Security-constrained Economic Dispatch Research Articles

Security constrained economic dispatch with VSC-HVDC connected wind farms

The rise in wind power in electrical networks creates complex challenges for transmission system operators (TSOs), particularly regarding real-time operation. TSOs rely on grid codes to enforce wind farm (WF) participation in primary frequency control (PFC), like conventional plants. This paper addresses this need by proposing a security constrained economic dispatch (SCED) model with VSC-HVDC connected WFs based on variable speed wind generators. A key differentiator from existing models is the explicit calculation of the spinning reserve and the droop parameter of the WFs. This method uses the deloading schemes related to blade pitch angle and mechanical rotor speed to ensure compliance with grid codes related to PFC. We show that the wind speed and these deloading schemes significantly impact the WF droop parameter. For efficient studies, linear shift factors are used to model the transmission grid and the VSC-HVDC connected WFs. The performance of the SCED model was assessed using two standard test systems that incorporate WFs connected by VSC-HVDC lines. Its effectiveness was confirmed by comparing it with the security constrained optimal power flow (SCOPF). The results showed agreement between both models, with differences less than 3 % and with the SCED saving about 70 % of the computing time.

Exploring Carbon Equilibrium in Integrated Electricity-Hydrogen System

Global carbon emissions from electricity and hydrogen production have grown rapidly in recent years. Some existing literature has proposed the method of reducing carbon emissions by power-to-hydrogen (P2H) technology. However, due to the fossil-based energy structure of electricity system, excessive electricity to hydrogen may lead to an increase in carbon emissions. To reduce carbon emissions effectively, a low carbon-driven optimal capacity configuration method for P2Hs is proposed in this paper to explore carbon equilibrium in integrated electricity-hydrogen system. A joint economic dispatch model for integrated electricity-hydrogen system is formulated. The electricity system model is a security-constrained economic dispatch model with P2H constraints. The hydrogen system model is a hydrogen supply chain model with pipeline pack constraints and Weymouth equation, whose sources are fossil fuel reforming and electrolytic hydrogen. We propose a second-order cone programming (SOCP)-based solution to transform the hydrogen system model into a mixed integer second order cone programming (MISCOP), which can be readily solved by commercial solvers. To preserve the internal information of each system, a decentralized algorithm based on optimality condition decomposition (OCD) is developed. Case study based on modified IEEE 30-bus and Belgium 20-node integrated energy system demonstrates the effectiveness of the proposed strategy.

DC-based security constraints formulation: A perspective of primal-dual interior point method

The DC network security constraints have been extensively studied in numerous power system problems, such as optimal power flow (OPF), security-constrained economic dispatch (SCED), and security-constrained unit commitment (SCUC). Power transfer distribution factors (PTDFs) are widely applied in DC network constraints. However, the PTDF matrix is extremely dense, making it difficult to solve security-constraint optimization problems. This paper investigates the computational inefficiency of PTDF-based security constraints from the perspective of matrix sparsity of primal–dual interior point method (IPM), and proposes a matrix transformation to restore sparsity during IPM iterations. It turns out that the transformation method is equivalent to solving the original optimization problem expressed in pure voltage angle. The regular B-θ formulation is also a variant of the proposed transformation. Numerical studies show that sparsity rather than the size of variables and constraints is the key factor impacting the speed of solving convex quadratic problems, i.e., OPF and SCED problems. The proposed transformation significantly outperforms the PTDF-based approach, achieving a 100x reduction in non-zero elements of the coefficient matrix and a 40x speed increase in barrier processes in a 25,000-bus network.

A Deep Reinforcement Learning Method for Unit Commitment with Renewable Energy Generators

To cope with the challenges of complex modeling, difficult solutions, and low efficiency brought by a significant amount of renewable energy units to the power system dispatch (PSD), a deep reinforcement learning method for unit commitment with renewable energy generators is proposed. Firstly, a PPO-based reinforcement learning method is utilized to promptly and effectively resolve the unit commitment. A mathematical optimization technique is employed to solve the security-constrained economic dispatch, considering the “N-1” security check. By integrating these two methods, the decision-making efficiency is enhanced while ensuring the security of the result. The proposed method’s efficiency is affirmed by case simulation.

Interpretable data‐driven contingency classification for real‐time corrective security‐constrained economic dispatch

AbstractHigh penetrations of renewable energy are crucial for low‐carbon power systems. However, the higher volatility of renewable power generation pushes real‐time operations closer to equipment limits. It is thus important to utilize flexibilities in the system through corrective security‐constrained economic dispatch (SCED) that allows generators to take corrective adjustments after contingencies. The corrective SCED problem, containing a large number of contingencies, and corresponding post‐contingency decisions and constraints, is very large in scale and difficult to solve using purely model‐based methods within the strict time limits of real‐time markets. To accelerate the solution process, this paper develops a novel interpretable data‐driven contingency classification method. Historical data and their potentially useful patterns are utilized in interpretable data‐driven decision tree classifiers. To directly consider continuous features, such as net load values, and to consider imbalanced datasets without much additional complexity, Improved Strong Optimal Classification Trees (ISOCTs) are developed with new branching threshold constraints and category weights in the objective function. ISOCTs are then embedded into a hybrid model‐based and data‐driven framework to guarantee the accuracy of the real‐time active contingency set and the resulting security of dispatch decisions. Numerical testing results demonstrate the classification accuracy, computational efficiency, and interpretability of the proposed approach.

Price formation in short-term electricity market scheduling

Price formation is important for monitoring/development of an electricity market since the short/long-run efficiencies depend on the prices representing the economic signals. However, existing approaches cannot capture the contribution of suppliers’ bidding behavior to short-term price formation. As a result, regulators cannot evaluate these contributions. This can result in market monitoring failure/inefficient regulatory decisions that entail short-run market distortion or compromised investment respectively. This paper proposes a novel approach enabling regulators to retrace these contributions for every single non-zero shadow price formed in a dynamic security-constrained economic dispatch (SCED) problem. The decomposition of dual variables in a linear representation of SCED is adopted to evaluate the marginal contribution of the offered prices. The proposed theory yields explicit functions mapping the SCED shadow prices (i.e., locational marginal prices, and marginal values of (i) binding generation capacity limits, (ii) binding transmission capacity limits, and (iii) binding ramping limits) to the offered prices. Counterintuitively, the results show that increasing the offered prices will not necessarily leads to an increase in the shadow prices, especially the locational marginal prices. In addition, it is shown that the offered prices can pose long-run implications by contributing to the shadow prices associated with the marginal value of transmission/generation capacity.

Stochastic Security-Constrained Economic Dispatch of Load-Following and Contingency Reserves Ancillary Service Using a Grid-Connected Microgrid during Uncertainty

In the context of the growing penetration of renewable power sources in power systems causing probabilistic contingency conditions, a suitable economic dispatch model is decisively needed. There is a lack of research in the field of probabilistic mathematical formulation considering the uncertainties due to the stochastic nature of renewables and contingency occurrence, as it is a very complex problem to be solved. The most appropriate model is the stochastic security-constrained economic dispatch (SSCED) model for optimized economic dispatch decisions during uncertainty. However, because of its complexity, it is rarely employed. This paper attempts to solve the complex SSCED problem in the presence of the uncertainty of resources and probabilistic contingency conditions, which is a novel effort in this regard. The SSCED is carried out over multiple periods to provide the load-following or contingency reserves. In the proposed SSCED, the uncertainty problem is addressed by modeling the stochastic wind energy power source by using “probability transition scenarios”. The uncertainty caused by probabilistic contingency conditions in the dispatch schedule is approximated using a “state-specific transition matrix”. The frequency control reserves in contingency conditions are co-optimized with energy, and stochastic security-constrained economic dispatch is achieved. The efforts are put forward to suggest a new market model in the presence of the uncertainty of renewable energy availability. Case studies are examined to show the potential technical and financial advantages of the proposed SSCED through co-optimization. Grid-connected microgrid owners offer frequency control ancillary services by providing load-following ramping reserves in the normal state and contingency reserves in the state of contingency. The probabilistic contingencies considered are generator failure and an underloading condition. A modified “IEEE 30 bus system” is considered a grid-connected microgrid for testing the proposed SSCED. The results show that the greater the flexibility of the resources, the greater the technical and economic benefits. The increase in ramping flexibility of a wind source results in almost an 8.1% reduction in operational costs compared to the base case. The contingency condition analysis shows that the presence of ramping reserves in the system enhances the power system performance, avoiding the cascading effects that ultimately cause a power system failure.

Impact Assessment and Defense for Smart Grids With FDIA Against AMI

Cyber-physical security has been becoming an important issue for many critical infrastructures in human society, including electrical power grids. This paper proposes an impact assessment framework for smart grids suffering false data injection attack against smart meters. Firstly, the propagation model of malicious false data codes in smart meter communication networks is established. Based on this, a security-constrained economic dispatch model is formulated to assess how false data codes would mislead the grid operator's actions. A defense strategy is proposed, which enhances the grid's vulnerability through effectively deploying defense resources in smart meter networks. Extensive numerical simulations are conducted to evaluate the impact of different attack scenarios as well as the effectiveness of the defense strategy.

Transmission Expansion Planning Considering a High Share of Wind Power to Maximize Available Transfer Capability

To have an effective transmission network and support free trading, the open and non-discriminatory access to transmission services for all market participants under all conditions is of significant concern. To this end, a sufficient value of available transfer capability (ATC) is required, which can significantly affect the electricity market efficiency. This paper constructs a methodology for reinforcing an existing transmission network considering wind power investment to enhance ATC. In this regard, a bi-level structure is adopted whose upper level is the joint transmission expansion planning (TEP) and wind power investment subject to the technical power grid limitations. After solving the upper level, a security-constrained economic dispatch (SC-ED) is formulated to acquire the optimal generation scheduling. Then, the lower level is designed to calculate the ATC. To solve this problem, the SC-ED is first replaced by its primal and dual feasibility constraints and strong duality equality. Then, these constraints are added to the upper level. The lower level is also replaced by its corresponding constraints. Consequently, a bilinear single-level optimization problem is extracted, which is further solved by employing Konno’s cutting plane algorithm. The experimental results on the IEEE 24-bus RTS show the proposed method’s effectiveness. It is indicated that the ATC can be improved by 27.2 % using the formulated model at the expense of more investment cost resulting in less load shedding and less wind curtailment.

Week-ahead Daily Peak Load Forecasting Using Hybrid Convolutional Neural Network

Peak load forecasting (PLF) is essential for the operation of large-scale power systems, such as security-constrained economic dispatch and rolling unit commitment. PLF is critical for peak load shaving and demand side management in distribution systems, too. Results obtained by PLF can assist market participants to develop their bidding schemes in power markets. This work presents a novel method, based on a hybrid convolutional neural network (CNN) that is cascaded with a fully-connected network, to explore week-ahead daily PLF. The proposed method uses a systematic grid search along with Adaptive Moment Estimation (Adam) optimizer to design the hybrid model. The grid search tunes the network structure and hyperparameters (such as kernel size) of the hybrid CNN while Adam optimizer adjusts the synaptic weights and parameters (e.g., values of a kernel). Realistic daily peak load data and meteorological (temperature) data in Taiwan are investigated. Simulation results obtained by the proposed hybrid deep learning model are better than those obtained by the traditional multi-layer neural network, recurrent neural network, vector auto-regressive moving average model and support vector machine.

Automatic Generation Control with Virtual Synchronous Renewables

As synchronous generators (SGs) are gradually displaced by renewable energy sources (RESs), the frequency stability of power systems deteriorates because RESs, represented by utility-scale solar and wind power sources, do not provide the inertial response, primary frequency response, secondary frequency response, and tertiary frequency regulation. As a result, the remaining SGs may not be sufficient to maintain the power balance and frequency stability. The concept and control strategies of virtual synchronous generators (VSGs) enable the inverter-based wind and solar power sources to emulate the outer characteristics of traditional SGs and participate in the active power and frequency control of power systems. This paper focuses on the automatic generation control (AGC) with virtual synchronous renewables (VSRs). First, the VSR strategy that enables the RESs to participate in AGC is introduced. Second, based on the interval representation of uncertainty, the output of RES is transformed into two portions, i.e., the dispatchable portion and the stochastic portion. In the dispatchable portion, the RESs can participate in AGC jointly with SGs. Accordingly, a security-constrained economic dispatch (SCED) model is built considering the RESs operating in VSR mode. Third, the solution strategy that employs the slack variables to acquire deterministic constraints is introduced. Finally, the proposed SCED model is solved based on the 6-bus and 39-bus systems. The results show that, compared with the maximum power point tracking (MPPT) mode, VSRs can participate in the active power and frequency control jointly with SGs, increase the maximum penetration level of RESs, and decrease the operating cost.

Learning optimization proxies for large-scale Security-Constrained Economic Dispatch

The Security-Constrained Economic Dispatch (SCED) is a fundamental optimization model for Transmission System Operators (TSO) to clear real-time energy markets while ensuring reliable operations of power grids. In a context of growing operational uncertainty, due to increased penetration of renewable generators and distributed energy resources, operators must continuously monitor risk in real-time, i.e., they must quickly assess the system’s behavior under various changes in load and renewable production. Unfortunately, systematically solving an optimization problem for each such scenario is not practical given the tight constraints of real-time operations. To overcome this limitation, this paper proposes to learn an optimization proxy for SCED, i.e., a Machine Learning (ML) model that can predict an optimal solution for SCED in milliseconds. Motivated by a principled analysis of the market-clearing optimizations of MISO, the paper proposes a novel just-in-time ML pipeline that addresses the main challenges of learning SCED solutions, i.e., the variability in load, renewable output and production costs, as well as the combinatorial structure of commitment decisions. A novel combined classification-plus-regression architecture is also proposed, to further capture the behavior of SCED solutions. Numerical experiments are reported on the French transmission system, and demonstrate the approach’s ability to produce, within a time frame that is compatible with real-time operations, accurate optimization proxies that produce relative errors below 1%. • Online risk estimation in power systems requires fast optimization proxies. • The variability of load, renewables, commitments, energy offers, complicates the learning. • The proposed just-in-time learning pipeline is grounded in ISOs’ operations. • A combined classification-then-regression architecture improves learning performance. • Experiments are conducted on real, industrial network, over multiple days.

Bilevel Model for Protection-Branch Measurements-Based Topology Attack Against DC and AC State Estimations

A topology attack, as a special class of false data injection attacks, tampers with topology information of a system to mislead the decision of the control center. This article conducts an in-depth study on topology attacks that aim to interfere with the judgment in topology information and pose potential damage by tampering with measurement data and protection information on branches, namely, protection-branch measurements-based topology attacks (PBT attacks). To achieve PBT attacks in actual networks, we study the protection settings and mechanisms in term of branches including transformers and transmission lines. Then, for the first time, we develop a bilevel model based on the protection configuration from the perspective of security-constrained economic dispatch. Meanwhile, since a bilevel model is constructed against dc state estimation, a conversion method in constructing attack vectors under PBT attacks against ac power system is proposed, which makes PBT attacks more suitable for actual power systems and more concealed. In a set of case studies on an IEEE 14-bus system, the simulation results verify the effectiveness of the model we proposed, analyze the vulnerability of network under PBT attacks, and then identify some critical branches that are defended to cope with PBT attacks. In addition, the comparison between PBT attacks and traditional cyber-overloaded attacks also shows a stronger threat of the studied attacks.

A Novel UPFC Model and its Convexification for Security-Constrained Economic Dispatch

Unified power flow controller (UPFC) gains growing application in power systems due to its power flow regulation ability. However, there is still a dilemma in the incorporation of UPFC into security-constrained economic dispatch (SCED). The modeling of UPFC involves nonlinear and nonconvex operational constraints, which is difficult to solve efficiently and accurately. Conventional methods adopted Taylor expansion or sensitivity analysis to realize the convexification of UPFC models, which leads to a loop structure and is subject to initial point choice. In this paper, a novel three-terminal injected UPFC model is proposed. In the proposed model, the voltage source variables are eliminated completely. Instead, only power injection variables are introduced to equivalently describe physical characteristics and constraints of UPFC. The nonlinear and nonconvex operational constraints of UPFC are transformed into mixed integer second-order cone form. Moreover, compared with conventional UPFC models, the control characteristic of UPFC is considered in a more accurate and practical manner in the proposed SCED, which helps to prevent potential risks of power flow over-limit under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -1 contingencies. Simulation results show the effectiveness and efficiency of the established solution.

A Cardinality Minimization Approach to Security-Constrained Economic Dispatch

We present a threshold-based cardinality inimization formulation for the security-constrained economic dispatch problem. The model aims to minimize the operating cost of the system while simultaneously reducing the number of lines operating in emergency operating zones during contingency events. The model allows the system operator to monitor the duration for which lines operate in emergency zones and ensure that they are within the acceptable reliability standards determined by the system operators. We develop a continuous difference-of-convex approximation of the cardinality minimization problem and a solution method to solve the problem. We also present mixed-integer programming reformulation of the cardinality minimization problem. Our numerical experiments demonstrate that the cardinality minimization approach reduces the overall system operating cost as well as avoids prolonged periods of high electricity prices during contingency events.

An Enhanced Energy Management System Including a Real-Time Load-Redistribution Threat Analysis Tool and Cyber-Physical SCED

It is possible to launch undetectable load-redistribution (LR) attacks against power systems even in systems with protection schemes. Therefore, it is imperative to detect LR attacks in power systems and establish corrective actions to provide secure dispatch points. This paper develops a systematic real-time LR threat analysis (RTLRTA) tool to flag LR attacks and identify all affected transmission assets. Since attackers might introduce some forms of random strategies to create LR attacks, we introduce different optimization models to generate random LR attacks to determine accurate thresholds for our detection index and test the tool’s functionality. Additionally, based on an estimation for the actual loads in the post-attack stage, we design a set of physical line flow security constraints (PLFSCs) that can be added to the existing security-constrained economic dispatch (SCED) models. This leads to appropriate responses to the identified LR attacks and provides secure dispatch points. We generate multiple scenarios of LR attacks and random errors for different target lines in the 2383-bus Polish test system to validate our proposed methods’ accuracy and functionality in detecting LR attacks and responding to them.

A linear outer approximation of line losses for DC-based optimal power flow problems

This paper proposes a novel and simple linear model to capture line losses for use in linearized DC models, such as optimal power flow (DC-OPF) and security-constrained economic dispatch (SCED). The Line Loss Outer Approximation (LLOA) model implements an outer approximation of the line losses lazily and typically terminates in a small number of iterations. Experiments on large-scale power systems demonstrate the accuracy and computational efficiency of LLOA and contrast it with classical line loss approaches. The results seem to indicate that LLOA is a practical and useful model for real-world applications, providing a good tradeoff between accuracy, computational efficiency, and implementation simplicity. In particular, the LLOA method may have significant advantages compared to the traditional loss factor formulation for multi-period, stochastic optimization problems where good reference points may not be available. The paper also provides a comprehensive overview and evaluation of approximation methods for line losses.

Economic Loss Utilized Probabilistic Defense against Load Redistribution Attacks by Selecting Optimal Critical Measuring Units

State Estimation (SE) reflects the real time operation of power system network in the present cyber-physical power world. However, prior research works depict that bad/false undetectable data can be injected into the system on compromising measuring devices like Remote Terminal Units or Phasor Measurement Units. If an attacker intrudes into the cyber network and injects successful undetectable bad data, then that attack is popular as False Data Injection Attack (FDIA). One practical FDIA is Load Redistribution Attack (LRA), which target bus active power injections and line active power flows. LRA harms SE and subsequently disturbs Security Constrained Economic Dispatch (SCED) which result in severe rise of power generation and load shedding costs. Hence to maintain grid’s security, defense is one of the optimistic options. Attacker or defender won’t have access or control over all units. So, certain critical measuring units must be considered to attack or defend the system. In this research article, a procedure is developed to select optimal critical units subjected to all possible attack resources and load variations. The developed procedure is analyzed on three loading scenarios of modified IEEE-14 bus test system. These critical units are set as basis to find an optimal attack-defense strategy among possible strategies, which is accomplished by static zero-sum game theory in which economic loss is utility. This study provides an in-sight of consequences due to LRA, critical units’ selection under load variations and probabilistic optimal attack-defense strategy of the modified IEEE-14 bus system at three loading conditions.Graphical Abstract

Security-constrained economic dispatch exploiting the operational flexibility of transmission networks

Dynamic line rating (DLR) and flexible ac transmission system (FACTS) are two technologies to enhance the utilization of existing transmission lines and exploit the inherent transmission-side flexibility. This paper coordinates DLR and FACTS in a two-stage security-constrained economic dispatch (SCED) model to enhance the power system flexibility in N-K contingency management and reduce operational cost. To utilize DLR while handling its uncertainty, spatial–temporal joint chance constraints (JCCs) are used. A scalable reformulation method for these JCCs is developed, which enables considering the spatial–temporal correlations between DLRs and co-optimizing the DLR utilization with system dispatch. To leverage the flexibility of FACTS, the adjustments of FACTS set points before and after the occurrence of any N-K line outage are modelled. The proposed SCED model is reformulated as a triple-level robust model, which avoids enumerating all possible N-K outages in the SCED model and obtains a more reasonable model size. To handle the presence of binary variables in the lowest level of the robust model, a nested column-and-constraint generation solution structure is designed. Case studies on IEEE 14 and 118-bus systems are conducted to verify the effectiveness of the proposed SCED model.

A Distributed and Robust Security-Constrained Economic Dispatch Algorithm Based on Blockchain

Distributed optimization algorithms for security-constrained economic dispatch (SCED) problems have been the subject of significant research interest in recent years. However, existing distributed SCED algorithms can be ineffective in the presence of malicious participants and inefficient in the absence of a coordinator. On the other hand, blockchain, an emerging technique known as the trust machine, has not shown its potential to address the above challenges in state-of-the-art literature. This paper proposes a blockchain-based distributed SCED algorithm. Using blockchain to form a coordination committee and enable balance among committee members, the proposed method allows the use of hierarchical SCED algorithms in the absence of a coordinator and can disable malicious participants. Numerical results show the robustness and necessity of the proposed blockchain-based SCED algorithm, by comparing the SCED results with and without blockchain.