Example Load Flow
As discussed already, renewable energy generation can affect both line loadings and voltages throughout the system. Load flow is a technique that allows the flows of real and reactive current throughout the network to be calculated, based on the location of the loads and sources and the line impedances. The network of Figure 6.1 is used here to illustrate the way in which load flow analysis is applied at a distribution level to assess the effect of connecting a renewable energy generator at a...
I
Figure 4.24 Circuit of a diode bridge rectifier with a smoothing capacitor and a supply impedance t vl__________________________ Figure 4.25 Waveforms of a diode bridge rectifier with a smoothing capacitor by a series of pulses shown as b in the figure. Because the duration of the pulses is short, their amplitude must be high, if the same average power is to be supplied to the load as it was supplied before the capacitor insertion. The downside of this arrangement is that the current drawn from...
Capacity Factor and Capacity Credit [
When renewables displace significant amounts of conventional generation plant, an extra conventional plant capacity margin is required to maintain system supply reliability. It is important to recognize that an additional plant margin will only be required at times of low electricity demand and high input from variable sources. At other times an additional margin will not be required as there will be sufficient conventional plant available to meet demand irrespective of the contribution from...
A AC Waveforms
In practice AC generators are designed to produce a voltage that, to all intents and purposes, is a pure sine wave. There is a good reason why pure sign waves are used in power networks. A sine wave is the only waveform that, when differentiated or integrated, results in a replica of itself. As will be shown later, electric power system components, including transformers, respond differentially to a sine wave excitation and thus the shape of the waveform is maintained throughout the network....
Power Transfer Equations
There is interest in exploring the mechanism by which power is injected into the grid by a synchronous generator. This can be done by means of the concept of complex power developed in Appendix A. The grid connected synchronous generator of Figure 4.7 will be considered. The complex power at end B of the line is given by Then 1B is expressed as a function of the line voltages using Kirchoff's voltage law, Substituting Equation 4.7 into Equation 4.6 gives I lt -jf - j e-5 Sb - y1 sin 5 j X Vb -...
References Epd
1 Smith, R.J. and Dorf, R.C. Circuits, Devices and Systems, 5th edition, John Wiley amp Sons, Ltd, Chichester. 2 Gross, C.A. Power System Analysis, John Wiley amp Sons, Ltd, Chichester, 1986. 3 Lander, C.W. PowerElectronics McGraw-Hill, Maidenhead, 1987. 4 Slootweg, H. and De Vries, E. 'Inside wind turbines fixed vs variable speed'. Renewable Energy World, January-February 31-40. 5 Pedersen, T.K. 'Semi-variable speed operation - a compromise ' Vestas-Danish Wind Technology A S, Denmark, EWEA...
Photovoltaic Systems
At the heart of a PV system is the PV module. Detailed descriptions of the different PV technologies and the basics of solar cell operation can be found in a wide range of textbooks, for example References 13 and 14 . PV modules produce output determined mainly by the level of incident radiation. They are characterized for given external conditions, by an I-V curve of the type shown in Figure 2.13 . The power, IV, depends on the operating point and is maximized for operation near to the knee of...
Applications to Renewable Energy Generators
All PV systems generate direct current and so power electronic converters, known as inverters, are required to connect them to power systems. As described in Chapter 2, PV modules have an I-V characteristic that depends on incident radiation intensity and to a lesser extent the solar spectrum and module temperature. Different types of PV have different shapes of I-V curve, characterized in simple terms by a fill factor, as explained in Chapter 2 . To maximise the output of any PV module, or...
The Synchronous Generator Equivalent Circuit
To analyse the power flows in electrical systems, component representations are required that can be incorporated into network or circuit models. To use the available circuit analysis tools described in Chapter 5 , it is necessary to build up these representations from basic circuit elements, namely resistors, inductors, capacitors and voltage or current sources Appendix A . Electrical power engineers over the years have developed a range of what are known as equivalent circuits for network...
Small Hydro
A small-scale hydro is commonly defined as being smaller than 5 MW. At even lower powers lt 100 kW , the so-called microhydro is subdivided into dammed and run of the river schemes in which there is no storage a further distinction is into high and low head. It is estimated that the world potential of small microhydro is around 500GW of which roughly only one-fifth has been exploited to date. A particular attraction of small microhydro is that the resource is often located in remote rural...
Frequency Control at Different Timescales [
The maintenance of frequency involves a response from generators over several timescales ranging from seconds to days. This response is not only required to follow the demand' s fast variability from second to second and its slow variability over the day, but also sudden substantial mismatches between generation and demand, for example during system faults. Figure 3.10 illustrates a typical system frequency trajectory plotted on a nonlinear time scale. From the origin of the graph until about 8...
Faults and Protection
Faults in power systems can be caused by a whole range of events. Lightning strikes, overhead lines breaking in storms and workmen digging through cables are common examples. Faults often result in the conductors being effectively shorted together or shorted to ground. In either case, very large currents can flow. The system must be designed to withstand these currents for short periods and to disconnect the faulted section quickly, so that the rest of the system continues to operate with a...
The Transmission System [
Figure 1.12 in Chapter 1 gave a pictorial view of a typical power system and the desirability of using various voltage levels for transmission were explained. Overhead lines, supported Renewable Energy in Power Systems Leon Freris and David Infield 2008 John Wiley amp Sons, Ltd Figure 5.1 Overhead lines at four different voltage levels. Courtesy of Murray Thomson Figure 5.1 Overhead lines at four different voltage levels. Courtesy of Murray Thomson on steel towers pylons , concrete towers or...
Fault Level Shortcircuit Level Weak Grids
In systems operating at various voltages, it is useful to multiply the fault current Isc by the nominal operating voltage before the fault . On a per-phase basis this is VphIsc, where Vph is phase-to-neutral voltage. In a balanced three-phase system, vph v a 3, where V is line-to-line voltage. Multiplying by 3 gives the three-phase fault level Sk where V is the nominal line-to-line voltage before the fault and Isc is the symmetrical three-phase fault current, as introduced above. The fault...
References Txu
1 National Grid Company NGC website www.nationalgrid.com uk . In particular, the 'Seven Year Statement' is very informative and now includes a large section on 'Embedded and Renewable Generation'. 2 ER G83 1 is available from the Energy Network Association www.energynetworks.org.uk. 3 McGrow, L. 'Beat the system', IETPower Engineering, April May 2006, 28-30. 4 Jenkins, N., Allan, R., Crossley, P., Kirchen, D. and Strbac, G. Embedded Generation, IEE Power and Engineering Series 31, Institution...
Threephase Equations
The synchronous machine equations were derived without any reference to its three-phase nature. Assuming that the voltages in Equations 4.8 and 4.9 are phase to neutral in volts, the equations will give the single-phase active and reactive powers in watts and VAR respectively. If the voltages are in kV then the active and reactive powers - both functions of voltage squared - will be in MW and MVAR. In a balanced three-phase system the three-phase P and Q will be three times the per-phase P and...
Wind Turbines
The power in the wind than can be extracted by a wind turbine is proportional to the cube of the wind speed and is given in watts by Figure 2.6 The Vestas V9G, Systems A S 3MW wind turbine. Reproduced with permission of Vestas Wind where p is the air density, A is the rotor swept area, U is the wind speed and Cp is the power coefficient that represents the aerodynamic efficiency of the rotor. The variability in power output from one wind turbine would therefore be expected to substantially...
Competitive Wholesale Markets in Other Countries Introduction
The England and Wales pool-based wholesale electricity market was ground-breaking when it was introduced. Since its introduction, other countries have introduced wholesale electricity markets based on power pools, bilateral forwards and futures markets and balancing markets. Broadly speaking, the wholesale price of electricity can be set in advance ex ante , in real time or after the event ex post . Ex ante prices can typically be set at the day-ahead stage. Clearly, it is not possible to know...
Reactive Power Management
The principle of conservation of reactive power described in Section A.13 requires that reactive power is scheduled so that as the consumer demand of Q varies over a day, appropriate Q resources are available to provide it. In Chapter 3 it was explained that a discrepancy between demand and supply of active power is manifested by rises or falls in frequency, a parameter that is common to the whole interconnected power system. In contrast, reactive power deficits or excesses manifest themselves...
v Vv sin at
respectively, where V and I are the peak values and lt and d are phase angles with respect to a reference sinusoid. Figure A.11 Phasor representation of AC quantities If two AC voltages are added together by being connected in series as in Figure A.13, their voltage magnitudes do not directly add or subtract as with scalar voltages in DC. Instead, these voltages are complex quantities, and just like the above phasors, which add up in a trigonometric fashion, an 8 volt source at 0 added to a 6...
Power Load Angle Characteristic Stability
Equation 4.8a is plotted in Figure 4.8 to illustrate the dependence of the generated active power on the load angle. Note that a synchronous generator SG connected to an infinite bus is capable of generating a maximum active power PBmax . at 8 90 . Any additional applied mechanical torque will increase the load angle beyond 90 , with a consequential decrease in electrical power. Physically, the peripheral magnetic forces linking the two fields together is insufficient to maintain the locking...
Fault Level Increase
As noted previously, fault level can be used as a measure of grid strength and can be compared with proposed generator capacity to give an indication of likely effects on line voltage. However, as shown in Figure 6.6, the fault level can itself be increased by the connection of embedded generators, particularly where synchronous machines are involved. This does not invalidate the previous comments on voltage effects, but it does represent another factor to be considered in the connection of a...
Offshore Wind Farm Development
An offshore installation has advantages over and above the reduction in turbine costs from the resulting economies of scale. The marine environment is windier resulting in an increased energy yield, and the winds are more persistent and less turbulent making system-wide integration easier. Very large wind turbines that might cause an unacceptable visual intrusion onshore may well be acceptable if sited away from the shore. Additionally, the transportation of exceptionally large or heavy items...
Transformer Basics
The transformer is an indispensable part of any power system operating at a range of voltages. The transformer mode of operation is included here as it provides a useful aid to the under- Figure 4.9 The Transformer. Reproduced from Reference 1 with permission of John Wiley amp Sons, Inc. Figure 4.9 The Transformer. Reproduced from Reference 1 with permission of John Wiley amp Sons, Inc. standing of the mode of operation of induction generators which are used extensively in wind turbines. The...
Introduction Jae
The previous section assessed the value of renewable energy generation when competing directly with other 'conventional' power generation sources in an open electricity market. Many countries have recognized that renewable energy would find it difficult to compete on Variability. As discussed, most renewable energy sources cannot easily be controlled and their output forecast with 100 accuracy. Cost. Many of the renewable energy technologies are not yet mature and thus cost more than...
Connection Voltage
The distribution system in the UK includes 400 V, 11 kV, 33kV and 132kV other countries have similar voltage levels. As mentioned in Section 5.7.4, the fault level at the point of connection which is a measure of network strength, is an important design parameter, not only for predicting currents under fault conditions, but also for predicting performance under normal operating conditions and in particular, voltage rise. The fault level at the PCC is very important when considering connecting a...
Structure of the Electrical Power System
Electricity is widely used because it is a supremely flexible form of energy. It can be readily and efficiently transported and is easily converted to other forms of energy. Mechanical energy can be provided by very efficient motors, light energy by increasingly efficient light Figure 1.12 Pictorial view of the components of a large power system Figure 1.12 Pictorial view of the components of a large power system fittings, heat energy by 100 efficient resistive elements, and power supply to...
Optimum Economic Dispatch
The aim is to load generating sets in response to demand changes so as to minimize the cost of supply. This is known as optimum economic dispatch OED and over the years sophisticated OED methods have been developed to identify the minimum cost solution and at the same time satisfy numerous engineering and operational requirements and constraints. Here the basic ideas that provide guidance in the task of adjusting the load on individual conventional or RE generators will be investigated in order...
Load Flow and Power System Simulation [
Section 5.4 looked at the maths describing an individual overhead line or underground cable. Mature power systems are likely to have thousands of such lines, all interconnected. The same basic maths applies to each and every line, but now the equations must be solved simultaneously. Structured procedures for such calculations are known as load flow. A basic load flow calculation provides information about the voltages and currents and complex power flows throughout a network, at a particular...
Wind Variability
The wind speed at a given location is continuously varying. There are changes in the annual mean wind speed from year to year annualI changes with season seasonal , with passing weather systems synoptic , on a daily basis diurnal and from second to second turbulence . All these changes, on their different timescales, can cause problems in predicting the overall energy capture from a site annual and seasonal , and in ensuring that the variability of energy production does not adversely affect...
A Phasor Addition
If phasors that are not in-phase or antiphase are added, their magnitudes add up quite differently to that of scalar quantities. Figure A.12 shows an example of such an addition. In fact, phasors add up in exactly the same way as vectors that represent velocities or forces in mechanical systems. As explained in Section A.4 the 'effective' value of an AC waveform is its RMS value hence AC quantities, unless stated otherwise, are always labelled in terms of their RMS value and are expressed by a...
Solar Thermal Electric Systems
Solar thermal electricity generation systems most commonly use solar concentrators to produce high temperatures that can drive heat engines with acceptable conversion efficiency. Two main types of generator suitable for large scale generation have so far been demonstrated, both requiring direct or beam radiation. Climates with cloudy or overcast conditions, where most of the radiation is diffuse, are thus unsuited to this technology. The two technologies are Large collections or solar farms of...
A Complex Power
The V and I phasors in Figure A.18 are shown again in Figure A.19 b in the form of a triangle. With the current as reference, the voltage V applied across the circuit is equal to the P i2r vi cos q c Power triangle P i2r vi cos q c Power triangle Figure A.19 The complex power triangle phasorial addition of the voltage VR across the resistor in phase with the current and voltage VX across the reactor in quadrature and leading the current . If the magnitude of each voltage phasor is divided by I...
A Rectangular Notation
Simple electric networks can be analysed through phasor diagrams. This is extremely tedious when a more challenging circuit is involved and becomes impossible for real life networks. Phasors can be represented mathematically by complex numbers and circuits can be analysed through algebraic manipulations without the laborious task of drawing phasors. There are two basic forms of complex number notation the polar, described earlier, and the rectangular or Cartesian. In the rectangular form, a...
Costing Pollution
The studies mentioned above along with several others have looked at overall damage potentials on health and the environment, assigning a cost penalty to each generating technology, depending on the fuel. This approach enables the difference in external costs between, for example, coal and wind, to be easily compared. Another approach calculates costs per pollutant, recognizing that different fuels generate different amounts of pollutant. Typically these penalties, as proposed by some states in...
Steady State Voltage Rise
The connection of a distributed generator usually has the effect of raising the voltage at the PCC and this can lead to overvoltages for nearby customers. The need to limit this voltage rise, rather than exceeding the thermal capacity of the line, often determines the limiting size of generator that may be connected to a particular location. An initial estimate of the voltage rise caused by connection of a generator can be obtained from analysis of the system as represented in a simplified form...
Thevenin Equivalent Circuit
Consider again the Icelandic national power system shown in Figure 5.12. It is often useful to be able to calculate performance at one particular node, without having to perform a full load flow or fault analysis of the entire network. This can be achieved by representing the network by its Thevenin equivalent, as explained in the Appendix. The values in the Thevenin equivalent circuit shown in Figure 5.15 must be calculated for the particular node in question. The magnitude of Zth can be found...
Point of Common Coupling PCC
A basic requirement in connecting any generator to a power system is that it must not adversely affect the quality of electricity supplied to other customers on the network. With this in mind, it is useful to identify again the point of common coupling PCC . Official definitions vary, but in simple terms the PCC is the point where the generator is connected to the public network as shown in Figure 6.1. In other words, the PCC is the point on the network, nearest to the generator, at which other...
Large Wind Turbines
Recent progress in wind turbine technology has been breathtaking. At the time of writing 5MW wind turbines are commercially available. Ten years ago, the largest wind turbine on the market was typically an 800 kW machine with most manufacturers offering 600 kW units. At present, most wind turbines are fitted with rotors of 60-90 m compared to the 35-45 m of the mid-1990s. Due to economies of scale, larger machines generate electricity at a lower cost per kW h , particularly in offshore...
Equal Incremental Cost Dispatch
The merit order philosophy is adequate and convenient for rough scheduling but as a precise tool of economic dispatch it is inaccurate. The reason for this is that cost curves are not quite linear as assumed above they are better described by a quadratic function as in the example of Figure 7.5 . Such curves can be used to determine the overall efficiency of the plant at various output levels. As previously, it can be assumed that only two plants A and B are supplying a demand Pd. Following the...
A The Th venin Equivalent Circuit
The one-port circuit of Figure A.1 was initially assumed to be passive, i.e consisting of R, L or C components. In contrast, active networks include energy sources. A valuable method of representing active networks by simpler equivalent circuits is based on the Th venin theorem. This theorem states that any one- port network consisting of passive elements and energy Figure A.27 Thevenin equivalent circuit sources can be replaced by an ideal voltage source VT the Thevenin voltage in series with...
ZLu f T
Figure 5.8 Resistance, inductance and capacitance of a three-phase overhead line or underground cable Figure 5.9 Single-phase equivalent circuit of a transmission line Figure 5.9 Single-phase equivalent circuit of a transmission line short length, the capacitance is substantial. For such cases, the circuit of Figure 5.9 can still be used for the first stage of the analysis. The capacitance can be lumped at the two ends of the line and its effect taken into account at a second stage in the...
The Asynchronous Generator
Asynchronous or induction machines operating as motors are the most widely used electromechanical converters. In an induction machine the stator is identical to the one for synchronous machines shown in Figure 4.3 in which three-phase currents supplied to the stator produce a rotating magnetic field RMF . The rotor, however, is radically different and it has neither an external magnetizing source nor permanent magnets. Instead, alternating currents are injected in the rotor from the stator...