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## Über dieses Buch

This book presents integrated optimization methods and algorithms for power system problems along with their codes in MATLAB. Providing a reliable and secure power and energy system is one of the main challenges of the new era. Due to the nonlinear multi-objective nature of these problems, the traditional methods are not suitable approaches for solving large-scale power system operation dilemmas. The integration of optimization algorithms into power systems has been discussed in several textbooks, but this is the first to include the integration methods and the developed codes. As such, it is a useful resource for undergraduate and graduate students, researchers and engineers trying to solve power and energy optimization problems using modern technical and intelligent systems based on theory and application case studies. It is expected that readers have a basic mathematical background.

## Inhaltsverzeichnis

### Modelling for Composite Load Model Including Participation of Static and Dynamic Load

Abstract
It is well recognized that voltage problems in power system is much affected through the connected loads. Different types of load can be modeled on their characteristics basis for computation of power system problems effectively. For different power system studies especially in the area of power system optimization problems that includes voltage control with reactive power compensation, transfer function $$\Delta Q{/}\Delta V$$ of composite load is required. This chapter gives a detailed mathematical modelling to compute the reactive power response with small voltage perturbation for composite load. Composite load is defined as a combination of static and dynamic load model. To develop this composite load model, the exponential load is used as a static load model and induction motors are used as a dynamic load model in this chapter. To analyze the dynamics of induction motor load, fifth, third and first order model of induction motor are formulated and compared using differential equations solver in MATLAB coding. Since the decentralized areas have many small consumers which may consist large numbers of induction motors of small rating, it is not realistic to model either a single large rating unit or all small rating induction motors together that are placed in the system. In place of using single large rating induction motor a group of motors are being considered and then aggregate model of induction motor is developed using law of energy conservation and this aggregate model is used as a dynamic load model. Transfer function of composite load is derived in this chapter by successive derivation for exponential model of static load and for fifth and third order induction motor dynamic load model using state space model.
Nitin Kumar Saxena, Ashwani Kumar

### A Novel Forward-Backward Sweep Based Optimal DG Placement Approach in Radial Distribution Systems

Abstract
The huge value of the electricity consumption in different residential, commercial, industrial and agricultural sectors lead to the load-generation mismatch, voltage drops, cascading failures, and wide area blackouts. Therefore, the use of renewable energy resources based distributed generation (DG) units is rapidly growing in order to satisfy not-supplied electrical demand and reduce greenhouse gas emissions. Meanwhile, optimal placement of DG units in radial grids is crucial for minimization of the total active power losses and the voltage drops. This chapter proposes a novel backward-forward sweep (BFS) based methodology for optimal allocation of DG micro-plants in radial distribution systems aiming to minimize total real power losses of the whole system. Voltage permitted range limit and feeder capacity criterion are considered as optimization constraints. Simulation of BFS based DG placement method is conducted on the 33-bus distribution network to investigate its performance under different scenarios.
Farkhondeh Jabari, Somayeh Asadi, Sahar Seyed-barhagh

### Optimal Capacitor Placement in Distribution Systems Using a Backward-Forward Sweep Based Load Flow Method

Abstract
Nowadays, the non-optimal placement of the shunt capacitors in distributed electricity systems may increase the total active power loss and lead to the voltage instability. Therefore, many researchers have recently focused on optimization of capacitor placement problem in radial and meshed distribution grids aiming to minimize transmission losses and improve the overall efficiency of the power delivery process. This chapter aims to present a backward-forward sweep (BFS) based algorithm for optimal allocation of shunt capacitors in distribution networks. The total real power loss of the whole system is minimized as the objective function. Moreover, the feeder current capacity and the bus voltage magnitude limits are considered as the optimization constraints. In addition, it is assumed that the sizes of capacitors are the known  scalars. The 1st capacitor is considered to be located at the 1st bus of the test system. Then, the BFS load flow is run and the objective function is saved as 1st row and 1st column component of a loss matrix. Secondly, the 1st capacitor is assumed to be installed at bus 2 and the BFS load flow is run to obtain objective function as 2nd row and 1st column component of loss matrix. When all buses are assessed for installation of capacitor 1 and losses are calculated in each scenario, similar analyses are carried out for the 2nd capacitor bank and the values of the active power loss are saved as the 2nd column of the loss matrix. The same strategy is applied to other capacitors. Finally, a loss matrix is formed with number of rows and columns equal to the number of buses and shunt capacitors, respectively. The best places for installation of capacitors are determined based on the components of the loss matrix. Simulation of BFS based capacitor placement problem is conducted on the 33-bus distribution network to demonstrate its robustness and effectiveness in comparison with other procedures.
Farkhondeh Jabari, Khezr Sanjani, Somayeh Asadi

### Optimal Capacitor Placement and Sizing in Distribution Networks

Abstract
Utilizing capacitor banks in order for local compensation of loads reactive power is common in distribution networks. Using capacitors has positive effects on networks such as power and energy loss reduction, voltage deviation and network harmonic reduction as well as improvement in network power factor. Capacitor placement is applied on the network in a form of single or multi-objective problems. Decreasing the total network loss is often the main reason for using capacitors in distribution networks. Capacitor placement approach involves the identification of location for capacitor placement and the size of the capacitor to be installed at the identified location. An optimization algorithm decides the location of the nodes where the capacitors should be placed. As we know, the capacitors are categorized in two main types of fixed and switchable capacitors. Selecting an appropriate type of capacitor is related to the topology of network, load value and economic situation. They are also different from coding point of view. In this section, the model of coding is presented at first, and then, the approach of applying is described based on optimization algorithm. The capacitors are often used for peak loads but they may be present in the network in off-peak due to the switching issues. The network voltage may be increased in off-peak with the presence of capacitors. Therefore, it is very important to consider both peak and off-peak in the capacitor sizing and placement problem. The proposed model is applied on IEEE 10 and 33-bus standard test cases in order to demonstrate the efficiency of the proposed model.
Arsalan Najafi, Ali Masoudian, Behnam Mohammadi-Ivatloo

### Binary Group Search Optimization for Distribution Network Reconfiguration

Abstract
In this chapter, the binary group search optimization algorithm (BGSO) is proposed to tackle with optimal network reconfiguration problem in distribution systems. Here, total loss minimization is considered as the objective which is solved subject to system radial operation and power flow constraints. Here, the basics of GSO algorithm is presented first and then, necessary modification for developing BGSO is discussed. The main part of this chapter deals with a source code, which expresses step by step implementation of BGSO method to optimal network reconfiguration problem. Needless to emphasize that the BGSO and associated source code presented in this chapter is a general engine that can be easily adjusted to any optimization problem with binary variables. In addition, the source code associated with the developed forward-backward sweep-based load flow study is also provided. The simulation studies are performed on different distribution networks to examine the scheme at various conditions and problem complexities. Comprehensive simulation studies conducted in this chapter verifies effectiveness of the BGSO and developed source code for solving optimal distribution network reconfiguration problem.

### Combined Heat and Power Economic Dispatch Using Particle Swarm Optimization

Abstract
Due to increased energy cost and limitations of fossil fuel energy sources, systems with higher efficiency such as combined heat and power (CHP) have become more popular. Optimal operation of the power system in the presence of CHP units which have non-linear and non-convex characteristics is getting more complicated. Difficulties of mentioned problem lead us to use heuristic and evolutionary methods. In this chapter, particle swarm optimization (PSO) is implemented in economic dispatch (ED) of CHP units. The main objective of ED problem is to obtain optimal output power and heat of each unit while the total generating cost is minimized and system operational constraints are satisfied. The results show the capability of this algorithm in solving CHP economic dispatch (CHPED) problem.
Farnaz Sohrabi, Farkhondeh Jabari, Pouya Pourghasem, Behnam Mohammadi-Ivatloo

### Combined Heat and Power Stochastic Dynamic Economic Dispatch Using Particle Swarm Optimization Considering Load and Wind Power Uncertainties

Abstract
Due to the increased cost of energy sources and related environmental problems, systems with higher efficiency such as combined heat and power (CHP) units are getting more popular. Renewable energy sources can be another alternative solution for the above mentioned problems. Scheduling of renewable-based systems are getting more complicated due to the intermittent behavior of these sources. In this chapter, a stochastic programming framework is utilized to model uncertainties in dynamic economic dispatch (DED) problem of CHP based systems integrating wind energy. Forecast errors of electrical load and wind power are assumed as the two sources of uncertainty. A heuristic method called particle swarm optimization (PSO) is used to attain optimal solution of the problem due to non-linearity, non-convexity, and complexity of the problem. The stochastic programming provides more comprehensive and realistic viewpoint about dispatch problem by considering a variety of most probable scenarios compared to a single scenario.

### Economic Dispatch of Multiple-Chiller Plants Using Wild Goats Algorithm

Abstract
Use of multiple-chiller systems in air-conditioning applications is known as a major factor in increasing electricity consumption. To obtain a significant energy saving in building space cooling, optimal operation of chillers as an energy-efficient manner is necessary. Therefore, this chapter aims to obtain the best performance of the multi-chiller systems, which can be attained by minimizing the total power consumption of chillers considering their partial load ratios (PLRs) as decision variables. In this chapter, optimal chiller loading (OCL) problem is implemented on three different case studies using a novel evolutionary algorithm, called wild goats algorithm (WGA). This algorithm is inspired from wild goats’ climbing, living in groups and based on cooperation between members of groups. Numerical results show the effectiveness of the WGA to solve the OCL problem.
Farkhondeh Jabari, Alireza Akbari Dibavar, Behnam Mohammadi-Ivatloo

### Optimization of Tilt Angle for Intercepting Maximum Solar Radiation for Power Generation

Abstract
In this study the novelty is determination of optimum tilt angles $$(\upbeta_{\text{opt}} )$$ for photovoltaic system at 11 different sites for Gujarat in India. The $$\upbeta_{\text{opt}}$$ is searched for maximum incident solar radiation (SR). For calculation SR values given by National Aeronautics and Space Administration (NASA) is utilized. It was found that the optimum tilt angle varies between 1° and 57° throughout the year in Gujarat, India. The monthly optimum tilt angle is maximum in December for different sites in Gujarat India. This study is useful for industry and researcher to install PV system in India to generate maximum power.

### Probabilistic Power Flow Analysis of Distribution Systems Using Monte Carlo Simulations

Abstract
Nowadays, population growth has led to increased electricity consumption in different residential, commercial and industrial district levels. This may leads to load-generation imbalance, voltage drop, cascaded failure and catastrophic blackout of interconnected power networks. To prevent from wide spread outages and uncontrolled islanding of large-scale and distributed grids, uncertainties associated with loads are considered in steady-state voltage stability analysis and reliability assessment. Therefore, this chapter aims to present a Monte Carlo simulations based probabilistic power flow method for finding all critical buses against variations of active and reactive loads. In this approach, backward-forward sweep based load flow is used to find optimal operating point of benchmark distribution grid in each scenario. Number of scenarios with bus voltage magnitude violation probability is used to cluster nodes into two critical and non-critical categories. Robustness and effectiveness of Monte Carlo based probabilistic power flow algorithm is revealed by simulations on 33-bus radial distribution system.

### Long-Term Load Forecasting Approach Using Dynamic Feed-Forward Back-Propagation Artificial Neural Network

Abstract
In recent years, due to increasing rate of electricity demand and power system restructuring with a limited investment in transmission expansion, large power systems may closely be operated at their stability margins. Meanwhile, uncertain and intermittent nature of electricity demand with traditional load forecasting error seriously effects on operation and planning of bulk power grids. Hence, this chapter aims to present a novel approach based on dynamic feed-forward back-propagation artificial neural network (FBP-ANN) for long-term forecasting of total electricity demand. A feed-forward back-propagation time series neural network consists of an input layer, hidden layers, and an output layer and is trained in three steps: (a) Forward the input load data, (b) Compute and propagate the error backward, (c) Update the weights. First, all examples of the training set are entered into the input nodes. The activation values of the input nodes are weighted and accumulated at each node in the hidden layer and transformed by an activation function into the node’s activation value. Hence, it becomes an input into the nodes in the next layer, until eventually the output activation values are found. The training algorithm is used to find the weights that minimize mean squared error. The main characteristics of FBP-TSNN are the self-learning and self-organizing. The proposed algorithm is implemented on Canada’s power network to prove its accuracy along with effectiveness, and then compared with real historical data.

### Multi-objective Economic and Emission Dispatch Using MOICA: A Competitive Study

Abstract
In this chapter, the application of multi-objective imperialist competitive algorithm is investigated for solving economic and emission dispatch problem. It is aimed to minimize two conflicting objectives, economic and environmental, while satisfying the problem constraints. In addition, nonlinear characteristics of generators such as prohibited zone and ramp up/down limits are considered. To check applicability of the MOICA, it is applied to 12 h of IEEE 30-bus test system. Then, results of MOICA are compared with those derived by non-dominated sorting genetic algorithm and multi-objective particle swarm optimizer. The finding indicates that MOICA exhibits better performance.