Essay: Transmission systems

From the earlier days, interconnected systems are being used worldwide for the transmission of electric power. Generation of electric power and its utilization can be far away with transmission line. There will be transmission losses in the form of heat energy along the transmission line because the lines are not perfectly conductor. The total power transmission loss is about 10% of generated power. The power loss can be decreased using optimal power flow with power losses as an objective function. This will increase the profitability of generating companies.
In restructured power systems, the energy trades can be done in two ways: 1. Energy auction or pools and 2. Bilateral contracts. Bilateral contracts are becoming more popular among the Independent System Operator (ISO) and market participants (i.e., the sellers and buyers of the electric energy). Bilateral contracts are financially safer for the market participants, because they can hedge against high price volatilities of real-time markets [3].
A bilateral transaction between a supplier and a buyer involves the injection of power at one location in the network and the extraction of the same amount of power, at another location, at the same time. Each bilateral transaction should be represented by a source (positive injection) connected to the point of injection and a sink (negative injection) connected to the point of extraction. The source and sink are assumed to have same size (transaction rate in MW). The power injections associated with different bilateral transactions can influence the loading on transmission interfaces can increase or decrease depending on the system operating conditions, transaction size, and the direction of power transfer and the number of transactions considered [2].
An important problem that arises during the operation of power system is optimizing the power flow. There can be various objective functions in OPF. Some of these are reduction in power generation cost, reduction in power transmission system losses, minimization of fuel emission during power generation which is related to environmental pollution, etc. Different techniques have been used for solving the optimal power flow problem [1]. An optimal power flow with cost minimization using Newton’s method is described. This is an analytical method in which we take derivative of gradient to speed up the convergence. This method has limitations in handling the constraints.
The difficulty arises in the fact that near the limit the penalty is small, so that optimal solution will tend to allow the variable, for example, a voltage to float over its limit. Another analytical method is the interior point method for the solution of constrained optimal power flow. This method is faster as compared to other conventional analytical methods. In [3], the authors describe loss reduction method using alterations in the hardware installations as well as software based constrained optimization. This shows the need of some good optimization technique with OPF which is the main aim of research work.
One of the optimization techniques to solve Assignment Problem is to apply Hungarian method. Hungarian mathematician Konig (1931) developed the Hungarian method of assignment which provides an efficient method of finding the optimal solution without having to make a direct comparison of every solution. It works on the principle of reducing the given cost matrix to an opportunity costs. If we can reduce the cost matrix to the extent of having at least one zero in each row and column, it will be possible to make optimal assignments