Abstract (english) | Since the beginning of the 21st century major changes have occurred in the development of power system. The conventional understanding of the power systems implied strictly centralized systems managed by vertically organized monopolistic companies that were mostly in a state ownership. Due to constantly increasing demand for electricity on global level, problems in ensuring reliable power supply were getting bigger which led to changes in conventional power systems in terms of system liberalization and decentralization. Also, interconnection of national transmission systems led to electricity market development. At the same time, due to climate changes and environment pollution, global energy politics turned towards more ecological energy sources and the development of renewable energy sources began to rapidly increase. Between them, the greatest potential lies in wind turbines and photovoltaics. In last decade total global installed power capacity of these two types of power plants is rapidly increasing, while total power capacity of conventional power plants stagnates. Both, the wind turbines and photovoltaics are intermittent sources whose power production depends on current weather conditions. High penetration of such power plants in power system can cause problems in system stability, production planning, system management and power supply reliability. In the second chapter the main characteristics of distribution network and impact of distributed generation was described. Current photovoltaics’ generation depends on current amount of light that falls on the photovoltaic panels and it changes during the day depending on the sun position and the amount of cloud cover. There are, also, differences in total daily electricity production due to day length. Most of photovoltaics are micro power plants that are built on the roofs of existing objects and are connected to low voltage distribution network. High penetration of such power plants in low voltage network affects on voltage conditions and, also, on electricity losses. Large share of electricity generation can cause overvoltages that can cause damage on electrical installations and appliances. Distribution system operators now have to deal with low voltages, when there in case of low or non-generation, and high voltages in periods of high insolation at the same time. Due to that, capacity of low voltage network for connection of photovoltaics is limited and depends on the technical characteristics and the daily load curve of the network. To raise this capacity and to ensure prescribed voltage conditions in network, it is necessary to introduce smart technologies that can manage the output power of photovoltaics. Also, high generation in low voltage network can increase energy losses and, thus, reduce total distribution system efficiency. The aim of doctoral thesis was to develop model for active power curtailment of photovoltaics in order to minimize power losses in low voltage network with high penetration of photovoltaics. The expected effects of the model were power losses minimization, increase of network capacity for connecting larger share of photovoltaics and improvement of voltage profile in low voltage network. The model was developed in three phases. The first phase was making of a three phase power flow calculation program which is described in chapter three. The first step was making three phase models of distribution system elements: lines, loads and transformers. A chosen method for power flow calculation was forward-backward sweep method which is suitable for power flow calculations in radial networks. The method is iterative and converges pretty fast. Iterative process consists of four steps that repeat until the given tolerance is achieved for every node. Distribution networks are mostly radial networks with lateral branches. To define connections between nodes before starting an iterative process, it is necessary to create an incidence matrix. For radial networks incidence matrices are upper triangle sparse matrices which means that the most of their elements are equal to zero. In iterative process of forward-backward sweep method it is necessary to calculate branch currents from the last towards the feeder node and then node voltages from the feeder node towards the last node. In classical forward-backward sweep method for every step of iterative process an upper triangular part of incidence matrix has to be read at least once. With increase of nodes number in network the number of read elements increases rapidly which extends the duration of calculation process. To speed up the calculation process, a procedure for creating a modified incidence matrix is developed by using breadth-first search method which gives an ordinal number to every node. Modified incidence matrix is created by using ordinal numbers. The advantage of such matrix writing is that all non-zero elements of the upper triangulat part are placed sequently. When reading the elements of the specific row process stops when the first zero element is read and the reading continues from the same column of the next row. The proposed procedure significantly reduces the number of total read elements and, thus, reduces the calculation duration. The programming code is made in Matlab and the tests of accuracy, duration and robustness was carried out. Calculation duration test compared the efficiency of classical forward-backward sweep method and the proposed procedure on networks with various numbers of nodes. The results showed that the calculation duration could be reduced up to three times by using the proposed procedure and its efficiency increases with increase of nodes number of the network. The second phase of the model was development of method for optimization output powers of photovoltaics which is described in the fourth chapter. The optimization problem is very complex. The number of unknown variables that need to be calculated is equal to number of photovoltaics connected to certain network. Solution of problem by using exact mathematical methods is hard to get or even impossible. For solving such optimization problems heuristic methods are usually used. In doctoral thesis an artificial bee colony method is chosen due to its simplicity, good results in solving multidimensional problems and its tools for avoiding of falling into local minimum. The method imitates behavior of bee colony in process of searching for food sources and nectar collecting. The colony consists of three groups of bees: employed bees, onlookers and scouts. Scouts are searching for potential food sources and return to the hive where they perform dance by which they send information to the onlookers about the food amount and the location of food sources. Based on the performed dance onlookers receive the information and decide which sources are better. After that they deliver the information to employed bees that then go and collect nectar. Mathematical model of artificial bee colony method consists of initial step and three steps that repeat in given nuber of cycles. In initial step colony is divided only on employed bees and scouts with equal share. In initial step for every employed bee a random solution is generated which represents an n-dimensional vector where n is equal to number of parameters that need to be optimized. Then starts the employed bee phase in which for every employed bee a new solution near the initial one is generated by random function. Fitness function is used for evaluation of the solutions quality and by using greedy selection only better solution is memorized. Every employed bee tries to find better solution in limited number of trials and if the better solution is not found, employed bee becomes scout. Then begins the onlookers phase in which the possibilities of every solution are calculated. By using roulette wheel selection the best potential sources are chosen. After that, onlooker try to find better solution near the old one in a same way as in employed bee phase. If they don’t succed in limited number of trials, they become scouts. In scout phase for every scout a new random solution is generated by using the formula from the initial step. The goal function for optimizing the output power of photovoltaics is minimum of the sum of power losses in every single branch. Photovoltaics are modeled as P-Q nodes, and three phase power plants are modeled symmetrically. The optimization program was made in Matlab and it uses the three phase power flow calculation program from the first phase of the thesis to calculate power losses. Lower and upper limit of photovoltaics could be set from 0 to the maximum measured power at the moment and is given in percentage. In the model an initial condition is that voltages in all nodes should be in prescribed range of ±10% of rated voltage. The optimization method is tested on a real low voltage network with high penetration of photovoltaics. An optimal output power of every photovoltaic is calculated for every 15-minute average period of the daily diagram. The results showed that significant reduction of power losses could be achieved by using this method. In addition, such method prevents from occurring overvoltages and the voltage differences between nodes are reduced. By active power curtailment this method increases the capacity of low voltage network for connection of larger share of photovoltaics. Due to long duration of optimization process, this method could only be used in extended real time. To speed up the method, a model of neural network is developed in the fifth chapter by using multilayer perceptron and radial basis function neural network. The data set for neural network training was created by using optimization method in case of the 100%, 90%, 75%, 60%, 45% and 30% of insolation during a summer sunny day. Total number of data set consists of 378 cases. Training of the neural network is done on 90% of the random chosen cases through phases of learning (70%), validation (15%) and testing (15%). Remaining 10% of the data set represents the independent data set which is used for testing the generalization properties of the trained model. Quality of the model is usually tested by linear regression which has to be done for every phase of training including the model testing on independent data set. Quality is evaluated by Pearson’s correlation coefficient. The models of neural networks were made by using multilayer perceptron neural network with one, two, three and four hidden layers and by using radial basis function neural network. The best model of multilayer perceptron neural network with one and with more than one hidden layers and of radial basis function neural network are chosen and tested on aforementioned low voltage network in the case of variable cloudiness where the total dialy generation curve is not smooth. Both models of multilayer perceptron neural network showed good generalization properties while the radial basis function model had many deviations between the output and the goal values. The model with best characteristics between the analyzed models was the model with three hidden layers. Total calculation duration of the model amounts less than two seconds which makes this model suitable for using in a real time. In the sixth chapter pros and cons of the proposed model and the approach is described. Pros are the flexibility of the optimization model which can be adjusted to various kinds of problems, power loss minimization, improvement of the voltage conditions in the network and the increase of the low voltage network capacity for connecting larger share of the photovoltaics. Photovoltaics’ generation dependence on a weather conditions is also described. The proposed method has the greatest impact during the sunny days, while during the variable cloudiness has moderate and during cloudy days has negligible impact. Statistically, sunny day ampunt less than 20% for continental part and less than 30% yearly for coastal part in Croatia which means that the most of the days are days with variable or high cloudiness when the curtailment of the active power is moderate to negligible. This information is very important for the owners of photovoltaics due to their loss of profit caused by reduced output power. Cons of the proposed method are that it is not harmonized with the applicable regulations, it reduces the profit of the photovoltaics and the part of the produced energy is wasted. Due to constantly increase of photovoltaics penetration countries with high installed capacity are introducing changes in regulations that could allow regulation and management of the photovoltaics including active power curtailment. Also, battery industry is developing very fast and in the very near future the usage of battery systems for energy storage could be expected. The proposed method in combination with the battery usage could show much better results and, what is the most important, produced energy that couldn’t be sent in network could be stored and thus increase the photovoltaics profitability. In the final chapter it can be concluded that it could not be technical possible to connect large share of photovoltaics in distribution grid without some kind of output power regulation and introducing smart technologies. The proposed method has fulfilled all set goals. The following expected scientific contributions are achieved in this doctoral thesis: - procedure of creating an incidence matrix in order to accelerate the classical forward-backward sweep power flow method in a branched radial networks, - method for optimization of output power of photovoltaics based on the artificial bee colony method in extended real time, - model of neural network for management of photovoltaics in a distribution network in real time with the goal of technical losses minimization. The goal of the future research should be consideration of battery usage in a combination with the proposed method that could improve the efficiency of the distribution network and also increase the photovoltaics utilization. |