A scheme suitable for the detection and identification of faults in power systems is presented. Two notable contributions are made: a re-modelling of faulty components of power systems that is applicable to both normal and faulty conditions, and a fault detection scheme for power systems. The faults are modelled as unknown inputs, decoupled from the state and output measurements through coordinate transformations, and then estimated through the use of observer theory. The proposed scheme is applied to a power system consisting of a synchronous generator, an exciter, a turbine and speed-governing system, and a network of lines and loads. The case where faults occur on the transmission network is considered. It is shown that the proposed fault detection procedure allows for the real-time identification of the occurrence of the faults and determines their exact locations. Results of detailed simulation studies involving disturbances and faults occurring in linear and nonlinear models of the power system are presented.
In the deregulated marketplace, generation companies sell energy through auctions or bilateral contracts in a daily market. The daily-price volatility creates the need to perform risk assessment. A procedure able to detect the profitability and risk of bidding in a day-ahead energy market is proposed for power producers. In a pool/bilateral market structure, generation companies are assumed to submit supply bids for the auction in the market pool and report the power amount involved in bilateral contracts to the market operator. The market-clearing process is simulated by solving an OPF-based problem that maximises the social welfare. Then, the expected profits are evaluated by running a Monte Carlo simulation, and the value at risk and conditional value at risk are calculated for quantifying risk of the producer portfolio. The proposed procedure provides suppliers with an efficient tool able to handle daily market-price uncertainties and to capture, in powerful aggregate risk measures, all relevant portfolio effects of market-risk exposure. Simulations are carried out in a 24-hour time frame to analyse the profit and the risk faced by one of the generating companies of the Italian electric-power system.
There is a high level of financial risk associated with the direct participation of wind generation in liberalised electricity markets, due to the stochastic nature of output and imbalance charges set by market prices. The positioning of generation with respect to the market is therefore critical to successful trading activities. Examined is the use of risk characterisation to select the best output level for a wind generator to trade, dependant on maximising revenue and managing marginal costs from imbalances in a competitive market situation. Trading strategies based on utility risk assessment are presented as a possible way to improve market participation for wind generators based on these criteria.
Electromagnetic interference calculations in the case of overhead lines and underground insulated conductors require the determination of the self and mutual impedances of all conductors in the arrangement. For the calculation of these impedances in nonhomogeneous soils, the use of the finite-element method is suggested. However, this is generally a complicated and time-consuming task. Analytic expressions for these impedances are derived by a solution of the electromagnetic field equations for the case of n-layer soil. The infinite integrals involved are evaluated using a numerically stable and efficient integration scheme. A typical transmission line/underground insulated pipeline arrangement is examined for various two-layer earth models and over a wide frequency range. The validity of the proposed methodology is justified by a proper finite-element method formulation. The inclusion of earth stratification leads to substantially different results for the calculated impedances. These differences affect significantly the levels of voltages and currents induced on the pipeline, even for power frequencies, justifying the need for a more detailed earth model representation.
A methodology has been developed for accurate distributed-parameter modelling of a transient on a buried bare conductor based on measured results. The developed bare conductor model including its frequency-dependent effect is implemented into the EMTP so that a transient simulation on a power system can be carried out by the EMTP. The EMTP simulation results agree well with measured results. Based on the wave propagation characteristics identified by the proposed method, it has been observed that the shunt conductance is dominant at a very low frequency and the series inductance plays an important role at an intermediate frequency. Finally the inductance and the shunt capacitance become dominant at a very high frequency. The observation explains most of the previous investigations. The results are expected to contribute to the derivation of analytical formulas for the series impedance and the shunt admittance, and also to predict transient induced voltages on control cables in substations.
A nonlinear coupled electrothermal model of underground cables having aluminum sheaths is developed. The mathematical model deals with the numerical evaluation of losses, heating and ampacity. The filament method, the advancing front method as well as the finite-element method combined with the mapped infinite elements are used. In particular, an improved modelling of heat sources is carried out, taking into account the influence of the nonuniform losses distribution of a particular sheath on the cable heating. Moreover, the calculation of losses is performed with respect to the nonuniform temperature distribution of a particular sheath. Some illustrative computational results leading to clear-cut concluding remarks are given.
Electricity markets with only a few large suppliers often exhibit less competitive behaviour than desired. The presence of transmission constraints further restrict competition among suppliers and provide more opportunities for suppliers to exercise market power. While it is generally acknowledged that long-term contracts provide good measures for mitigating market power in the spot market, thus reducing undesired price spikes, it is not clear how effective these contracts are if the market is severely limited due to transmission constraints. An analytical approach through finding a Nash equilibrium is presented for studying the effects of long-term contracts on market equilibrium in a bid-based pool with transmission constraints. Surprisingly the analysis shows that the presence of long-term contracts may result in reduced expected social welfare.
In a competitive-market environment, deregulation of the electricity industry and thus transmission open access make it even more important to allocate the cost of transmission service fairly. The proposed method can deal with the problem of reactive-power decomposition which could not easily be resolved previously. An equivalent line circuit based on the nominal-T model for reactive-power decomposition is presented. Graph theory and the proportional-sharing principle are employed to trace power flow; the results are then employed to determine the real-power contribution of generators to lines and loads and the reactive-power contribution of generators and lines to loads. The proposed method is illustrated by means of a simple example. Because complex power rather than real power is considered, numerical results from the proposed method are more reasonable than those from the method which considers only real power.
The paper proposes a methodology that determines control strategies of load shedding for restoring power-flow solvability in unsolvable cases using a new tool of outage-continuation power flow (OCPF). A specified outage from a set of multiple contingencies is modelled with a homotopy function, including a parameter representing the outage. The new tool traces the path of solutions satisfying the power-flow equations with respect to variations of the parameter. At the nose point, it performs a sensitivity analysis with a normal vector to identify the most effective control variables. With the sensitivity information, location of load shedding is determined; then, an adequate amount of control is decided by applying a searching method. In numerical simulation, an illustrative example of the proposed framework is shown applied to the New England 39-bus system.
The growing interest in using electrical power networks as an alternative broadband communication medium has spurred many to study the channel characteristics and to formulate channel models of these power networks. Existing channel-modelling techniques for power-line communications (PLC) typically assume that the power networks are connected in tree or radial topology. This assumption is not entirely valid as many electrical circuits in residential homes, commercial and industrial facilities may be wired in ring topology. Using the concept of scattering parameters a novel method derives analytical expressions for the channel transfer function and input impedance of ring-based PLC networks. The derived transfer function and input impedance are successfully verified against measurements conducted on a practical electrical power network in the frequency band from 1 to 30 MHz.
An approach to line protection that is based on fault characteristics extracted by means of wavelet transforms is presented. Analysis of the spectral energy of the phase voltage signals for different frequency bands enables faults to be detected, classified and faulted phases selected. The proposed approach points to the development of ultra-high-speed protective relaying and has been applied to a series-compensated line. The system has been simulated with MICROTRAN and the protection with MATLAB. The results show the feasibility of implementing this algorithm.
Spinning reserve (SR) is probably the most important resource used by power system operators to respond to sudden generation outages and to prevent load disconnections. Although its availability has a substantial value, because it mitigates the considerable social and economic costs of outages, the provision of SR is costly. Unit commitment programs customarily include a reserve constraint in their optimisation procedure to ensure that a fixed amount of SR is scheduled. This approach is sub-optimum, because it considers explicitly neither the cost of providing this amount of reserve, nor the value that consumers place on not being disconnected. In practice, this means that the amount of SR scheduled is likely to be excessive during some periods and insufficient during others. To overcome this problem, a new formulation of the unit commitment optimisation problem is proposed, where the value of the reserve is included in the objective function. To achieve this, a method is developed for quick estimation of the expected energy not served of each combination of generating units considered during the optimisation process.
The paper presents a method for the decentralised solution of the optimal-power-flow (OPF) problem of large, interconnected power systems. The method decomposes the central OPF problem of a multiarea system into independent OPF subproblems, one for each area. The mathematical decomposition method is based on the decoupling of the first-order (KKT) conditions of the original system-wide OPF problem. The solutions of the OPF subproblems of the different areas are co-ordinated through a pricing mechanism until they converge to the system-wide OPF solution. The method requires no parameter tuning for reaching convergence or faster convergence. Results from the application of the method to several IEEE test systems are presented.
The paper studies the impacts of learning behaviour of electrical-power suppliers on electricity-spot-market equilibrium under repeated linear supply-function bidding. In the markets, the supplier will conduct 'learning' to improve his strategic bidding in order to obtain greater profit. Therefore, it is significant to explore the impacts of such learning behaviour on market equilibria and market-clearing price (MCP). First the mathematical model for supplier's optimal bidding is established. This is then used to solve for market equilibrium. It is shown that supply-function equilibrium is a Nash equilibrium; and that under certain conditions the overall learning behaviour will reduce the MCP, which in turn increases consumers' surplus and decreases suppliers' profits, while in some other conditions the results are just the contrary. In either case, the MCP at equilibrium induced by the overall learning behaviour reflects the true relationship of supply and demand. Numerical results support the analytical conclusions very well.
A power system is an inherently highly nonlinear and complex system. Many tuning methods involving parameter optimisation used in the past, were often based on small-signal stability theory and linearised system equations. Such optimisation usually involves the optimising of frequency-domain characteristics such as damping and damping factors of the system critical eigenvalues. The use of frequency-domain information does not allow for the direct improvement of the time-domain characteristics of the system response, e.g. settling time. A simple method is proposed that directly optimises the nonlinear system by using system time response to large disturbances. The properties of the method and its application specifics are discussed in detail. The effectiveness of the method in the co-ordinated tuning of multiple power system stabilisers is illustrated on a multimachine test power system.
The paper presents a simple, robust, and efficient method for determining the maximum-loading point (MLP), and consequently the security margin to voltage collapse of electric-power systems. The computation procedure is based on a proper utilisation of sensitivity techniques. The load increments influence the behaviour of the reactive power injected by generators (slack and PV buses), thus making sensitivity analysis a very interesting tool for voltage-stability analysis and applications. The MLP is obtained accurately after a few load-change steps. Initially, load increments towards the MLP are defined through sensitivity analysis. If an overestimated load increment drives the system outside the feasible (stable) operating region, a very simple optimisation-based procedure aimed to minimising the power mismatches determines the load adjustment to drive the system back to the feasibility boundary. Simulation results for a range of system sizes are shown to validate the proposed method.
The paper presents a set of formulas for directly predicting the performance of rate-of-change-of-frequency (ROCOF) relays used to detect islanding of embedded synchronous generators. The formulas are analytically derived from the dynamic model of the generator and relay. Dynamic simulation results obtained using a representative distribution system confirm the validity and accuracy of the formulas. The formulas presented are a useful tool for protection engineers; they can be used, for example, to assess the effectiveness of anti-islanding schemes based on ROCOF relays, or to assist the selection of relay settings, significantly reducing the number of repeated dynamic simulations necessary to carry out such studies.
Voltage support of transmission lines by var compensation is now carried out mostly on transmission buses. The authors show that var compensation on distribution buses and deregulation of transmission voltages is not only feasible in certain circumstances but also economically advantageous. This opens the prospect of the distribution sector offering voltage support to the transmission sector as an ancillary service. The considered system is a 400 km long, 230 kV, heavily loaded (800 MW) radial transmission line which feeds several remote load centres spaced along its length. Analysis of the benefits and demonstration of feasibility, steady-state stability and robustness in the face of short-circuit faults are presented.
In a deregulated power system, it is usually required to determine the shares of each load and generation in line flows, to permit fair allocation of transmission costs between the interested parties. The paper presents a new method of determining the contributions of each load to line flows and losses. The method is based on power-flow topology and has the advantage of being the least computationally demanding of similar methods.
A linear time-varying fuzzy load model for solving the short-term electric load forecasting problem is presented. The model utilises a moving window of current values of weather data as well as the recent past history of load and weather data. The parameters of this model are assumed to be fuzzy numbers with a triangular membership function yielding a fuzzy load that has both central and spread values. Both the load and load error are predicted for the following 24hours on an hourly basis. The forecasting method is based on state space and the Kalman filtering prediction approach in conjunction with fuzzy rule-based logic. The technique is used recursively to estimate the optimal load forecast fuzzy parameters for each hour of the day. The central values of the fuzzy parameters represent the crisp forecast values while the spread values represent the amount of variation of the forecast. The predicted load spread value provides an approximate envelope of the extremes the load possibly takes. The effectiveness of the approach is demonstrated on real load and weather data which show the load forecast with a mean absolute percent error of less than 0.7% and absolute percent error standard deviation of 0.9%.
