Cost Of Generating Units Research Articles

A State-of-the-Art Review on Optimization Methods and Techniques for Economic Load Dispatch with Photovoltaic Systems: Progress, Challenges, and Recommendations

Fossil fuel is considered to be the primary power generation source. As this source is not that eco- and environmentally friendly, researchers are constantly searching for an alternative source for power generation. Renewable energy has drawn much attention in this regard in recent times. For solving economic load dispatch issues, numerous operational constraints must be considered. Due to the restructuring of the power sector, there is competition between different power systems organizations. Increasing fossil fuel costs drive power-producing utilities to adopt a cost-effective technique for dispatching actual power output. Due to the presence of nonlinearity and non-convexity in the fuel of cost function of generators, the economic load dispatch is often considered a complex optimization problem. Many researchers have been optimizing fuel costs to solve the economic power dispatch problem. This paper offers a critical analysis of ELD that takes into account both traditional and non-traditional energy sources. The review covers a variety of algorithms, including hybrid algorithms for integrating renewable energy sources (RES). The paper also focuses on several restricted optimization techniques and contemporary algorithms including PSO, Jaya, GWO, SMO, TLBO, Rao, MRao-2, and MFO to reduce the fuel cost of generation units using large-scale solar PV. Moreover, this paper provides a comprehensive overview of the current state of economic load dispatch and provides valuable insights for electricity researchers and practitioners. It also discusses future technologies and next steps in the field of ELD, emphasizing the need for more environmentally friendly and cost-effective power generation and distribution solutions. Overall, the paper demonstrates the benefits of renewable energy sources as well as optimization techniques for creating a more sustainable and efficient power generation system.

Design and off-design performance analysis of a liquid carbon dioxide energy storage system integrated with low-grade heat source

Nowadays, developing the renewable energy has become the worldwide consensus. Nevertheless, the intermittency and volatility of renewable electricity bring great challenges to the stability of the power grid. Liquid carbon dioxide energy storage is recognized as one of the most promising technologies to overcome these difficulties. In this paper, a liquid carbon dioxide energy storage system integrated with the low-grade heat source is proposed. Based on the preliminary geometric parameters of system components, investigations on the system design and off-design performances are carried out. Results of parametric analysis indicate that the pseudo-critical point corresponding to 8 MPa is recommended as the design point for compressor inlet, and the minimum value of LCOE could reach 9.49 cents/kWh. Under design conditions, the system exergy efficiency reaches 48.42% and the roundtrip efficiency is 63.60%. Moreover, 10.70 cents/kWh of the per unit generation cost is advantageous in the large-scale energy storage systems. With the variations of input power (70%∼120%) and output power level (50%∼100%), the surplus water ratio could reach 23.63% at 50% load level, while the variation range of exergy efficiency is 15.56%∼48.42%. Meanwhile, the roundtrip efficiency varies from 22.16% to 63.60% under off-design conditions, and the maximum value is achieved at the design point. All the results identify the feasibility of the integrated energy storage system.

Day-Ahead Electricity Market Price Forecasting Considering the Components of the Electricity Market Price; Using Demand Decomposition, Fuel Cost, and the Kernel Density Estimation

This paper aims to improve the forecasting of electricity market prices by incorporating the characteristics of electricity market prices that are discretely affected by the fuel cost per unit, the unit generation cost of the large-scale generators, and the demand. In this paper, two new techniques are introduced. The first technique applies feature generation to the label and forecasts the transformed new variables, which are then post-processed by inverse transformation, considering the characteristic of the fuel types of marginal generators or prices through two variables: fuel cost per unit by the representative fuel type and argument of the maximum of Probability Density Function (PDF) calculated by Kernel Density Estimation (KDE) from the previous price. The second technique applies decomposition to the demand, followed by a feature selection process to apply the major decomposed feature. It is verified using gain or SHapley Additive exPlanations (SHAP) value in the feature selection process. In the case study, both showed improvement in all indicators. In the Korean Electricity Market, the unit generation cost for each generator is calculated monthly, resulting in a step-wise change in the electricity market price depending on the monthly fuel cost. Feature generation using the fuel cost per unit improved the forecasting by eliminating monthly volatility caused by the fuel costs and reducing the error that occurs at the beginning of the month. It improved the Mean Squared Percentage Error (MAPE) of 3.83[%]. Using the argument of the maximum PDF calculated by KDE improved the forecasting during the test period, where discrete monthly variations were not included. The resulting MAPE was 3.82[%]. Combining these two techniques resulted in the most accurate performance compared to the other techniques used, which had a MAPE of 3.49[%]. The MAPE of the forecasting with the decomposed data of the original price was 4.41[%].

Research on the Economic Dispatch of Power Systems with a High Proportion of Renewable Energy based on Improved PSO

The penetration rate of renewable energy sources represented by wind power and photovoltaics in the power grid is increasing, adding complexity to unit dispatch. In this paper, a multi-objective optimization model is established for power systems containing wind power and photovoltaic economic dispatch. Firstly, the power generation cost of traditional units, the emission cost of traditional units, the power generation costs of wind turbines and photovoltaics, and the output characteristics of wind power and photovoltaics are analyzed. Secondly, a multi-objective economic dispatch model with the lowest power generation cost, the smallest emission cost, and the smallest power generation cost of new energy units are established, and the power flow balance constraint, supply and demand balance constraint, unit output constraint, and node voltage constraint are considered. Then the improved particle swarm algorithm is proposed to solve the multi-objective function to obtain better convergence and optimal solution. Finally, the simulation is carried out in the IEEE-30 node system and the HRP-38 system, which compares and illustrates the similarities and differences of the solution results of various algorithms under multi-objective and verifies the effectiveness of the algorithm.

A hybrid dynamic economics emissions dispatch model: Distributed renewable power systems based on improved COOT optimization algorithm

This study proposes a hybrid dynamic economics emissions dispatch (HDEED) model for a distributed power system containing thermal generating units, wind farms and photovoltaic plants. The construction of novel distributed power system has been a significant means of tackling the energy crisis. (1) the relationship between each generation unit of the power generation system is analyzed, as well as the power balance constraint, transmission loss constraint, output capacity of each generation unit and slope constraint of the power system; and (2) the operating cost objective function is established with the objective of minimizing unit's generation cost, pollutant emission objective function, and the satisfaction weight coefficient. A novel and improved COOT optimization algorithm is presented to enhance convergence performance and solution speed in solving the problem by introducing a chaotic initialization strategy. A mutation strategy and an improved chain movement of the model solution are verified. The result shows that for the HDEED problem, the ICOOT algorithm reduces the operating cost targets by 1.28%, 6.99% and 7.44% and the pollutant emission targets by 2.98%, 5.46% and 10.88% compared to other algorithms. The developed model provides an effective solution for improving the operational stability, economy and cleanliness of system.

Exploiting the operational flexibility of AA-CAES in energy and reserve optimization scheduling by a linear reserve model

Advanced Adiabatic Compressed Air Energy Storage (AA-CAES) is expected to play a crucial role in providing energy shifting and fast regulation to variable renewable energy generation because of its large capacity and fast response. However, due to the complex operation characteristics of AA-CAES, there are few studies on AA-CAES optimal operation providing energy and reserve for power systems. Therefore, a new robust scheduling approach is proposed, in which the operation of AA-CAES is precisely characterized by the synergetic energy and reserve market. To fully exploit the operational flexibility of AA-CAES, this paper proposes a linear reserve model of AA-CAES by quickly switching working modes. The energy storage-reserve constraint is established to ensure the deliverability of reserve services. Then, an enhanced column and constraint generation (C&CG) algorithm is proposed to solve the proposed model. Finally, the proposed method is applied to the Garver-6 bus and IEEE-118 bus systems in the MATLAB operating environment. Numerical simulation results indicate that AA-CAES participating in power system scheduling can reduce the generation and reserve cost of conventional units, and improve wind power accommodation. By quickly switching the working mode, the adjustable reserve margin of AA-CAES can be effectively improved. In addition, compared with the existing nested C&CG algorithm, the enhanced C&CG algorithm effectively improves the solution efficiency of the proposed model.

A Slime Mould Algorithm Programming for Solving Single and Multi-Objective Optimal Power Flow Problems with Pareto Front Approach: A Case Study of the Iraqi Super Grid High Voltage

Optimal power flow (OPF) represents one of the most important issues in the electrical power system for energy management, planning, and operation via finding optimal control variables with satisfying the equality and inequality constraints. Several optimization methods have been proposed to solve OPF problems, but there is still a need to achieve optimum performance. A Slime Mould Algorithm (SMA) is one of the new stochastic optimization methods inspired by the behaviour of the oscillation mode of slime mould in nature. The proposed algorithm is characterized as easy, simple, efficient, avoiding stagnation in the local optima and moving toward the optimal solution. Different frameworks have been applied to achieve single and conflicting multi-objective functions simultaneously (Bi, Tri, Quad, and Quinta objective functions) for solving OPF problems. These objective functions are total fuel cost of generation units, real power loss on transmission lines, total emission issued by fossil-fuelled thermal units, voltage deviation at load bus, and voltage stability index of the whole system. The proposed algorithm SMA has been developed by incorporating it with Pareto concept optimization to generate a new approach, named the Multi-Objective Slime Mould Algorithm (MOSMS), to solve multi-objective optimal power flow (MOOPF) problems. Fuzzy set theory and crowding distance are the proposed strategies to obtain the best compromise solution and rank and reduce a set of non-dominated solutions, respectively. To investigate the performance of the proposed algorithm, two standard IEEE test systems (IEEE 30 bus IEEE 57 bus systems) and a practical system (Iraqi Super Grid High Voltage 400 kV) were tested with 29 case studies based on MATLAB software. The optimal results obtained by the proposed approach (SMA) were compared with other algorithms mentioned in the literature. These results confirm the ability of SMA to provide better solutions to achieve the optimal control variables.

A Partnership of Virtual Power Plant in Day-Ahead Energy and Reserve Markets Based on Linearized AC Network-Constrained Unit Commitment Model

This paper presents coordinated energy management as a virtual power plant (VPP) framework with a wind farm, a storage system, and a demand response program in the transmission network according to the cooperation of VPPs in day-ahead energy and reserve markets. This strategy is based on a bilevel method, where it maximizes the expected VPP revenue in the proposed markets subject to constraints of renewable and flexible sources and the VPP reserve model in the upper-level problem. Also, a market-clearing model based on network-constrained unit commitment (NCUC) is explained in the lower-level problem so that it minimizes the expected operating cost of generation units constrained to a linearized AC-NCUC model. The scenario-based stochastic programming (SBSP) models the uncertainties of loads and WF power generation. Then, the master/slave decomposition method solves the bilevel problem to achieve an optimal solution at a low computational time. Also, since the lower-level problem is mixed-integer linear programming, the Benders decomposition algorithm is adopted to solve this problem. Finally, the suggested approach is implemented on IEEE test networks in GAMS software, and numerical results confirm the efficiency of the coordinated VPP management in DA energy and reserve markets and its capabilities in improving network operation.

Topology-Aware Learning Assisted Branch and Ramp Constraints Screening for Dynamic Economic Dispatch

Multi-interval or dynamic economic dispatch (D-ED) is the core of various power system management functions. This optimization problem contains many constraints, a small subset of which is sufficient to enclose the D-ED feasible region. This paper presents a topology-aware learning-aided iterative constraint screening algorithm to identify a feasibility outlining subset of network and generating units ramp up/down constraints and create a truncated D-ED problem. We create a colorful image from nodal demand, thermal unit generation cost, and network topology information. Convolutional neural networks are trained for constraint status identification using colorful images corresponding to system operating conditions and transfer learning. Filtering inactive line flow and ramp up/down constraints reduces the optimization problem's size and computational burden, resulting in a reduction in solution time and memory usage. Dropping all inactive branch and ramp constraints may activate some of these originally inactive constraints upon solving the truncated D-ED. A loop is added to form a constraints coefficient matrix iteratively during training dataset preparation and algorithm utilization. This iterative loop guarantees truncated D-ED results feasibility and optimality. Numerical results show the proposed algorithm's effectiveness in constraint status prediction and reducing D-ED size and solution time.

Research on double-tier bidding model for gas-fired units

This paper proposes a double-tier bidding(DTB) model on the generation side to introduce gas-fired units(GFU) into the market bidding by analyzing the electricity cost of the whole society and the generation cost of gas-fired units. With the introduction of a sub-process, the GFUs are incorporated into the main bidding process or the sub-process independently, and the bidding prices of each process are cleared separately. Based on the traditional market bidding algorithm, the DTB model can effectively solve the problem of increasing market price after units with higher generation costs join the market. Besides, transmission congestion and power shortages during peak hours caused by the drawback of market mechanism can be avoided. In addition, recessive electricity price subsidy from markets is visualized, realizing the non-price advantages of low-emission units. Thus, the promotion of the overall optimal social benefits and the implementation of the low-carbon development concept are realized. Moreover, the algorithm incorporates a transverse comparison method of generation costs to restrict the market speculation of power suppliers. Numerical example shows that this algorithm is effective and feasible, and can be adopted in other areas with similar market characteristics.

Power distribution network design considering the distributed generations and differential and dynamic pricing

In this study, a power distribution network design model is developed considering voltage control, as well as differential and dynamic pricing schemes. The objective is to maximize power distribution network profits under uncertain demands and parameters, such as power generation capacity, investment and generation cost of renewable distributed generation units, and the penalty budget for unsatisfied demands. The model determines the percentage of the power supply to the customer groups, the amount of power supplied to each customer group, the technology and capacity of renewable distributed generation units, and the prices offered. The proposed pricing scheme is differential for different types of customers with allowable voltage limits. The price is dynamic according to the planning time, including low, medium, and peak times. A fuzzy stochastic programming approach is developed to solve this problem. By simultaneously using triangular crisp numbers and probabilistic variables, the fuzzy stochastic programming integrates the fuzzy and stochastic approaches to deal with the uncertainty of demand and parameters. The numerical analysis shows that, as the confidence level decreases, the capacity of renewable distributed generation units and the profit increase. The results also show that when the decision maker responds to the uncertainty in demand with a high confidence level, the optimum profit can be obtained; approximately 55.90% of the power is supplied to low-demand customers.

The gravitational search algorithm for incorporating TCSC devices into the system for optimum power flow

<span lang="EN-US">This paper proposes a gravitational search algorithm (GSA) to allocate the thyristor-controlled series compensator (TCSC) incorporation with the issue of reactive power management. The aim of using TCSC units in this study is to minimize active and reactive power losses. Reserve beyond the thermal border, enhance the voltage profile and increase transmission-lines flow while continuing the whole generation cost of the system a little increase compared with its single goal base case. The optimal power flow (OPF) described is a consideration for finding the best size and location of the TCSCs devices seeing techno-economic subjects for minimizing fuel cost of generation units and the costs of installing TCSCs devices. The GSA algorithm's high ability in solving the proposed multi-objective problem is tested on two 9 and 30 bus test systems. For each test system, four case studies are considered to represent both normal and emergency operating conditions. The proposed GSA method's simulation results show that GSA offers a practical and robust high-quality solution for the problem and improves system performance.</span>

Thermoeconomic Optimization of Steam Pressure of Heat Recovery Steam Generator in Combined Cycle Gas Turbine under Different Operation Strategies

The optimization of the steam parameters of the heat recovery steam generators (HRSG) of Combined Cycle Gas Turbines (CCGT) has become one of the important means to reduce the power generation cost of combined cycle units. Based on the structural theory of thermoeconomics, a thermoeconomic optimization model for a triple pressure reheat HRSG is established. Taking the minimization of the power generation cost of the combined cycle system as the optimization objective, an optimization algorithm based on three factors and six levels of orthogonal experimental samples to determine the optimal solution for the high, intermediate and low pressure steam pressures under different gas turbine (GT) operation strategies. The variation law and influencing factors of the system power generation cost with the steam pressure level under all operation strategies are analyzed. The research results show that the system power generation cost decreases as the GT load rate increases, T4 plays a dominant role in the selection of the optimal pressure level for high pressure (HP) steam and, in order to obtain the optimum power generation cost, the IGV T3-650-F mode should be adopted to keep the T4 at a high level under different GT load rates.

Probabilistic optimal power flow calculation method considering sequential features and correlations of multi-uncertain source-load scenarios

In order to accurately evaluate the influence of the correlation and sequential feature of wind power, PV power, and load on the economic operation of a power system, a sequential probabilistic optimal power flow calculation method based on multi-uncertain source-load scenarios generated by a multi-generative adversarial network (MGAN) is proposed. First, the historical datasets of wind power, PV power, and load in adjacent areas were collected, and their probability distributions in 24 time periods were analyzed. The results showed that the probability distribution of different periods had obvious differences, which were defined as time sequence differences in this paper. Second, a novel neural network called MGAN for scenario generation was designed. Based on the historical data of each time period, the correlated wind power, photovoltaic (PV) power, and load scenarios were generated by MGAN. Finally, in the modified IEEE 118-bus system, in which two wind power sources, two PV power sources, and two loads with correlation were integrated, probabilistic optimal power flow calculations were carried out for 24 periods with the goal of the lowest power generation cost of thermal power units. The experimental results showed that the power generation cost fluctuation ranges that considered the time sequence difference were reduced by 60% on average compared with the nonconsidered. The proposed method can effectively reduce the power generation cost budget.

Multi-objective Analysis of Sustainable Generation Expansion Planning based on Renewable Energy Potential: A case study of Bali Province of Indonesia

This article analyzes the role of renewable energy in producing sustainable generation expansion planning. The generation expansion planning is carried out using an optimization model which has two objective functions, namely the objective function of planning costs and the objective function of emissions. Multi-objective analysis was performed using the epsilon constraint method to produce the Pareto set. Solution points are selected from the Pareto set generated using the fuzzy decision making method. The process of determining the best solution points is based on three scenarios. Furthermore, calculations were carried out to obtain 7 indicators of sustainability covering economic, social, and environmental aspects. The sustainability index is calculated based on several predetermined policy options. The model is implemented using data obtained from the electricity system in Bali Province, Indonesia. From the analysis, the planning scenario by implementing renewable energy sources in the generation of electrical energy, namely scenario 3, results in an increase in the sustainability index with the highest value during the planning period. However, scenario 3 produces two sustainability indices from the economic aspect, namely the unit cost of generation and shared electricity cost to GDP, which is the lowest when compared to other scenarios.

Optimal scheduling of a micro-grid with multi-period islanding constraints using hybrid CFCS technique

This paper proposes an efficient technique for optimum scheduling of micro-grids with multi-period islanding restrictions. The proposed method is joint implementation of Cuttle Fish Algorithm (CFA) and Crow Search Algorithm (CSA); is known CFCS method. Here, the CFA search behavior is modified by the CSA update position. The proposed CFCS system is utilized for optimal scheduling of micro-grid and considerably decreases the calculation load. The main purpose of proposed work is diminish the micro-grid operation cost together with the dispatch-able units operation cost, cost of power transmission as main grid with inconvenience cost recognized with consumers. The cost of power transmission from main phase can be positive or negative based on the flow direction of transmission line linking the microcircuit to main phase. Negative cost that represents an export of power to main grid emerges as economic advantage of micro-grid. Cost of inconvenience implies the penalty of modifiable loads programming outside the time intervals particular by the consumers. Constant penalty factor is utilized for prioritizing loads with respect to operation sensitivity inside the particular time intervals, in which a superior value of the penalty factor implies a least flexible load based on time interval operation settings. The value of the penalty factor is chosen reasonably greater to unit generation cost and market price. In proposed technique, the CFCS is used for establishing the correct program of the MG combinations according to load side power range. The CFCS method, objective function can be defined as system data subject to equality and inequality limitations. At that time, CFCS model is performed at MATLAB/Simulink working platform and performance is estimated to existing techniques.

Design and cost analysis of fish friendly kaplan tubine: A case study

The development of small hydropower has some environmental challenges, one of which is related to fish passage both upstream and downstream. These migrations are ecological imperatives for populations of fish. The development of waterways in hydropower, can restrict or delay fish migration, increase predation, affect water quantity and quality, and subject fish to direct damage and stress. There is no single solution for designing up and downstream passageways. In present investigation, a typical Kaplan based Mainmatti Small Hydropower Project has been selected as a case study. Design of conventional as well as modified fish friendly Kaplan blade has been carried out based on analytical approach. Further, effect of modification in runner diameter on different operating and design parameters i.e. flow velocity, twist angle and efficiency were discussed for five different design cases. Cost analysis of conventional as well as modified fish friendly design cases has been carried out and optimal design of fish friendly runner blade has been proposed. It has been observed that at 3.34 m runner diameter, change in turbine efficiency is minimum, and percentage change in unit generation cost is low which is suitable for the optimal selection of runner diameter.

Experimental analysis of photovoltaic-thermal collectors with closely spaced tubes

ABSTRACT Solar Photovoltaic (PV) systems have become increasingly popular in the last decade due to continuous increase in conversion efficiency and significant reduction in per unit generation cost. Photovoltaic-thermal (PV/T) collectors have been gaining popularity to utilize Sun’s spectrum effectively for production of electricity and utilization of waste heat. In the present study, two independent serpentine PV/T collectors having small gap between tube columns are designed to obtain desired temperature for domestic use with limited collector area and to achieve better cooling uniformity. PV/T-I has a copper absorber plate attached to the rear surface of the PV module and tubes are brazed to the plate, while PV/T-II has only tube for fluid flow which is glued to the PV back. Both the PV/T’s have a back cover to protect the tubing from moisture and dust. PV/T’s are tested under outdoor conditions during September–December, 2018. The developed PV/T’s are analyzed using the energetic and exergetic method. The average energy and exergy efficiency for PV/T-I is found to be 62.28 ± 5.53% and 12.27 ± 5.58%, whereas for PV/T-II average energy and exergy efficiency found to be 51.13 ± 5.53% and 13.4 ± 5.58%, respectively.

Energy Trading in Local Electricity Market With Renewables—A Contract Theoretic Approach

Emerging smart grid technologies and increased penetration of renewable energy sources (RESs) direct the power sector to focus on RESs as an alternative to meet both baseload and peak load demands in a cost-efficient way. A key issue in such schemes is the design and analysis of energy trading techniques involving complex interactions between an aggregator and multiple electricity suppliers (ESs) with RESs fulfilling a certain demand. This is challenging because ESs can be of various categories, such as small/medium/large scale, and they are self-interested and generally have different preferences toward trading based on their types and constraints. This article introduces a new contract theoretic framework to tackle this challenge by designing optimal contracts for ESs. To this end, a dynamic pricing scheme is developed such that the aggregator can utilize to incentivize the ESs to contribute to both baseload and peak load demands according to their categories. An algorithm is proposed that can be implemented in a distributed manner by trading partners to enable energy trading. It is shown that the trading strategy under a baseload scenario is feasible, and the aggregator only needs to consider the per unit generation cost of ESs to decide on its strategy. The trading strategy for a peak load scenario, however, is complex and requires consideration of different factors, such as variations in the wholesale price and its effect on the selling price of ESs, and the uncertainty of energy generation from RESs. Simulation results demonstrate the effectiveness of the proposed scheme for energy trading in the local electricity market.

Squirrel search algorithm for economic dispatch with valve-point effects and multiple fuels

ABSTRACT This paper bestows a new swarm intelligence approach, Squirrel Search Algorithm (SSA) to solve Economic Load Dispatch (ELD) of the thermal unit by addressing the valve point loading effects and multiple fuel options. SSA inspires the foraging behavior of squirrels which is based on dynamic jumping and gliding strategies. The main intention of the ELD problem is to minimize the total generation cost of units while assuring various system constraints. Renovate strategy and selection rules are used in the SSA algorithm to handle the constraints appropriately. The practicability of the proposed algorithm is tested on six different power test systems having different sizes and intricacies. Simulation results ascertain that the proposed SSA approach outperforms the other existing heuristic optimization techniques in terms of solution quality, robustness, and computational efficiency. Consequently, the proposed SSA can be an efficient approach for solving the ELD problems with valve point loading impacts and multi-fuel options.