Load Uncertainty Research Articles

Unit commitment of power systems considering system inertia constraints and uncertainties

AbstractLarge‐scale integration of renewable energy into the power grid results in a lack of system inertia, posing challenges to the optimal operation and scheduling of systems considering frequency stability. This article proposes a unit commitment model that considers both inertia constraints and the uncertainty of load and renewable energy. First, the time‐domain expression of the system frequency response is calculated based on the aggregated System Frequency Response (SFR) model, considering the system's maximum frequency deviation and the maximum Rate of Change of Frequency (RoCoF) limit. This calculation determines the minimum inertia requirement for the system. Furthermore, inertia constraints suitable for mixed‐integer programming model are derived to address the nonlinearity of conventional frequency constraints. Second, considering the uncertainties of load and wind energy from renewable sources, a unit commitment model with inertia constraints is constructed, and a robust method is used to solve the uncertainties. Finally, the accuracy of the proposed inertia constraints and unit commitment model is validated using case study of IEEE standard test cases and a provincial power grid in China.

A new multi-objective-stochastic framework for reconfiguration and wind energy resource allocation in distribution network incorporating improved dandelion optimizer and uncertainty

Improving the reliability and power quality of unbalanced distribution networks is crucial for ensuring consistent and reliable electricity supply. In this research, multi-objective optimization of unbalanced distribution networks reconfiguration integrated with wind turbine allocation (MORWTA) is implemented considering uncertainties of networks load, and also wind power incorporating a stochastic framework. The multi-objective function is defined by the minimization of power loss, voltage sag (VS), total harmonic distortion (THD), voltage unbalance (VU), energy not-supplied (ENS), system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), and momentary average interruption frequency (MAIFI). A new improved dandelion optimizer (IDO) with adaptive inertia weight is recommended to counteract premature convergence to identify decision variables, including the optimal network configuration through opened switches and the best location and size of wind turbines in the networks. The stochastic problem is modeled using the 2m + 1 point estimate method (PEM) combined with K-means clustering, taking into account the mentioned uncertainties. The proposed stochastic methodology is implemented on three modified 33-bus, and unbalanced 25-, and 37-bus distribution networks. The results demonstrated that the MORWTA enhanced all study objectives in comparison to the base networks. The results also demonstrated that the IDO had superior capability to solve the deterministic- and stochastic-MORWTA in comparison to the conventional DO, grey wolf optimizer (GWO), particle swarm optimization (PSO), and arithmetic optimization algorithm (AOA) in terms of achieving greater objective value. Moreover, the results demonstrated that when the stochastic-MORWTA model is considered, the power loss, VS, THD, VU, ENS, SAIFI, SAIDI, and MAIFI are increased by 18.35%, 9.07%, 10.43%, 12.46%, 11.90%, 9.28%, 12.16% and 14.36%, respectively for 25-bus network, and also these objectives are increased by 12.21%, 10.64%, 12.37%, 9.82%, 14.30%, 12.65%, 12.63% and 13.89%, respectively for 37-bus network compared to the deterministic-MORWTA model, which is related to the defined uncertainty patterns.

Two-Stage Robust Optimization of Integrated Energy Systems Considering Uncertainty in Carbon Source Load

Integrated Energy Systems (IESs) interconnect various energy networks to achieve coordinated planning and optimized operation among heterogeneous energy subsystems, making them a hot topic in current energy research. However, with the high integration of renewable energy sources, their fluctuation characteristics introduce uncertainties to the entire system, including the corresponding indirect carbon emissions from electricity. To address these issues, this paper constructs a two-stage, three-layer robust optimization operation model for IESs from day-ahead to intra-day. The model analyzes the uncertainties in carbon emission intensity at grid-connected nodes, as well as the uncertainty characteristics of photovoltaic, wind turbine, and cooling, heating, and electricity loads, expressed using polyhedral uncertainty sets. It standardizes the modeling of internal equipment in the IES, introduces carbon emission trading mechanisms, and constructs a low-carbon economic model, transforming the objective function and constraints into a compact form. The column-and-constraint generation algorithm is applied to transform the three-layer model into a single-layer main problem and a two-layer subproblem for iterative solution. The Karush–Kuhn–Tucker (KKT) condition is used to convert the two-layer subproblem into a linear programming model. A case study conducted on a park shows that while the introduction of uncertainty optimization increases system costs and carbon emissions compared to deterministic optimization, the scheduling strategy is more stable, significantly reducing the impact of uncertainties on the system. Moreover, the proposed strategy reduces total costs by 5.03% and carbon emissions by 1.25% compared to scenarios considering only source load uncertainty, fully verifying that the proposed method improves the economic and low-carbon performance of the system.

Wavelet-based convolutional neural network for non-intrusive load monitoring of next generation shipboard Power Systems

In this study, a non-intrusive load monitoring (NILM) framework is developed for next generation shipboard power systems (SPS) based on a discrete wavelet transform signal processing and a convolutional neural network (CNN). We have applied the developed NILM method to a four-zone medium voltage direct current (MVDC) SPS to evaluate the effectiveness of the proposed method. Each zone of the MVDC SPS consists of multiple components, such as propulsion load, pulsed load, high ramp rate load, cooling load, and hotel load. The current signals from the main generators are the main inputs to the NILM model. The current signals are first processed through a discrete wavelet transform to create a coefficient vector that reflects the status of all the components in each zone. Then, a multi-class classification problem is formulated and solved using a CNN architecture model to monitor the load statuses in real time. The results of case studies show that the developed NILM model in comparison with benchmark methods can (i) accurately monitor the status of all components with a total accuracy of over 98%, (ii) identify unique pulsed loads with a total accuracy of over 99%, and (iii) sustain the functionality of load monitoring under extreme events such as cyber/physical attacks, load uncertainty, and noisy inputs.

An improved meta-heuristic method for optimal optimization of electric parking lots in distribution network

In this study, a stochastic multi-objective structure for optimization of the intelligent electric parking lots (EPLs) is implemented in the distribution network for minimizing the power losses annual costs, power purchased from the main grid, unsupplied energy of subscribers, cost of vehicles to the grid as well as minimizing the network voltage deviations considering battery degradation cost (BDC) and network load uncertainty (NLUn). In this research, the unscented transformation method (UTM) is used for NLUn modeling and this method is easily applicable and has a low computational cost. An improved meta-heuristic algorithm named improved fire hawks optimization (IFHO) is utilized for decision variables finding defined as the site and size of the EPLs in the distribution network. The conventional fire hawks optimization (FHO) algorithm is inspired by the fire hawks foraging behavior and in this research, the Taylor-based neighborhood technique (TBNT) is used to reduce the dependency and the possibility of becoming trapped in local optimal. To evaluate the proposed methodology, the simulations are implemented in three scenarios (1) EPLs optimization without BDC and NLUn based-UTM, (2) EPLs optimization with BDC and without NLUn, and (3) EPLs optimization with BDC and NLUn. The results of the third scenario considering BDC and NLUn showed that the EPLs optimization integrated with a multi-objective framework by finding the EPL's optimal size and capacity in the network via the IFHO has reduced the annual losses, voltage deviations, ENS cost, and substation cost by 21.06%, 12.15%, 70.82%, and 39.10%, respectively compared to the base distribution network. Additionally, the results demonstrated that incorporating the BDC and NLUn, the annual losses, voltage oscillations, ENS cost, grid cost, and EPLs have increased in comparison with the EPLs optimization without BDC and NLUn based-UTM. In addition, the TBNT based-IFHO superiority has been confirmed in different scenarios by achieving better values of the objectives and also obtaining the convergence process with lower convergence tolerance and higher convergence accuracy.

Robust optimization of community energy sharing considering source-load uncertainty and demand response

Community energy consumption is a crucial aspect of the overall societal energy consumption landscape. The allocation rate of distributed photovoltaic (PV) systems within communities is steadily increasing. However, managing and optimizing the consumption of PV resources while mitigating the impact of their inherent randomness and volatility, along with minimizing electricity costs, presents a significant challenge. This paper proposes a mechanism for community energy sharing that utilizes rooftop PV systems, energy storage systems, and bi-directional electric vehicles. To achieve the goal of finding the minimum cost of electricity in the worst scheduling scenarios, a two-stage robust optimization model is established. This model considers the two-sided uncertainty of source and load as well as flexible load demand response. The simulation outcomes prove the proposed method's efficacy in substantially mitigating residential electricity costs and enhancing PV utilization. Notably, during peak summer demand, a substantial 24.78% reduction in electricity costs was achieved, while PV utilization witnessed a significant 16.52% increase.

Optimal Scheduling of the Active Distribution Network with Microgrids Considering Multi-Timescale Source-Load Forecasting

Integrating distributed generations (DGs) into distribution networks poses a challenge for active distribution networks (ADNs) when managing distributed resources for optimal scheduling. To address this issue, this paper proposes a day-ahead and intra-day scheduling approach based on a multi-microgrid system. It starts with a CNN-LSTM-based generation and load forecasting model to address the impact of generation and load uncertainties on the power grid scheduling. Then, an optimal day-ahead and intra-day scheduling framework for ADN and microgrids is introduced using predicted generation and load information. The day-ahead scheduling is responsible for optimizing the power interactions between ADN and the connected microgrids, while intra-day scheduling focuses on minimizing the operational costs of microgrids. The effectiveness of the proposed scheduling strategy is verified via case studies performed on a modified IEEE 33-node ADN. The results show that the network loss of ADN and the operation costs of microgrids are reduced by 17.31% and 32.81% after the microgrid is integrated into the ADN. The peak-valley difference in microgrids decreased by 13.12%. The simulation shows a significant reduction in operational costs and load fluctuations after implementing the proposed day-ahead and intra-day scheduling strategy. The seamless coordination between the day-ahead scheduling and intra-day scheduling allows for the precise adjustment of transfer power, alleviating peak load demand and minimizing network losses in the ADN system.

A multi-objective coordinating model for distribution network with EVs, energy storage, and reactive power compensation devices

Promoting electric vehicles (EVs) is regarded as an effective solution for reducing carbon emissions and addressing growing environmental concerns. However, the increasing number of EVs has significantly heightened the demand for electric power charging, posing challenges to distribution systems. Studies have shown that a coordination strategy combining various compensation devices, such as energy storage systems and reactive power compensation devices, can enhance the integration capability of EVs. Furthermore, EVs can be managed as controllable loads that can be shed at low costs, contributing to the flexibility of the distribution network. This paper explores the uncertainties of EV load sizes and the coordination of active and reactive power. A multi-objective optimization model was developed to augment the flexibility of the distribution network and mitigate the risk of load shedding. The Monte Carlo method is utilized to simulate scenarios with EV load uncertainties. To simplify the power flow calculations in the proposed convex optimization model, the Distflow equation was adopted. Case study results demonstrate that managing EV loads in the distribution network can significantly reduce load shedding costs by 80 %, and the proposed EV charging strategy can effectively eliminate load shedding costs in most scenarios.

Design of a optimal robust adaptive neural network-based fractional-order PID controller for H-bridge single-phase inverter

Adaptive Neural Network- based Fractional-order PID Control (NN-FO-PID) approach is designed for H-bridge inverter. This inverter has an LC filter to decrease the level of Total Harmonic Distortion (THD) that can affect the efficiency of the system. In addition, the reduction of THD and stability insurance of the filter are challenging performances. To fulfill this function, a fractional order proportional integrated derivative (FO-PID) controller is developed for the inverter. A few merits of the Fractional-Order notion as a useful technique include reduced sensitivity to noise and parametric fluctuation; however, for a wider range of disturbances, such as noise, this approach shows an unsuitable practical application based on its fixed gain values. Moreover, having parameters uncertainties including parametric variations, load uncertainty, supply voltage variation uplifts this challenging condition severely, and the parameters need to be adjusted once more for more dependable operations. As a result, the control parameters must be optimized once more to provide ideal operations. Here, an adaptive mechanism is proposed based on neural network structure to optimize the gains of the FO-PID controller for better performances. In real applications, this approach has some benefits, since it uses the Black-box technique, which does not necessitate a precise mathematical model of the system, resulting in a reduced computational burden, simple implementation, and reduced dependence on the model’s states. Even under extremely difficult circumstances, the artificial neural network structure effectively optimizes the FO-PID gains in real-time. This benefit can reduce the amount of THD-level for the inverter, properly. Additionally, to have a proper response in the first step condition, and trying to reduce the level of dangerous conditions, based on benefits of the ant lion optimization method, it is considered to select the initial values of the FO-PID controller gains. Here to verify the superiority of the proposed controller, PID and FO-PID controllers are offered to drive a comparison with this method, which are optimized using the PSO optimization algorithm. The analysis of simulation data shows that the suggested control strategy is appropriate for maintaining stability as well as adequately compensating for disturbances and uncertainties in the inverter. Furthermore, with the help of this controller, THD level decreased lower than 2 percent.

A two-stage optimal operation strategy for community integrated energy system considering dynamic and static energy characteristics

The community integrated energy system (CIES) can provide users with reliable and economical energy supply through centralized utilization of various energy equipment. However, due to the significant difference in inertia between different energy sources, the response speed of equipment using different energy sources varies greatly, making it difficult to cooperate well and limiting their ability to cope with source-load uncertainty. Based on this consideration, a two-stage optimal operation strategy for CIES is proposed to utilize dynamic and static energy separately. First, the dynamic and static energy are defined and divided, and their different functions are analyzed. Based on this, a two-stage optimal operation architecture is proposed. Then, a day-ahead interval optimal operation model considering dynamic and static energy matching is established. In which, the uncertainty of source and load is characterized by nonlinear interval numbers, and the interval possibility degree is used for deterministic transformation of nonlinear interval numbers. Thirdly, a dynamic and static energy replacement mechanism based on model predictive control is given, and an intra-day rolling optimal operation model considering dynamic and static energy replacement is established. Finally, a CIES is used as an example to demonstrate the rationality and effectiveness of the proposed strategy. Simulation results show that the proposed strategy can effectively utilize different types of energy equipment and significantly reduce the adverse effects of source-load uncertainty.

Optimal capacity configuration and operation strategy of typical industry load with energy storage in fast frequency regulation

As the potential and competent load-side resources for frequency response and control in modern power grids, typical industrial load can compensate for the deficiency of frequency response capability for new-type power systems. However, the operational flexibility is seriously enforced by the operation conditions uncertainties of industrial load. With “Online Calculation, and Real-time Matching” as the core, based on fuzzy mathematical theory, the coordinated operation strategy of typical industrial loads and energy storage systems (ESS) is proposed to finish fast frequency regulation (FFR) tasks. And an optimal capacity configuration model of industrial loads with ESSs is established to evaluate the whole economic profitability in FFR. Specially, in terms of algorithms, a novel Two-layer Parallel Particle Swarm Optimization and Genetic Algorithm (TPPSGA) is innovatively designed in this manuscript. Comparing with traditional heuristic algorithms, TPPSOGA improves computation speed by 6.84 times. Simulation results show that our proposed strategy can reasonably estimate the frequency capability of industrial load by membership degree function, and prove that the industrial load participating in FFR with the support of ESSs is able to get more revenue and stability than industrial load or ESSs separately is in regulation of FFR. The economic analyze in market price and ESS parameters can help the load agent to screen the suitable-type ESS and its capacity to serve for FFR and enhance the flexibility in load-side frequency regulation.

A novel improved hybrid neural network for predicting heating load in airport building

In order to guarantee the efficient and energy-saving operation and control of airport heating systems, accurate heating load prediction is extremely critical. In view of the relatively little research on heating load prediction of airport buildings, besides, out of these, the fact that the actual characteristics of the airport itself and its production operations should be considered, resulting in inferior performance. Framed in this goal, Initially, the heating area is partitioned. Subsequently, a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm synthesizes it with fuzzy entropy (FE) to decompose the heating load, and the maximum information coefficient integrated with the distance correlation coefficient is utilized for the feature selection. After that, a multi-strategy improved artificial bee colony algorithm (MIABC) algorithm is used to optimize the radial basis function (RBF)neural network and the gated recurrent unit (GRU) neural network, respectively, and the two are combined to construct the hybrid prediction model of the heating load. Finally, actual heating load data is used to verify the prediction performance of the proposed model. Besides, the results show that the root mean square error (RMSE), mean absolute percentage error (MAPE), range of relative error (RRE), and mean bias error (MBE) of the proposed model are 0.465, 1.08 %, 11.42 % and 0.082, respectively, the coefficient of determination (R2) is 0.997, and the prediction accuracy reaches 98.92 %. Additionally, it has more robustness and generalization power, effectively overcoming the heating load's uncertainties and laying a foundation for controlling, monitoring, and managing the buildings' operation.

Multi-objective robust dynamic pricing and operation strategy optimization for integrated energy system based on stackelberg game

The integrated energy system (IES) with hydrogen storage has become one of the most important developments in multi-energy coupling field, where the severe conflict of interests between different entities leads to great challenges to the economy and low-carbon operation. A multi-objective robust dynamic pricing and operation strategy optimization method based on the Stackelberg game is proposed for the hydrogen-containing energy storage (HES) IES. Firstly, the HES-IES trading framework is established based on the introduction of an integrated energy operator (IEO) and a load aggregator (LA). Secondly, a multi-objective robust Stackelberg game model is developed with the IEO as the leader and the LA as the follower, considering the minimization of operating costs and carbon emissions of the IEO and the minimization of integrated energy costs of the LA as the objectives. Finally, the compromise planning and the max-min fuzzy are addressed to solve the multi-objective model, which adopts the adaptive differential evolution (ADE) algorithm. In addition, the robust optimization (RO) with adjustable coefficients is employed to tackle uncertainties of source and load. The results show that this method can effectively balance the operating costs and carbon emissions of the system, improve the benefit of the IEO, reduce the costs of the LA, and avoid the uncertainty risk. Compared with traditional algorithms, the ADE algorithm has significant advantages in the number of iterations and solving time. In summary, the multi-objective robust dynamic pricing and operation strategy optimization proposed in this paper could effectively achieve the benefit balance between the IEO and the LA, also further improve the economy and robustness of the system and reduce carbon emissions.

A novel efficient RFEM for reliability analysis and design of multi-line dynamically installed anchor for floating offshore wind turbines

A novel multi-line dynamically installed anchor was previously proposed by the authors to allow for the mooring of multiple floating offshore wind turbine, resulting in a significant reduction in the total number and cost of anchors required for floating wind farms. Considering the spatial variability of soil properties and the uncertainty of environmental loads, the present study performs reliability analysis and design of the multi-line dynamically installed anchor. Firstly, a strategy to repeatedly use fundamental random variables is proposed and validated for reducing the number of random variables used in Karhunen-Loève expansion in the simulation of random field of soil properties when the ratio of the soil domain dimension to the scale of fluctuation is large. Then, the efficiency, accuracy, and robustness of the RFEM (random finite element method) combined with K-MCS (Kriging model and Monte Carlo simulation) based on the proposed strategy are validated through examples of random capacity of foundations. Next, the random capacities and probabilistic VHMT failure envelopes of the multi-line dynamically installed anchor in spatially variable soil are investigated. Finally, the reliability design of multi-line dynamically installed anchors is conducted and compared with that of multi-line pile anchors, in which both the spatial variability of soil and the uncertainty of loads are condidered. The results show that the costs for multi-line dynamically installed anchors are obviously less than those of multi-line pile anchors.

Decentralized coordinated optimal dispatching of multi-area interconnected electricity-gas-heat system based on inertia Bregman ADMM

The coordinated interconnection of multi-area interconnected electricity-gas-heat systems (MIEGHS) has become a typical feature of the modern energy internet. While enhancing system operational efficiency, it also introduces complexity and uncertainty into system operation. In consideration of these factors, a decentralized coordinated robust optimization scheduling framework for MIEGHS is proposed to facilitate coordinated optimization. Firstly, a two-stage robust stochastic optimal dispatching model for a single-area integrated electricity-gas-heat system (IEGHS) is established, considering the uncertainty of wind power output and load. Secondly, a decentralized self-regulation control model for MIEGHS is proposed based on the principle of consistency constraints. Next, considering both the timeliness and convergence of the traditional alternating direction method of multipliers (ADMM) in solving problems, an improved ADMM method based on inertial Bregman distance is presented for the optimized solution of the proposed model. Finally, the effectiveness and superiority of the presented model and methods are verified by three interconnected IEGHS.

Eco-environmental dispatch of power system with high penetration wind farms considering demand/source side uncertainties

In this paper, a stochastic economic-emission dispatch (EE-D) of a power system with wind farms and flexible loads is proposed. The EE-D is defined as a stochastic multi-objective optimization problem, and a heuristic hybrid multi-objective algorithm is also proposed to solve it. The proposed algorithm is a combination of the lightning search algorithm and multi-objective particle swarm optimization (hLSA-MOPSO). The simulations are conducted in two sections. In the first section, the performance of the proposed algorithm is evaluated by optimizing standard benchmark functions. In the second section, the EE-D problem is solved optimally, considering the impact of uncertainties and the participation of flexible loads, as well as without considering them. Simulations are conducted on a standard 40-unit power system that includes two wind farms. Additionally, a sensitivity analysis is performed to examine the effects of uncertainties and flexible loads on cost and emissions. The sensitivity analysis demonstrates that increasing the penetration rate of wind farms results in reduced costs and emissions. However, it also reveals that the impact of this increase diminishes as the penetration rate continues to rise. Also, the uncertainty analysis reveals that the simultaneous uncertainty of load and wind has the most significant impact on costs and emissions.

Medium-voltage feeder blocks division method considering source-load uncertainty and characteristics complementary clustering

Existing feeder block division methods fail to consider the complementary characteristics and uncertainty between power sources and loads, which result in excessive feeder blocks, low inter-block balance, and significant disparity in net load peak-valley difference. To address these issues, a medium-voltage feeder block division method that considers the uncertainty and complementary characteristics of sources and loads is proposed. Firstly, based on the probability density characteristics of sources and loads, an uncertainty model of DG output and load demand is established. Secondly, considering the constraints of block maximum load rate and feeder non-crossing, a feeder block division model is established. Additionally, a set of center circles is defined, and based on this, an improved K-means clustering algorithm is proposed. The initial clustering centers based on the center circles is set, and the clustering centers based on the arcs of the center circles corrected. And the weighted distances between power sources and clustering centers are calculated. An algorithm flow for improved K-means clustering feeder block division is designed accordingly. Finally, the case studies show that the result of block division is improved.

Stochastic Techno-Economic Optimization of Hybrid Energy System with Photovoltaic, Wind, and Hydrokinetic Resources Integrated with Electric and Thermal Storage Using Improved Fire Hawk Optimization

In this paper, a stochastic techno-economic optimization framework is proposed for three different hybrid energy systems that encompass photovoltaic (PV), wind turbine (WT), and hydrokinetic (HKT) energy sources, battery storage, combined heat and power generation, and thermal energy storage (Case I: PV–BA–CHP–TES, Case II: WT–BA–CHP–TES, and Case III: HKT–BA–CHP–TES), with the inclusion of electric and thermal storage using the 2m + 1 point estimate method (2m + 1 PEM) utilizing real data obtained from the city of Espoo, Finland. The objective function is defined as planning cost minimization. A new meta-heuristic optimization algorithm named improved fire hawk optimization (IFHO) based on the golden sine strategy is applied to find the optimal decision variables. The framework aims to determine the best configuration of the hybrid system, focusing on achieving the optimal size for resources and storage units to ensure efficient electricity and heat supply simultaneously with the lowest planning cost in different cases. Also, the impacts of the stochastic model incorporating the generation and load uncertainties using the 2m + 1 PEM are evaluated for different case results compared with the deterministic model without uncertainty. The results demonstrated that Case III obtained the best system configuration with the lowest planning cost in deterministic and stochastic models and. This case is capable of simply meeting the electrical and thermal load with the contribution of the energy resources, as well as the CHP and TESs. Also, the IFHO superiority is proved compared with the conventional FHO, and particle swarm optimization (PSO) achieves the lowest planning cost in all cases. Moreover, incorporating the stochastic optimization model, the planning costs of cases I–III are increased by 4.28%, 3.75%, and 3.57%, respectively, compared with the deterministic model. Therefore, the stochastic model is a reliable model due to its incorporating the existence of uncertainties in comparison with the deterministic model, which is based on uncertain data.

Uncertain Scheduling of the Power System Based on Wasserstein Distributionally Robust Optimization and Improved Differential Evolution Algorithm

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method.

Failure assessment of deteriorated steel light poles

Steel poles are extensively used as street light posts and various other applications within the power distribution network. For partially buried pole, the effect of corrosion below and at the ground level significantly controls the overall load capacity. In this study, number of in-service steel pole specimens extracted from field were assessed for the corrosion damage. The level of corrosion was estimated by remaining wall thickness measured using ultrasonic testing and the surface corrosion was estimated using 3D laser scanning to adopt an appropriate existing model for buried steel structures. A relationship between maximum and average corrosion pit depth and loss of embedment depth was then developed. Finally, the corrosion parameters, combined with uncertainty in loading and soil properties were employed to perform time-dependent reliability assessment for steel light poles which can be used to assist the asset maintenance team in planning the replacement or strengthening works for steel pole.