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Electricity TariffThe electricity tariff is defined as the rate at which the electrical energy is sold to a consumer.However, the tariff should include the total cost of producing and supplying electrical energy plus the profit to the power company. In practice, the tariff cannot be same for all types of consumers because the cost of production of electrical energy depends upon the magnitude of electrical energy consumed by the user and his load conditions. Therefore, the tariff is fixed by considering the different types of consumers such as domestic, industrial and commercial, etc.Objective of TariffLike any other product, the electrical ... Read More
The power factor of the load connected to the power system considerably affects the voltage regulation and efficiency of a transmission line.Effect of Load Power Factor on Voltage RegulationThe expression for percentage voltage regulation of a transmission line, when a load of lagging power factor is connected to the system, is given by, $$\mathrm{\%\:Voltage \:Regulation\:=\:\frac{\mathit{IR}\:cos\:\phi _{\mathit{R}}\:+\:\mathit{IX_{\mathit{L}}}cos\:\phi _{\mathit{R}} }{\mathit{V_{\mathit{R}}}}\:\times \:100\%\:\:\:...\left ( 1 \right )}$$Where, suffix R denotes the receiving end quantities.Also, the percentage voltage regulation for leading power factor is given by, $$\mathrm{\%\:Voltage \:Regulation\:=\:\frac{\mathit{IR}\:cos\:\phi _{\mathit{R}}\:-\:\mathit{IX_{\mathit{L}}}cos\:\phi _{\mathit{R}} }{\mathit{V_{\mathit{R}}}}\:\times \:100\%\:\:\:...\left ( 2 \right )}$$Therefore, from equations (1) and (2), the following points can ... Read More
Variable Load on Power StationThe load on an electric power system changes from time to time due to uncertain demands of the consumers, this variation in load of a power station is termed as variable load on power station.An electric power station is designed to meet the load requirements of the consumers. From the standpoint of equipment needed and operating routine, an ideal load on a power station would be of constant magnitude and of steady duration.However, in actual practice, such a steady load on the power station cannot be realised. It is because the consumers require different blocks of ... Read More
Power FactorThe cosine of angle between voltage and current in an AC circuit is called the power factor of the circuit. In other words, the power factor is defined as the ratio of active power to the apparent power in the circuit, i.e., $$\mathrm{Power\: factor, cos\:\phi\:=\:\frac{Active\: power\: (in \:Watts)}{Apparent\: power\: (in\: VA)}}$$Where, $\phi$ is the power factor angle.Causes of Low Power FactorFrom the economic point of view, the low power factor of the load connected to a power system is undesirable. The main causes of low power factor are given as follows −The AC electric motors consist of inductive winding. ... Read More
In this problem, we are given a 2D binary matrix. Our task is to Find the number of islands Using DFS.Island is a ground of 1 or more connected 1’s in the matrix.Let’s take an example to understand the problem, Input : bin[][] = {{ 1 0 0 0} {0 1 0 1} {0 0 0 0} {0 0 1 0}} Output : 3 ExplanationIslands are −bin00 - bin11bin13bin32 Solution ApproachTo solve the problem using DFS, we will use the DFS technique for exploring all the neighbours (maximum possible 8 of a number in the matrix) and ... Read More
In this problem, we are given an integer value N. Our task is to find Nth Even Fibonacci Number.Fibonacci Series generates subsequent number by adding two previous numbers. The Fibonacci series starts from two numbers − F0 & F1. The initial values of F0 & F1 can be taken 0, 1 or 1, 1 respectively.Let’s take an example to understand the problem, Input : N = 4 Output : 144Solution ApproachA simple solution to the problem is using the fact that every third number in the fibonacci sequence is even and the sequence of even numbers also follows the recursive ... Read More
The numpy.matrix method is used to interpret a given input as a matrix. It returns a matrix from an array-like object. Its syntax is as follows −numpy.matrix(data, dtype=None, copy=bool)where, data - It is the input data.dtype - It represents the data type of the output matrix.copy - If the input data is already an ndarray, then this flag copy determines whether the data is to be copied (default behavior), or whether a view is to be constructed.Example 1Let us consider the following example −# import numpy library import numpy as np # matrix function y = np.matrix([[4, 5], [7, ... Read More
The numpy.triu() method can be used to get the upper triangle of an array. Its syntax is as follows −Syntaxnumpy.triu(m, k=0)where, m - number of rows in the array.k - It is the diagonal. Use k=0 for the main diagonal. k < 0 is below the main diagonal and k > 0 is above it.It returns a copy of the array after replacing all the elements above the kth diagonal with zero.Example 1Let us consider the following example −# import numpy library import numpy as np # create an input matrix x = np.matrix([[6, 7], [8, 9], [10, 11]]) ... Read More
The numpy.vander() method is used to generate a Vandermonde (Vander) matrix. A Vander matrix contains a geometric progression in each row, for example, $$\mathrm{A =\begin{bmatrix}1 & 2 & 4 \1 & 3 & 9 \1 & 5 &25\end{bmatrix} or\: B = \begin{bmatrix}1 & 4 & 16 \1 & 6 &36 \end{bmatrix}}$$SyntaxIts syntax is as follows −numpy.vander(x, N=None, increasing=False)ParametersIt accepts the following parameters −x - This is the input array.N - It is the number of columns in the output. By default, it is None.Increasing - If increasing=True, then the power increases from left to right. If increasing=False, then powers are ... Read More
We can use the numpy.tril() method to get the lower triangle of an array. Its syntax is as followsSyntaxnumpy.tril(m, k=0)where, m - number of rows in the array.k - It is the diagonal. Use k=0 for the main diagonal. k < 0 is below the main diagonal and k > 0 is above it.It returns a copy of the array after replacing all the elements above the k thdiagonal with zero.Example 1Let us consider the following example −# import numpy library import numpy as np # create an input matrix x = np.matrix([[20, 21, 22], [44 ,45, 46], [78, ... Read More