Decision-Making for Crisis Management of Power Distribution Networks

This paper suggests a model to solve crises in power distribution network by using spreadsheets in order to make an optimum decision in this regard. Importance of crisis management in power distribution network is investigated from various aspects. Reductions in off times and immediate returns of power, as well as undistributed energy along subscribers` satisfaction are parameters considered in crisis management power distribution network. This paper solves a case about this issue by spreadsheets in order to provide a new model for decision makers to facilitate solving these kinds of problems.


Introduction
Power distribution network is the endpoint of long, expensive process of power generation, transfer and distribution.The task of this sector is to deliver generated power to subscribers and consumers.In fact, in case of failure incidence in distribution sector, all the expenses to generate and transfer power would be fruitless.On the other hand, due to extent of power distribution network, it is subject to various adverse events.Many of these events occur because of network exhaustion or unpredictable events such as atmospheric ones and unexpected events.Therefore, network reliability is a crucial parameter in distribution network exploitation.On the other hand, occurrences such as storm, flood, and earthquake results in simultaneous blackouts in distribution network.In turn, these blackouts results in subscribers` dissatisfaction as well as increase in undistributed energy of distribution sector that is considerable in terms of economic.Decision-making in such situation is a difficult and complex process that should be taken by network managers to decrease failure time and undistributed energy.Since facilities are restricted during crisis, decisions should be taken considering several parameters and attempts to find optimum.Currently, crisis management decisions are made in distribution sector practically without using advanced software models, while using existing facilities such as advanced computer models and algorithms blackout times and undistributed energy can be reduced to the lowest.In the present article, different types of decision-making models during crisis are examined and a model is presented using Excel spreadsheet to show their performance.

Necessity of Using Decision-making Models
Decision-making models can be traced back to pre-IIWW periods.At that time, many mathematicians like Kolmogorov began using linear decision-making models.After IIWW, with complexity of decision-making issues, "operational research" was introduced as an effective method to solve very complicated issues [2].In today world, company managers are faced with complex challenges.At the moment, many of successful companies in various fields try to implement different processes in format of various decisionmaking models.Currently, different issues in social, martial, and economic issues are solved using decision-making models.From environment pollution control to increase in airline profitability, all are achieved through precise computer modeling.Now, there is no successful company not using different modeling method for its decisions [1].Power distribution companies due to their important role is the field of country`s power supply, can benefit from these models to significantly increase their performance.In this article, only one example of efficient decisionmaking models during crisis is presented, though there are many models can be used in distribution companies.Major benefits of using decision-making models are: 1.A marked decrease in blackout time 2. Decrease in undistributed energy, and thus economy saving 3. Decrease in expenses of fixing outage and efficient use of existing facilities 4. Increase in subscribers` satisfaction 5. Decrease in tension and stress in workplace, and thus decrease in accidents during work In fact, it can be said that decision-making models are powerful tools guiding managers during crisis.In this article, a simple model of linear planning is introduced to make an optimal decision during crisis.Since proposed model is solved using Excel software in Windows it can easily be integrated into other network management software such as ENOX or other software.Using proposed methods and adding them to network management software can incredibly increase network management capabilities.
3 Decision-making Models and Their Implementation Decision-making models are divided into two categories: 1) deterministic models in which all parameters are assumed deterministic, and 2) probability models that are provided in uncertain situation [3].In these models occurrence of a phenomenon is dependent to its possibility.For example, entrance of a company into business context s dependent to its industry`s possible status.It has to be mentioned that in both of these categories data are qualitative or quantitative.In most of decision-making models it is tried to replace qualitative data with quantities ones.For a model to be applied in a real context, it should have some features.Figure 1 shows decisionmaking cycle and its application in real context.

Sensitivity Analysis Results Employing
The cycle in Figure 1 is consisted of 3 phases of formulation, solving, and interpretation, each of which has several subsets.Is formulation phase, it is first necessary to define the issue clearly and completely [5].In the case of crisis management of power distribution network to relove outages using existing maintainance teams with minimum time and cost is inevitable.

Model Creation
To solve all the decision-making issues there are several models that are selected according to the conditions.In crisis management of distribution network "assignment" model is selected which is a subset of "transportation" models.In this kind of model the aim is to find the best available facility assignment to capacity or external needs.For example, parts supply or medicine distribution is of important functions of this model.In crisis management of distribution network the aim is to assign maintenance groups to network incidents such that minimum outage time and undistributed energy occurs.In the example solved problem it is assumed that region power has two service centers for incidents.The number of these centers is high or low according to the area.For example, power of Shemiran region as a subset of Tehran Power Distribution Company has 3 operational zones.Nevertheless, the number and location of operational zones and groups located in them can be solved as an "operational study" problem named "Set-covering" using Excel software, but addressing this subject is out of the scope present study.Figure 2 shows a schematic of an assumed scenario in an assumed area.DOI: 10.12948/issn14531305/19.4.2015.01

Fig. 1. A schematic of an assumed crisis scenario in an area with two operational zones
In this scenario it is assumed that 14 simultaneous incidents have occurred in the network.Circles indicate defect occurrence and its number determines its type.Thus, number 1 shows outage of low voltage air network and other numbers accordingly show outage in related sectors.In this way, 1-1 is the outage number 1 and type 1.On the other hand, groups of these 3 zones are located as table (1) shows.Also, it is assumed that region groups are single-purpose and only can solve breakdowns of their own zone.To create the model, variables should be defined first.Accordingly, variables to be optimized must be determined.In this order, variable Xijk is defined as follows: Xijk= departure of group type 1 from center I to k th breakdown These variables are defined binary (1 and 0).In this way, 1 variable means related group departure towards related defect.For example, if XA12 is 1, this shows that one of group types 1 of center A has to departure towards defect type 1 with number 2. Type and number of defects are specified in Figure 2. Assumed distance of breakdowns with centers A and B are specified in table (2).Therefore, assuming constant speed of groups` cars objective function can be defined as sum of driving distance of groups that is equal to multiply of binary variable of X in the distance between center and the breakdown that is shown with variable Y. thus, objective function is as follows: Function Z should be minimized so that groups` access time to breakdown reaches to its minimum.But is minimum should be followed by certain conditions and constraints of the problem.Since number of available groups in each center is restricted according to table (1), following constraints should be considered to solve the problem.These constraints are extracted from each groups` restrictions from table (1)

Answer Analysis and Sensitivity
After solving problem and testing answer compatibility, Solver setting provides a report of answers and sensitivity analysis.Menus related to analysis and answers reports are presented in Figure 5.

Fig. 2 .
Fig. 2. Solved model using Solver Add-in of Excel

Fig 4 .Fig 5 .
Fig 4. How to determine variables and objective function in Solver

Table 2 .
Composition of expert groups located in regions