Arnold, C.P., Watson, N.R. Power System Analysis Software The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton CRC Press llc. 2000
Arnold, C.P., Watson, N.R. “Power System Analysis Software” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
68 Power system analysis Software 68.1 Introduction .2 Early Analysis Programs Load Flow(Power Flow).Fault Analysis. Transient Stability Fast Transients. Reliability. Economic Dispatch and Unit Commitment 8.3 The Second Generation of programs Graphics. Protection. Other Uses for Load Flow Analysis Extensions to Transient Stability Analysis. Voltage Collapse SCADA.Power Quality. Finite Element Analysis C P Arnold and Grounding. Other Programs N.R. Watson 68.4 Further Development of Programs University of canterbury. New zealand 68.5 Conclusions 68.1 Introduction Power system software can be grouped in many different ways, e.g., functionality, computer platform, etc. but here it is grouped by end user. There are four major groups of end users for the software major utilities of ele consultants Large comprehensive program packages are required by utilities. They are complex, with many different anctions and must have very easy input/output(IO). They serve the needs of a single electrical system and may be tailor-made for the customer. They can be integrated with the electrical system using SCADA (Super visory Control And Data Acquisition). It is not within the scope of this chapter to discuss the merits of these programs. Suffice to say that the component programs used in these packages usually have the same generic/development roots as the programs used by the other three end user groups The programs used by the other three groups have usually been initially created in the universities. They start life as research programs and later are used for teaching and/or consultancy programs Where the consultant is also an academic, then the programs may well retain their crude research style IO. However, if they are to be used by others who are not so familiar with the algorithms, then usually they are modified to make them more user friendly. Once this is achieved, the programs become commercial and are used by consultants and utilities. These are the types of programs that are now so commonly seen in the engineering journals quite often bundled together in a generic package c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 68 Power System Analysis Software 68.1 Introduction 68.2 Early Analysis Programs Load Flow (Power Flow) • Fault Analysis • Transient Stability • Fast Transients • Reliability • Economic Dispatch and Unit Commitment 68.3 The Second Generation of Programs Graphics • Protection • Other Uses for Load Flow Analysis • Extensions to Transient Stability Analysis • Voltage Collapse • SCADA • Power Quality • Finite Element Analysis • Grounding • Other Programs 68.4 Further Development of Programs Program Suites 68.5 Conclusions 68.1 Introduction Power system software can be grouped in many different ways, e.g., functionality, computer platform, etc. but here it is grouped by end user. There are four major groups of end users for the software: • major utilities • small utilities, and industry consumers of electricity • consultants • universities Large comprehensive program packages are required by utilities. They are complex, with many different functions and must have very easy input/output (IO). They serve the needs of a single electrical system and may be tailor-made for the customer. They can be integrated with the electrical system using SCADA (Supervisory Control And Data Acquisition). It is not within the scope of this chapter to discuss the merits of these programs. Suffice to say that the component programs used in these packages usually have the same generic/development roots as the programs used by the other three end user groups. The programs used by the other three groups have usually been initially created in the universities. They start life as research programs and later are used for teaching and/or consultancy programs. Where the consultant is also an academic, then the programs may well retain their crude research style IO. However, if they are to be used by others who are not so familiar with the algorithms, then usually they are modified to make them more user friendly. Once this is achieved, the programs become commercial and are used by consultants, industry, and utilities. These are the types of programs that are now so commonly seen in the engineering journals quite often bundled together in a generic package. C.P. Arnold and N.R. Watson University of Canterbury, New Zealand
68.2 Early Analysis Programs Two of the earliest programs to be developed for power system analysis were the fault and load flow(power flow) programs. Both were originally produced in the late 1950s. Many programs in use today are either based on these two types of program or have one or the other embedded in them Load Flow(Power Flow) The need to know the flow patterns and voltage profiles in a network was the driving force behind the development of load flow programs Although the network is linear, load flow analysis is iterative because of nodal(busbar)constraints. At most busbars the active and reactive powers being delivered to customers are known but the voltage level is not far as the load flow analysis is concerned, these busbars are referred to as PQ buses. The generators are scheduled to deliver a specific active power to the system and usually the voltage magnitude of the generator terminals is fixed by automatic voltage regulation. These busbars are known as PV buses. losses in the system cannot be determined before the load flow solution, one generator busbar only has its voltage magnitude specified. In order to give the required two specifications per node, this bus also has its voltage angle defined to some arbitrary value, usually zero. This busbar is known as the slack bus. The slack bus is a mathematical requirement for the program and has no exact equivalent in reality. However, in operating practice, the total load plus the losses are not known. When a system is not in power balance, i. e, when the input power does not equal the load power plus losses, the imbalance modifies the rotational energy stored in the system. The system frequency thus rises if the input power is too large and falls if the input power is too little. Usually a generating station and probably one machine is given the task of keeping the frequency constant by varying the input power. This control of the power entering a node can be seen to be similar to the slack bus. The algorithms first adopted had the advantages of simple programming and minimum storage bu t were slow to converge requiring many iterations. The introduction of ordered elimination, which gives implicit inversion of the network matrix, and sparsity programming techniques, which reduces storage requirement allowed much better algorithms to be used. The Newton-Raphson method gave convergence to the solution in only a few iterations Using Newtonian methods of specifying the problem, a Jacobian matrix containing the partial derivatives of the system at each node can be constructed. The solution by this method has quadratic onvergence. This method was followed quite quickly by the Fast Decoupled Newton-Raphson method. This exploited the fact that under normal operating conditions, and providing that the network is predominately reactive, the voltage angles are not affected by reactive power flow and voltage magnitudes are not effected by real power flow. The Fast Decoupled method requires more iterations to converge but each iteration uses less omputational effort than the Newton Raphson method. A further advantage of this method is the robustness of the algorithm Further refinements can be added to a load flow program to make it give more realistic results. Transformer n-load tap changers, voltage limits, active and reactive power limits, plus control of the voltage magnitudes at buses other than the local bus help to bring the results close to reality. Application of these limits can slow The problem of obtaining an accurate, load flow solution, with a guaranteed and fast convergence has resulted in more technical papers than any other analysis topic. This is understandable when it is realized that the load flow solution is required during the running of many other types of power system analyses. While improvements have been made, there has been no major breakthrough in performance. It is doubtful if such an achievement overall time of the anal quired to prepare the data and process the results represents a significant part of the is possible as the time re Fault Analysis A fault analysis program derives from the need to adequately rate switchgear and other busbar equipment for the maximum possible fault current that could flow through them c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 68.2 Early Analysis Programs Two of the earliest programs to be developed for power system analysis were the fault and load flow (power flow) programs. Both were originally produced in the late 1950s. Many programs in use today are either based on these two types of program or have one or the other embedded in them. Load Flow (Power Flow) The need to know the flow patterns and voltage profiles in a network was the driving force behind the development of load flow programs. Although the network is linear, load flow analysis is iterative because of nodal (busbar) constraints. At most busbars the active and reactive powers being delivered to customers are known but the voltage level is not. As far as the load flow analysis is concerned, these busbars are referred to as PQ buses. The generators are scheduled to deliver a specific active power to the system and usually the voltage magnitude of the generator terminals is fixed by automatic voltage regulation. These busbars are known as PV buses. As losses in the system cannot be determined before the load flow solution, one generator busbar only has its voltage magnitude specified. In order to give the required two specifications per node, this bus also has its voltage angle defined to some arbitrary value, usually zero. This busbar is known as the slack bus. The slack bus is a mathematical requirement for the program and has no exact equivalent in reality. However, in operating practice, the total load plus the losses are not known. When a system is not in power balance, i.e., when the input power does not equal the load power plus losses, the imbalance modifies the rotational energy stored in the system. The system frequency thus rises if the input power is too large and falls if the input power is too little. Usually a generating station and probably one machine is given the task of keeping the frequency constant by varying the input power. This control of the power entering a node can be seen to be similar to the slack bus. The algorithms first adopted had the advantages of simple programming and minimum storage but were slow to converge requiring many iterations. The introduction of ordered elimination, which gives implicit inversion of the network matrix, and sparsity programming techniques, which reduces storage requirements, allowed much better algorithms to be used. The Newton-Raphson method gave convergence to the solution in only a few iterations. Using Newtonian methods of specifying the problem, a Jacobian matrix containing the partial derivatives of the system at each node can be constructed. The solution by this method has quadratic convergence. This method was followed quite quickly by the Fast Decoupled Newton-Raphson method. This exploited the fact that under normal operating conditions, and providing that the network is predominately reactive, the voltage angles are not affected by reactive power flow and voltage magnitudes are not effected by real power flow. The Fast Decoupled method requires more iterations to converge but each iteration uses less computational effort than the Newton Raphson method. A further advantage of this method is the robustness of the algorithm. Further refinements can be added to a load flow program to make it give more realistic results. Transformer on-load tap changers, voltage limits, active and reactive power limits, plus control of the voltage magnitudes at buses other than the local bus help to bring the results close to reality. Application of these limits can slow down convergence. The problem of obtaining an accurate, load flow solution, with a guaranteed and fast convergence has resulted in more technical papers than any other analysis topic. This is understandable when it is realized that the load flow solution is required during the running of many other types of power system analyses. While improvements have been made, there has been no major breakthrough in performance. It is doubtful if such an achievement is possible as the time required to prepare the data and process the results represents a significant part of the overall time of the analysis. Fault Analysis A fault analysis program derives from the need to adequately rate switchgear and other busbar equipment for the maximum possible fault current that could flow through them
Initially only three-phase faults were considered and it was assumed that all busbars were operating at unity per unit voltage prior to the fault occurring. The load current flowing prior to the fault was also neglected By using the results of a load flow prior to performing the fault analysis, the load currents can be added to the fault currents allowing a more accurate determination of the total currents flowing in the system. Unbalanced faults can be included by using symmetrical components. The negative sequence network is similar to the positive sequence network but the zero sequence network can be quite different primarily because of ground impedance and transformer winding configurations Transient Stability After a disturbance, due usually to a network fault, the synchronous machine's electrical loading changes and the machines speed up(under very light loading conditions they can slow down). Each machine will react differently depending on its proximity to the fault, its initial loading and its time constants. This means that the angular positions of the rotors relative to each other change. If any angle exceeds a certain threshold(usually between 140@and 160%)the machine will no longer be able to maintain synchronism. This almost always results in its removal from service Early work on transient stability had concentrated on the reaction of one synchronous machine coupled to a very large system through a transmission line. The large system can be assumed to be infinite with respect to the single machine and hence can be modeled as a pure voltage source. The synchronous machine is modeled by the three phase windings of the stator plus windings on the rotor representing the field winding and the eddy current paths. These are resolved into two axes, one in line with the direct axis of the rotor and the other line with the quadrature axis situated 90%(electrical) from the direct axis. The field winding is on the direct axis Equations can be developed which determine the voltage in any winding depending on the current flows in all the other windings. A full set of differential equations can be produced which allows the response of the machine to various electrical disturbances to be found. The variables must include rotor angle and rotor speed which can be evaluated from a knowledge of the power from the turbine into, and power to the system out of the machine. The great disadvantage with this type of analysis is that the rotor position is constantly changing as it rotates. As most of the equations involve trigonometrical functions relating to stator and rotor windings, the matrices must be constantly reevaluated. In the most severe cases of network faults the results, once the dc transients decay, are balanced. Further, on removal of the fault the network is considered to be balanced.There is thus much computational effort involved in obtaining detailed information for each of the three phases which is of little value to the power system engineer. By contrast, this type of analysis is very important to machine designers. However, programs have been written for multi-machine systems using this method. Several power system catastrophes in the U.S. and Europe in the 1960s gave a major boost to dev transient stability programs. What was required was a simpler and more efficient method of representing the machines in large power systems Initially, transient stability programs all ran in the time domain. A set of differential equations is developed describe the dynamic behavior of the synchronous machines. These are linked together by algebraic equations for the network and any other part of the system that has a very fast response, i.e, an insignificant time constant, relative to the synchronous machines. All the machine equations are written in the direct and quadrature axes of the rotor so that they are constant regardless of the rotor position. The network is written in the real and imaginary axes similar to that used by the load flow and faults programs. The transposition between these axes only requires knowledge of the rotor angle relative to the synchronously rotating frame of reference of the Later work involved looking at the response of the system, not to major disturbances but to the build-up of oscillations due to small disturbances and poorly set control systems. As the time involved for these disturbances to occur can be large, time domain solutions are not suitable and frequency domain models of the system were produced. Lyapunov functions have also been used, but good models have been difficult to produce. However, they are now of sufficiently good quality to compete with time domain models where quick estimates of stability are needed such as in the day to day operation of a system. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Initially only three-phase faults were considered and it was assumed that all busbars were operating at unity per unit voltage prior to the fault occurring. The load current flowing prior to the fault was also neglected. By using the results of a load flow prior to performing the fault analysis, the load currents can be added to the fault currents allowing a more accurate determination of the total currents flowing in the system. Unbalanced faults can be included by using symmetrical components. The negative sequence network is similar to the positive sequence network but the zero sequence network can be quite different primarily because of ground impedance and transformer winding configurations. Transient Stability After a disturbance, due usually to a network fault, the synchronous machine’s electrical loading changes and the machines speed up (under very light loading conditions they can slow down). Each machine will react differently depending on its proximity to the fault, its initial loading and its time constants. This means that the angular positions of the rotors relative to each other change. If any angle exceeds a certain threshold (usually between 140° and 160°) the machine will no longer be able to maintain synchronism. This almost always results in its removal from service. Early work on transient stability had concentrated on the reaction of one synchronous machine coupled to a very large system through a transmission line. The large system can be assumed to be infinite with respect to the single machine and hence can be modeled as a pure voltage source. The synchronous machine is modeled by the three phase windings of the stator plus windings on the rotor representing the field winding and the eddy current paths. These are resolved into two axes, one in line with the direct axis of the rotor and the other in line with the quadrature axis situated 90° (electrical) from the direct axis. The field winding is on the direct axis. Equations can be developed which determine the voltage in any winding depending on the current flows in all the other windings. A full set of differential equations can be produced which allows the response of the machine to various electrical disturbances to be found. The variables must include rotor angle and rotor speed which can be evaluated from a knowledge of the power from the turbine into, and power to the system out of the machine. The great disadvantage with this type of analysis is that the rotor position is constantly changing as it rotates. As most of the equations involve trigonometrical functions relating to stator and rotor windings, the matrices must be constantly reevaluated. In the most severe cases of network faults the results, once the dc transients decay, are balanced. Further, on removal of the fault the network is considered to be balanced. There is thus much computational effort involved in obtaining detailed information for each of the three phases which is of little value to the power system engineer. By contrast, this type of analysis is very important to machine designers. However, programs have been written for multi-machine systems using this method. Several power system catastrophes in the U.S. and Europe in the 1960s gave a major boost to developing transient stability programs. What was required was a simpler and more efficient method of representing the machines in large power systems. Initially, transient stability programs all ran in the time domain. A set of differential equations is developed to describe the dynamic behavior of the synchronous machines. These are linked together by algebraic equations for the network and any other part of the system that has a very fast response, i.e., an insignificant time constant, relative to the synchronous machines. All the machine equations are written in the direct and quadrature axes of the rotor so that they are constant regardless of the rotor position. The network is written in the real and imaginary axes similar to that used by the load flow and faults programs. The transposition between these axes only requires knowledge of the rotor angle relative to the synchronously rotating frame of reference of the network. Later work involved looking at the response of the system, not to major disturbances but to the build-up of oscillations due to small disturbances and poorly set control systems. As the time involved for these disturbances to occur can be large, time domain solutions are not suitable and frequency domain models of the system were produced. Lyapunov functions have also been used, but good models have been difficult to produce. However, they are now of sufficiently good quality to compete with time domain models where quick estimates of stability are needed such as in the day to day operation of a system
CHARLES PROTEUS STEINMETZ (1865-1923) C harles Steinmetz(1865-1923)came to the United States in 1889 from breslau Germany, where he was a student at the University of Breslau. He joined the inventor Rudolf Eickemeyer in building electric appara tus at Yonkers, New York, and at age 27 he for- ulated the law of hysteresis, which made it possible to reduce the loss of efficiency in elec trical apparatus. When Eickemeyer's firm was bought by General Electric, Steinmetz joined the new company, beginning a 31-year relationship that ended only with his death. His improvements in methods of making cal- culations of current in alternating current cir- cuits revolutionized power engineering, and his theory of electrical transients stood as another important contribution. In the midst of his GE career, Steinmetz was also a professor at Union College and a vocal champion of civic and polit- Charles Proteus Steinmetz(1865-1923) ical causes. Courtesy of the IEEE Center for the History of Electrical Engineering. Fast Transients While the transient stability program assumed a fast transient response was equivalent to an instantaneous response and only concentrated on the slower response of the synchronous machines, the requirement to model the fast transient response of traveling waves on transmission lines brought about the development of programs that treated variables with large time constants as if they were constants and modeled the variables with very small time constants by differential equations. The program is based on the equations governing voltage and current wave propagation along a lossless line Attenuation is then included using suitable lumped resistances. A major feature of the method is that inductance and capacitance can both be represented by resistance in parallel with a current source. This allows a purely resistive network to be formed Whereas, with the most other programs, source code was treated as intellectual property, the development of the fast transient program was done by many different researchers who pooled their ideas and programs An electromagnetic transient program developed quickly and it probably became the first power systems analysis tool to be used for many different purposes throughout the world. From this base, numerous commercial In parallel with the development of electromagnetic transient programs, several state variable programs were produced to examine the fast transient behavior of parts of the electrical system, such as ac transmission lines and HVdc transmission systems. As these programs were specifically designed for the purpose they were intended, it gave them certain advantages over the general purpose electromagnetic transient program c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Fast Transients While the transient stability program assumed a fast transient response was equivalent to an instantaneous response and only concentrated on the slower response of the synchronous machines, the requirement to model the fast transient response of traveling waves on transmission lines brought about the development of programs that treated variables with large time constants as if they were constants and modeled the variables with very small time constants by differential equations. The program is based on the equations governing voltage and current wave propagation along a lossless line. Attenuation is then included using suitable lumped resistances. A major feature of the method is that inductance and capacitance can both be represented by resistance in parallel with a current source. This allows a purely resistive network to be formed. Whereas, with the most other programs, source code was treated as intellectual property, the development of the fast transient program was done by many different researchers who pooled their ideas and programs. An electromagnetic transient program developed quickly and it probably became the first power systems analysis tool to be used for many different purposes throughout the world. From this base, numerous commercial packages have been developed. In parallel with the development of electromagnetic transient programs, several state variable programs were produced to examine the fast transient behavior of parts of the electrical system, such as ac transmission lines and HVdc transmission systems. As these programs were specifically designed for the purpose they were intended, it gave them certain advantages over the general purpose electromagnetic transient program. CHARLES PROTEUS STEINMETZ (1865–1923) harles Steinmetz (1865–1923) came to the United States in 1889 from Breslau, Germany, where he was a student at the University of Breslau. He joined the inventor Rudolf Eickemeyer in building electric apparatus at Yonkers, New York, and at age 27 he formulated the law of hysteresis, which made it possible to reduce the loss of efficiency in electrical apparatus. When Eickemeyer’s firm was bought by General Electric, Steinmetz joined the new company, beginning a 31-year relationship that ended only with his death. His improvements in methods of making calculations of current in alternating current circuits revolutionized power engineering, and his theory of electrical transients stood as another important contribution. In the midst of his GE career, Steinmetz was also a professor at Union College and a vocal champion of civic and political causes. (Courtesy of the IEEE Center for the History of Electrical Engineering.) C