Stochastic Load Demand Research Articles

Comparison of stability regions for a line distribution network with stochastic load demands

We compare stability regions for different power flow models in the process of charging electric vehicles (EVs) by considering their random arrivals, their stochastic demand for energy at charging stations, and the characteristics of the electricity distribution network. We assume the distribution network is a line with charging stations located on it. We consider the Distflow and the Linearized Distflow models, and we assume that EVs have an exponential charging requirement, that voltage drops on the distribution network stay under control, and that the number of charging stations N goes to infinity. We investigate the stability of utility-optimizing power allocations in large distribution networks for both power flow models by controlling the arrival rate of EVs to charging stations. For both power flow models, we show that, to obtain stability, the maximum feasible arrival rate, i.e., stability region of vehicles, is decaying as 1/N^2, and the difference between those arrival rates is up to constants, which we compare explicitly.

Performance Enhancement of an Islanded Microgrid with the Support of Electrical Vehicle and STATCOM Systems

Modern electrical power systems now require the spread of microgrids (MG), where they would be operating in either islanded mode or grid-connected mode. An inherent mismatch between loads and sources is introduced by changeable high renewable share in an islanded MG system with stochastic load demands. The system frequency is directly impacted by this mismatch, which can be alleviated by incorporating cutting-edge energy storage technologies and FACTS tools. The investigated islanded MG system components are wind farm, solar PV, Electric vehicles (EVs), loads, DSTATCOM, and diesel power generator. An aggregated EVs model is connected to the MG during uncertain periods of the generation of renewable energy (PV and wind) to support the performance of MGs. The ability to support ancillary services from the EVs is checked. DSTATCOM is used to provide voltage stability for the MG during congestion situations. The MG is studied in three scenarios: the first scenario MG without EVs and DSTATCOM, the second scenario MG without DSTATCOM, and the third scenario MG with all components. These scenarios are addressed to show the role of EVs and DSTATCOM, and the results in the third scenario are the best. The system voltage and frequency profile is the best in the last scenario and is entirely satisfactory and under the range of the IEEE standard. The obtained results show that both EVs and DSTATCOM are important units for improving the stability of modern power grids. The Matlab/Simulink program is considered for checking and validating the dynamic performance of the proposed configuration.

Decomposition-Coordination-Based Voltage Control for High Photovoltaic-Penetrated Distribution Networks under Cloud-Edge Collaborative Architecture

With the integration of high proportional photovoltaics (PVs) into distribution networks, the superposition of uncertain output power of PVs and stochastic load demand fluctuations have posed a serious challenge to voltage stability. In this paper, a multitimescale decomposition-coordination-based voltage control method is proposed under the cloud-edge cooperative architecture. The distribution network is firstly decomposed into several subnetworks. In each subnetwork, the edge computing device is equipped to realize the distributed control and provide external computing resources for the cloud center. Then, a multitimescale control scheme containing the interval dispatch stage and the real-time time-window stage is proposed. In the interval dispatch stage, a cloud-edge collaborative calculation strategy considering balanced resource allocation is well designed to obtain the global optimal power flows and the corresponding reference operating points of the voltage control equipment. Meanwhile, in the real-time time-window stage, a consensus-based voltage correction mechanism under the optimal power flow boundary constraints is designed to avoid the voltage violations caused by unexcepted power fluctuations deviating from the representative scenarios. Simulation results with the improved 33-bus and IEEE 123-bus systems have demonstrated the effectiveness of our proposed method.

Fractional Cascade LFC for Distributed Energy Sources via Advanced Optimization Technique Under High Renewable Shares

Unpredictable high renewable shares in standalone microgrid (MG) system with stochastic load demands introduces an unavoidable mismatch among loads and sources. This mismatch directly impacts the system frequency that can be mitigated via applying a suitable load frequency control (LFC) scheme. This brief proposes a maiden attempt of marine predator algorithm (MPA) assisted one plus proportional derivative with filter-fractional order proportional-integral ((1+PDF)-FOPI) controller to obtain the proper power flow management among loads and sources. The investigated MG system consists of a photovoltaic (PV) system, a wind turbine (WT) generator (WTG), and a diesel engine generator (DG) as the distributed energy sources, and an ultracapacitor (UC) and a flywheel are chosen as the energy storage elements (ESEs). Various system nonlinearities such as governor dead-band (GDB) and generation rate constraint (GRC) are also considered reflecting the practical scenario. Five state-of-the-art optimization techniques and three traditional controllers, PID, FOPID, and PI-PD, are vividly compared to assess the proposed scheme’s performance. The parametric uncertainties are considered to obtain the robust performance of the proposed control scheme. An eigenvalues-based stability evaluation of the considered plant employing the proposed LFC scheme is also included in this work. In the worst situation, the maximum frequency deviation is obtained as -0.016 Hz, which is entirely satisfactory and under the range of the IEEE standard. Finally, a modified New England IEEE-39 test bus system is chosen to perform the real-time validation.

The stochastic short-term hydropower generation scheduling considering uncertainty in load output forecasts

Load demand forecasts for short-term hydropower generation scheduling (STHGS) has stochastic essence which is impacted by multiple uncertainties from hydrometeorology, streamflow and compensation operation. These dynamically changed uncertainties propagate to startup or shutdown transition, load dispatch and water consumption of hydro-units. However, dynamic uncertainty propagation process is not expounded effectively and its effects on STHGS are ignored to some extent when planners made short-term hydropower plan, leading to potential decision error. Moreover, computation efficiency and precision are also crucial for managers to make reliable decisions and adjustments timely. To this end, framework is developed to provide efficient model solver and identify effect of uncertain load demand forecast on STHGS. The framework contains: (1) stochastic load demand forecast based on martingale model of forecast evolution (MMFE); (2) enhanced shuffled frog leaping algorithm (SFLA) incorporating parallel computing; (3) risk quantification and evolvement revelation based on risk of exceedance (ROE). The STHGS for Three Gorges hydropower station (TGHS) is studied to demonstrate framework. The stochastic STHGS model is efficient solved by algorithms proposed. The propagation of forecast uncertainty and effect of different uncertainty levels and temporal correlations on STHGS is exhibited and fully discussed based on power load scenarios dynamically updated by MMFE.

A Hybrid Optimization Algorithm for Solving of the Unit Commitment Problem Considering Uncertainty of the Load Demand

Unit commitment problem (UCP) is classified as a mixed-integer, large combinatorial, high-dimensional and nonlinear optimization problem. This paper suggests solving the UCP under deterministic and stochastic load demand using a hybrid technique that includes the modified particle swarm optimization (MPSO) along with equilibrium optimizer (EO), termed as MPSO-EO. The proposed approach is tested firstly on 15 benchmark test functions, and then it is implemented to solve the UCP under two test systems. The results are basically compared to that of standard EO and previously applied optimization techniques in solving the UCP. In test system 1, the load demand is deterministic. The proposed technique is in the best three solutions for the 10-unit system with cost savings of 309.95 USD over standard EO and for the 20-unit system it shows the best results over all algorithms in comparison with cost savings of 1951.5 USD over standard EO. In test system 2, the load demand is considered stochastic, and only the 10-unit system is studied. The proposed technique outperforms the standard EO with cost savings of 40.93 USD. The simulation results demonstrate that MPSO-EO has fairly good performance for solving the UCP with significant total operating cost savings compared to standard EO compared with other reported techniques.

A stochastic load demand-oriented synergetic optimal control strategy for variable-speed pumps in residential district heating or cooling systems

For a residential district heating or cooling (RDHC) system in the “part-time part-space (PTPS)” service mode, the thermal load demands of end users are notably stochastic.To reducing the energy consumption of centralized variable-speed pumps (VSPs) in RDHC systems, this study presents a stochastic load demand-oriented synergetic optimal control strategy for VSPs in RDHC systems. In this strategy, the spatial and temporal distribution of the stochastic load demands (SLDs) in a residential district is predicted using the stochastic occupant behavior (SOB) method. The operation regulation of the RDHC system is mathematically described based on graph theory. A synergetic optimization mathematical model is developed based on each end user’s SLD as well as the operation regulation characteristics of the RDHC system. This synergetic optimization mathematical model is subsequently solved using particle swarm optimization (PSO) algorithm. Thus, an optimal hourly pump frequency ratio is obtained. A case study is performed to comprehensively compare the proposed synergetic optimal control (SOC) strategy with the conventional constant pressure difference control (CPDC) strategy. The results show that for the same load demands, the energy consumption of the pumps throughout the heating season under the SOC strategy is 62.9% lower than that under the CPDC strategy.

Incorporating high-resolution demand and techno-economic optimization to evaluate micro-grids into the Open Source Spatial Electrification Tool (OnSSET)

For decades, electrification planning in the developing world has often focused on extending the national grid to increase electricity access. This article draws attention to the potential complementary role of decentralized alternatives – primarily micro-grids – to address universal electricity access targets. To this aim, we propose a methodology consisting of three steps to estimate the LCOE and to size micro-grids for large-scale geo-spatial electrification modelling. In the first step, stochastic load demand profiles are generated for a wide range of settlement archetypes using the open-source RAMP model. In the second step, stochastic optimization is carried by the open-source MicroGridsPy model for combinations of settlement size, load demand profiles and other important techno-economic parameters influencing the LCOE. In the third step, surrogate models are generated to automatically evaluate the LCOE using a multivariate regression of micro-grid optimization results as a function of influencing parameters defining each scenario instance. Our developments coupled to the OnSSET electrification tool reveal an important increase in the cost-competitiveness of micro-grids compared to previous analyses.

Latin Hypercube Sampling Method for Location Selection of Multi-Infeed HVDC System Terminal

Owing to the stochastic states of power systems with large-scale renewable generation, the impact of high-voltage direct current (HVDC) systems on the stability of the power system should be examined in a probabilistic manner. A probabilistic small signal stability assessment methodology to select the best locations for multi-infeed high-voltage direct current systems in alternating current (AC) grids is proposed in this paper. The Latin hypercube sampling-based Monte Carlo simulation approach is taken to generate the stochastic operation scenarios of power systems with the consideration of several stochastic factors, i.e., load demand and power generation. The damping ratio of the critical oscillation modes and the controllability of power injection to oscillation modes are analyzed by the probabilistic small signal stability. A probabilistic index is proposed to select the best locations of high-voltage direct current systems for improving the damping of the oscillation modes. The proposed methodology is applied to an IEEE 39 bus system considering the stochastic load demand and power generation. The results of probabilistic small signal stability assessment and a time-domain simulation show that the installation of a high-voltage direct current system on the selected locations can effectively improve the system damping.

Optimal reactive power dispatch with uncertainties in load demand and renewable energy sources adopting scenario-based approach

Optimizing reactive power flow in electrical network is an important aspect of system study as the reactive power supports network voltage which needs to be maintained within desirable limits for system reliability. A network consisting of only conventional thermal generators has been extensively studied for optimal active and reactive power dispatch. However, increasing penetration of renewable sources into the grid necessitates power flow studies incorporating these sources. This paper presents a formulation and solution procedure for stochastic optimal reactive power dispatch (ORPD) problem with uncertainties in load demand, wind and solar power. Appropriate probability density functions (PDFs) are considered to model the stochastic load demand and the power generated from the renewable energy sources. Numerous scenarios are created running Monte-Carlo simulation and scenario reduction technique is implemented to deal with reduced number of scenarios. Real power loss and steady state voltage deviation of load buses in the network are set as the objectives of optimization. Success history based adaptive differential evolution (SHADE) is adopted as the basic search algorithm. SHADE has been successfully integrated with a constraint handling technique, called epsilon constraint (EC) handling, to handle constraints in ORPD problem. The effectiveness of a proper constraint handling technique is substantiated with case studies for deterministic ORPD on base configurations of IEEE 30-bus and 57-bus systems using SHADE-EC algorithm. The single-objective and multi-objective stochastic ORPD cases are also solved using the SHADE-EC algorithm. The results are discussed, compared and critically analyzed in this study.

Innovative appraisement of smart grid operation considering large-scale integration of electric vehicles enabling V2G and G2V systems

Upgrading the internal combustion engine (ICE) driven cars to the electric vehicles (EVs) offers the opportunity to reduce the fossil fuel consumption, emission rates and total driving costs. However, the large scale utilization of the EVs introduces a stochastic load demand to the power grid. The effect of EVs charging demand on the distribution network operation should be investigated properly. This paper proposed a novel model to study the effects of power exchange between the grid and EVs on the power system demand profile, the operation stability index, and the reliability indices. To this end, the operation instability indices are introduced by the range and standard deviation of the load factor of the network components to evaluate the system stability. Further, the CAIFI,11Customer Average Interruption Frequency Index. SAIDI,22System Average Interruption Duration Index. SAIFI,33System Average Interruption Frequency Index. and ASAI44Average Service Availability Index. reliability indices are calculated for various vehicle-to-grid (V2G) and grid-to-vehicle (G2V) power level to estimate the impact of different level of power exchange on system reliability. We introduced an EV charging scheduling approach which considers the specification of Li-Ion battery and the limitations for increasing battery life. The power exchange profile for V2G is also calculated using the constant power method to discharge the energy at different levels for times which cars are parked at the workplace. Due to the stochastic nature of EVs, the minimal path method is used to compute the stability and reliability parameters and the backward–forward algorithm is used to load flow analysis. The proposed model is evaluated via modified IEEE 33-bus test system.

Statistical Cooperative Power Dispatching in Interconnected Microgrids

Load demand management in the context of grid-connected microgrids is the scope of this paper. This issue is formulated as a power dispatching problem between distributed power sources with the objective of grid operational cost minimization. Under the assumption of time-varying demands and supplies at individual microgrids, a cooperative power dispatching algorithm of interactions among microgrids is proposed for power sharing within the grid. This is done through a communication infrastructure in the grid and a set of defined parameters known as purchase prices at individual microgrids. As a result of this algorithm, power flows within the grid are regulated to smooth power generations at microgrids despite the stochastic load demands. Numerical results demonstrate the effectiveness of the proposed load management scheme in comparison with no power sharing scheme in the grid operational cost point of view. Moreover, optimal solution of the power problem verifies these results.

Optimal Generation Scheduling of Hydrothermal Power Systems

In this paper decomposition and coordination techniques are applied to minimize the operation al cost of hydrothermal power systems. Through this for muXation large systems are dealt with by a more general and precise model that includes thermal operation costs and hydroelectric power generation as nonlinear functions, water head variations, stochastic load demands, hydraulic networks with cascade plants, time delays, and spilling. An economic interpretation and an example are given.