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MINISTRY OF EDUCATION AND TRAINING VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY ----------------------------- Ngo Ngoc Thanh PROPOSED OPTIMAL CONTROL ALGORITHMS FOR PHOTOVOLTAIC ARRAYS RECONFIGURATION Major: Control and Automation Technology Code: 9.52.02.16 SUMMARY OF ENGINEERING DOCTORAL DISSERTATION Ha Noi – 2020 This work is completed at: Graduate University of Science and Technology Vietnam Academy of Science and Technology Supervisor: Assoc.Prof.Dr. Pham Thuong Cat Prof.Dr. Nguyen Phung Quang Reviewer 1: ……………………………………………………..........................………. ……………………………………………………………………………........................ Reviewer 2: ………………………………………………………………........................ …………………………………………………………………………............................ Reviewer 3: ………………………………………………………………........................ ……………………………………………………………………………........................ This Dissertation will be officially presented in front of the Doctoral Dissertation Grading Committee, meeting at: Graduate University of Science and Technology Vietnam Academy of Science and Technology At …………. hrs ……. day ……. month……. year ……. This Dissertation is available at: 1. Library of Graduate University of Science and Technology 2. National Library of Vietnam INTRODUCTION 1. Introduction Photovoltaic panels during the working process in solar power plants can receive inconsistent solar irradiance levels in many cases due to the partial shading. In the context of partial shading, the system capacity shows a significant decrease, in addition to the phenomenon of Misleading (confusion due to the maximum power point). Development of a solar system reconfiguration strategy based on the irradiance equalization method is a key area of research, whereby the solar system restructuring is the rearrangement of the connection circuitry of photovoltaic panels for the purposes of increased output power and device protection when the solar system works in heterogeneous lighting conditions. Therefore, the topic “Proposed optimal control algorithms for photovoltaic arrays reconfiguration” was selected for this thesis to contribute to solving problems in the solar system reconfiguration strategy. 2. Thesis objectives and tasks ✓ Establishing a mathematical model, putting forward an algorithm applied for seeking the solar system's irradiance equalization configuration under the heterogeneous lighting conditions. ✓ Establishing a mathematical model, putting forward an algorithm applied for choosing an optimal circuit switching method, from the initial connection configuration to the irradiance equalization configuration. 3. Research scope ✓ Studying primary sources, connecting photovoltaic panels with the use of TCT connection circuit. ✓ Without considering constraints on equipment production costs, economic nature when putting into practice. 4. New findings of the thesis ✓ Establishing the mathematical model, applying Dynamic programming (DP) algorithm and proposing Smartchoice (SC) algorithm for selecting the irradiance equalization configuration to find ways of arranging connection positions of photovoltaic panels so that optimal system power and local maximum points elimination can be achieved. ✓ Proposing the mathematical model, applying the Munkres assignment algorithm (MAA) and proposing an improved MAA for selecting the optimal circuit switching method aimed at extending the life of switching matrix in the solar system. ✓ Building a simulation toolkit on Matlab-Simulink and Micrsoft Visual Studio in order to assess the performance and accuracy of algorithms used for proving new methods of the thesis. 5. Thesis structure: The thesis is broken down into 4 chapters. Chapter 1: Solar system structure and system performance improvement strategy under partial shading conditions. Chapter 2: Introduction to the optimal control theory Chapter 3: Development of a system restructuring strategy using optimal control theory Chapter 4: Simulation and experiment 1 Chapter 1: SOLAR SYSTEM STRUCTURE AND SYSTEM PERFORMANCE IMPROVEMENT STRATEGY UNDER PARTIAL SHADING CONDITIONS. 1.1 Introduction to the solar system 1.1.3 Solar power Solar power is generated from either the conversion of sunlight into electricity, or directly by using photovoltaic panels, or indirectly through thermal energy using the concentrated solar power. 1.1.4 Photovoltaic panels connecting structures There are basically two main connection standards for photovoltaic panels: serial and parallel. The advantage and disadvantage of parallel connection circuit are that the current is the total current of photovoltaic panels, and the voltage is equal to the minimum voltage of photovoltaic panels, respectively. The advantage and disadvantage of serial connection circuit are that the voltage is the total voltage of photovoltaic panels, and the current is equal to the minimum current of photovoltaic panels, respectively. Figure 1-13 shows 6 different connection methods of photovoltaic panels commonly used. Although there are many special connection structures with lots of advantages being studied and applied, the most commonly exploited solution currently in practice is SP connection circuit as Figure 1-13c and TCT connection circuit as Figure 1-13d. Hình 1-13. Photovoltaic panel connection circuits; (a) Series array; (b) Parallel array; (c) Series-Parallel array (SP); (d) Total-Cross-Tied array (TCT); (e) Bridge-Link array; (f) Honey-Comb array 1.1.5 Basic structure of grid-connected solar system with power storage There are three main parts: photovoltaic panels connection array, converters and load (local load or grid). In addition, extra batteries can be used for storage and power stabilization purposes. 1.2 Introduction to the system performance improvement strategy under partial shading conditions. 1.2.1 Effects of partial shading The reduction in capacity of the solar system in the context of shading is shown in Figure 1-21. In the context of partial shading, the system capacity shows a significant decrease, in addition to the phenomenon of misleading (confusion due to the maximum power point). 2 1.2.2 Power attenuation minimization techniques due to the partial shading Currently, the studies to reduce the loss of solar energy system in the world are classified into three main groups: Distributed MPP, multi-level converter and solar system restructuring method. Photovoltaic panel circuits restructuring was first proposed by Salameh et al., used for the operation and speeding of electric vehicles using solar panels. Sherif and Boutros did propose the photovoltaic panel circuits restructuring by using Figure 1-21. Shading, partial shading, and misleading transistors and circuit breakers. losses for a photovoltaic array. Shading, partial shading, and misleading losses for a photovoltaic array. Nguyen and Lehman used the restructuring circuit inside the photovoltaic panels and proposed two optimal algorithms to control the restructuring circuit. Velasco et al. applied the restructuring method to the grid system and proposed a mathematical model for it. However, all is only at the local optimal level, instead of offering an overall optimal configuration. Velasco proposed the EI (Equalization Index), understood as the difference between the row with the highest total solar irradiance compared to the row with the lowest total solar irradiance; accordingly, the configuration with the lowest EI is known as the overall optimal configuration. The most optimal configuration requires the minimum illumination difference level received by the photovoltaic panels in each parallel circuit. 1.2.5 Comparison of methods presented The methods in the solar system restructuring strategy have different advantages and disadvantages, as shown in Table 1-9 below. Table 1-9. Comparison of irradiance equalization algorithms using TCT connection circuit Tác giả Chiến lược Thuật toán điều khiển Số khóa Yêu cầu dữ liệu Ghi chú - 2.NPV.m-throw current, voltage static and dynamic part Irradiance Deterministic and NSW = (2.m.NPV)DPST + equalization Random search (m)SPDT Velasco- Irradiance Quesada equalization Romano Storey Irradiance equalization Best worst sorting Matam and Irradiance Arrange in descending Barry equalization order of radiation Irradiance Reconfiguration equalization algorithm Jazayeri Mahmoud and ElSaadany Irradiance equalization NSW = NPV.(m2-m)SPST 24-DPST relays Greedy algorithm 3 irradiance current, voltage supports row with different number modules supports row with different number modules current, voltage, Dynamic PV array is formed irradiance - irradiance - irradiance using PV modules supports row with different number modules fixed part along with adaptive part 1.3 Conclusions of Chapter 1 In Chapter 1, the author gives an overview of the grid-connected solar system including its components, model connecting such basic components and photovoltaic panel connection structures. In the next section, the author presents an overview of the solar system performance improvement strategy under heterogeneous lighting conditions for TCT connection circuit and SP connection circuit based on the irradiance equalization method. Advantages and disadvantages of optimal algorithms in other studies, statistical table of characteristics of listed methods have been analyzed to get an overview of evaluation of the pros and cons of such methods. Chapter 2: INTRODUCTION TO THE OPTIMAL CONTROL THEORY 2.1 Introduction to the optimal control theory The optimal control is aimed to find the optimal signal u* so that the objective function Q can reach the maximum or minimum value. The most basic methods of optimal control are broken down into two main groups: static optimization control and dynamic optimization control. 2.2 Formulation of the optimal control problem 2.2.1 Control circuit structure in the solar system Although the circuit structures have very diverse forces, they all share the same characteristics of control function block diagram for the solar panels shown in Figure 2-1. Accordingly, a power electronic control system for solar panels is divided into three functional levels. Figure 2-1. Block diagram of grid-connected electronic power control function for solar panels. The research objective of this thesis is to propose a photovoltaic panel connection restructuring method enabling the system always work with the highest efficiency. Photovoltaic panel connection restructuring is shown in Figure 2-2 (CT2). 4 1 2 n1 1 n2 2 nm m PV Reconfiguration techniques. HANOI May 2013 (a) (b) (c) Figure 2-2. Photovoltaic array reconfiguration: (a) TCT topology, (b) Dynamic electrical scheme, (c) Dynamic Figure 2-7: Connection topologies of the PV array configuration by using DES The restructuring unit is located in front of the inverter to change the photovoltaic panels connection, so the control circuit applied in the restructuring unit is under level 2 - the typical control level of solar panels. 2.2.2 Restructuring unit 14 The location of restructuring unit is shown in Figure 2-3. Reconfigura tion system Hình 2-3. Bộ tái cấu trúc trong hệ thống NLMT hòa lưới có dự trữ Hình 2-4. Các thành phần trong bộ tái cấu trúc The restructuring unit (CT1) depicted in Figure 2-4 is mainly composed of a switching matrix and a controller. Initially, the controller functioned as measuring the current, voltage of photovoltaic panels, estimating lighting levels, and finding the highest connection configuration for system capacity. Then, it ordered the opening and closing of keys in the switching matrix, switching the photovoltaic panel connection configuration from the initial configuration to the optimal configuration. 2.2.3 Proposal on the Control system In this thesis, an open control system is proposed to be applied by the PhD student in order to build a restructuring unit according to the flowchart in Figure 2-5 (CT2). Measurement of panels’ current and voltage Seeking the optimal switching configuration and method Closing and opening of keys in the switching matrix Figure 2-5. An open control system for the restructuring unit 5 2.2.4 Proposal on the optimal control method The proposed optimal control method applied in the restructuring unit as shown in Figure 2-6 (see CT2) includes 2 main problems: Seeking the irradiance equalization configuration and selecting the optimal switching method. Solar irradiance and current connection position of each photovoltaic panel are the input data of this method. The new connection position of each photovoltaic panel is the method’s outcome. Thus, this is a problem of which the model's input, output and state variables are independent of time, and the output value at a time is dependent on the input value and states at that time only. Static optimization control method is selected to apply for the two above Figure 2-6. Flowchart of the algorithm for the system optimization problems. reconfiguration 2.3 Some optimal problems used in the thesis. 2.3.1 Subset sum problem The subset sum problem was introduced by Knapsack for the first time in 1990. It is stated as follows: Given AS with a set of nAS items and a knapsack, wj being the weight of item j; c is the capacity of that knapsack. Requirements: Select a subset of the items of which the total weight is closest to, without exceeding, c 𝑛𝐴𝑆 That is, finding the maximum value of 𝑧 = ∑𝑗=1 𝑤𝑗 𝑥𝑗 satisfying the condition that 𝑛 𝐴𝑆 ∑𝑗=1 𝑤𝑗 𝑥𝑗 ≤ 𝑐 with 𝑥𝑗 = 0 𝑜𝑟 1, 𝑗 ∈ 𝑁 = {1, . . , 𝑛𝐴𝑆 } 1, 𝑖𝑛 𝑐𝑎𝑠𝑒 𝑜𝑓 𝑠𝑒𝑙𝑒𝑐𝑖𝑛𝑔 𝑡ℎ𝑒 𝑖𝑡𝑒𝑚 𝑗 so that 𝑥𝑗 = { 0, 𝑖𝑛 𝑐𝑎𝑠𝑒 𝑜𝑓 𝑛𝑜𝑡 𝑠𝑒𝑙𝑒𝑐𝑖𝑛𝑔 𝑡ℎ𝑒 𝑖𝑡𝑒𝑚 𝑗 Generalize the problem with the objective function of maximum weight z: 𝑛𝐴𝑆 ( 2-8 ) maximize z = ∑ 𝑤𝑗 𝑥𝑗 𝑗=1 Constraint: 𝑛𝐴𝑆 ( 2-9 ) ∑ 𝑤𝑗 𝑥𝑗 ≤ 𝑐 𝑗=1 𝑗 ∈ 𝑁 = {1, . . , 𝑛𝐴𝑆 } 𝑗 ∈ 𝑁 = {1, . . , 𝑛𝐴𝑆 } 𝑥𝑗 = 0 𝑜𝑟 1, { 𝑤𝑗 ≥ 0 6 2.3.2 Munkres' Assignment Algorithm (MAA) This is the first task division problem proposed by author James Munkres. It is stated as follows: Contents of the problem: Given nM workers (iM = 1, 2, ... , nM) and nM tasks (jM = 1, 2, ... , nM). In order to assign the worker iM to perform the task jM, cost of CiMjM ≥ 0 as required. The problem is to assign which task to which worker (each worker only performs one task; each task is performed by one worker only) to incur the lowest total cost? General C matrix in Figure 2-7: Worker Task 1 2 ... nM 1 C11 C12 𝐶1𝑛𝑀 2 C21 C22 𝐶2𝑛𝑀 ... nM 𝐶𝑛𝑀1 𝐶𝑛𝑀2 𝐶𝑛𝑀𝑛𝑀 Figure 2-7. Matrix general C The mathematical model of this problem is as follows: 𝑛𝑀 𝑛𝑀 ( 2-14 ) 𝑧𝑀 = ∑ ∑ 𝐶𝑖𝑀𝑗𝑀 𝑥𝑖𝑀𝑗𝑀 → 𝑚𝑖𝑛 𝑖𝑀=1 𝑗𝑀 =1 Provided that: 𝑛 Each worker only performs one task: ∑𝑗𝑀𝑀=1 𝑥𝑖𝑀 𝑗𝑀 = 1 , 𝑖𝑀 = 1, … , 𝑛𝑀 Each task is performed by one worker only: ∑𝑛𝑖𝑀𝑀=1 𝑥𝑖𝑀𝑗𝑀 = 1 , 𝑗𝑀 = ( 215 ) ( 216 ) 1, … , 𝑛𝑀 ( 217 ) 𝑥𝑖𝑀𝑗𝑀 = 0 ℎ𝑎𝑦 1 , 𝑖𝑀 = 1 , … , 𝑛𝑀 ; 𝑗𝑀 = 1 , … , 𝑛𝑀 due to the availability of conditions (2-15) (2-16), the conditions (2-17) can be replaced with ( 218 ) 𝑥𝑖𝑀𝑗𝑀 integer ≥0, iM = 1 , 2 , ... , nM ; jM = 1 , 2 , ... , nM 2.4 Conclusions of Chapter 2 Chapter 2 provides an overview of the optimal control problem, thereby proposing the optimal control method and formulating the optimal control problem used in the thesis. The first section gives an overview of the optimal control problem, provides definitions, limiting conditions, and classification of the optimal control problem. In the next section, the author formulates an optimal control problem used in the restructuring unit. For the last section, there are two optimization problems presented as the basis for proposing the optimal algorithms for the thesis: Subset sum problem and Munkres' Assignment Algorithm. The application of optimal control in the photovoltaic panels connection restructuring problem will increase the efficiency of the solar system under lighting conditions. The static optimization problem, with the open control system, is proposed to be applied by the author to build a structure that is fast acting and applicable to large solar systems. 7 Chapter 3: DEVELOPMENT OF A SYSTEM RESTRUCTURING STRATEGY USING OPTIMAL CONTROL THEORY 3.1 Irradiance equalization strategy with TCT connection circuit Irradiance equalization method for TCT connection circuit (Figure 1-13d) is the rearrangement of photovoltaic panel connection positions in order to balance the total solar irradiance at the parallel connections in TCT circuit (CT1,5). The Irradiance equalization method, improving the efficiency of the solar system can be generalized according to the diagram in Figure 2-6. This method is designed to make the solar system always operate at the highest efficiency with repetition in a certain period of time. 3.2 Measurement of current and voltage of photovoltaic panels During operation, the photovoltaic panels are connected to each other, and their current and voltage are interdependent as analyzed in section 1.1.4. It is big challenge to measure the current and voltage exactly generated by each photovoltaic cell as a basis for estimating the solar irradiance received by each photovoltaic panel. In this thesis, the measurement method shown in Figure 3-2 (for example, the measurement circuit for 4 Figure 3-2. Current and voltage acquisition circuit photovoltaic panels) (CT9) is used. 3.3 Solar irradiance estimation After measuring the current and voltage at each photovoltaic panel, the solar irradiance calculation formula (3-1) of each photovoltaic panel is applied. 𝐺𝑆 = 𝐺𝑆𝑇𝐶 𝐼𝐿𝑆𝑇𝐶 + 𝜇1𝑠𝑐 (𝑇𝑐 − 𝑇𝐶 𝑆𝑇𝐶 ) [𝐼 + 𝐼0 (𝑒 𝑉+𝐼𝑅𝑆 𝑇 𝑛𝑆𝐴𝑑 𝑘 𝑞𝑐 − 1) + 𝑉 + 𝐼𝑅𝑆 ] 𝑅𝑆ℎ (3-1) 3.4 Proposal of the mathematical model (s) and 02 algorithms for Seeking the irradiance equalization configuration The mathematical model, DP algorithm application method and SC algorithm prposal are announced in (CT8), (CT1) and (CT3), respectively. 3.4.1 Mathematical model establishment 𝑛𝑖 𝑛𝑖 (3-4) 𝐸𝐼 = max (∑ 𝐺𝑖𝑗 ) − min (∑ 𝐺𝑖𝑗 ) → 0 𝑖=1,𝑚 𝑖=1,𝑚 𝑗=1 𝑗=1 𝑛1 + 𝑛2 + 𝑛3 + . . . +𝑛𝑚 = 𝑛 𝐺𝑖1 + 𝐺𝑖2 + 𝐺𝑖3 + . . . + 𝐺𝑖𝑛𝑖 = 𝐺𝑖 𝑛𝑖 > 0 𝐺𝑖𝑗 ≥ 0 Constraints: 𝑖 = 1, 𝑚 ; 𝑗 = 1, 𝑛𝑖 { 8 (3-5)