On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia

Analysis of distrubances in large interconnected power systems

World economies increasingly demand reliable and economical power supply and distribution. To achieve this aim the majority of power systems are becoming interconnected, with several power utilities supplying the one large network. One problem that occurs in a large interconnected power system is the regular occurrence of system disturbances which can result in the creation of intra-area oscillating modes. These modes can be regarded as the transient responses of the power system to excitation, which are generally characterised as decaying sinusoids. For a power system operating ideally these transient responses would ideally would have a “ring-down” time of 10-15 seconds. Sometimes equipment failures disturb the ideal operation of power systems and oscillating modes with ring-down times greater than 15 seconds arise. The larger settling times associated with such “poorly damped” modes cause substantial power flows between generation nodes, resulting in significant physical stresses on the power distribution system. If these modes are not just poorly damped but “negatively damped”, catastrophic failures of the system can occur. To ensure system stability and security of large power systems, the potentially dangerous oscillating modes generated from disturbances (such as equipment failure) must be quickly identified. The power utility must then apply appropriate damping control strategies. In power system monitoring there exist two facets of critical interest. The first is the estimation of modal parameters for a power system in normal, stable, operation. The second is the rapid detection of any substantial changes to this normal, stable operation (because of equipment breakdown for example). Most work to date has concentrated on the first of these two facets, i.e. on modal parameter estimation. Numerous modal parameter estimation techniques have been proposed and implemented, but all have limitations [1-13]. One of the key limitations of all existing parameter estimation methods is the fact that they require very long data records to provide accurate parameter estimates. This is a particularly significant problem after a sudden detrimental change in damping. One simply cannot afford to wait long enough to collect the large amounts of data required for existing parameter estimators. Motivated by this gap in the current body of knowledge and practice, the research reported in this thesis focuses heavily on rapid detection of changes (i.e. on the second facet mentioned above). This thesis reports on a number of new algorithms which can rapidly flag whether or not there has been a detrimental change to a stable operating system. It will be seen that the new algorithms enable sudden modal changes to be detected within quite short time frames (typically about 1 minute), using data from power systems in normal operation. The new methods reported in this thesis are summarised below. The Energy Based Detector (EBD): The rationale for this method is that the modal disturbance energy is greater for lightly damped modes than it is for heavily damped modes (because the latter decay more rapidly). Sudden changes in modal energy, then, imply sudden changes in modal damping. Because the method relies on data from power systems in normal operation, the modal disturbances are random. Accordingly, the disturbance energy is modelled as a random process (with the parameters of the model being determined from the power system under consideration). A threshold is then set based on the statistical model. The energy method is very simple to implement and is computationally efficient. It is, however, only able to determine whether or not a sudden modal deterioration has occurred; it cannot identify which mode has deteriorated. For this reason the method is particularly well suited to smaller interconnected power systems that involve only a single mode. Optimal Individual Mode Detector (OIMD): As discussed in the previous paragraph, the energy detector can only determine whether or not a change has occurred; it cannot flag which mode is responsible for the deterioration. The OIMD seeks to address this shortcoming. It uses optimal detection theory to test for sudden changes in individual modes. In practice, one can have an OIMD operating for all modes within a system, so that changes in any of the modes can be detected. Like the energy detector, the OIMD is based on a statistical model and a subsequently derived threshold test. The Kalman Innovation Detector (KID): This detector is an alternative to the OIMD. Unlike the OIMD, however, it does not explicitly monitor individual modes. Rather it relies on a key property of a Kalman filter, namely that the Kalman innovation (the difference between the estimated and observed outputs) is white as long as the Kalman filter model is valid. A Kalman filter model is set to represent a particular power system. If some event in the power system (such as equipment failure) causes a sudden change to the power system, the Kalman model will no longer be valid and the innovation will no longer be white. Furthermore, if there is a detrimental system change, the innovation spectrum will display strong peaks in the spectrum at frequency locations associated with changes. Hence the innovation spectrum can be monitored to both set-off an “alarm” when a change occurs and to identify which modal frequency has given rise to the change. The threshold for alarming is based on the simple Chi-Squared PDF for a normalised white noise spectrum [14, 15]. While the method can identify the mode which has deteriorated, it does not necessarily indicate whether there has been a frequency or damping change. The PPM discussed next can monitor frequency changes and so can provide some discrimination in this regard. The Polynomial Phase Method (PPM): In [16] the cubic phase (CP) function was introduced as a tool for revealing frequency related spectral changes. This thesis extends the cubic phase function to a generalised class of polynomial phase functions which can reveal frequency related spectral changes in power systems. A statistical analysis of the technique is performed. When applied to power system analysis, the PPM can provide knowledge of sudden shifts in frequency through both the new frequency estimate and the polynomial phase coefficient information. This knowledge can be then cross-referenced with other detection methods to provide improved detection benchmarks.

SSE based parallel solution for power systems network equations

Streaming SIMD Extensions (SSE) is a unique feature embedded in the Pentium III class of microprocessors. By fully exploiting SSE, parallel algorithms can be implemented on a standard personal computer and a theoretical speedup of four can be achieved. In this paper, we demonstrate the implementation of a parallel LU matrix decomposition algorithm for solving power systems network equations with SSE and discuss advantages and disadvantages of this approach.

Real-time simulation for power systems based on parallel computing - an empirical study

Abstract Computer simulation is a versatile and commonly used tool for the design and evaluation of systems with different degrees of complexity. Power distribution systems and electric railway network are areas for which computer simulations are being heavily applied. A dominant factor in evaluating the performance of a software simulator is its processing time, especially in the cases of real-time simulation. Parallel processing provides a viable mean to reduce the computing time and is therefore suitable for building real-time simulators. In this paper, we present different issues related to solving the power distribution system with parallel computing based on a multiple-CPU server and we will concentrate, in particular, on the speedup performance of such an approach.

Interpreting regional frequencies from synchronized phasor measurement in multi-area power systems

In this paper a new approach is proposed for interpreting of regional frequencies in multi machine power systems. The method uses generator aggregation and system reduction based on coherent generators in each area. The reduced system structure is able to be identified and a kalman estimator is designed for the reduced system to estimate the inter-area modes using the synchronized phasor measurement data. The proposed method is tested on a six machine, three area test system and the obtained results show the estimation of inter-area oscillations in the system with a high accuracy.

Variable structure control for power systems stabilization

The application of variable structure control (VSC) for power systems stabilization is studied in this paper. It is the application, aspects and constraints of VSC which are of particular interest. A variable structure control methodology has been proposed for power systems stabilization. The method is implemented using thyristor controlled series compensators. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller. The results demonstrate the effectiveness of the methodology proposed as an useful tool to suppress the oscillations in power systems.

Unit commitment in power systems with plug-in hybrid electric vehicles

With the continued development of renewable energy generation technologies and increasing pressure to combat the global effects of greenhouse warming, plug-in hybrid electric vehicles (PHEVs) have received worldwide attention, finding applications in North America and Europe. When a large number of PHEVs are introduced into a power system, there will be extensive impacts on power system planning and operation, as well as on electricity market development. It is therefore necessary to properly control PHEV charging and discharging behaviors. Given this background, a new unit commitment model and its solution method that takes into account the optimal PHEV charging and discharging controls is presented in this paper. A 10-unit and 24-hour unit commitment (UC) problem is employed to demonstrate the feasibility and efficiency of the developed method, and the impacts of the wide applications of PHEVs on the operating costs and the emission of the power system are studied. Case studies are also carried out to investigate the impacts of different PHEV penetration levels and different PHEV charging modes on the results of the UC problem. A 100-unit system is employed for further analysis on the impacts of PHEVs on the UC problem in a larger system application. Simulation results demonstrate that the employment of optimized PHEV charging and discharging modes is very helpful for smoothing the load curve profile and enhancing the ability of the power system to accommodate more PHEVs. Furthermore, an optimal Vehicle to Grid (V2G) discharging control provides economic and efficient backups and spinning reserves for the secure and economic operation of the power system

RCA method for fault diagnosis in digital substations of power systems

The authors present a Cause-Effect fault diagnosis model, which utilises the Root Cause Analysis approach and takes into account the technical features of a digital substation. The Dempster/Shafer evidence theory is used to integrate different types of fault information in the diagnosis model so as to implement a hierarchical, systematic and comprehensive diagnosis based on the logic relationship between the parent and child nodes such as transformer/circuit-breaker/transmission-line, and between the root and child causes. A real fault scenario is investigated in the case study to demonstrate the developed approach in diagnosing malfunction of protective relays and/or circuit breakers, miss or false alarms, and other commonly encountered faults at a modern digital substation.

Dynamic equivalent state estimation for multi-area power systems with synchronized phasor measurement units

This paper proposes a new approach for state estimation of angles and frequencies of equivalent areas in large power systems with synchronized phasor measurement units. Defining coherent generators and their correspondent areas, generators are aggregated and system reduction is performed in each area of inter-connected power systems. The structure of the reduced system is obtained based on the characteristics of the reduced linear model and measurement data to form the non-linear model of the reduced system. Then a Kalman estimator is designed for the reduced system to provide an equivalent dynamic system state estimation using the synchronized phasor measurement data. The method is simulated on two test systems to evaluate the feasibility of the proposed method.

Candidate radial-inflow turbines and high-density working fluids for geothermal power systems

Optimisation of Organic Rankine Cycle (ORCs) for binary-cycle geothermal applications could play a major role in determining the competitiveness of low to moderate temperature geothermal resources. Part of this optimisation process is matching cycles to a given resource such that power output can be maximised. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration: the selection of working fluid and appropriate operating conditions as well as optimisation of the turbine design for those conditions will determine the amount of power that can be extracted from a resource. In this paper, we present the rationale for the use of radial-inflow turbines for ORC applications and the preliminary design of several radial-inflow machines based on a number of promising ORC systems that use five different working fluids: R134a, R143a, R236fa, R245fa and n-Pentane. Preliminary meanline analysis lead to the generation of turbine designs for the various cycles with similar efficiencies (77%) but large differences in dimensions (139–289 mm rotor diameter). The highest performing cycle, based on R134a, was found to produce 33% more net power from a 150 °C resource flowing at 10 kg/s than the lowest performing cycle, based on n-Pentane.

Candidate radial-inflow turbines and high-density working fluids for geothermal power systems

Optimisation of Organic Rankine Cycles (ORCs) for binary-cycle geothermal applications could play a major role in the competitiveness of low to moderate temperature geothermal resources. Part of this optimisation process is matching cycles to a given resource such that power output can be maximised. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration. Due to the temperature differences in geothermal resources a one-size-fits-all approach to surface power infrastructure is not appropriate. Furthermore, the traditional use of steam as a working fluid does not seem practical due to the low temperatures of many resources. A variety of organic fluids with low boiling points may be utilised as ORC working fluids in binary power cycle loops. Due to differences in thermodynamic properties, certain fluids are able to extract more heat from a given resource than others over certain temperature and pressure ranges. This enables the tailoring of power cycle infrastructure to best match the geothermal resource through careful selection of the working fluid and turbine design optimisation to yield the optimum overall cycle performance. This paper presents the rationale for the use of radial-inflow turbines for ORC applications and the preliminary design of several radial-inflow turbines based on a selection of promising ORC cycles using five different high-density working fluids: R134a, R143a, R236fa, R245fa and n-Pentane at sub- or trans-critical conditions. Numerous studies published compare a variety of working fluids for various ORC configurations. However, there is little information specifically pertaining to the design and implementation of ORCs using realistic radial turbine designs in terms of pressure ratios, inlet pressure, rotor size and rotational speed. Preliminary 1D analysis leads to the generation of turbine designs for the various cycles with similar efficiencies (77%) but large differences in dimensions (139289 mm rotor diameter). The highest performing cycle (R134a) was found to produce 33% more net power from a 150°C resource flowing at 10 kg/s than the lowest performing cycle (n-Pentane).