Integral planning of primary-secondary distribution systems using mixed integer linear programming

Distribution systems (DS) are a focal connection point for existing and new renewable energy sources. DS have increasing sizes; they connect increasing numbers of renewable energy sources and have a mandate to operate as financial entities seeking to maximize their profits in an electricity market. To achieve these goals, DS require highly efficient planning tools. In this paper, we propose a successive fuzzy mixed integer linear programming (MILP) method for optimally placing and sizing capacitors in a DS that explicitly models induction run wind electric generators (WEGs). The optimization problem is linearized, transformed into a fuzzy MILP model and is solved successively while updating the solution vector. The fuzzy MILP method employs fuzzy models of voltage constraints that are often violated in a planned system that lacks reactive power support. The use of fuzzy constraints makes the proposed solution method very robust by avoiding infeasibility and reducing the need for user expertise. Further, the fuzzy MILP method represents the dual objectives of capacitor cost and annual energy loss minimization as fuzzy sets with individual satisfaction functions. The method maximizes the minimum of these satisfaction functions during optimization. Tests on 69-bus and 2002-bus DS show that the method performs well and is robust.

This paper presents an approach to deal with the problem of operational planning and expansion planning of distribution systems. Operational planning is to choose a new system configuration, out of the existing system, to meet the load profile in a better way, more reliably and with fewer losses. The expansion planning considers additions to the existing system. To evaluate the goodness of a new addition, one should know how the system would operate with that new addition included-hence an operational planning problem should be solved. Thus an operational planning problem should be solved for each expansion plan to be considered. In this paper, the authors present the development of, and experience with, an evolutionary computation approach to address, and to actually solve, the operational planning and expansion-planning problems for real-size distribution systems. Results for a 385-node, 442-branch network are presented.

A constructive heuristic algorithm (CHA) to solve distribution system planning (DSP) problem is presented. The DSP is a very complex mixed binary nonlinear programming problem. A CHA is aimed at obtaining an excellent quality solution for the DSP problem. However, a local improvement phase and a branching technique were implemented in the CHA to improve its solution. In each step of the CHA, a sensitivity index is used to add a circuit or a substation to the distribution system. This sensitivity index is obtained by solving the DSP problem considering the numbers of circuits and substations to be added as continuous variables (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an efficient nonlinear optimization solver. Results of two tests systems and one real distribution system are presented in this paper in order to show the ability of the proposed algorithm.

This paper presents a new mixed-integer linear programming (MILP) model to solve the multistage long-term expansion planning problem of electrical distribution systems (EDSs) considering the following alternatives: increasing the capacity of existing substations, constructing new substations, allocating capacitor banks and/or voltage regulators, constructing and/or reinforcing circuits, and modifying, if necessary, the system's topology. The aim is to minimize the investment and operation costs of the EDS over an established planning horizon. The proposed model uses a linearization technique and an approximation for transforming the original problem into an MILP model. The MILP model guarantees convergence to optimality by using existing classical optimization tools. In order to verify the efficiency of the proposed methodology, a 24-node test system was employed.

Reactive power planning has always been a key research area in power distribution engineering; technically and economically. However, the problem needs to be revisited to consider several aspects of modern distribution systems, such as a high penetration level of renewable resources with intermittent nature; the microgrid concept and the possibility of system operation in grid-connected or isolated single microgrid mode, or isolated multiple microgrids; and probabilistic or hourly load profile. Motivated by these needs and considering all these aspects, this paper presents a generalized approach for probabilistic optimal reactive power planning in modern distribution systems. A new index is defined to probabilistically assess the success of microgrids in terms of real and reactive power adequacy and voltage limit constraints. Afterward, the reactive power planning is performed to reduce the annual energy losses of the grid-connected system and increase the defined microgrid success index. The problem formulation and solution algorithms are presented in this paper. The well-known PG&E 69-bus distribution system is selected as a test case, and through several sensitivity studies, the effect of optimization coefficients on the design and the robustness of the algorithm are investigated. A cost–benefit case study is also presented to determine the optimum total size of distributed reactive sources for the system under study.

Multi-objective planning of electrical distribution systems using dynamic programming

The rising penetration of intermittent renewable distributed generation leads to uncertainties in the planning of electric distribution networks. Fully considering the uncertainties pertinent to wind power generation, photovoltaic power generation and load demand, this paper proposes a scenariobased model for the planning of active distribution systems. The solution obtains the optimal capacities and locations of wind and photovoltaic based distributed generators in the distribution system, whilst minimizing the active and reactive power losses as well as voltage deviation. A scenario matrix is generated using the heuristic moment matching technique that captures the stochastic moments and correlation among historical wind and photovoltaic power, and electricity demand. The scenario matrix is then incorporated to propose a stochastic planning model that considers a multi-objective index for minimizing power losses and voltage deviation. Finally, the effectiveness of the proposed planning model is confirmed using case-studies in 53-bus and IEEE 123-bus distribution systems.

A comprehensive framework for optimal day-ahead operational planning of self-healing smart distribution systems

This paper aims to develop and apply an approach for short-, medium- and long-term scenario planning. Construction of water demand scenarios is of the utmost importance for planning, design and operation of distribution systems, providing useful information to promote more efficient use of water resources. The proposed approach offers a new perspective for water utilities to obtain coherent and plausible descriptive scenarios as well as realistic water demand projections. This approach was applied to network sectors in existing water distributions systems, using extensive network flow data. Descriptive scenarios for water demand, considering trends and the uncertainties of the future, were obtained, together with improved Multiple Linear Regression (MLR) models, with the inclusion of the key variable temperature and by using historical billed consumption, socio-demographic and infrastructure data. In addition, water demand projections for short- and long-term periods were obtained through the inclusion of future trends in the MLR models. Results from MLR models show enhanced empirical relations between water demand variables and water consumption key factors. This approach was validated using different distribution systems and the results have demonstrated the efficiency of the developed models for the projection of water demand.

A new parallel and decomposition approach to solve the medium- and low-voltage planning of large-scale power distribution systems

Receding horizon load restoration for coupled transmission and distribution system considering load-source uncertainty

Enhancing the resilience of power distribution systems to extreme weather events is of critical concern. Upgrading the distribution system infrastructure by system hardening and investing in smart grid technologies effectively enhances grid resilience. Existing distribution system planning methods primarily consider the persistent cost of the expected events (such as faults and outages likely to occur) and aim at improving system reliability. The resilience to extreme weather events requires reducing the impacts of the high impact low probability (HILP) events that are characterized by the tail probability of the event impact distribution. Thus, the resilience-oriented system upgrades solutions need to be driven by the risks imposed by extreme weather events on the power grid infrastructure rather than persistent costs. This paper aims to develop a risk-based approach for the long-term resilience planning of active power distribution systems against extreme weather events. The proposed approach explicitly models (1) the impacts of HILP events using a two-stage risk-averse stochastic optimization framework, thus, explicitly incorporating the risks of HILP events in long-term planning decisions, and (2) the advanced distribution grid operations (in the aftermath of the event) such as intentional islanding into infrastructure planning problem. The inclusion of risk in the planning objective provides additional flexibility to the grid planners to analyze the trade-off between risk-neutral and risk-averse planning strategies.

A randomised controlled trial comparing lateral skull computerised radiographs with or without a grid

Effectiveness of an electrical distribution system depends on the stability of its voltage profile. Several methods such as Static Compensator (SC), Thyristor Controlled Series Compensation (TCSC) and Series Capacitor have been applied for the stability of the system. However, these methods have been characterized by harmonic variation and low efficiency. Therefore, this research paper applied Shunt Switching Capacitor (SSC) on 11 kV distribution system located at Monatan, Ibadan, Oyo State in order to investigate the stability of the system during outages. Hourly data on bus voltage of the system were collected to determine the average bus voltage and voltage drop of the distribution system for stability evaluation using IEEE statutory limits method. Load Flow Model (LFM) of the distribution system was developed with incorporation of Capacitor Switching Compensation (CSC). This was solved using Kirchoff’s Current Law( KCL) analysis to improve the average bus voltage and voltage drop of the distribution system while simulation was done using MATLAB R2015a. The results of the average bus voltage and voltage drop of the distribution system were 10.5 and 4.2 , respectively. The CSC model improved the average bus voltage and voltage drop by 6 % and 33 % respectively. The research showed that incorporating capacitor switching as a compensation technique enhanced the stability of the distribution systems. The research is useful in the planning and optimization of electrical distribution systems. Keywords: Electrical Distribution System, Voltage, Capacitor Switching Compensation, Load Flow Models, Monatan 11 kV Distribution System, Voltage Drop, MATLAB. DOI: 10.7176/NCS/14-02 Publication date: August 31 st 2022

This work proposes an immune inspired memetic algorithm for the expansion planning of electric distribution systems. This algorithm is based on a clonal selection algorithm and a local search method which is built using network distance concepts abstracted from continuous spaces. The memetic algorithm is intended to find not only the optimal solution for the design conditions, but a whole set of viable solutions, that can be considered as alternatives under perturbed operation conditions. Those alternatives are used for handling with load evolution uncertainties, which are inherently related with long term evaluation of the distribution system. The post-optimization analysis of solutions has been made using a Monte Carlo simulation and a multiobjective sensitivity analysis, in order to estimate their robustness under perturbed load conditions. The results achieved by the proposed algorithm in a practical problem indicate that this method can be more suitable for designing distribution system under load evolution uncertainties.