- : Ms Word, Ms Word Format
- : 100 Pages
- : ₦5000
- : 1-5 Chapters
- Click to DOWNLOAD Materials
TRANSIENT STABILITY ANALYSIS OF NIGERIA POWER SYSTEM: MULTIMACHINE APPROACH
ABSTRACT
The recent power sector reform in Nigeria has thrown up enormous challenges in this sector, ranging from the construction of more power stations, construction of new transmission lines and substations. The existing network of 8-plants and 26 bus-bars expanded to the proposed network of 16 generating plants with 49 bus-bars. This network expansion requires reappraisal for power evacuation capabilities, relay systems setting and establishment of stability margins for adverse system fault conditions on the network. Power flow evaluations of the existing and proposed 330KV networks were done using the Newton-Raphson technique. The transient stability analysis of the two networks was also simulated by direct method using ode45 MATLAB programmed functions. The critical clearing time of 0.21second and stability margin of 0.238 were established for a three-phase fault at bus 16, line 13 – 16 of the existing Grid. In the proposed Grid, the critical clearing times and stability margins for three-phase faults at buses 3 (line 3 – 44) and 31 (line 2 – 31) were established as 0.21second, 0.238 and 0.29second, 0.448 respectively. The results provided a suite of specifications and standards for the proposed grid system. An algorithm for coherent generators was developed with which the 16 machines in proposed network were reduced to 13 machines system. The network reduction was carried out through coherent generators aggregation and construction of dynamic equivalents representing the aggregated generators.
Key words: existing network, proposed network, power flow, transient stability, coherent generators, dynamic equivalents, clearing time, stability margin, swing curve.
TABLE OF CONTENTS
Title page i
Certification ii
Dedication iii
Acknowledgment iv
Abstract v
Table of contents vi List of tables ix
List of figures x
List of abbreviations and symbols xiv
CHAPTER ONE
1.0 Introduction 1
1.1 Background knowledge 3
1.2 Problem statement 5
1.3 Objectives 6
1.4 Justification of study 7
1.5 Scope of study 7
1.6 Structure of the thesis 8
CHAPTER TWO 9
2.0 Literature Review 9
2.1 Load flow study 11
2.2 Transient stability analysis 13
2.2.1 Coherent generator-based transient stability analysis 18 CHAPTER THREE
3.0 Methodology 22
3.1 Power system equipment and networks 22
3.2 The synchronous generator 22
3.2.1 Bulk power generation in power networks 27
3.2.2 abc – odq frame of reference 28
| 3.2.3 Transient parameters of the synchronous generator | 34 | ||||
| 3.2.4 The generator in the transient state | 44 | ||||
| 3.3 The transmission system | 48 | ||||
| 3.3.0 The transmission systems model | 48 | ||||
| 3.3.1 Transmission line model | 49 | ||||
| 3.3.2 The transformer model with complex ratio | 51 | ||||
| 3.3.3 The in-phase transformer model | 51 | ||||
| 3.3.4 Phase shifting transformer model | 53 | ||||
| 3.3.5 The unified power network model | 54 | ||||
| 3.3.6 The unified power flow equation | 60 | ||||
| 3.3.7 Substation controls | 60 | ||||
| 3.3.7.1 Load – break switches | 60 | ||||
| 3.3.7.2 Circuit breakers | 61 | ||||
| 3.4 Power system protection | 61 | ||||
| 3.4.1 Generator protection | 62 | ||||
| 3.4.2 Line protection | 63 | ||||
| 3.5 National grid data | 64 | ||||
| 3.5.1 Generation data | 64 | ||||
| 3.5.2 Transmission line data | 65 | ||||
| 3.6 Theory of power flow and stability computations | 68 | ||||
| 3.6.1 Single machine to infinite bus system | 68 | ||||
| 3.6.2 Method of solutions of power flow problems | 74 | ||||
| 3.6.3 Power flow equations | 75 | ||||
| 3.6.4 Gauss Seidel method | 76 | ||||
| 3.6.5 Newton Raphson method | 79 | ||||
| 3.7 Modelling of multimachine power system | 85 | ||||
| 3.8 Multimachine transient stability equations | 88 | ||||
| 3.8.1 The rotor swing equation | 88 | ||||
| 3.9 Step by step solution of swing equation | 94 | ||||
3.10 Data preparation for transient stability 99
3.11 Coherent generator identification 104
3.11.1 Mathematical formulation 104
3.11.2 Coherent generators dynamic equivalent
Construction technique 109
3.11.2.1 Mathematical formulation 110
3.11.2.2 The algorithm for the coherent machines
identification and dynamic equivalents construction 114
CHAPTER FOUR
4.0 Power flow and stability of the Existing and Proposed
National grids 115
4.1 Derivation of Existing national grid injected current equation 115 4.2 Derivation of Proposed national grid injected current equation 119
CHAPTER FIVE
5.0 Result and Discussion 135
5.1 Existing network power flow results 135
5.2 Proposed network power flow results 136
5.3 Result of transient stability analysis of existing network under three-phase fault at some selected
buses and lines. 138
5.4 Result of transient stability analysis of proposed network under three-phase fault at some selected
buses and lines. 147
5.4.1 Results of generators-coherency check and aggregation
for a three-phase fault at bus 3 line 3-44. 161
CHAPTER SIX
6.0 Conclusion and Recommendations 166
6.1 Conclusion 166
6.2 Recommendations 168
| Contribution to knowledge | 170 |
| References
Appendix A: Existing 330KV National Grid bus data, power flow results, and line flow and losses. |
171 |
| A1: Existing 330KV National Grid bus data | 183 |
| A2: Existing 330KV National Grid power flow results | 184 |
| A3: Existing 330KV National Grid line flow and losses
Appendix B: Proposed 330KV National Grid bus data, power flow results and line flow and losses. |
185 |
| B1: Proposed 330KV National Grid bus data | 188 |
| B2: Proposed 330KV National Grid power flow results | 190 |
| B3: Proposed 330KV National Grid line flow and losses
Appendix C: Proposed 330KV National Grid bus data based on coherent generators aggregation application. C1: Ybus matrix for proposed 330KV Nigeria power system at |
192 |
| faulted bus 3 | 198 |
| C2: Proposed Grid generator fault-induced power variation C3: Study and external systems generators classified based | 199 |
| on fault-on percentage power variation
C4: - index data for proposed grid generators |
200 |
| coherency check
C5: – Index data for proposed grid generators |
201 |
| coherency check | 202 |
| C6: Aggregated grid generator groups data | 203 |
| C7: New Grid Generators data for aggregation | 203 |
| C8: New Grid systems bus data after aggregation | 204 |
| C9: Line data for New Grid system after aggregation | 206 |
| Appendix D: MATLAB SOFTWARE PROGRAMS | 209 |
CHAPTER ONE
1.0 Introduction
Despite an installed capacity of about 5610MW in the Nigerian National Grid as at 2001, the available capacity dropped to below 2000MW. Electricity supply to private, commercial and industrial consumers became grossly inadequate and erratic. Many industries had to close down causing a downturn of the national economy, and the quality of life of the citizens reduced considerably. The general outcry of industry chieftains and the energy starved consumers kick-started a national debate on the problems of the power industry sector; it became obvious that a number of problems led to the near collapse of the sector. There was a dearth of generating capacity and its planners had not considered the pattern of the load demand and the rapid increase of national population. Besides the high dependence of the sector on foreign technology, the lack of skilled maintenance staff and lack of new investment over a long period had a negative impact on the industry. The Federal Government of Nigeria virtually declared an Energy Emergency and took a number of steps aimed at improving the fortunes of the sector.
The Power Sector Reform Act which was enacted in 2005, led to the unbundling of PHCN into eighteen companies (six generation, one transmission and eleven distribution companies) to reduce administrative bureaucracy and increase the speed of response of the companies to consumer complaints. The new legal framework also instituted the National Electricity Regulatory Commission (NERC) to license and regulate bodies engaged in electricity generation. The private sector obtained licenses to own power plants under the Independent Power Producers (IPPs) thereby opening the door to new investments in the power sector. The Transmission Company of Nigeria (TCN) became the backbone of the sector that can enter into power purchase agreements with the IPPs. The Federal Government also assisted the PHCN to build four new Gas fired power plants at Geregu, Omotosho, Papalanto and Afam. The Government in addition set up the National Integrated Power Project (NIPP) to build seven new power plants in the oil producing areas of the country. The outlook for future installed power generation capacity in the country became much brighter as shown in table1.1 (Achibong, 2007).
Table 1.1: Expected new power stations and their capacities
| Expected New Power Stations | Expected Capacities(MW) |
| 7 NIPP Power Stations | 2,556 |
| 4 FG Power Stations | 1,434 |
| 2 State Owned IPPs | 800 |
| 5 Joint Venture IPPs | 2,780 |
| 10 Private IPPs | 5,391.5 |
| Total Capacity | 12,961.5 |
The existing national grid was made up of 5000km of 330kV transmission lines and 6000km of 132KV transmission lines with twenty five (25) 330KV and eighty nine (89) 132KV substations. The distribution facilities included 55,143km of 33KV and 11KV distribution lines. The proposed grid system would have an increased installed generating capacity of about 18,571.5MW. About 7000km of transmission facility were planned under NIPP (Achibong, 2007). It is expected that the addition of new power plants and transmission facilities would alter considerably the performance criteria of the grid system. In the light of the above the system operators have to face the challenges of ensuring that the stability of the system is maintained using new criteria to be developed. These challenges arising from the rapidly expanding grid system have to be systematically appraised through research and operational experiences to identify areas of weaknesses and corrective measures to be imposed to ensure system stability. In order to meet the expectation of the Nigerian economic planners to make the country one of the twenty most developed economies by the year 2020, the power industry must be pulled out of the present state to provide a stable and secure supply of electricity.
1.1 Background Knowledge
Through load flow studies, the solutions of the steady-state operating conditions of electric power transmission systems are provided, and these are most frequently performed in power system analysis (Ekwue et al., 1991). The essence of load flow is to find out the real and reactive powers flowing in each line along with the magnitude and phase angle of the voltage at each bus of the system for specific loading conditions (Okoro et al., 2007). In performing load flow studies, the network bus-bars are classified into three based on the direction of power flow in a particular bus and the specified variables. The three types of buses include load bus, voltage controlled bus, and reference or slack bus. In load bus, the real and reactive power are specified, while the voltage magnitude and phase angle of the voltage are unknown. In a voltage controlled bus, the real power and voltage magnitude are specified, while reactive power and phase angle of voltage are unknown. The last is known as the reference or slack bus because it takes up the slack in losses (Elgerd, 1979). It is also known as swing bus. In this bus, real and reactive power demands are unknown, while voltage magnitude and load angle are specified.
Power system stability concerns the power system’s response to disturbances (Fouad et al., 1992), and a disturbance is a sudden change in an operating condition or an operating parameter of the power system (IEEE Task Force, 1982). When the linearization of the system equations for the purpose of analysis is justified after a disturbance, such disturbance is considered small; otherwise, it is regarded as large. In other words, a small disturbance is a disturbance for which the equations that describe the dynamics of the power system may be linearized for analysis purposes (Machowski et al., 1997). Small disturbance include small variations in loads and generation. In power system stability studies, the period of interest is the transient period prior to the attainment of new steady state conditions. The power system is considered to operate at steady state when the operating parameters are assumed constant for the purpose of analysis. Under this condition, the peak-to-peak amplitude of the system current waveform is assumed time invariant (constant). When a disturbance occurs in a power system initially operating at steady state, the stability concern becomes whether an acceptable steady state condition could be reached as a fall out of the transient. If the disturbance is considered large, the stability concern is referred to as “transient stability”. Examples of large disturbances include: short-circuits on transmission line, loss of generation, loss of large load, loss of a tie between two subsystems etc. when the disturbance is small, it is referred to as “steady state stability”. Transient stability is thus, the ability of the power system to maintain synchronism when subjected to a severe transient disturbance. The resulting system response to such disturbance involves large excursions of generator rotor angle which is influenced by the non-linear power-angle relationship (Kundur, 1994). Stability is dependent on both the initial operating state of the system and the severity of the disturbance. In carrying out transient stability studies, particularly in problems involving electromechanical transients, slow varying phase is assumed and this assumption is justified considering the high moments of inertia exhibited by turbine – generator sets (Bergen et al., 2000). Transient stability as earlier defined concerns but not limited to the maintenance of synchronism between generators following a severe disturbance. The general purpose transient analysis involves quality investigation of the power system dynamic behaviour (Fouad et al., 1992). The equations describing the dynamic behaviour of a power system are highly nonlinear. These nonlinear equations describe the dynamic behaviour of the synchronous generators in the system. In transient stability analysis, the generator parameters such as rotor angels, internal emfs, terminal voltages, currents, etc. are particularly of interest. These parameters in turn influence the behaviour of other network parameters such as voltage at key buses, real power and reactive power flow in transmission lines, etc. Also the operation of various stability controls is equally investigated.
In the event of a major fault like a short-circuit, the transient reactance X’d is subjected to change, thus leading to change in the electric power output of the generator, P’e and thereby altering the power balance within the system. The altered power balance results to energy transfer between the generators, leading to rotor oscillations. The three states associated with the system disturbance have various transient reactance values which include the pre-fault transient reactance, X’dpre, the fault-on transient reactance, X’df, and the post-fault transient reactance, X’dpost.
1.2 Problem Statement
In the past two decades, the Nigeria power system has been characterized by incessant interruptions caused by inadequacies in power generation capacity, transmission and distribution facilities etc. These lapses have resulted in shutting down of industries, loss of jobs, downturn of national economy, drop in the quality of life of citizens, high cost of living occasioned by high cost of production and so on. In recognition of these challenges, the Federal Government through its power reform, has opened up the power sector by licensing independent power producers, and expanding the Nigeria power system through National Integrated Power Projects aimed at building more power generating stations to boost generation capacity as well as reinforcing the existing power transmission and distribution facilities through building new transmission lines across the country; and refurbishing, replacing of aging facilities, and construction of more transmission and distribution substations. The anticipated positive changes in the Nigeria power system will obviously throw up stability challenges to the system operators. The challenges include:
- System protection coordination
- Stability of the grid system after specified faults
- Voltage profiles and utilization of transmission capacities of the power network
- Power Evacuation and reactive power management for system stability
- Identification of remedial actions such as FACTs placement to ensure system stability.
- Objectives
The achievement of a secure and stable power system is not for operations alone; hence considerable planning and research are necessary for system performance development. The work should provide research inputs that are needed for secure operation of the national grid. These inputs include determination of the adequacy of the generation expansion schemes to meet the national power demand, accessment of the network configuration and operating conditions of the Nigeria power system vis-à-vis the reliability criteria. Others include to investigate and analyze system upsets when subjected to severe disturbances as well as ascertain the disturbance types the system can withstand, determination of the critical clearing time for superimposed operating condition and the adequacy of the transmission facilities for bulk power evacuation with the new generating stations.The result of these will enable the system managers to make informed decisions and take guided steps toward ensuring the security and stability of the Nigeria power system.
- Justification of study
The proposed expanded National grid considered in this research consists of 16 power plants and 49 busbars interconnected by 330KV transmission lines. There is therefore need for a comprehensive investigation of the performance and stability analysis of the expanded grid. Transient stability study of the Nigeria power system is thus required to assess the system’s response to the transient conditions following major disturbances. Such studies are fundamental when new generating and transmitting facilities are added to the system (Saadat, 2002). This research is very auspicious at this period when a lot of generating plants and transmission facilities are being constructed across the country through the National Integrated Power Projects. Through this research, the technical information on the system stability, voltage profile and transmission capabilities, types of disturbances the system can withstand, safe margins for system operating limits etc. can be provided. This information when managed properly will enhance efficient power system operation.
- Scope of study
The research covered existing (8- machines, 26-bus system) and proposed (16- machines, 49 – bus system) Nigeria power system at 330KV voltage level. Separate load flow studies and transient stability studies are carried out for these two networks under specified fault conditions at various locations in both systems. The method adopted in this research is such that the structure of the network is preserved to such extent that the accuracy of the result is not compromised. The method involved identification of coherent machine groups, coherent machines aggregation, network reduction and construction of coherency-based dynamic machine equivalents, to represent different coherent generators groups; and integration of these subsystems to form a new network comprising the study area machines, external area machines and the rest of system machines.
- Structure of the thesis
The thesis has been arranged in such a manner as to facilitate understanding and promote coherency. In this regard, the introduction, background study, problem statements, objectives and the study scope are covered in chapter one; while chapter two dwelt on the literature review. Chapter three focused on the methodology which considered the power system equipment and networks, national grid data, theory of power flow and stability computations. Chapter four covers the power flow and stability evaluation of the existing and proposed national grids. Chapter five dwelt on the results and discussion, while chapter six covers recommendations and conclusion.
TRANSIENT STABILITY ANALYSIS OF NIGERIA POWER SYSTEM: MULTIMACHINE APPROACH
