A Customer-Focused Resilience Enhancement Planning Framework in Distribution Systems Through a Leader-Follower Approach

This paper presents a novel planning framework to enhance the resilience of energy supply to customers in power distribution systems. The framework involves three key stakeholders: the regulator as the governing entity that enforces regulatory mechanisms to oversee the performance of the distribution system operator (DSO); the DSO that reinforces the infrastructure by placing emergency distributed generations and hardening sections, implements necessary operational decisions, and facilitates customers’ participation by introducing appropriate incentives; and customers who may (i) gain the desired resilience through investing in self-generation, (ii) rely on the resilience provided by the DSO along with paying the agreed-upon insurance premiums, or (iii) opt for a mix of both approaches. The proposed framework is designed through a four-step process. First, the regulatory mechanisms are established by setting a standard resilience index for the penalty and reward model as well as a revenue cap for the DSO under a revenue-cap regulation using customized optimization problems aimed at optimizing DSO’s costs without customers’ participation. Next, an integrated resilience enhancement optimization problem that coordinates the strategies of the DSO and customers is formulated as a mixed-integer linear programming model, focusing on the global objective functions of the DSO and customers. Finally, the economic benefits are distributed between the DSO and customers who are justified for investment in self-generation using a suggested method based on Monte-Carlo estimation, in which the Fisher-Yates shuffle technique and a designated optimization problem are employed. Applied to the IEEE 33-bus test system for two case studies, the proposed framework is proven to be effective in enhancing resilience, achieving regulatory objectives, and providing economic benefits for both the DSO and customers, creating a mutually beneficial scenario for all parties involved.

We propose a comprehensive framework for the optimal day-ahead scheduling of power distribution systems (PDS), based on a mixed-integer linear programming (MILP) model. The interaction between transmission system operator (TSO) and distribution system operator (DSO) is considered, where TSO informs DSO of the day-ahead forecast concerning the expected power flow (PF) commitment at the TSO-DSO interconnection points and the violation costs. We propose a MILP model to determine the optimal voltage and power settings of distributed energy resources (DERs), such as dispatchable distributed generators and energy storage units and optimal adjustments of capacitor banks controlled by current. The objective function includes the minimization of energy losses, voltage violations, power curtailment of DERs using volt-watt strategy, and violation of TSO-DSO interconnection PF commitment. Furthermore, we propose a method to estimate the degree of uncertainty in the PF commitment. Therefore, the proposed method can help achieve an optimal operation of the distribution system; in addition, the TSO can best model uncertainty at TSO-DSO interface points and thereby procure reduced amounts of resources to address these uncertainties. Numerical results obtained for a system based on real data highlight the several potential applications of the proposed framework.

Traditionally, the distribution system operator (DSO) is responsible for the reliable operation of power distribution systems. However, the advent of micro-grids in electric power distribution systems promotes a new role of DSO where it is responsible for aggregating the widely dispersed distributed energy resources (DERs), small thermal generation units, and flexible loads into the electricity markets. This paper presents an optimal demand response (DR) bidding framework for aggregators in the distribution network, that help integrate the uncertainty of the power output of the wind turbine. In the proposed framework, the load aggregators collect and submit DR offers to the DSO to make their contribution to the market operation. The load reduction offers include load curtailment, load shifting, and the generation from DERs. The DSO solves market clearing problem using the proposed DR model for the day-ahead market using a mixed-integer linear programming (MILP) model. The proposed approach for DR participation and market clearing is implemented using a 6-bus test system, and the merits of the proposed DR model are demonstrated using two cases for hourly unit commitment and ten scenarios for wind variability.

Power distribution systems (PDS) are the infrastructure and equipment used to distribute electricity from the transmission system to end-users, such as homes and businesses. PDS are usually designed to operate in a radial mode, where power flows from one substation to the end user through a series of feeders. The extension of distribution lines to attend new customers along with the growing demand for electricity result in increased energy losses and voltage reductions. Various solutions have been proposed to solve these issues, such as selecting the optimal set of conductors, optimizing the placement of voltage regulators, using capacitor banks, reconfiguring the distribution system, and implementing distributed generation. A well-known approach for reducing energy losses and enhancing voltage profile is the optimal conductor selection (OCS). While this can be beneficial, it may not be sufficient to fully reduce technical losses and improve the system voltage profile; therefore, it must be combined with other strategies. This paper presents a new approach that combines the OCS with the optimal placement of capacitor banks (OPCB) to minimize technical losses and improve the voltage profile in PDS. The main contribution of this paper is the integration of these two problems into a single mixed integer linear programming (MILP) model, therefore guaranteeing the achievement of globally optimal solutions. Three test systems of 27, 69, and 85 buses were used to illustrate the effectiveness of the proposed modeling approach. The results indicate that the combination of OCS and OPCB effectively minimizes energy losses and enhances the voltage profile. In all cases, the solutions obtained by the proposed MILP approach were better than those previously reported through metaheuristics for the combined OCS and OPCB problem.

An aggregator undertakes multiple tasks in smart distribution network such as energy trading, grouping and providing market access to demand response (DR) resources, coordinating distributed generations (DG), efficiently controlling smart appliances of consumers and communicating with the distribution system operator (DSO). In this project, a bi-Ievel model is proposed for a load aggregator of day-ahead energy procurement in a smart distribution system with DR and DG into consideration. The upper level simulates the decision-making process of a load aggregator to maximize its profit through optimal energy purchase and flexible energy management strategy with DG power outputs uncertainties. The decision-maker of the lower level is DSO, who takes the responsibility for the economic dispatch of the distribution system and determines load shedding in a comprehensive way. A single level mixed-integer linear programming (MILP) model is developed for considering two level problems with the idea of mathematical programming problem with equilibrium constraints (MPEC) and Karush-Kuhn-Tucker (KKT) condition. A highly efficient commercial solver CPLEX is utilized to solve the developed model. Finally, a modified IEEE 33-bus distribution system is employed to demonstrate the essential features of the developed model and method.

Mixed Integer linear programming and constraint programming models for the online printing shop scheduling problem

Having multiple optimal solutions to weights affects to a great extent the consistency of operations related to weights. The cross efficiency method is the most frequently studied topic in data envelopment analysis (DEA) literature. Originally, the cross efficiency method included the efficiency evaluations that were obtained for a decision making unit (DMU) by the classical DEA for the reuse of optimal weights in other DMUs. As the optimal weights in classical DEA solutions usually have multiple solutions, this reduces the usefulness of the cross evaluation. Lam (J Oper Res Soc 61:134–143, 2010) proposed a mixed-integer linear programming (MILP) formulation based on linear discriminant analysis and super efficiency method to choose suitable weight sets to be used in cross efficiency evaluation. In this study, Lam’s MILP model has been modified to reduce the steps during the solution process. The model also becomes a linear programming model after the modification to make it easier to use and to reduce the computational complexity. Numerical examples indicate that the proposed weight determination model both reduces the steps and minimizes computational complexity. Furthermore, it has similar performance with Lam’s MILP model for the cross efficiency evaluation.

A major water and energy provider in Central Texas is the Lower Colorado River Authority (LCRA). It supplies water and electricity to over a million persons. Approximately 10 percent of that electricity is generated from hydroelectric power plants on the six dams in the Highland Lakes system on the lower Colorado River. A real-time scheduling system has been developed and is being implemented into the LCRA Energy Management System (EMS) to optimally schedule the hourly operation of thirteen hydropower generating units in concert with the three steam-electric power stations operated by the LCRA. The hydro scheduling system uses a mixed integer linear programming (MILP) model of the Highland Lakes to determine the optimal hydro generation based on forecasted power and water demands and hydrologic conditions over the next 72 hours. The MILP model maximizes hydropower generation while satisfying hourly and daily constraints on generation capacity, lake storage and flow releases. The solution to the scheduling model is provided in real-time to the EMS which uses the results to determine generation unit commitment in the LCRA power system.

Mixed-integer linear programming and constraint programming formulations for solving distributed flexible job shop scheduling problem

In this paper, we consider the job shop scheduling problem (JSS) with non-anticipatory, per-machine, sequence-dependent setup times (SDST). The contributions of this paper are twofold. First, we propose a formulation in the form of a mixed-integer linear programming (MILP) model to modelize the aforementioned problem. Second, we play a pioneering effort for the effective adaptation of a novel metaheuristic known as electromagnetism-like algorithm (EMA) to solve the foregoing problem under the minimization of makespan. Afterwards, we evaluate the performance of the proposed MILP model, the EMA, and other effective metaheuristic algorithms from the literature on two different sets of benchmarks: small-sized and large-sized instances. The rationale behind applying the MILP model and the other algorithms at the small-sized instances is to compare the solutions obtained by the metaheuristic algorithms and the optimal solutions obtained by the MILP model (optimality gap analysis). Subsequently, to demonstrate the competitiveness of the EMA against some effective algorithms in the literature, we conduct an experimental design based on Taillard's benchmark, which is considered as large-sized instances. The purpose of conducting this very experiment is to show whether the acceptable performance of the EMA is transferrable to large-sized instances. The computational evaluations simply manifest the superiority of our proposed algorithm vs the other high-performing algorithms over both small and large instances.

Novel MILP and CP models for distributed hybrid flowshop scheduling problem with sequence-dependent setup times

The periodic vehicle routing problem (PVRP) is an extension of the well-known vehicle routing problem. In this paper, the PVRP with time windows and time spread constraints (PVRP-TWTS) is addressed, which arises in the high-value shipment transportation area. In the PVRP-TWTS, period-specific demands of the customers must be delivered by a fleet of heterogeneous capacitated vehicles over the several planning periods. Additionally, the arrival times to a customer should be irregular within its time window over the planning periods, and the waiting time is not allowed for the vehicles due to the security concerns. This study, proposes novel mixed-integer linear programming (MILP) and constraint programming (CP) models for the PVRP-TWTS. Furthermore, we develop several valid inequalities to strengthen the proposed MILP and CP models as well as a lower bound. Even though CP has successful applications for various optimization problems, it is still not as well-known as MILP in the operations research field. This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance of the proposed MILP and CP models by modifying the well-known benchmark set from the literature. The extensive computational results show that the CP model performs much better than the MILP model in terms of the solution quality.

The self-healing ability of distribution systems (DSs) against extreme events can be significantly boosted by strategically dispatching mobile emergency resources (MERs). In recent years, the penetration of hydrogen energy in energy systems has increased dramatically. Hydrogen energy and its related infrastructure, such as hydrogen refueling stations (HRSs) and mobile fuel cell vehicles (MFCVs), exhibit great potential for enhancing the self-healing ability of DSs. In this work, a two-layer hierarchical strategy for improving the restorative self-healing ability of hydrogen-penetrated DS (HPDS) with multiple microgrids (MGs) and HRSs is proposed considering their interactions and MERs such as mobile energy storages and MFCVs. In the lower layer, an optimal energy management strategy is presented for MGs considering the coordination between hydrogen and electricity via the electrolyzer and fuel cell in the HRSs. In the upper layer, an energy sharing (ES) strategy is proposed for the distribution system operator (DSO) to dispatch MERs in order to minimize the power imbalance among MGs and reduce the unserved load. Since MERs can be dispatched for many times to swap energy and hydrogen between MGs or HRSs, the concept of the equivalent time network (ETN) is introduced, and based on the ETN, a mixed integer linear programming (MILP) model is innovatively proposed to represent the traveling pattern of MERs and to optimize their ES path among MGs. Finally, the two-layer hierarchical strategy is formulated as MILP models and solved using the commercial solver. Case studies on a modified IEEE 33 bus distribution system (DS) and a regional DS in China verify the effectiveness of the proposed strategies.

The paradigm shift in adopting electrified public transportation, enabled by long-range battery electric buses (BEBs) and associated charging infrastructure, inflict operational challenges to both power distribution and transit systems. This article takes an opportunistic look at the paradigm shift and develops a model for optimally scheduling the spatio-temporal charging flexibility of BEBs as a source of operational flexibility for power distribution systems. The proposed model co-optimizes the timing and location of BEBs' charging in the transit system with the operation of the power distribution system, while respecting the operational constraints and requirements of both power distribution and public transit systems. In the proposed model, the BEBs transit system is mathematically modeled by a graph and the associated BEB charging stations are mapped into the power distribution nodes. The BEBs' transit schedule constrains the spatio-temporal charging opportunities to all BEBs over the scheduling horizon. The proposed model is implemented on the IEEE 33-bus power distribution system coupled with the transit system of Park City, UT, USA, with BEB routes. The numerical results showcase the economic and operational benefits of the proposed model for the power distribution system operator and transit system operator.

One of the key distinctions between extreme weather events and random events in distribution systems is the level of predictability. The distribution system operator (DSO) can anticipate the upcoming extreme weather event and its effects, which is impossible in random events. Thus, the DSO can prepare the system by taking appropriate actions to tackle the upcoming event. This characteristic provides the DSO with operational situational awareness (SA) against extreme weather events. Considering this DSO’s capability in evaluating the system resilience against extreme weather events results in a more realistic resilience estimate. This paper proposes a model for resilience-oriented distribution system planning (RODP) in which the value of the DSO’s SA is considered and modeled (namely, SA-RODP). The proposed two-stage stochastic model is formulated as a mixed-integer linear programming (MILP) problem. In the first stage, hardening sections and installing emergency distributed generations (DGs), battery energy storage systems (BESSs), and automatic switches are modeled. The second stage contains the DSO’s decisions corresponding to operation scenarios. These decisions are made in two successive operation periods, namely, the preventive operation period (before the event to prepare the system) and the emergency operation period (during and after the event to mitigate the effects of the event). The DSO’s decisions in the preventive operation period are made according to each scenario, reflecting the DSO’s SA. The objective function of SA-RODP comprises the investment costs of the first stage and the expected operation cost of the second stage. The model constraints include the investment constraints and power flow and operational requirements constraints in each scenario. The model’s effectiveness is validated by several numerical simulations on the IEEE 33-bus test system. SA-RODP model simultaneously reduces the required investment cost and boosts the system resilience compared to conventional RODP frameworks in which the DSO’s SA is not considered. Further, this model increases the DSO’s capability to confront extreme weather events.