ReGrid: Frequency and voltage regulation in electrical grids

Transcription

1 # ReGrid: Frequency and voltage regulation in electrical grids I. Introduction 2 II. Table of contents 1. Assessing the solar thermal potential (potential analysis) 6 2. Awareness raising: broad campaigns targeting the general public 8 3. Awareness raising: targeted campaigns to develop specific market areas Financial incentives: VAT reductions Financial incentives: public loans at preferential conditions Regulatory measures: energy efficiency requirements for buildings Regulatory measures: solar obligations Building permits solar thermal in listed buildings Quality Assurance: product standards and certification Health & Safety requirements Qualification of skilled personnel Research & Development programmes 25 III. Further Reading 27 1

2 Table of Content LIST OF ABBREVIATIONS...3 LIST OF SYMBOLS...4 LEARNING TARGETS BASIC CONCEPTS WHY FREQUENCY AND VOLTAGE CONTROL? CONTROL VARIABLES FOR FREQUENCY AND VOLTAGE STABILITY IN AN ELECTRICAL POWER SYSTEM POWER QUALITY IN ELECTRICAL GRIDS CONTROL OF INTERCONNECTED POWER SYSTEMS REQUIREMENTS IN DIFFERENT INTERCONNECTED SYSTEMS PROVISION OF ANCILLARY SERVICES IN ELECTRICAL GRIDS ELECTRICAL SYSTEM FREQUENCY AND ACTIVE POWER REGULATION FREQUENCY CONTROL IN POWER SYSTEMS EXCERPT: ELECTRICAL SYSTEM FREQUENCY AS A COMMUNICATION LINK FOR ACTIVE POWER SHARING REACTIVE POWER AND VOLTAGE CONTROL EFFECTS OF ACTIVE AND REACTIVE POWER FLOWS ON VOLTAGE LOAD FLOW CALCULATIONS MITIGATION OF VOLTAGE STABILITY PROBLEMS/REACTIVE POWER MANAGEMENT INTEGRATION OF RENEWABLE ENERGY GENERATION IN POWER SYSTEMS VOLTAGE EFFECTS ACTIVE AND REACTIVE POWER FROM RENEWABLE ENERGY GENERATORS CODES AND REGULATIONS SUMMARY REFERENCES AND RECOMMENDED FURTHER READING GLOSSARY

3 List of abbreviations AC DC ENTSO-E FACTS IEEE kv LV MV PWM PV RE STATCOM TSO UCTE VAR Alternating current Direct current European Network of Transmission System Operators for Electricity Flexible alternating current transmission system Institute of Electrical and Electronics Engineers Kilovolts Low voltage Medium voltage Pulse width modulation Photovoltaic Renewable energy Static synchronous compensator Transmission system operator Union for the Coordination of Transmission of Electricity Volt-ampere reactive 3

4 List of symbols AC Symbol Description AC generator providing a sinusoidal voltage source Resistor Inductor Voltage node Load Earth Capacitor Thyristor Transformer DC-AC inverter Solar photovoltaic generation 4

5 Learning targets After studying this chapter you will: Understand the basic technological principles governing the operation of electrical power systems. Be aware of the parameters that affect frequency and voltage stability in power systems. Be familiar with the methods and tools available to guarantee frequency and voltage stability in the event of contingencies in power systems. Learn about the principles governing power flow in electrical power systems in additional mathematical modules. Understand the differences in electrical grid interfacing between conventional generation units and renewable energy generation units. 1 Basic concepts The purpose of this section is to introduce the main electrical concepts necessary for an understanding of the operation of electrical systems. A very simple electrical circuit can be built by connecting a 100W (watt) incandescent light bulb to an electrical socket. 100 watts is the nameplate rated electrical power of the incandescent bulb. The electrical power supplied by the mains to the incandescent light bulb enables it to do work (in this case in the form of light). The simplest way to calculate the electrical power in watts (W) consumed by an appliance such as an incandescent bulb is to multiply the applied voltage, in volts (V), by the current which flows through it, in amps (A). Voltage is the difference in electrical potential between two points. The higher the potential, the more energy that can be transferred between those points. In good conductor materials, electrons are not tightly bound to the nucleus of the atom. When a voltage is applied, these free electrons wander from atom to atom, constituting an electrical current. There are two types of current, as shown in figure 1. When free electrons flow at a steady rate in one direction only, the current is said to be direct current (DC). When the amount of free electrons and their direction change cyclically, usually sinusoidally, the current is called alternating current (AC). The number of times the current waveform reaches its positive peak per second is called the current frequency. In Europe, the AC electricity delivered by utility companies has a frequency of 50 cycles per second, or 50Hz (hertz). 5

6 Figure 1: a) Direct current (DC) waveform, b) Alternating current (AC) waveform. Source: RENAC The amount of electrical energy used by an appliance is found by multiplying its consumed power by the length of time of operation. Thus, for example, a 100W incandescent light bulb that is operated for 10 hours will consume 100Wx10h, that is to say 1000Wh or 1kWh (kilowatt hours) of energy. Electrical circuits are composed of a limited amount of different components. The basic circuit elements which can be found in electrical models of power systems are generators, resistors and inductors. Generators are usually modelled as voltage sources. Voltage sources generate a given voltage independent of the current drawn from the generator. The general expression for the sinusoidal voltage waveform delivered by a conventional generator is: v(t) = V peak sin (ωt + θ) (0.1) where v(t) is the voltage, a function of time; V peak is the amplitude of the voltage waveform; ω is the angular frequency (measured in radians/s); and θ is the phase angle (radians) shows the different parameters that define a voltage sinusoidal waveform. Figure 2: AC voltage sinusoidal waveform. Source: RENAC 6

7 The meaning of the peak voltage (V peak ) is straightforward. The angular frequency ω of a sinusoidal waveform is related to the linear frequency f mentioned above by the following expression: ω = 2π (radians/cycle) f (cycles/s) = 2πf (0.2) Regarding the phase angle θ, it must be mentioned that any sine wave that does not pass through zero at t = 0 has a phase shift. θ is the phase angle in degrees or radians that the waveform has shifted either left or right from the reference point along the horizontal reference axis. There will usually be a phase difference of the same frequency between two sinusoidal waveforms. Sinusoidal waveforms can be represented by vectors called "phasors", where the vector length is determined by the peak amplitude and the direction given by the phase angle θ (see figure 3). Figure 3: Phasor representation of sinusoidal waveforms. Source: RENAC Resistors are passive elements that model the effect of electrical resistance in electrical circuits, defined as the opposition of a material to the flow of an electric current. As stated by Ohm s law, the voltage drop through a resistance is directly proportional to the current across it. The constant of proportionality is the resistance value R measured in ohms (Ω). 7

8 Figure 4: Symbol and voltage-current relationship in a resistor. Source: RENAC When connecting an AC voltage generator to a resistor, the voltage across the resistor is the same as the voltage delivered by the generator. The current that flows though the resistor can be calculated using the expression as follows: I = v(t) R = V peak sin (ωt) (0.3) R The phase angle of the resulting current is the same as the phase angle of the voltage (zero), as can be observed in Fig. 5 b) and c). Figure 5: a) AC voltage generator connected to a resistor, b) Voltage and current through the resistor, c) Phasor representations. Source: RENAC Another passive element that is often used in electrical circuits that model power systems is an inductor. An inductor is a passive electrical component which stores energy in a magnetic field. The effect of an inductor in a circuit is to oppose changes in current through by developing a voltage across it proportional to the rate of change of the current. The relationship between the time-varying voltage v(t) across an inductor with inductance L and the time-varying current i(t) passing through it is described by the following expression: v(t) = L di(t) dt (0.4) 8

9 The inductor is again connected to an AC voltage generator, as in the case of the resistor. The voltage across the inductor is the same as the voltage delivered by the generator. The current can be calculated using relation (0.4): i(t) = 1 v(t)dt = 1 V L L peaksin (ωt)dt = V peak cos (ωt) (0.5) ωl The current and voltage waveforms are illustrated in Fig. 6. As can be observed from relation (0.5) and b): The current through the inductor has the same frequency as the applied voltage. The current lags behind the voltage by a quarter of a cycle. Referring to relation (0.2), where the concept of angular frequency was introduced, a complete cycle is equivalent to an angle of 2π. Therefore, a waveform lagging behind by a quarter cycle corresponds to a phase shift angle of θ = 90. The corresponding phasors for voltage and current are illustrated in c). The proportionality factor between voltage and current is not just the inductance L, but the reactance Lω. The reactance will be denoted by the abbreviation X in the remainder of the module, and depends on the inductance value of the inductor and on the frequency of the voltage applied through the inductor. Figure 6: a) AC voltage generator connected to an inductor, b) Voltage and current through the inductor, c) Phasor representations. Source: RENAC The expressions derived for the relation between current and voltages for different electrical components form the foundation for the introduction of the very important concepts of apparent (S), real (P) and reactive power (Q). 9

10 In order to calculate the instantaneous power supplied by the voltage source to the resistor and inductor, it is necessary to multiply the waveforms of the voltage and current. The results are illustrated in Fig. 7, with the green waveform being the instantaneous power transferred from the generator to the load (resistor or inductor). In the case of the resistive circuit, the product of voltage and current is positive at all times, indicating that the power flow direction does not change. Real power is transferred from the generator and is dissipated at the resistor. The situation changes in the second circuit, with an inductor as the load. During every cycle, for half of the cycle the product of voltage and current is positive, but for the other half of the cycle the product is negative. On average, exactly as much energy flows from the generator to the inductor as flows back. There is no net energy flow over one cycle; only a transfer of reactive energy takes place. Certain appliances do not have a purely resistive or inductive character. A good example is a motor. There is a portion of the current absorbed by a motor which is in phase with the voltage in the motor. This is the current that creates real power in the motor and which can be used to create mechanical work. There is another part of the current which is required by the stator of the motor to create the magnetic field necessary for the motor to operate. As mentioned above, inductors are the components that store magnetic energy. The stator of a motor can therefore be modelled as an inductor and, as we have seen, the current in an inductor lags behind the voltage by 90 degrees. This magnetising current in the motor does not create real power, but reactive power. Figure 7: Instantaneous power in resistive and inductive circuits. Source: RENAC 10

11 A concept that is very useful in analysing the relation between load current and magnetising current that is to say, real and reactive power is what is known as the power triangle. For appliances like motors, voltage V and current I are not in phase, but instead present a certain phase shift θ. The pure product of the current drawn by the motor (amps) and the voltage (volts) across the motor equals the apparent power consumed by the motor (S, measured in volt-amperes). The real power consumed by the motor, which can be used to produce mechanical torque, is the horizontal projection, which is given by the expression S*cosθ=V*I*cosθ (measured in watts). The vertical projection is the reactive power, which cannot be converted into work, and in the case of motors is mainly used to magnetise the stator. Reactive power can be calculated using the expression S*sinθ=V*I*sinθ, and is measured in VAR (volt-amperes reactive). Figure 8: Power triangle. Source: RENAC The power factor of an AC electric power system is defined as the ratio of the real power (P) flowing to the load to the apparent power in the circuit (S). In purely resistive circuits, voltage and current waveforms are in phase and therefore all the apparent power is real power and can be consumed. In this type of circuit the power factor is 1. Circuits containing purely resistive loads, for example a filament lamp, have a power factor of 1. When the load is not purely resistive e.g. induction motors the apparent power does not equal real power. The power factor will consequently be less than 1. The apparent power is a vector quantity that can be represented as a complex number: either in rectangular format with real and imaginary components, such as S = P + jq or in polar format S θ with S being the amplitude (S=V*I). is simply a symbol to denote that the value beside it is an angle, in this case θ, the phase shift of the apparent power S. 11

12 2 Why frequency and voltage control? The main purpose of an electrical power system is to efficiently deliver reliable electricity to consumers. Voltage and system frequency are the main variables to guarantee the stability of an electrical system. The simplest electrical power system consists of a single electric generator and a load. An electric generator converts rotational kinetic energy to electric energy. The law of energy conservation requires that, at any instant, the power demanded by the load is supplied by the generator and/or by energy stored within the system 1. If the consumption in the load increases, the extra energy demand is initially supplied by the rotational inertia of the generator through a decrease of its speed. The frequency of the voltage in an electrical generator is directly proportional to the rotational speed of its rotor. All the alternators connected to an electrical system rotate with the same electrical angular speed, according to the relation f = p n 60 where f is the frequency, p the number of poles in the alternator and n the rotational speed of the rotor in rpm (revolutions per minute). Consequently, the decrease in rotational speed will be accompanied by a proportionate decrease in the frequency of the voltage generated by the generator. An electrical power system consisting of thousands of interconnected generators and loads behaves much like a simple one-generator one-load system, with the frequency being the same for the whole interconnected power system. However, there is never a perfect equilibrium between generation and demand in a power system; since the amount of storage is usually rather limited in a power system when compared with the load demanded, there will be frequency shifts as a result of the imbalances between generation and demand, as shown in Fig. 9. Frequency drifts downwards when demand exceeds supply and vice versa. (1.0) 1 Leon Freris, David Infield (2008): Renewable Energy in Power Systems. John Wiley & Sons, New York, NY. p

13 Figure 9: Frequency behavior due to imbalances between generation and demand. Source: RENAC Regarding the first variable necessary to guarantee the stability of an electrical system, there are several reasons why it is desirable to keep frequency in a power system within narrow bounds, as mentioned by Freris et al [2]: It ensures that electric motors operate at a virtually constant speed. A fixed speed is required in many consumer applications where an AC electric motor is used to drive a device at an approximately constant rate, e.g. a pump in a washing machine. In electronic applications, the mains frequency can be used as a basis for timing various processes. Transformers are sensitive to frequency variations and may be overloaded if the frequency drifts substantially from the nominal value. Finally, and most importantly, in traditional power stations the performance of the generators is dependent on the performance of all the auxiliary electric motor drives that deliver fuel and air to the boiler, oil to bearings and cooling services to several systems. If these auxiliaries underperform due to low speed caused by low frequency, power station output can be reduced. This phenomenon could lead to a runaway situation with cascaded shutdowns of power stations and blackouts. Regarding the second variable voltage manufacturers of electrical appliances design their products to operate with a certain nominal voltage in order to achieve effective performance and comply with safety standards. The electrical grid operator is therefore obliged by law to provide electricity at consumer terminals at voltage levels that do not deviate from a nominal value by more than a certain percentage. So, for example, following voltage harmonisation, electricity supplies within the European Union are now nominally 230 V ± 6% at 50 Hz 2. Operating appliances outside the specified voltage level range can lead to overheating, malfunctions, reductions of the expected equipment lifetime, etc. Electric drives and motors are affected by voltages below and above the nameplate voltages: 2 CENELEC Harmonisation Document HD 472 S1:

14 Since power is proportional to the product of current and voltage, when electric motors are subjected to voltages below the nameplate rating, current must increase to provide the same amount of power, which increases the build-up of heat within the motor. Furthermore, the mechanical torque is inversely proportional to the square of the voltage. Thus a 10% reduction from nameplate voltage would reduce the torque by a factor of 0.9 x 0.9, that is to say, the resulting torque would be 81% of the original value. Contrary to what would be expected, a higher than nominal voltage also leads to overcurrents. High voltage to a motor tends to push the magnetic portion of the motor into saturation. This causes the motor to draw excessive current in an effort to magnetise the iron beyond the point to which it can easily be magnetised 3. In order to achieve voltage stability at consumer terminals, the voltage at all nodes in a power system must be maintained within limits. This is a task which is performed by TSOs and DSOs (transmission system operators and distribution system operators), which are the entities entrusted with carrying electrical power over long distances, allowing for generation and consumption to be geographically separated. The lower voltage levels of an electrical power system are commonly named distribution systems, while higher voltage levels are commonly named transmission systems. Increasing the voltage reduces the current in the transmission lines, and hence the size of conductors and distribution losses, making it more economical to distribute electrical power over long distances. Fig. 10 shows a simplified diagram of an electrical power system with different voltage levels. Transformers are the interfaces between the different voltage levels. 3 Discussing the operation of electrical motors is beyond the scope of this webinar, but further details can be consulted in references [2] and [8]. 14

15 Figure 10: Voltage levels in electrical power systems. Source: RENAC Furthermore, the following table lists typical voltage ranges for the different voltage levels present in electrical grids. Voltage level Low voltage Medium voltage High voltage Voltage range <400V, for industrial applications up to 690V 6kV to 30kV From 50kV to 750kV Table 1: Voltage ranges for different voltage levels in electrical grids. Source: RENAC 2.1 Control variables for frequency and voltage stability in an electrical power system Frequency As explained in the previous section, for a near constant frequency to be maintained, the production and consumption of active power has to be in equilibrium at every point in time. The better the balance between generation and consumption, the smaller the frequency variation in the grid, and consequently the better the electricity quality. The electricity demand for a single load is characterised by a high variability. Fig. 11 shows the load curve for a single household in Germany, with a time resolution of 1 min and partially averaged. With a finer time resolution the variability would be higher and the ratio between minimum and maximum demand would be greater (for example, due to power spikes from switching off appliances, etc.). 15

16 Figure 11: Demand curve for a household in Germany. Source: RENAC However, the electricity consumption of different consumers is not correlated. By combining the loads of different electricity accounts, the demand curve is smoothed and the ratio of peak demand to lowest demand decreases. This effect becomes stronger as more electrical power systems are interconnected. For large power systems, demand aggregation and interconnection makes it fairly feasible to forecast the expected load for the day ahead, thus facilitating the task of scheduling the generation required to supply the demand, plus a reserve which will be needed to regulate frequency in the system. Figure 12: Power generation scheduling in electrical power systems. Source: RENAC The transmission system operator is the entity in charge of plant scheduling. In systems in liberalised electricity markets, the main criteria used to decide which generators meet which 16

17 part of the demand is economic, and allocation is usually carried out through bidding systems. In national power systems without electricity markets, the dispatch centre is responsible for allocation. Base load is usually defined as the minimum level of demand on an electrical power system over 24 hours. This continuous energy demand is covered by what are known as base load plants, which are production facilities delivering electricity at a constant rate, usually at a low cost relative to other production facilities available to the system 4. Their efficiency decreases at less than full output. Base load power plants include coal, nuclear and biogas plants. Medium load power plants operate for between 20% and 60% of the day, typically during the daytime and early afternoon. They fill the gap between the base load and peaks in electricity demand. Intermediate load power can be increasingly supplied by renewable energy sources such as wind and solar power. To meet peak demand, peak load power stations are designed to run for short periods of time each day. They can be started quickly from cold, and vary the quantity of electrical output by the minute. Gas-fired plants as well as hydro-electricity are typically used to provide peak load power. As mentioned in section 0, if power consumption is greater than production, the grid frequency is below the nominal value. Similarly, if production is greater than consumption the grid frequency is above the nominal value. A certain portion of the peak power generation capacity available in a power system which is highly responsive to changes in electrical demand is used to guarantee frequency stability in the system. These reserves will be used by the different frequency control levels (primary, secondary and tertiary) which will be explained in detail in section 5.1. The active power reserves that can be activated automatically by frequency changes are usually classified as below: 17 The frequency response reserve is provided by generators usually equipped with governors. Following a loss in supply, the additional energy demand is initially supplied by the rotational inertia of the generator, and its speed is decreased due to the increased mechanical load. The function of a governor is to sense any changes in speed and to adjust the fuel supplied to the prime mover so that the speed (and therefore the frequency) is controlled. The frequency response reserve is used for primary frequency control and, therefore, is usually named primary reserve. The spinning reserve is extra generating capacity available by increasing the power output of generators already in operation (used as secondary/minute reserve). The operating reserve includes generating capacity available within a short period of time to meet demand in case a generator goes down or there is a disruption in supply (used as secondary/minute reserve). The replacement or long-term reserve is reserve power provided by generators that require a longer start-up time (30-60 min) and is used to relieve the generating capacity available to meet demand in case a generator goes down, in case there is a disruption in supply or to cover system capacity or congestion. 4 "Energy Dictionary - Baseload plant". Source: EnergyVortex.com: Accessed

18 The Time responses for different kinds of reserve power are illustrated in Fig Voltage 18 Figure 13: Time response for different kinds of reserve power. Source: RENAC In order to guarantee voltage stability at the different nodes in an electrical power system, the line impedances in the transmission system must be considered. The Fig. shows a simplified equivalent circuit of a transmission line. Cables used in overhead lines or underground cables are made out either of copper, aluminium, steel and alloys. These materials present a small but not negligible resistance to the flow of electrical current when considering the long distances covered by transmission lines. The most common method for alternating current power transmission and distribution are three-phase systems, where three circuit conductors carry three alternating currents (of the same frequency) that reach their instantaneous peak values at different times 5. Fig. 14 shows a high voltage overhead line. The steel towers carry doublecircuit three-phase lines with two conductors per phase bundle. Furthermore, an earth wire conductor has been strung at the top of the steel towers in order to shield the phase conductors from direct lightning strikes and to provide a low impedance path in case of faults. The current that is carried by single-phase conductors creates a magnetic field around the conductor. When the current changes, the magnetic flux changes correspondingly. Consequently a voltage is generated within the conductor itself as well as in the conductors around it. Therefore, conductors in a transmission line behave like an inductor. The conductors exhibit self and mutual inductance. As explained in the introductory section 1, the reactance X L can be calculated easily once the line inductance has been obtained. 5 William D. Stevenson, Jr. (1975): Elements of Power System Analysis. Third Edition, McGraw-Hill, New York, NY. p. 2. ISBN:

19 Figure 14: High voltage overhead lines. Source: RENAC Assuming that the three-phase system is balanced, the transmission line can be simplified to the single-line circuit in Fig. 15 a). Both the line resistance R L and the line reactance X L have been included. Fig 15 b) shows the voltage drops across the different elements of the transmission line. As already mentioned in section 1, due to the presence of an inductive element the current I is not going to be in phase with the voltage U A. The voltage drop in the line resistance U R =R L *I will be in phase with the current I, while the voltage drop in the line reactance X L will lead the current by 90. I R L X L U AB U R U X U A U A U AB U B I U B - U AB U X U R a) b) Figure 15: Equivalent circuit of a transmission/distribution line and phasor diagram of voltages and currents. Source: RENAC 19

20 In order to calculate the voltage at the two ends of this transmission line, the voltage across the line impedance is calculated according to Ohm s law 6 : U AB = U A U B = I Z L = I (R L + jx L ) (1.1) The complex impedance Z L includes the resistance R L as well as the reactance X L mentioned before. Due to the reactive and inductive character of the line impedance, there will be active power (P) flowing through the line as well as reactive power Q. The apparent power S flowing through the transmission line is related to the voltage and current by where I* is the complex conjugate 7 of I. S = P + jq = U A I (1.2) Combining equations (1.1) and (1.2), a general relationship for the voltage drop can be obtained: U AB = U = I Z L = S U A Z L = (P jq) (R L+jX L ) U A = (PR L+QX L ) U A + j (PX L QR L ) U A (1.3) Usually the main interest is in the real (or scalar) value of the voltage drop in the line impedance, which equals the voltage difference between the two nodes A and B. As can be observed in figure 15 b), this scalar difference is mainly influenced by the real part of U AB (its horizontal component). Equation (1.4) can be simplified to the scalar relationship: U real PR L+QX L U A (1.4) This relation provides a convenient way to estimate the voltage drop in a transmission line given the active and reactive power carried by the line. Expression (1.4) can be further simplified if the characteristics of the transmission line analysed are taken into account. Due to the geometry and low resistance of the conductors used, medium and high voltage transmission lines present a higher value of reactance X L than resistance R L. This transmission line ratio, often denoted X/R, varies depending on the voltage level. 6 The detailed derivation can be found in: Leon Freris, David Infield (2008): Renewable Energy in Power Systems. John Wiley & Sons, New York, NY. p The complex conjugate of a complex number is another complex number with the same real part but with imaginary parts of equal magnitude and opposite signs. For example, 2+5i and 2 5i are complex conjugates. 20

21 Line voltage (kv) X/R Table 2: Transmission line parameters. Source: Leon Freris, David Infield: Renewable Energy in Power Systems, John Wiley & Sons High X/R ratios mean that the first term in equation (1.4) will be small compared to the second term, and therefore the following approximation can be made: U real QX L U A U Q (1.5) Equation 1.5 provides a very important insight into the voltage stability of electrical power systems: network voltages at the different nodes of the middle and high voltage distribution layers of an electrical power system are mainly determined by reactive power flows. Therefore, in order to guarantee voltage stability and maintain a flat network voltage profile, it is necessary to control components of the electrical power system capable of absorbing or injecting reactive power. 21

22 3 Power quality in electrical grids Different IEEE 8 standards define power quality in a different manner, but an overall valid definition would be a set of conditions for the provision of electrical power so that the user of an electric system can utilise electrical energy from the distribution system in their intended manner without interference, interruption or significant loss of performance. Ideal power quality for an electrical system with a defined line-neutral voltage for each phase of 230V and 50Hz providing electrical power to single- and three-phase loads is represented by the corresponding single-phase and three-phase waveforms of voltage depicted in Fig. 16. Figure 16: Ideal single- and three-phase voltage waveforms. Source: RENAC There are several types of distortions of the voltage waveforms that might occur in an electrical power system. The following table summarises the main distortions that frequency and voltage instability might cause: 8 Institute of Electrical and Electronics Engineers 22

23 Disturbance types Description Causes Deviations in the frequency of the transmission system from the nominal value (50, 60Hz) during several cycles. Imbalances between demand and supply. Variation in the amplitude of one or more phases relative to the other three-phase voltages and their nominal value. Imbalance in the electrical loads on the phases, lightning, etc. Variations or repetitive fluctuations in the voltage amplitude, either positive or negative, for several cycles. In an extreme case an outage occurs, when there is a zero voltage condition for one or several phases. Sudden variations in electrical loads, ground faults, lightning, etc. Table 3: Overview of power quality disturbances relating to voltage and frequency instability. Source: RENAC 23

24 Different frequency quality indices can be used in order to characterise the frequency quality in a power system: The absolute frequency deviation f = f f n where f n is the rated frequency (50Hz or 60Hz) and f is the actual frequency (Hz). The relative frequency deviation (in %) f = f f n 100 f n f n The integral deviations during the day 24h I integral = f dt Various standards address the issues of power quality in electric systems. Standards are needed so that all end users (industrial, commercial and residential) and transmission and distribution suppliers (the utilities) speak the same language when discussing power quality issues 9. Standards also define recommended limits for events that degrade power quality. A good overview of applicable standards (e.g. IEEE Standards 519 and 1159) to power quality can be obtained from references [3] (chapter 3) and [4]. 0 9 Alexander Kusko and Marc T. Thompson: Power Quality in Electrical Systems. McGraw-Hill Professional. p. 15. ISBN: DOI: /

25 4 Control of interconnected power systems The positive effect of interconnecting electrical systems in terms of the smoothing of electrical demand curves associated with aggregating electrical loads has already been mentioned in section 2.1. Furthermore, the interconnection of electrical systems presents other advantages: It increases the possibilities for electricity trading. It improves the reliability of electricity supply. The overall peak load is lower than the sum of the peak loads of the individual interconnected power systems. This in turn reduces the installed capacity needed. As a consequence the reserve capacity needed is also lower. It produces more favourable operational conditions for individual generation units, increasing their efficiency which again reduces fuel consumption. Interconnection also has some drawbacks. It increases complexity and also the impact of disturbances, since the number of electricity consumers affected is higher in large interconnected systems. Therefore, the stability of power systems is a major concern in the operation of large interconnected power systems. Power systems can be expanded by connecting the power systems of several countries to work synchronously, i.e. with a common nominal frequency. Dy Liacco [5] classified the possible states in an electrical power system into five different states according to their operational conditions. These are classified in relation to the grid or load/frequency risk levels and urgency of actions related to risks of propagation. A prerequisite for power system reliability is a Normal operating state. Any other state decreases system reliability. During this state there is no risk to interconnected system operation. Frequency and voltage are within their predefined allowed limits. After one or more contingencies the new state will be Alert, which implies some degree of risk to interconnected system operation, although the system is still within acceptable limits. If the situation deteriorates, there may be a transition to an Emergency state. The system, however, would still be intact, and emergency control action could be initiated to restore the system to an alert state. If these measures are not taken in time or are ineffective, the system will break down and reach an In Extremis state. This state is equivalent to a partial or total blackout, which is characterised by a partial or total absence of voltage in the transmission power system. Restoration is carried out from this state, gradually re-energising and re-synchronising the power system. From this state, the system can transition to either the alert or the normal state, depending on the circumstances. 25

26 Figure 17: Electrical power system operating states. Overall, the stability of interconnected electrical power systems requires effective control of its operational conditions in normal and emergency states. 4.1 Requirements in different interconnected systems The control performance requirements for an interconnected system are normally prescribed and regulated by a coordinating authority 10. A good example of an interconnected system is the European Network of Transmission System Operators for Electricity (ENTSO-E), representing 41 transmission system operators from 34 European countries. Through the ENTSO-E grid, 532 million customers are served, and 880GW net generation capacity is connected, supplying 3,200TWh of electricity consumption through 305,000km of transmission lines managed by the TSOs Antonio Gómez-Expósito, Antonio Conejo, Claudio Cañizares (2009): Electric Energy Systems Analysis and Operation. CRC Press. ISBN:

27 The operation of the ENTSO-E/UCTE system is regulated through the UCTE Operation Handbook. The Handbook prescribes the following requirements regarding frequency regulation: Activation of primary control: primary control is activated if the frequency deviation exceeds ±20mHz. The quasi-steady-state deviation in the synchronous area must not exceed ±180mHz. The instantaneous frequency must not drop below 49.2Hz. Load shedding (automatic or manual, including the possibility to shed pumping units) starts at a system frequency of 49.0Hz (or below). The electrical grids of several countries within the scope of the ReGrid project - Morocco, Algeria and Tunisia - are synchronous with ENTSO. Frequency Deviation Actions 50Hz 0 Nominal frequency 49.98Hz / 50.02Hz ± 20mHz Activation of primary control 49.95Hz / 50.05Hz ± 50mHz Disturbed operation 48.8Hz / 50.2Hz 200mHz Maximum steady-state frequency deviation 49.2Hz / 50.8Hz 800mHz Maximum instantaneous frequency deviation 49Hz / 51Hz > 1000mHz Load shedding frequency criterion Table 4: Maximum thresholds of grid frequency for safe operation. Source: ENTSO-E (Draft Network Code on Load-Frequency Control and Reserves, Jan. 2013) 4.2 Provision of ancillary services in electrical grids Apart from frequency and voltage regulation, there are further ancillary services needed to guarantee stable operation of electrical grids. (System) ancillary services are services necessary for the operation of an electric power system provided by the system operator and/or by power system users according to IEC Some examples of ancillary services are: 27 Black start: includes all the services and activities necessary for a transition from the restoration state explained in section 0 (gradual re-energising, re-synchronising of the power system, restoration of unsupplied load, etc.). Islanded operation, which is also part of the above mentioned power system restoration process as a follow up to the black start. Reduction and compensation for active power losses in the transmission system, since the transportation of active or reactive power in the network leads to active power losses. These power losses must be compensated, either by producing or supplying power in addition to the power delivered to end consumers. 5 Electrical system frequency and active power regulation

28 As already described in previous sections, imbalances between electricity supply and demand for active power lead to increases or drops in grid frequency. Disturbances in this balance, causing a deviation of the system frequency from its set-point values, will be offset initially by the kinetic energy of the rotating generating sets and motors. In practice, the grid frequency almost never equals the nominal grid frequency, as can be observed in Real-time frequency graph of Continental Europe. Source: ENTSO-E. Figure 18: Real-time frequency graph of Continental Europe. Source: ENTSO-E Tthe tolerance ranges for grid frequency are kept strictly small. Consequently, in order to compensate imbalances, synchronous electrical systems need rapid responses in order to follow variability of demand as well as respond to sudden mismatches between active power generation and consumption, such as during system faults. 5.1 Frequency control in power systems Frequency stability involves responses from generators over different time scales. Fig. 19 illustrates the behaviour of a synchronous electrical power system after a disturbance. In undisturbed conditions, the system frequency is maintained within strict limits. At some point in time a contingency occurs, which in this example provokes an excess of consumption compared to generation. Fig. 19 indicates two magnitudes used to quantify the rate at which the frequency drops after the contingency. The first one is the dynamic frequency deviation, which is governed mainly by the following 12 : The amplitude and development over time of the disturbance affecting the balance between power output and consumption. The kinetic energy of rotating machines in the system. The number of generators subject to primary control, the primary control reserve and its distribution between these generators. The dynamic characteristics of the machines (including controllers). The dynamic characteristics of the loads, particularly the self-regulating effect of the loads. The second one is the quasi-steady-state frequency deviation, which is mainly influenced by the following: 12 ENTSO-E s Continental Europe Synchronous Area Operation Handbook. Available at: 28

29 The drop of all generators subject to primary control in the synchronous area. The sensitivity of consumption to variations in system frequency. The frequency control structure of synchronous interconnected electrical systems performs three levels of control, called primary, secondary and tertiary frequency control. After a disturbance, as soon as the frequency exceeds a predefined threshold value, a control mechanism is activated within 15 to 30 seconds. This is denoted as primary frequency control and aims to restore the balance between generated and consumed active power at a certain frequency level. Figure 19: Frequency behaviour after a grid disturbance. Source: Adapted from ENTSO-E Operation Handbook Conventional power plants usually have primary frequency or droop controllers installed. In the case of conventional fossil fuelled generators, the steam flow from the boiler to the turbine is regulated by a valve. The control signal to open or close the valve is provided by a governor, which measures the rotational speed of the generator, compares it to the reference value (50 or 60Hz) and, based on the error signal, opens or closes the steam valve. This proportional control is the droop of the generator, expressed as: s G = f f n P PGn (4.1) 29

30 f n and P Gn are the nominal frequency and nominal power of the generator, ΔP is the decay in generator power when the increase in frequency Δf in the system takes place. Fig 20 shows a diagram of variations in the generating output of two generators (a and b) with different droop under equilibrium conditions. The droop of the generator is the slope of the P/f (power/frequency) characteristic of a generator. The contribution of generator a (which has the controller with the smaller droop) to correcting the disturbance will be greater than that of generator b, which has the controller with the greater droop. The frequency offset (Δf a ) at which the primary control reserve of generator a will be exhausted (i.e. where the power generating output reaches its maximum value Pmax) will be smaller than that of generator b (Δf b ) 13. Figure 20: Frequency power characteristics of two different generators equipped with a governor. Source: ENTSO-E Operation Handbook The second step is to bring the system frequency back to the set-point value. This task is accomplished by the secondary frequency control, which delivers reserve power at short notice. Secondary reserves must be able to increase active power output within 15 seconds and be able to maintain the response for a further 30 minutes. Hydropower and pumped storage plants are commonly used as secondary reserves. Beyond primary and secondary reserves, power systems have tertiary reserves (also called minute reserves). The tertiary frequency control involves a manual or automatic change in the dispatching of power. Changes may be achieved by 14 : 30 Connecting and tripping power (gas turbines, reservoir and pumped storage power stations, increasing or reducing the output of generators in service). Redistributing the output from generators participating in secondary control. Changing the power interchange programme between interconnected undertakings. 13 ENTSO-E s Continental Europe Synchronous Area Operation Handbook. Available at: 14 ENTSO-E s Continental Europe Synchronous Area Operation Handbook. Available at:

31 Load control (e.g. centralised tele-control). Overall, the combined action of primary, secondary and tertiary frequency control must guarantee that the variations in frequency caused by the contingency are rapidly decreased. The response time and the return of the system frequency to its initial value are monitored by using what is called the trumpet method 15. In order to assess the quality and compliance of frequency control, trumpet-shaped curves of the type: H(t) = f 0 ± A e t/t (4.2) have been defined on the basis of values obtained from experience and the monitoring of system frequency over a period of years. In equation (4.2), A is an experimental value, which is equal to 1.2* Δf 2 (Δf 2 being the maximum frequency deviation expected f 0 is the set frequency value. The system frequency must be restored to within a margin of d = ± 20mHz of the setpoint frequency by 900 seconds (15 minutes) after the start of an incident. Hence, the time constant T of the trumpet curve results from the relation: T = 900 ln ( A for T 900s and d = 20mHz (4.3) d ) Figure 21: Frequency variation during a fault in a power network. Source: ENTSO-E Operation Handbook 15 UCTE Operation Handbook. Available at: 31

32 5.2 Excerpt: electrical system frequency as a communication link for active power sharing The droop properties of conventional generators introduced in section 5.1 can be used as a load sharing scheme in interconnected electric power systems with multiple generators. Figure 22: Two generators connected to a load. Source: RENAC Fig. 22 hows two generators connected to a load through two transmission lines. As listed the X/R ratio for medium and high voltage lines is rather high, and so the transmission line is predominantly inductive. Therefore, for the purposes of simplified analysis, the transmission lines will be represented by pure inductances. The complex power provided to the load by the generator i is given by: S i = P i + jq i = V I i (4.4) where I i is the complex conjugate of the generator i current, which can be expressed as a function of the line voltages using Kirchoff s voltage law: I i = ( E i δ i V 0 ) (4.5) X i 90 Substituting (4.5) into (4.4) and using Euler s formula to break the total power into real and imaginary: S i = V I i = V ( E i X i (δ i 90 ) V X i 90 ) = V ( E i X i sinδ i + j V X i j E i X i cosδ i ) (4.6) 32

33 The former relation gives us the active and reactive power flowing from the i th generator: P i = VE i X i sinδ i (4.7) Q i = V2 X i VE i X i cosδ i (4.8) Relations (4.7) and (4.8) are important in power systems technology as they describe the flow of active and reactive power in grid-connected synchronous generators. Equation (4.7) states that real power flow (P i ) is mostly influenced by the phase shifts of the power generators (δ i ). Equation (4.8) shows that the reactive power flow (Q i ) between the generator i and the load depends on the difference between the load voltage (V) and the voltage at the generator I (E i ). Therefore, the flow of active power (P) and reactive power (Q) in an electrical power system can be regulated by altering the voltage magnitudes and power angles. While the power phase deviation angles can be controlled by altering the system frequency. It is for these reasons the droop method uses frequency instead of phase to control the active power flows and the share of loads between the generators connected to an electrical system. 33

34 6 Reactive power and voltage control There are several definitions of voltage stability. The IEEE defines voltage stability as the ability of a power system to maintain steady voltages after a disturbance (IEEE-CIGRE, 2004) 16. Voltage disturbances are commonly associated with reactive power deficiencies. 6.1 Effects of active and reactive power flows on voltage Expression (1.4) obtained in section 2.1: U real = PR +QX U provides a method to estimate the voltage drops in transmission and distribution lines. According to this expression, both active and reactive power flows over distribution and transmission lines will affect the voltage profiles of the different nodes in the network. Which component active power flow or reactive power flow affects voltage stability more strongly depends upon whether the corresponding lines are predominantly resistive (R L >X L ) or reactive (X L >R L ). In the event that the line is predominantly resistive, the term PR will generally be more important in the relation than QX, and therefore voltage nodes will be affected by active power flow due to voltage drops at the resistive part of the line impedance. The opposite happens when the line is predominantly reactive. The line parameters are different for distribution/low voltage lines and for transmission/medium and high voltage lines: Distribution lines are predominantly resistive. Consequently voltage in distribution lines is affected by active power flow rather than by reactive power flow. The higher the voltage of the line, the stronger the reactive character of the line impedance. Therefore, in medium and especially in high voltage lines, voltage profiles are affected more by the flow of reactive power. 6.2 Load flow calculations The equations obtained in section 5.2 can also be applied to a transmission line linking two buses as depicted in Fig P. Kundur, J. Paserba, V. Ajjarapu, G. Anderson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. V. Custem, V. Vittal: Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions in IEEE Transactions on Power Systems. Vol. 19, No. 2, August p

35 Figure 23: Transmission line linking two nodes. Source: RENAC The equations can be generalised for the transmission line as follows 17 : 0 = P L V 1V 2 X L sinδ 0 = Q L V 2 2 X L V 1V 2 X L cosδ 0 = Q G V 1 2 X L + V 1V 2 X L cosδ There are several variables associated with each transmission line linking nodes of the electrical grid: active and reactive power injected or extracted at the bus; bus voltage; and voltage phase angle. These equations are not linear since they contain products of variables and trigonometric functions. Electrical power systems have thousands of interconnected nodes, and the equations listed above need to be solved for all the nodes simultaneously. These are the types of calculations that are carried out by power system simulation packages. 6.3 Mitigation of voltage stability problems/reactive power management Voltage, unlike frequency, is not the same in all the nodes of an electrical power system. Equipment used to mitigate voltage stability problems behaves with certain time constants that need to be taken into consideration, and as such different time windows need to be considered. The simplest differentiation is between short-term and long-term voltage stability. Short-term voltage stability (with a time frame of several seconds) comprises the time between voltage digression after a disturbance occurs and the activation of a transformer tap changer close to loads. Short-term voltage stability dynamics are associated with the behaviour of induction motors after a voltage disturbance. So, for example, a short circuit on the distribution/transmission grid will slow induction motors, which in turn leads to high currents 17 Leonard L. Grigsby (2007): Power System Stability and Control. CRC Press. 35