Mechanical Consideration of Transmission Line | Power Systems - Electrical Engineering (EE) PDF Download

Mechanical Design of Overhead Lines

Sag and Tension

Supports at Same Level

where, S = Sag at mid point in meter.
Z = Length of span in meter.
W = Conductor weight kg/m
T = Conductor tension [assumed constant over the whole span] newton

Effect of Ice and Wind Loading

The weight of ice per unit length of conductor,

w_i =πp (2π + I²) kg/m

where, p = Density of ice (910 kg/m³)

Wind Loading

Wind loading w_a per unit length

= 2 (r + t) p kg/m

where, p = Wind pressure in kg/m²

r = Radius of conductor

l = Thickness of ice coating

Total loading on conductor per metre length

Spacing between conductors (without sparing)

where S = Sag in metre

V = Line voltage in kV

Supports at different level

where, I_c = Span of a complete parabola.

Voltage Control: The voltage of the generator is proportional to the speed and excitation (flux) of the generator.

The speed is constant, the excitation is used to control the voltage. Therefore, the voltage control system is also called as excitation control system or automatic voltage regulator (AVR)

 The control of voltage and reactive power is a major issue in power system operation. This is because of the topological differences between distribution and transmission systems, different strategies have evolved. This paper contains contributions of novel reactive power control and voltage stability schemes for distribution and transmission systems. A particular interest is taken to the development of control schemes to avoid so-called voltage collapse, which can result in widespread outages. In order to achieve efficient and reliable operation of power system, the control of voltage and reactive power should satisfy the following objectives:

1. Voltages at all terminals of all equipment in the system are within acceptable limits
2. System stability is enhanced to maximize utilization of the transmission system
3. The reactive power flow is minimized so as to reduce RI² and XI² losses.

Voltage control using tap changing transformers is the basic and easiest way of controlling voltages in transmission, sub-transmission and distribution systems. In high voltage and extra high voltage lines On Load Tap Changing (OLTC) transformers are used while ordinary off-load tap changers prevail in distribution circuits. It is to be noted that tap changing transformers do not generate reactive power.

From a system point of view, the regulation of the voltage and reactive power is usually organized in three levels; primary, secondary and tertiary voltage regulation.

• The Primary Voltage Regulation (PVR) refers to the local automatic response of the controllers.
• The Secondary Voltage Regulation (SVR) is an automatic control that coordinates the actions of PVRs at a zonal level. The secondary regulation level is not implemented in all Transmission System Operators TSOs since its added cost and complication are not always justified.
• The Tertiary Voltage Regulation (TVR) refers to the manual optimization of the voltage and reactive power at a regional or national system level (area).

The regulation scheme with three levels is referred to (i) hierarchical voltage regulation, whereas the regulation scheme without SVR is referred to (ii) Centralized Voltage Regulation (CVR). 

Frequency Control: Frequency all over a synchronous power grid is the same in steady state.

Maintaining a nearly constant frequency (one may allow frequency to vary over a very narrow band) is considered an important requirement of power system operation. Frequency in a power system is intimately related to the electrical speed of synchronous generators. The difference between mechanical and electrical torques govern acceleration of a rotor of a generator. Therefore to maintain a constant speed, mechanical input and electrical output power need to be continually matched.

If the system is connected to numerous loads in a power system, then the system frequency and speed change with the characteristics of the governor as the load changes. If it’s not required to maintain the frequency constant in a system then the operator is not required to change the setting of the generator. But if the constant frequency is required the operator can adjust the velocity of the turbine by changing the characteristics of the governor when required. If a change in load is taken care by two generating stations running parallel then the complex nature of the system increases. The ways of sharing the load by two machines are as follow:

• Suppose there are two generating stations that are connected to each other by tie line. If the change in load is either at A or at B and the generation of A is regulated so as to have constant frequency then this kind of regulation is called as Flat Frequency Regulation.
• The other way of sharing the load is that both A and B would regulate their generations to maintain the frequency constant. This is called parallel frequency regulation.
• The third possibility is that the change in the frequency of a particular area is taken care of by the generator of that area thereby maintain the tie-line loading. This method is known as flat tie-line loading control.
• In Selective Frequency control each system in a group is taken care of the load changes on its own system and does not help the other systems, the group for changes outside its own limits.
• In Tie-line Load-bias control all the power systems in the interconnection aid in regulating frequency regardless of where the frequency change originates.  

The transmission lines that connect an area to its neighboring area are called tie-lines. Power sharing between two areas occurs through these tie-lines. Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency constant.

Speed Governing System

• Mathematical Modelling of a Generator
  With the use of swing equation of a synchronous machine to small perturbation, we have
  
  Or in terms of small change in speed
  
• Mathematical Modelling of Load
  The load on a power system consists of variety of electrical drives. The load speed characteristic of the load is given by:
  ΔPe = ΔPL + D Δω
  where ΔPL is the non-frequency sensitive change in load,
  DΔω is the load change that is frequency sensitive.
  D is expressed as % change in load divided by % change in frequency.
• Mathematical Modelling of Prime Mover
  The source of power generation is the prime mover. It can be hydraulic turbines near waterfalls, steam turbine whose energy come from burning of coal, gas and fuels. The model of turbine relates the changes in mechanical power output ΔP_m and the changes in the steam valve position ΔP_V.
  
  where the turbine constant is in the range of 0.2 -2.0s.
• Mathematical Modelling of Prime Mover
  When the electrical load is increased suddenly then the electrical power exceeds the input mechanical power. This deficiency of power in load side is compensated from the kinetic energy of the turbine. Due to this reason, the energy that is stored in the machine is decreased and the governor sends a signal for supplying more volumes of water, steam or gas to increase the speed of the prime mover to compensate deficiency in speed.
  
  The command ΔP_g is transformed through an amplifier to the steam valve position command ΔP_V. We assume here a linear relationship and considering simple time constant we get this  s-domain relation
  
  Combining all the above block diagrams, for an isolated area system we get the following
  

Automatic Generation Control(AGC)

1. If the load on the system is suddenly increased, then the speed of the turbine drops before the governor could adjust the input of the steam to this new load. As the change in the value of speed decreases the error signal becomes lesser and the position of the governor and not of the fly balls gets nearer to the point required to keep the speed constant.
2. One way to regain the speed or frequency to its actual value is to add an integrator on its way. The integrator will monitor the average error over a certain period of time and will overcome the offset. 
3. Thus as the load in the system changes continuously the generation is adjusted automatically to restore the frequency to its nominal value. This method is known as automatic generation control.
4. In an interconnected system consisting of several areas, the task of the AGC is to divide the load among the system, stations, and generators so to achieve maximum economy and uniform frequency.

Automatic Generation Control(AGC) in a Single Area

With the main LFC loop, change in the system load will result in a steady state frequency deviation, depending on the speed regulation of the governor. To reduce the frequency deviation to zero we need to provide a reset action by using an integral controller to act on the load reference setting to alter the speed set point. This integral controller would increase the system type by 1 which forces the final frequency deviation to zero. The integral controller gain needs to be adjusted for obtaining a satisfactory transient response.

Automatic Generation Control(AGC) in Multi Area System

Interconnected areas in a power system

Load frequency control deals with the control mechanism needed to maintain the system frequency. The topic of maintaining the system frequency constant is commonly known as Automatic Load Frequency Control (ALFC). It has got other nomenclatures such as Load Frequency Control, Power Frequency Control, Real Power Frequency Control and Automatic Generation Control.

The basic role of ALFC is:

1. To maintain the desired megawatt output power of a generator matching with the changing load,
2. To assist in controlling the frequency of larger interconnection,
3. To keep the net interchange power between pool members, at the predetermined values.