Grid-connected Photovoltaic models for three-phase load flow analysis

An unbalanced electric power system can occur due to unequal lines and/or loads in each phase of the system. For a system with a high level of unbalance, the assumption that the system is balanced becomes incorrect. For a case like this, the system must be analyzed using three-phase approaches because single-phase analysis techniques can no longer be used to obtain accurate results. Therefore, the development of three-phase models of all components of the electric power system, including the wind turbine generating system (WTGS), is very important so that the system can properly be analyzed and its performance can correctly be evaluated. This paper proposes a method to incorporate WTGS in a three-phase load flow analysis of an unbalanced distribution system. The proposed method is based on the previously published single-phase two-port network model. In this paper, the single-phase two-port network model is modified and extended so that it can be applied to unbalanced systems. The model is then included in the three-phase distribution system load flow (DSLF) analysis. The proposed method is validated using 12-node and 19-node distribution systems.

The transition from a vertically integrated to a horizontally integrated structure in the electricity system results in an increase in uncertainty at various levels. The new power system topology mandates the inclusion of uncertain behavior in the standard power flow studies, which were previously not necessary. Three-phase load flow has been extensively used for power system analysis in balanced and unbalanced cases. In this paper, an efficient Latin Hypercube Monte-Carlo simulation (LHMCS) approach for a three-phase transmission system load flow has been developed, which can be used for uncertainty quantification and determining the probability distribution of various parameters. The proposed method has been tested using the IEEE-118 bus test system for different cases.

This paper presents the estimation method of solar irradiance in W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> based on the short circuit current output produce by the photovoltaic module. The proposed solar irradiance estimation method is derived using photovoltaic mathematical model. Therefore, photovoltaic module modeling is required to develop the proposed estimation method. The modeling includes the identification of photovoltaic module diode ideality factor using recursive iteration and series resistance identification using photovoltaic model equation. The reminding modeling parameters can be obtained from the given photovoltaic module manufacturer datasheet. With all the required parameters in place the solar irradiance can be estimated using equation derived from the photovoltaic model. The proposed solar irradiance estimation method is evaluated using a 80W 36 cells polycrystalline photovoltaic module in the field and the results are validated with a World Meteorological Organization certified second class pyranometer. This paper demonstrates that the solar irradiance can be estimated by the short circuit current output measured from the photovoltaic module with acceptable accuracy. This contributes to the elimination of the installation of expensive pyranometer.

Advanced three-stage photovoltaic system phasor model for grid integration dynamic studies

Three-phase distribution network optimal load flow (T-OLF) cannot be exactly linearized to mixed integer second order cone programming(MI-SOCP) like single-phase branch flow based OLF. Hence, interior point based OLF (IP-OLF) and mixed integer nonlinear programming based OLF (MINLP-OLF) are both tried out to cope with T-OLF in this paper. For IP-OLF, a quadratic three-phase transformer model is proposed to guarantee IP-OLF applying constant Hessian matrix during iterative process. For MINLP-OLF, to gain better optimization results, a Mixed-Integer Quadratically-Constrained Quadratic Program model (MIQCQP) of T-OLF is formulated via binary scheme and big-M method. Numerical tests implemented on simple 4-bus system, IEEE 13-bus and IEEE 34-bus distribution test feeders verify the validity of proposed models and algorithms.

Long term supporting schemes for photovoltaic (PV) system installation have led to accommodating large numbers of PV systems within load pockets in distribution grids. High penetrations of PV systems can cause new technical challenges, such as voltage rise due to reverse power flow during light load and high PV generation conditions. Therefore, new strategies are required to address the associated challenges. Moreover, due to these changes in distribution grids, a different response behavior of the distribution grid on the transmission side can be expected. Hence, a new equivalent model of distribution grids with high penetration of PV systems is needed to be addressed for future power system studies. The thesis contributions lie in three parts. The first part of the thesis copes with the PV modelling. A non-proprietary PV model of a three-phase, single stage PV system is developed in PSCAD/EMTDC and PowerFactory. Three different reactive power regulation strategies are incorporated into the models and their behavior are investigated in both simulation platforms using a distribution system with PV systems. In the second part of the thesis, the voltage rise problem is remedied by use of reactive power. On the other hand, considering large numbers of PV systems in grids, unnecessary reactive power consumption by PV systems first increases total line losses, and second it may also jeopardize the stability of the network in the case of contingencies in conventional power plants, which supply reactive power. Thus, this thesis investigates and develops the novel schemes to reduce reactive power flows while still keeping voltage within designated limits via three different approaches: 1. decentralized voltage control to the pre-defined set-points 2. developing a coordinated active power dependent (APD) voltage regulation Q(P) using local signals 3. developing a multi-objective coordinated droop-based voltage (DBV) regulation Q(V) using local signals In the third part of the thesis, furthermore, a gray-box load modeling is used to develop a new static equivalent model of a complex distribution grid with large numbers of PV systems embedded with voltage support schemes. In the proposed model, variations of voltage at the connection point simulate variations of the model’s active and reactive power. This model can simply be integrated into load-flow programs and replace the complex distribution grid, while still keeping the overall accuracy high. The thesis results, in conclusion, demonstrate: i) using rms-based simulations in PowerFactory can provide us with quite similar results using the time domain instantaneous values in PSCAD platform; ii) decentralized voltage control to specific setpoints through the PV systems in the distribution grid is fundamentally impossible due to the high level voltage control interaction and directionality among the PV systems; iii) the proposed APD method can regulate the voltage under the steady-state voltage limit and consume less total reactive power in contrast to the standard characteristic Cosf (P) proposed by German Grid Codes; iv) the proposed optimized DBV method can directly address voltage and successfully regulate it to the upper steady-state voltage limit by causing minimum reactive power consumption as well as line losses; v) it is beneficial to address PV systems as a separate entity in the equivalencing of distribution grids with high density of PV systems.

Particle swarm optimisation with adaptive mutation strategy for photovoltaic solar cell/module parameter extraction

As countries attach importance to environmental protection, clean energy has become a hot topic. Among them, solar energy, as one of the efficient and easily accessible clean energy sources, has received widespread attention. An essential component in converting solar energy into electricity are solar cells. However, a major optimization difficulty remains in precisely and effectively calculating the parameters of photovoltaic (PV) models. In this regard, this study introduces an improved rime optimization algorithm (RIME), namely ERINMRIME, which integrates the Nelder-Mead simplex (NMs) with the environment random interaction (ERI) strategy. In the later phases of ERINMRIME, the ERI strategy serves as a complementary mechanism for augmenting the solution space exploration ability of the agent. By facilitating external interactions, this method improves the algorithm’s efficacy in conducting a global search by keeping it from becoming stuck in local optima. Moreover, by incorporating NMs, ERINMRIME enhances its ability to do local searches, leading to improved space exploration. To evaluate ERINMRIME's optimization performance on PV models, this study conducted experiments on four different models: the single diode model (SDM), the double diode model (DDM), the three-diode model (TDM), and the photovoltaic (PV) module model. The experimental results show that ERINMRIME reduces root mean square error for SDM, DDM, TDM, and PV module models by 46.23%, 59.32%, 61.49%, and 23.95%, respectively, compared with the original RIME. Furthermore, this study compared ERINMRIME with nine improved classical algorithms. The results show that ERINMRIME is a remarkable competitor. Ultimately, this study evaluated the performance of ERINMRIME across three distinct commercial PV models, while considering varying irradiation and temperature conditions. The performance of ERINMRIME is superior to existing similar algorithms in different irradiation and temperature conditions. Therefore, ERINMRIME is an algorithm with great potential in identifying and recognizing unknown parameters of PV models.

Different types of photovoltaic (PV) cell technologies have been commercially used for various applications. These cell technologies can be categorized as multi-crystalline, mono-crystalline and thin film. Due to the differences in PV cell technologies, a single PV model is unable to model all the output characteristics. The single and double diode PV models have been widely used for modeling the output characteristic of a PV module. This paper introduces a generalized multi-dimension diode PV model which can be used to select the most suitable dimension for a particular PV cell technology. The results confirm that the single diode PV model is suitable for the multi-crystalline and mono-crystalline PV modules. For the thin film PV module, a multi-dimension diode PV model is required to achieve a low modeling error.

Three-phase voltage imbalance occurs by variety of connecting points of single-phase loads. In order to improve three-phase voltage imbalance, connecting points of single-phases loads are exchanged. System planner has to decide how to exchange connection of single-phase loads with the minimum planning cost in order to improve three-phase voltage imbalance. However, since there are many patterns of connection for single-phase loads, it is not easy to determine the optimal connection pattern for single-phase loads with the minimum planning cost under the constraint for improving voltage imbalance. In this paper, authors propose a computational method to support the planner's decision of single-phase loads connection systematically. The proposed method, which is based on effective enumeration algorithm, can obtain the optimal single-phase loads connection pattern, which satisfies with constraint of voltage balance and has the minimum total number of single-phase loads exchanged from previous single-phase loads connection. In the proposed method, three-phase iterative load flow calculation is applied to calculate rate of three-phase voltage imbalance. Three-phase iterative load flow calculation has two simple procedures: (Procedure1) addition of load currents from terminal node of feeder to root one, and (Procedure2) subtraction of voltage drop from root node of feeder to terminal one. In order to check the validity of the proposed method, numerical results are shown for a distribution system model with DG.

The increasing demand for electrical energy has made it inevitable to bring forth an environment-friendly energy resource which has to be robust as well as economic. Solar energy fulfils these criteria significantly, and to cultivate such energy, a reliable photovoltaic (PV) model is required. But most of the typical PV system undergoes a low energy conversion ratio because of improper choice of PV parameters. To build a proficient PV model, the estimation of precise and accurate parameters is mandatory. This paper portrays the Sine Cosine Algorithm (SCA) for the estimation of photovoltaic (PV) module parameters. Unknown parameters of the PV model of a single diode PV module are estimated under the standard test condition (STC). PV parameter estimation using SCA has shown a significant minimum value of the fitness function hence maximizing the convergence. A comparative study has been done between SCA and other existing popular techniques named as the nonlinear least square (NLS) method and the modified Newton–Raphson (N-R) method. From the power–voltage (P-V) and current–voltage (I-V) characteristics, it’s found that the SCA model matches more accurately with the datasheet values.KeywordsRenewable energyPhotovoltaicSingle diode modelSine cosine algorithmParameter estimation

Photovoltaic (PV) technology is gaining much interest as a clean, sustainable, noise-free source of energy. However, the non-linear behavior of PV modules and their dependency on varying environmental conditions require thorough study and analysis. Many PV modeling techniques have been introduced in the literature, yet they exhibit several complexity levels for parameter extraction and constants estimation for PV power forecast. Comparatively, a simple, accurate, fast, and user friendly PV modeling technique is proposed in this paper featuring the least computational time and effort. Based on function representation of PV curves’ available in PV datasheets, an empirical mathematical equation is derived. The proposed formula is considered a generic tool capable of modeling any PV device under various weather conditions without either parameter estimation nor power prediction. The proposed model is validated using experimental data of commercial PV panels’ manufacturers under various environmental conditions for different power levels. The obtained results verified the effectiveness of the proposed PV model.

While addressing the issue of improving the performance of Photovoltaic (PV) systems, the simulation results are highly influenced by the PV model accuracy. Building the PV module mathematical model is based on its I-V characteristic, which is a highly nonlinear relationship. All the PV cells’ data sheets do not provide full information about their parameters. This leads to a nonlinear mathematical model with several unknown parameters. This paper proposes a new application of the Grasshopper Optimization Algorithm (GOA) for parameter extraction of the three-diode PV model of a PV module. Two commercial PV modules, Kyocera KC200GT and Solarex MSX-60 PV cells are utilized in examining the GOA-based PV model. The simulation results are executed under various temperatures and irradiations. The proposed PV model is evaluated by comparing its results with the experimental results of these commercial PV modules. The efficiency of the GOA-based PV model is tested by making a fair comparison among its numerical results and other optimization method-based PV models. With the GOA, a precise three-diode PV model shall be established.

Random learning gradient based optimization for efficient design of photovoltaic models

Photovoltaic (PV) model is used in simulation study to validate the system design of a PV system. With an accurate PV model for use in circuit orientated software, the behavior of PV array under different environmental conditions can be observed for study. In this paper, the unknown parameters of a single diode PV model are identified using the Particle Swarm Optimization (PSO) approach with log barrier constraint. The proposed method has been applied to a PV module KC65T and has shown accurate modeling result.