referred to as real power (i.e., watts) from the electrical energy source. In addition to real power, what is referred to as reactive power is also drawn from the electrical energy source to produce the magnetic fields in the motor. The total power consumed by the motor is, therefore, the sum of both real and reactive power.

Inductive loads.

3) CAPACITIVE LOAD:

A capacitor is a device made of two metal conductors separated by an insulator called a dielectric (i.e., air, paper, glass, and other non-conductive materials). These dielectric materials become charged when voltage is applied to the attached conductors. Capacitors can remain charged long after the voltage source has been removed. Examples of capacitor loads are TV picture tubes, long extension cords, and components used in electronic devices.

Opposite to inductors, the current associated with capacitors leads (instead of lags) the voltage because of the time it takes for the dielectric material to charge up to full voltage from the charging current. Therefore, it is said that the current in a capacitor leads the voltage. The units (measurement) of capacitance are called farads.

Similar to inductors, the power associated with capacitors is also called reactive power, but has the opposite polarity. Thus, inductors have positive VARs and capacitors have negative VARs. Note, the negative VARs of inductors can be cancelled by the positive VARs of capacitors, to leading a net zero reactive power requirement.

As a general rule, capacitive loads are not items that people purchase at the store in massive quantities like they do resistive and inductive loads. For that reason, power companies must install capacitors on a regular basis to maintain a reactive power balance with the inductive demand.

Capacitive loads.

CLASSIFICATION OF POWER SYSTEM STABILITY

Power system stability is a single problem, however, it is impractical to deal with it as such. Instability of the power system can take different forms and is influenced by a wide range of factors. Analysis of stability problems, including identifying essential factors that contribute to instability and devising methods of improving stable operation is greatly facilitated by classification of stability into appropriate categories. These are based on the following considerations:

Ø The physical nature of the resulting instability related to the main system parameter in which instability can be observed.

Ø The size of the disturbance considered indicates the most appropriate method of calculation and prediction of stability.

Ø The devices, processes, and the time span that must be taken into consideration in order to determine stability.

Figure 7.1 Possible classification of power system stability into various categories and
subcategories.

1) ROTOR ANGLE STABILITY:

Rotor angle stability is concerned with the ability of interconnected synchronous machines of a power system to remain in synchronism under normal operating conditions and after being subjected to a disturbance. It depends on the ability to maintain/restore equilibrium between electromagnetic torque and mechanical torque of each synchronous machine in the system. Instability that may result occurs in the form of increasing angular swings of some generators leading to their loss of synchronism with other generators.

The rotor angle stability problem involves the study of the electromechanical oscillations inherent in power systems. A fundamental factor in this problem is the manner in which the power outputs of synchronous machines vary as their rotor angles change. The mechanism by which interconnected synchronous machines maintain synchronism with one another is through restoring forces, which act whenever there are forces tending to accelerate or decelerate one or more machines with respect to other machines. Under steady-state conditions, there is equilibrium between the input mechanical torque and the output electrical torque of each machine, and the speed remains constant. If the system is perturbed, this equilibrium is upset, resulting in acceleration or deceleration of the rotors of the machines according to the laws of motion of a rotating body. If one generator temporarily runs faster than another, the angular position of its rotor relative to that of the slower machine will advance. The resulting angular difference transfers part of the load from the slow machine to the fast machine, depending on the power-angle relationship. This tends to reduce the speed difference and hence the angular separation. The power-angle relationship, as discussed above, is highly nonlinear. Beyond a certain limit, an increase in angular separation is accompanied by a decrease in power transfer; this increases the angular separation further and leads to instability. For any given situation, the stability of the system depends on whether or not the deviations in angular positions of the rotors result in sufficient restoring torques.

It should be noted that loss of synchronism can occur between one machine and the rest of the system, or between groups of machines, possibly with synchronism maintained within each group after separating from each other.

The change in electrical torque of a synchronous machine following a perturbation can be resolved into two components:

1) SYNCHRONIZING TORQUE: component, in phase with a rotor angle perturbation.

2) DAMPING TORQUE: component, in phase with the speed deviation.

System stability depends on the existence of both components of torque for each of the synchronous machines. Lack of sufficient synchronizing torque results in aperiodic or non-oscillatory instability, whereas lack of damping torque results in oscillatory instability.

For convenience in analysis and for gaining useful insight into the nature of stability problems, it is useful to characterize rotor angle stability in terms of the following two categories:

1) SMALL SIGNAL (OR STEADY STATE) STABILITY:

is concerned with the ability of the power system to maintain synchronism under small disturbances. The disturbances are considered to be sufficiently small that linearization of system equations is permissible for purposes of analysis. Such disturbances are continually encountered in normal system operation, such as small changes in load.

Small signal stability depends on the initial operating state of the system. Instability that may result can be of two forms:

(i) Increase in rotor angle through a non-oscillatory or aperiodic mode due to lack of synchronizing torque, or

(ii) Rotor oscillations of increasing amplitude due to lack of sufficient damping torque.

In today’s practical power systems, small signal stability is largely a problem of insufficient damping of oscillations. The time frame of interest in small-signal stability studies is on the order of 10 to 20 s following a disturbance. The stability of the following types of oscillations is of concern:

Ø LOCAL MODES: or machine system modes, associated with the swinging of units at a generating station with respect to the rest of the power system. The term ‘‘local’’ is used because the oscillations are localized at one station or a small part of the power system.

Ø INTERAREA MODES: associated with the swinging of many machines in one part of the system against machines in other parts. They are caused by two or more groups of closely coupled machines that are interconnected by weak ties.

Ø CONTROL MODES: associated with generating units and other controls. Poorly tuned exciters, speed governors, HVDC converters, and static VAR compensators are the usual causes of instability of these modes.

Ø TORSIONAL MODES: associated with the turbine-generator shaft system rotational components. Instability of torsional modes may be caused by interaction with excitation controls, speed governors, HVDC controls, and series-capacitor-compensated lines.

2) LARGE DISTURBANCE ROTOR ANGLE STABILITY OR TRANSIENT STABILITY:

As it is commonly referred to, is concerned with the ability of the power system to maintain synchronism when subjected to a severe transient disturbance. The resulting system response involves large excursions of generator rotor angles and is influenced by the nonlinear power-angle relationship.

Transient stability depends on both the initial operating state of the system and the severity of the disturbance. Usually, the disturbance alters the system such that the post-disturbance steady state operation will be different from that prior to the disturbance. Instability is in the form of aperiodic drift due to insufficient synchronizing torque, and is referred to as first swing stability. In large power systems, transient instability may not always occur as first swing instability associated with a single mode; it could be as a result of increased peak deviation caused by superposition of several modes of oscillation causing large excursions of rotor angle beyond the first swing.

The time frame of interest in transient stability studies is usually limited to 3 to 5 sec following the disturbance. It may extend to 10 sec for very large systems with dominant inter-area swings.

Power systems experience a wide variety of disturbances. It is impractical and uneconomical to design the systems to be stable for every possible contingency. The design contingencies are selected on the basis that they have a reasonably high probability of occurrence.

As identified in Fig. 7.1, small signal stability as well as transient stability is categorized as short term phenomena.

2) FREQUENCY STABILITY:

Frequency stability is concerned with the ability of a power system to maintain steady frequency within a nominal range following a severe system upset resulting in a significant imbalance between generation and load. It depends on the ability to restore balance between system generation and load, with minimum loss of load.

Severe system upsets generally result in large excursions of frequency, power flows, voltage, and other system variables, thereby invoking the actions of processes, controls, and protections that are not modeled in conventional transient stability or voltage stability studies. These processes may be very slow, such as boiler dynamics, or only triggered for extreme system conditions, such as volts/hertz protection tripping generators. In large interconnected power systems, this type of situation is most commonly associated with islanding. Stability in this case is a question of whether or not each island will reach an acceptable state of operating equilibrium with minimal loss of load. It is determined by the overall response of the island as evidenced by its mean frequency, rather than relative motion of machines. Generally, frequency stability problems are associated with inadequacies in equipment responses, poor coordination of control and protection equipment, or insufficient generation reserve.

Over the course of frequency instability, the characteristic times of the processes and devices that are activated by the large shifts in frequency and other system variables will range from a matter of seconds, corresponding to the responses of devices such as generator controls and protections, to several minutes, corresponding to the responses of devices such as prime mover energy supply systems and load voltage regulators.

Although frequency stability is impacted by fast as well as slow dynamics, the overall time frame of interest extends to several minutes. Therefore, it is categorized as a long-term phenomenon in Fig. 7.1.

3) VOLTAGE STABILITY:

Voltage stability is concerned with the ability of a power system to maintain steady voltages at all buses in the system under normal operating conditions, and after being subjected to a disturbance. Instability that may result occurs in the form of a progressive fall or rise of voltage of some buses. The possible outcome of voltage instability is loss of load in the area where voltages reach unacceptably low values, or a loss of integrity of the power system.

Progressive drop in bus voltages can also be associated with rotor angles going out of step. For example, the gradual loss of synchronism of machines as rotor angles between two groups of machines approach or exceed 180 degree would result in very low voltages at intermediate points in the network close to the electrical center. In contrast, the type of sustained fall of voltage that is related to voltage instability occurs where rotor angle stability is not an issue.

The main factor contributing to voltage instability is usually the voltage drop that occurs when active and reactive power flow through inductive reactance associated with the transmission network; this limits the capability of transmission network for power transfer. The power transfer limit is further limited when some of the generators hit their reactive power capability limits. The driving forces for voltage instability are the loads; in response to a disturbance, power consumed by the loads tends to be restored by the action of distribution voltage regulators, tap changing transformers, and thermostats.

Restored loads increase the stress on the high voltage network causing more voltage reduction. A rundown situation causing voltage instability occurs when load dynamics attempts to restore power consumption beyond the capability of the transmission system and the connected.

While the most common form of voltage instability is the progressive drop in bus voltages, the possibility of overvoltage instability also exists and has been experienced at least on one. It can occur when EHV transmission lines are loaded significantly below surge impedance loading and under excitation limiters prevent generators and/or synchronous condensers from absorbing the excess reactive power. Under such conditions, transformer taps changers, in their attempt to control load voltage, may cause voltage instability.

Voltage stability problems may also be experienced at the terminals of HVDC links. They are usually associated with HVDC links connected to weak AC systems. The HVDC link control strategies have a very significant influence on such problems.

As in the case of rotor angle stability, it is useful to classify voltage stability into the following subcategories:

1. LARGE DISTURBANCE VOLTAGE STABILITY:

Is concerned with a system’s ability to control voltages following large disturbances such as system faults, loss of generation, or circuit contingencies.

This ability is determined by the system-load characteristics and the interactions of both continuous and discrete controls and protections. Determination of large disturbance stability requires the examination of the nonlinear dynamic performance of a system over a period of time sufficient to capture the interactions of such devices as under-load transformer tap changers and generator field-current limiters. The study period of interest may extend from a few seconds to tens of minutes. Therefore, long term dynamic simulations are required for analysis.

2. SMALL DISTURBANCE VOLTAGE STABILITY:

Is concerned with a system’s ability to control voltages following small perturbations such as incremental changes in system load. This form of stability is determined by the characteristics of loads, continuous controls, and discrete controls at a given instant of time. This concept is useful in determining, at any instant, how the system voltage will respond to small system changes. The basic processes contributing to small disturbance voltage instability are essentially of a steady state nature. Therefore, static analysis can be effectively used to determine stability margins, identify factors influencing stability, and examine a wide range of system conditions and a large number of post contingency scenarios. A criterion for small disturbance voltage stability is that, at a given operating condition for ever y bus in the system, the bus voltage magnitude increases as the reactive power injection at the same bus is increased. A system is voltage unstable if, for at least one bus in the system, the bus voltage magnitude (V) decreases as the reactive power injection (Q) at the same bus is increased. In other words, a system is voltage stable if V- Q sensitivity is positive for ever y bus and unstable if V-Q sensitivity is negative for at least one bus.

The time frame of interest for voltage stability problems may vary from a few seconds to tens of minutes. Therefore, voltage stability may be either a short term or a long-term phenomenon.

Voltage instability does not always occur in its pure form. Often, the rotor angle instability and voltage instability go hand in hand. One may lead to the other, and the distinction may not be clear. However, distinguishing between angle stability and voltage stability is important in understanding the underlying causes of the problems in order to develop appropriate design and operating procedures.

TRANSIENT STABILITY CONSIDERATIONS IN SYSTEM OPERATION

While it is true that power systems are designed to be transiently stable, and many of the methods described above may be used to achieve this goal, in actual practice, systems may be prone to being unstable. This is largely due to uncertainties related to assumptions made during the design process.

These uncertainties result from a number of sources including:

LOAD AND GENERATION FORECAST: The design process must use forecast information about the amount, distribution, and characteristics of the connected loads as well as the location and amount of connected generation. These all have a great deal of uncertainty. If the actual system load is higher than planned, the generation output will be higher, the system will be more stressed, and the transient stability limit may be significantly lower.

SYSTEM TOPOLOGY: Design studies generally assume all elements in service, or perhaps up to two elements out-of-service. In actual systems, there are usually many elements out-of-service at any one time due to forced outages (failures) or system maintenance. Clearly, these outages can seriously weaken the system and make it less transiently stable.

DYNAMIC MODELING: All models used for power system simulation, even the most advanced, contain approximations out of practical necessity.

DYNAMIC DATA: The results of time-domain simulations depend heavily on the data used to represent the models for generators and the associated controls. In many cases, this data is not known (typical data is assumed) or is in error (either because it has not been derived from field measurements or due to changes that have been made in the actual system controls that have not been reflected in the data).

DEVICE OPERATION: In the design process it is assumed that controls and protection will operate as designed. In the actual system, relays, breakers, and other controls may fail or operate improperly.

To deal with these uncertainties in actual system operation, safety margins are used. Operational (short-term) time-domain simulations are conducted using a system model, which is more accurate (by accounting for elements out on maintenance, improved short-term load forecast, etc.) than the design model. Transient stability limits are computed using these models. The limits are generally in terms of maximum flows allowable over critical interfaces, or maximum generation output allowable from critical generating sources. Safety margins are then applied to these computed limits. This means that actual system operation is restricted to levels (interface flows or generation) below the stability limit by an amount equal to a defined safety margin. In general, the margin is expressed in terms of a percentage of the critical flow or generation output. For example, an operation procedure might be to set the operating limit at a flow level 10% below the stability limit.

A growing trend in system operations is to perform transient stability assessment on-line in near-real-time. In this approach, the power flow defining the system topology and the initial operating state is derived, at regular intervals, from actual system measurements via the energy management system (EMS) using state-estimation methods. The derived power flow together with other data required for transient stability analysis is passed to transient stability software residing on dedicated computers and the computations required to assess all credible contingencies are performed within a specified cycle time. Using advanced analytical methods and high-end computer hardware, it is currently possible to assess the transient stability of vary large systems, for a large number of contingencies, in cycle times typically ranging from 5 to 30 min. Since this on-line approach uses information derived directly from the actual power system, it eliminates a number of the uncertainties associated with load forecasting, generation forecasting, and prediction of system topology, thereby leading to more accurate and meaningful stability assessment.

TRANSIENT STABILITY CONSIDERATIONS IN SYSTEM DESIGN

Transient stability is an important consideration that must be dealt with during the design of power systems. In the design process, time-domain simulations are conducted to assess the stability of the system under various conditions and when subjected to various disturbances. Since it is not practical to design a system to be stable under all possible disturbances, design criteria specify the disturbances for which the system must be designed to be stable. The criteria disturbances generally consist of the more statistically probable events, which could cause the loss of any system element and typically include three phase faults cleared in normal time and line-to-ground faults with delayed clearing due to breaker failure. In most cases, stability is assessed for the loss of one element (such as a transformer or transmission circuit) with possibly one element out-of-service in the pre-disturbance system. In system design, therefore, a wide number of disturbances are assessed and if the system is found to be unstable (or marginally stable) a variety of actions can be taken to improve stability. These include the following:

REDUCTION OF TRANSMISSION SYSTEM REACTANCE: This can be achieved by adding additional parallel transmission circuits, providing series compensation on existing circuits, and by using transformers with lower leakage reactances.

HIGH SPEED FAULT CLEARING: In general, two-cycle breakers are used in locations where faults must be removed quickly to maintain stability. As the speed of fault clearing decreases, so does the amount of kinetic energy gained by the generators during the fault.

DYNAMIC BRAKING: Shunt resistors can be switched in following a fault to provide an artificial electrical load. This increases the electrical output of the machines and reduces the rotor acceleration.

REGULATE SHUNT COMPENSATION: By maintaining system voltages around the power system, the flow of synchronizing power between generators is improved.

REACTOR SWITCHING: The internal voltages of generators, and therefore stability, can be increased by connected shunt reactors.

SINGLE POLE SWITCHING AND RE-CLOSING: Most power system faults are of the single-line-to-ground type. However, in most schemes, this type of fault will trip all three phases. If single pole switching is used, only the faulted phase is removed, and power can flow on the remaining two phases thereby greatly reducing the impact of the disturbance. The single-phase is reclosed after the fault is cleared and the fault medium is deionized.

STEAM TURBINE FAST VALVING: Steam valves are rapidly closed and opened to reduce the generator accelerating power in response to a disturbance.

GENERATOR TRIPPING: Perhaps one of the oldest and most common methods of improving transient stability, this approach disconnects selected generators in response to a disturbance that has the effect of reducing the power, which is required to be transferred over critical transmission interfaces.

HIGH SPEED EXCITATION SYSTEMS: As illustrated by the simple examples presented earlier, increasing the internal voltage of a generator has the effect of proving transient stability. This can be achieved by fast acting excitation systems, which can rapidly boost field voltage in response to disturbances.

SPECIAL EXCITATION SYSTEM CONTROLS: It is possible to design special excitation systems that can use discontinuous controls to provide special field boosting during the transient period thereby improving stability.

SPECIAL CONTROL OF HVDC LINKS: The DC power on HVDC links can be rapidly ramped up or down to assist in maintaining generation/load imbalances caused by disturbances. The effect is similar to generation or load tripping.

CONTROLLED SYSTEM SEPARATION AND LOAD SHEDDING: Generally considered a last resort, it is feasible to design system controls that can respond to separate, or island, a power system into areas with balanced generation and load. Some load shedding or generation tripping may also be required in selected islands. In the event of a disturbance, instability can be prevented from propagating and affecting large areas by partitioning the system in this manner. If instability primarily results in generation loss, load shedding alone may be sufficient to control the system.

FACTORS INFLUENCING TRANSIENT STABILITY

Many factors affect the transient stability of a generator in a practical power system. From the small system analyzed above, the following factors can be identified:

Ø The post-disturbance system reactance as seen from the generator. The weaker the post-disturbance system, the lower the Pmax will be.

Ø The duration of the fault clearing time. The longer the fault is applied, the longer the rotor will be accelerated and the more kinetic energy will be gained. The more energy that is gained during acceleration, the more difficult it is to dissipate it during deceleration.

Ø The inertia of the generator. The higher the inertia, the slower the rate of change of angle and the lesser the kinetic energy gained during the fault.

Ø The generator internal voltage (determined by excitation system) and infinite bus voltage (system voltage). The lower these voltages, the lower the Pmax will be.

Ø The generator loading before the disturbance. The higher the loading, the closer the unit will be to Pmax, which means that during acceleration, it is more likely to become unstable.

Ø The generator internal reactance. The lower the reactance, the higher the peak power and the lower the initial rotor angle.

Ø The generator output during the fault. This is a function of faults location and type of fault.

METHODS OF ANALYSIS OF TRANSIENT STABILITY

1) MODELING:

The basic concepts of transient stability presented above are based on highly simplified models. Practical power systems consist of large numbers of generators, transmission circuits, and loads.

For stability assessment, the power system is normally represented using a positive sequence model.

The network is represented by a traditional positive sequence power flow model, which defines the transmission topology, line reactances, connected loads and generation, and pre disturbance voltage profile.

Generators can be represented with various levels of detail, selected based on such factors as length of simulation, severity of disturbance, and accuracy required. The most basic model for synchronous generators consists of a constant internal voltage behind a constant transient reactance, and the rotating inertia constant (H). This is the so-called classical representation that neglects a number of characteristics: the action of voltage regulators, variation of field flux linkage, the impact of the machine physical construction on the transient reactances for the direct and quadrature axis, the details of the prime mover or load, and saturation of the magnetic core iron. Historically, classical modeling was used to reduce computational burden associated with more detailed modeling, which is not generally a concern with today’s simulation software and computer hardware. However, it is still often used for machines that are very remote from a disturbance (particularly in very large system models) and where more detailed model data is not available.

In general, synchronous machines are represented using detailed models, which capture the effects neglected in the classical model including the influence of generator construction (damper windings, saturation, etc.), generator controls (excitation systems including power system stabilizers, etc.), the prime mover dynamics, and the mechanical load. Loads, which are most commonly represented as static voltage and frequency dependent components, may also be represented in detail by dynamic models that capture their speed torque characteristics and connected loads. There are a myriad of other devices, such as HVDC lines and controls and static VAR devices, which may require detailed representation.

Finally, system protections are often represented. Models may also be included for line protections (such as mho distance relays), out-of-step protections, loss of excitation protections, or special protection schemes.

Although power system models may be extremely large, representing thousands of generators and other devices producing systems with tens-of-thousands of system states, efficient numerical methods combined with modern computing power have made time-domain simulation readily available in many commercially available computer programs. It is also important to note that the time frame in which transient instability occurs is usually in the range of 1–5 s, so that simulation times need not be excessively long.

2) ANALYTICAL METHODS:

To accurately assess the system response following disturbances, detailed models are required for all critical elements. The complete mathematical model for the power system consists of a large number of algebraic and differential equations, including

Ø Generators stator algebraic equations
Ø Generator rotor circuit differential equations
Ø Swing equations
Ø Excitation system differential equations
Ø Prime mover and governing system differential equations
Ø Transmission network algebraic equations
Ø Load algebraic and differential equations

While considerable work has been done on direct methods of stability analysis in which stability is determined without explicitly solving the system differential equations, the most practical and flexible method of transient stability analysis is time domain simulation using step by step numerical integration of the nonlinear differential equations. A variety of numerical integration methods are used, including explicit methods (such as Euler and Runge-Kutta methods) and implicit methods (such as the trapezoidal method). The selection of the method to be used depends largely on the stiffness of the system being analyzed. In systems in which time-steps are limited by numerical stability rather than accuracy, implicit methods are generally better suited than the explicit methods.

3) SIMULATION STUDIES:

Modern simulation tools offer sophisticated modeling capabilities and advanced numerical solution methods. Although each simulation tools differs somewhat, the basic requirements and functions are the same.

i) INPUT DATA:

1. Power flow: Defines system topology and initial operating state.

2. Dynamic data: Includes model types and associated parameters for generators, motors, protections, and other dynamic devices and their controls.

3. Program control data: Specifies such items as the type of numerical integration to use and time-step.

4. Switching data: Includes the details of the disturbance to be applied. This includes the time at which the fault is applied, where the fault is applied, the type of fault and its fault impedance if required, the duration of the fault, the elements lost as a result of the fault, and the total length of the simulation.

5. System monitoring data: This specifies the quantities that are to be monitored (output) during the simulation. In general, it is not practical to monitor all quantities because system models are large, and recording all voltages, angles, flows, generator outputs, etc., at each integration time step would create an enormous volume. Therefore, it is a common practice to define a limited set of parameters to be recorded.

ii) OUTPUT DATA:

1. Simulation log: This contains a listing of the actions that occurred during the simulation. It includes a recording of the actions taken to apply the disturbance, and reports on any operation of protections or controls, or any numerical difficulty encountered.

2. Results output: This is an ASCII or binary file that contains the recording of each monitored variable over the duration of the simulation. These results are examined, usually through a graphical plotting, to determine if the system remained stable and to assess the details of the dynamic behavior of the system.

POWER SYSTEM STABILITY