Power Balance Constraints Research Articles

A Bi-Level Peak Regulation Optimization Model for Power Systems Considering Ramping Capability and Demand Response

In the context of constructing new power systems, the intermittency and volatility of high-penetration renewable generation pose new challenges to the stability and secure operation of power systems. Enhancing the ramping capability of power systems has become a crucial measure for addressing these challenges. Therefore, this paper proposes a bi-level peak regulation optimization model for power systems considering ramping capability and demand response, aiming to mitigate the challenges that the uncertainty and volatility of renewable energy generation impose on power system operations. Firstly, the upper-level model focuses on minimizing the ramping demand caused by the uncertainty, taking into account concerned constraints such as the constraint of price-guided demand response, the constraint of satisfaction with electricity usage patterns, and the constraint of cost satisfaction. By solving the upper-level model, the ramping demand of the power system can be reduced. Secondly, the lower-level model aims to minimize the overall cost of the power system, considering constraints such as power balance constraints, power flow constraints, ramping capability constraints of thermal power units, stepwise ramp rate calculation constraints, and constraints of carbon capture units. Based on the ramping demand obtained by solving the upper-level model, the outputs of the generation units are optimized to reduce operation cost of power systems. Finally, the proposed peak regulation optimization model is verified through simulation based on the IEEE 39-bus system. The results indicate that the proposed model, which incorporates ramping capability and demand response, effectively reduces the comprehensive operational cost of the power system.

Multi-objective-based economic and emission dispatch with integration of wind energy sources using different optimization algorithms

In this work, a study of economic and emission dispatch issues based on the multi-objective optimization is solved, and generation costs and emissions are reduced by utilizing multi-objective optimization techniques. This optimization is carried out in an IEEE-30 bus system, with and without the integration of wind energy sources, with equality and inequality constraints. The equality constraints are the power balance constraints, stipulating that to have an optimal solution, the generated power must be adequate to satisfy the load demand plus losses. The inequality constraints are a collection of limitations for active power generation, reactive power generation, generator bus voltage, and load bus voltage. To track the hourly load demand, a daily load profile is established using the IEEE-30 bus system. The generation costs and emissions in the system are optimized using multi-objective particle swarm optimization and multi-objective Ant–Lion Optimization approaches. In order to determine the goals’ minimum values, a fuzzy min–max technique is applied. The values that have been minimized are then compared to determine how well wind energy integration has reduced the generation costs and emissions. Two case studies are performed in this work. For Case 1, the total generation costs and emissions using MOPSO are less, with a difference of $42.763, while MOALO has lower emissions, with a difference of 157.337 tons. For Case 2, with the implementation of wind energy, MOPSO has lower total generation costs, with a difference of $51.678, and lower emissions, with a difference of 459.446 tons.

Robust Optimization Research of Cyber-Physical Power System Considering Wind Power Uncertainty and Coupled Relationship.

To mitigate the impact of wind power uncertainty and power-communication coupling on the robustness of a new power system, a bi-level mixed-integer robust optimization strategy is proposed. Firstly, a coupled network model is constructed based on complex network theory, taking into account the coupled relationship of energy supply and control dependencies between the power and communication networks. Next, a bi-level mixed-integer robust optimization model is developed to improve power system resilience, incorporating constraints related to the coupling strength, electrical characteristics, and traffic characteristics of the information network. The upper-level model seeks to minimize load shedding by optimizing DC power flow using fuzzy chance constraints, thereby reducing the risk of power imbalances caused by random fluctuations in wind power generation. Furthermore, the deterministic power balance constraints are relaxed into inequality constraints that account for wind power forecasting errors through fuzzy variables. The lower-level model focuses on minimizing traffic load shedding by establishing a topology-function-constrained information network traffic model based on the maximum flow principle in graph theory, thereby improving the efficiency of network flow transmission. Finally, a modified IEEE 39-bus test system with intermittent wind power is used as a case study. Random attack simulations demonstrate that, under the highest link failure rate and wind power penetration, Model 2 outperforms Model 1 by reducing the load loss ratio by 23.6% and improving the node survival ratio by 5.3%.

Distributed predefined-time optimal economic dispatch for microgrids

With the massive popularization of distributed generators, optimal economic dispatch has been a key optimization problem to maintain stable and efficient work of the whole system. In this paper, a new smooth reconstruction penalty function with continuous and piecewise linear differential is designed to deal with generation power constraints, which promotes to obtain a better suboptimal solution compared with the existing smooth penalty methods. A distributed predefined-time optimal economic dispatch strategy is presented by utilizing a time-based function. By employing the proposed strategy, the minimization of the generation cost with transmission loss under the power balance constraint and generation minimum/maximum constraints can be realized within a predefined settling time. The performance of the proposed optimization strategy is evaluated by simulations and hardware-in-the-loop experiments in terms of validity verification, robustness to load change and topology reconfiguration, plug-and-play functionality, and comparison with the existing results to illustrate the advantages of fast convergence and near optimal results.

A day‐ahead energy management strategy for electric vehicles in parking lots considering multi‐scenario simulations and hydrogen storage system

AbstractThis article investigated the charge and discharge management structure of electric vehicles (EVs) in intelligent parking lots (IPLs). It seems that with the expansion of renewable energy sources (RESs) as clean energy and investigation of the effects of EVs on the operation and planning of future distribution networks around the way EVs exchange energy with each other and the upstream network operator, RESs such as solar and wind sources, along with hydrogen storage are essential. Therefore, a new stochastic multi‐scenario approach for charge/discharge management of EVs parked in IPL was proposed, in which a newly developed model for the IPL with a hydrogen storage system (HSS) consisting of a fuel cell, an electrolyzer, and a hydrogen storage tank was presented. In the proposed model, the constraints of upstream network and power balance constraints, with the operating constraints related to the IPL, including EVs, renewable energy sources, and the hydrogen storage system, were formulated as the most important objectives of the optimization problem. The optimization algorithm, Competitive Swarm Optimizer (CSO), was formulated for implementation, and its results were compared with those of the PSO and GWO algorithms. The CSO must handle a variety of practical, large‐scale optimization problems. Based on the obtained results, the excess energy purchased from the upstream network or renewable sources was used as hydrogen storage for consumption during peak hours. As expected, the technical constraints and financial goals of the system were met, and the proposed system was evaluated on a 33‐bus network. As the expected benefits will be the most beneficial with the presence of renewable sources, the final profit will be reduced by taking into account uncertainty for charge/discharge management in EVs such as the uncertainty of electric load, market price, wind turbine, and photovoltaic cell sources. Nonetheless, the profit obtained from renewable resources is preferable to losses resulting from the uncertainty of the system, and according to expectation, the performance of the system for managing the optimal charging and discharging of EVs in the IPL will be acceptable with the maximum profit for the grid.

Managing power balance and reserve feasibility in the AC unit commitment problem

Incorporating the AC power flow equations into unit commitment models has the potential to avoid costly corrective actions required by less accurate power flow approximations. However, research on unit commitment with AC power flow constraints has been limited to a few relatively small test networks. This work investigates large-scale AC unit commitment problems for the day-ahead market and develops decomposition algorithms capable of obtaining high-quality solutions at industry-relevant scales. The results illustrate that a simple algorithm that only seeks to satisfy unit commitment, reserve, and AC power balance constraints can obtain surprisingly high-quality solutions to this AC unit commitment problem. However, a naive strategy that prioritizes reserve feasibility leads to AC infeasibility, motivating the need to design heuristics that can effectively balance reserve and AC feasibility. Finally, this work explores a parallel decomposition strategy that allows the proposed algorithm to obtain feasible solutions on large cases within the two hour time limit required by typical day-ahead market operations.

Distributionally robust optimization configuration method for island microgrid considering extreme scenarios

The marine climate conditions are intricate and variable. In scenarios characterized by high proportions of wind and solar energy access, the uncertainty regarding the energy sources for island microgrid is significantly exacerbated, presenting challenges to both the economic viability and reliability of the capacity configuration for island microgrids. To address this issue, this paper proposes a distributionally robust optimization (DRO) method for island microgrids, considering extreme scenarios of wind and solar conditions. Firstly, to address the challenge of determining the probability distribution functions of wind and solar in complex island climates, a conditional generative adversarial network (CGAN) is employed to generate a scenario set for wind and solar conditions. Then, by combining k-means clustering with an extreme scenario selection method, typical scenarios and extreme scenarios are selected from the generated scenario set, forming the scenario set for the DRO model of island microgrids. On this basis, a DRO model based on multiple discrete scenarios is constructed with the objective of minimizing the sum of investment costs, operation and maintenance costs, fuel purchase costs, penalty costs of wind and solar curtailment, and penalty costs of load loss. The model is subjected to equipment operation and power balance constraints, and solved using the columns and constraints generation (CCG) algorithm. Finally, through typical examples, the effectiveness of this paper’s method in balancing the economic viability and robustness of the configuration scheme for the island microgrid, as well as reducing wind and solar curtailment and load loss, is verified.

Energy storage capacity optimization of optical storage microgrid considering customer satisfaction and depth of energy storage discharge

Abstract The influence of the depth of battery discharge (DOD) and user satisfaction on the capacity configuration of the optical storage microgrid cannot be ignored. In this paper, the minimum comprehensive cost of an optical storage microgrid is taken as the objective function, and the model is established by considering the SOC after DOD, user satisfaction with electricity consumption, power balance, and other constraints. The numerical examples show that the proposed method can allocate suitable energy storage capacity for optical microgrids and ensure user satisfaction.

Distributed optimal operation of PV-storage-load micro-grid considering renewable and load uncertainties

Micro-grid is one of the important carriers for renewable energy integration. Optimizing the operation mode of micro-grid can improve economic benefits and reduce risks brought by uncertainties. To maximize the economic benefits of photovoltaic-storage-load micro-grid, a chance-constrained optimal operation model considering renewable and load uncertainties is proposed in this paper. Firstly, the photovoltaic (PV) power and load forecast error distribution function based on fitting method is obtained. Then, a probabilistic power balance constraint based on chance constrained theory is established to reflect risks brought by uncertainties. To protect the information privacy of different entities, the alternating direction multiplier method (ADMM) with self-adaptive parameters is used to the proposed optimal model in a distributed way. Case study demonstrates that the proposed model can achieve a profit and risk balance of micro-grid scheduling by setting different confidence levels, and the information privacy of micro-grid operator and users is well protected.

Optimal allocation method for MIES-based shared energy storage using cooperative game theory and CSP

To further promote the efficient use of energy storage and the local consumption of renewable energy in a multi-integrated energy system (MIES), a MIES model is developed based on the operational characteristics and profitability mechanism of a shared energy storage station (SESS), considering concentrating solar power (CSP), integrated demand response, and renewable energy output uncertainty. We propose a corresponding MIES model based on co-operative game theory and the CSP and an optimal allocation method for MIES shared energy storage. The model considers the maximum operating benefit of the SESS as the upper objective function and the minimum operating cost of the MIES as the lower objective function. First, the Karush–Kuhn–Tucker conditions of the lower-layer model are transformed into constraints of the upper-layer model, and the Big-M method is used to linearize the nonlinear problem and convert the two-layer nonlinear model into a single-layer linear model. Second, based on the Nash negotiation theory, the benefits of each IES in the MIES are allocated. Finally, the fuzzy chance constraints are used to relax the power balance constraints, and the trapezoidal fuzzy numbers are transformed into a deterministic equivalence class to assess the impact of renewable energy output uncertainty on system operation. The validity and rationality of the proposed two-layer model are verified through simulation, and the results demonstrate that the proposed shared storage capacity leasing model can effectively reduce the total operation cost, increase the profitability of the shared storage operator, and increase the utilization rate of the SESS.

Assessing and comparing a DDPG model and GA optimization for a heat and power virtual power plant operating in a power purchase agreement scheme

This paper proposes a deep deterministic policy gradient (DDPG) model for the operation management of a solar power-based virtual power plant (VPP) having a PPA with the grid and supplying power and thermal energy to consumers. The VPP serves to balance the solar power intermittency, cover the demand whenever solar power is absent, and ensure an efficient supply of energy. The literature in this field has introduced optimization algorithms to determine the power plant's output power or heat on a rolling-horizon basis. Using the function approximation category, which involves reinforcement learning with neural networks, to solve the simultaneous thermal and power operation management of VPPs is still not well developed. The challenges imposed in this model are sourced from the non-linearity of the CCHP, the power and thermal balance constraints, and the consideration of continuous variables rather than discrete ones. A case study is simulated in Egypt to assess and compare the models. Compared to the genetic algorithm optimization, the proposed DDPG model achieved 3% more profit, 12% higher carbon dioxide (CO2) emissions, and 9% lower natural gas consumption. The DDPG solution was 57% faster than the GA. The results of the DDPG model proved that machine learning methods could outperform optimization in terms of optimality achievement and speed of solution. The DDPG improved the operation of energy storage units and was able to recognize the supply-demand operational pattern, ensuring the scalability of the VPP to cope with different energy demand levels.

Renewable energy incentives for project owners representing communities with heavily subsidised fossil fuel-based electricity

The significance of renewable energy (RE) as an essential component of sustainable cities is widely acknowledged. Nevertheless, the global transition towards RE faces numerous hurdles, including RE financing, particularly in regions where electricity generation from fossil fuels is heavily subsidized. This necessitates the formulation of effective incentives that can encourage project owners to invest in the transition towards RE. This manuscript proposes a comprehensive framework for incentivizing RE project owners and offers three types of incentives: capital-based, production-based, and grid support incentives. The effectiveness of the proposed set of incentives is evaluated through a detailed techno-economic analysis which aims to minimize Net Present Cost while considering power balance and grid constraints. It encompasses various aspects of RE systems, including optimal sizing of photovoltaics, batteries, inverters, and optimal power flow, at different levels of RE penetration. Additionally, the framework explores the possibility of achieving 100 % RE through off-grid systems, shedding light on potential challenges and opportunities. Further, economic indicators such as the Cost of Energy, Payback Period, Return on Investment, and Internal Rate of Return are also analyzed to evaluate the acceptability of the proposed framework. Results demonstrate that the presented incentivizing framework has the potential to facilitate RE adoption, positioning it as a valuable policy and investment opportunity for RE project owners. This yields substantial benefits including reduced financial burdens, improved return on investment, and access to diverse revenue streams.

Stochastic optimal scheduling of wind power and pumped-storage hydropower complementary systems with multiple uncertainties

The joint operation of wind farms (WFs) and pumped-storage hydropower plants (PSHPs) is an effective way to smooth out the random fluctuations of wind power and improve its consumption rate. In this paper, a novel method to describe the multiple uncertainties of wind power outputs is proposed. A WFs-PSHP joint optimal scheduling model based on chance-constrained programming is then developed. The optimization model aims to maximize the total generation profit of the WFs-PSHP complementary system, and comprehensively considers the hydraulic constraints, unit operation constraints and system power balance constraint of the PSHP. To improve the model solving efficiency, this study converts the previous model with high-dimensional, non-convex, nonlinear and stochastic characteristics to the deterministic mixed integer linear programming (MILP) one. The optimization results demonstrate that the PSHP not only compensates for the fluctuations in wind power output, but also increases the total generation profit of this complementary system to 966.48 × 104 CNY, which is 17.56 % higher than that of independent operation.

Distributed Control of HVAC-BESS under Solar Power Forecasts in Microgrid System

This paper investigates an energy management problem in the microgrid by scheduling heating ventilation air conditioning (HVAC) and battery energy storage system (BESS) with a distributed algorithm. A multi-layer energy management architecture is presented at a system-level to co-optimize the HVAC-BESS by taking into account solar energy forecasts. A surplus-based consensus algorithm is proposed to solve the optimization problem, where the local power mismatch is introduced as a surplus term, and the HVAC-BESS can thus be co-scheduled to maximize renewable energy efficiency at the peak generation time. A set of the convex cost functions are formulated to minimize the HVAC's user dissatisfaction degree and alleviate power loss during the BESS operation. The goal is to collectively minimize the total energy cost in a distributed manner, subject to individual load constraints and power balance constraints. It is theoretically proved that a global convergence of the proposed algorithm is achieved provided that the directed network is strongly connected. The results from a number of case studies are promising, demonstrating the effectiveness and robustness of the algorithm under practical scenarios.

Research on Park Energy System Based on Grid Connection of Renewable Energy Power Generation

With the maximum consumption of renewable energy, the minimum emission of pollutants and the minimum comprehensive investment cost as the optimization objectives, the operation model of the park’s energy system considering the thermal power balance constraint, natural gas balance constraint and power grid power constraint was proposed, and the scenic power generation and electricity equipment of the park were studied. By comparing different operation scenarios, the influence of adding different equipment on the operation optimization of the whole park under the thermoelectric coupling is comprehensively analyzed. The balance curve of equipment output and related energy use is analyzed on a yearly cycle, indicating that the power supply grid of the park based on the thermoelectric coupling has great reliability and effectiveness in the consumption of renewable energy, and its economy is also significantly improved.

A self-healing restoration of power grid based on two-stage adaptive decision-making strategy to enhance grid resilience

Large-scale power outages can affect the economy of the country and jeopardize the lives of millions of people, so there is a need for a fast, reliable, and self-healing tool to reduce these losses. Hence, the power system restoration performance can be improved by considering both restoring and operating performance, however, current restoration strategies only consider the restoring performance but ignore the operational performance which can enhance the power system resiliency. Given this background, challenging tasks such as optimal restoration planning (ORP) and optimal real-time operation (ORO) are planned to be tackled by developing an adaptive decision-making strategy (ADMS). In order to reduce the effects of emergency power outages on power systems, this study presents the ADMS, a two-stage self-healing restoration approach. Moreover, a novel metric of capacity accessibility (NMCA) is developed to determine the capacity adequacy status during severe events. The proposed ADMS has two steps, each of which is conducted at a certain time, and is referred to as ORP for the first stage and ORO functions for the second stage. The goal of the ORP optimization model is to maximize system-wide power capacity for electricity demand under extreme events by considering practical constraints, including non-black-start generators (NBSGs) constraints, network topology constraints, and power balance constraints. In order to reduce generation costs, the ORO optimization model adjusts the generated output power to enhance one or more operating performance metrics. The first stage problem is formulated using mixed-integer linear programming (MILP), and it is resolved using the branch-and-bound technique. Moreover, the interior point method solves AC optimal power flow for the second stage. Finally, simulation studies are performed on the modified IEEE 118-bus power systems. The outcomes demonstrate the effectiveness of the proposed strategy for planning (ORP) and real-time operation (ORO); the proposed two-stage strategy is capable of providing an optimal solution for a high-performance online restoration decision support system; the proposed strategy can adapt against the system conditions and contingencies.

Capacity optimization of a wind-photovoltaic-electrolysis-battery (WPEB) hybrid energy system for power and hydrogen generation

Utility-scale (>10 MW) Wind-Photovoltaic-Electrolysis-Battery (WPEB) system is an emerging technology that adopts open loop “Power-to-H2” architecture for large-scale green hydrogen production. It applies to curtailment reduction in the area with abundant wind and solar energy resources. The traditional residential-scale (0–1 MW) or commercial/facility-scale (1–10 MW) WPEB systems usually adopt the close loop “Power-to-H2-to-Power” structure for power supply in the microgrid. The capacity optimization of the commercial-scale, residential-scale WPEB system have been studied extensively, but the researches for utility-scale WPEB system are rare. This work proposes a multi-constraints single objective capacity optimization method for the utility-scale WPEB system. The optimization objective is to minimize the levelized cost of electricity (LCOE) and the constraints of power balance, annual grid sales rate (AGSR), wind/PV/electrolysis station capacity are considered. The feasible domain is identified by the 8760-h production simulation and the gradient descent method is applied to search the optimal solution. The main conclusions are summarized below: (1) Increasing the wind-to-generation capacity ratio can reduce the LCOE, required grid sales capacity, and net generation curve fluctuation. (2) The lower and upper limits of the electrolysis station capacity are determined by the AGSR constraint and the LCOE target. (3) The battery bank time-shifts electricity to reduce the downtime of the electrolysis station. Thus, its power capacity should be no less than the minimum load ratio of the electrolysis station and the discharge duration greater than 1 h is preferred. Overall, this work provides a capacity optimization roadmap for the utility-scale WPEB system which plays a significant role in renewable electricity-based hydrogen production and curtailment reduction.

NSGA-III integrating eliminating strategy and dynamic constraint relaxation mechanism to solve many-objective optimal power flow problem

Increasing optimizing criteria in modern power systems promotes the birth of many-objective optimal power flow (Ma-OPF) problems in which more than three optimizing objective functions are considered. The increasing optimizing objectives as well as complex constraints of power balance and other system limits bring a decrease in selection pressure and challenges of constraint handling techniques for traditional multi-objective evaluation algorithms. Aiming at the solving difficulties of Ma-OPF problems, an improved NSGA-III integrating eliminating strategy and dynamic constraint relaxation mechanism (NSGA-III-EDR) is proposed. In the proposed approach, a new elimination strategy that eliminates the associated points having the largest angle with the corresponding reference line is employed to increase the selection pressure of the algorithm. An integrated constraint handling method, which employs a repair strategy based on assigning decision variables to feasible values and a penalty function approach together to handle power flow equality constraints, is also introduced into the NSGA-III-EDR. Aiming at lacking feasible solutions of the algorithm in the early searching stage, a strategy of relaxing constraint violations as well as a dynamic updating strategy for the tolerated threshold value of distinguishing feasible and infeasible solutions at the early evolution is proposed. Moreover, an improved domination sorting rule based on the proposed constraint handling method and the relaxing strategy to constraint violations is employed to promote the generation of feasible solutions. The effectiveness and feasibility of the proposed improved NSGA-III-EDR approach are studied and evaluated on different test cases of a famous standard IEEE 30-bus power system as well as the larger power systems of IEEE 57-bus and IEEE 118-bus. The numerical results show that the proposed NSGA-III-EDR method can provide solutions to many-objective OPF problems with tremendous potential compared with the traditional NSGA-III and other algorithms illustrated in the literature.

Optimization Method of Energy Storage Configuration for Distribution Network with High Proportion of Photovoltaic Based on Source–Load Imbalance

After a high proportion of photovoltaic is connected to the distribution network, it will bring some problems, such as an unbalanced source and load and voltage exceeding the limit. In order to solve them, this paper proposes an optimization method of energy storage configuration for a high-proportion photovoltaic distribution network considering source–load imbalance clustering. Taking the minimum total voltage deviation, the minimum total power loss and the minimum total operating cost as the objective function, and considering various constraints such as power balance constraints and energy storage operation constraints, a mathematical model for energy storage configuration optimization is established. Firstly, the source–load imbalance of the distribution network with a high proportion of photovoltaic is defined. Therefore, according to the 24 h photovoltaic and load data, the 24 h source–load imbalance can be obtained, and the optimal k value can be determined by the elbow rule, so that 24 h a day can be clustered into k periods by the k-means algorithm. Then, the fuzzy comprehensive evaluation method is used to determine the weight factors of each objective function in each period, and three scenes are determined according to the different amount of energy storage. Then, the hybrid particle swarm optimization algorithm proposed in this paper is used to solve the model, and the minimum objective function value, optimal position and optimal capacity of each energy storage grid in each scene are obtained. Finally, it is applied to an example of IEEE33. In the results, the total voltage deviation is increased by more than 10%, the total power loss is increased by more than 8% and the total operating cost is increased by more than 12%, which verifies the effectiveness of the proposed model.

CSP-IES economic dispatch strategy with generalized energy storage and a conditional value-at-risk model

To promote the efficient use of energy storage and renewable energy consumption in the integrated energy system (IES), an economic dispatch strategy for the concentrating solar power (CSP)-IES with generalized energy storage and a conditional value-at-risk (CVaR) model is proposed. First, considering the characteristics of energy storage and distributed power supply timing, a CSP-IES configuration is established by using a CSP plant to achieve thermal decoupling of the combined heat and power unit and by defining the thermal storage system of the CSP plant and the battery as the actual energy storage. Second, the fuzzy response of the logistic function is used to optimize the time-of-use tariff to guide load shifting, and the load shifting is defined as virtual energy storage. Third, the CSP-IES economic dispatch model is established to consider the carbon emission allowance model. Finally, considering the system uncertainty, a fuzzy chance constraint is used to relax the system power balance constraint, and then the trapezoidal fuzzy number is transformed into a deterministic equivalence class, and the CVaR model is used as a risk assessment index to quantify the risk cost of the system due to uncertainty. The CSP-IES economic dispatch model with CVaR is constructed. The feasibility and effectiveness of the proposed optimization model are verified by comparing various scenarios.