- Email: [email protected]
Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy
Energy xxx (2016) 1e10
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy Mostafa Esmaeeli a, b, Ahad Kazemi b, Heidarali Shayanfar b, Gianfranco Chicco c, Pierluigi Siano d, * a
Faculty of Industrial and Computer Engineering, Birjand University of Technology, Birjand, Iran Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran Energy Department, Politecnico di Torino, Torino, Italy d Department of Industrial Engineering, University of Salerno, Fisciano, Italy b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2015 Received in revised form 31 October 2016 Accepted 5 November 2016 Available online xxx
Technical and financial uncertainties may put distribution system planning at risk. In this paper, a new risk-based planning method is proposed which pays more attention to low-probability and high consequences events in energy supplying systems. The proposed approach is adopted for determining the optimal structure of a Medium Voltage network where risk-based determination of the radial network structures is implemented through an uncertainty model of the system's variables based on discrete states, called scenarios. The cost of distribution system planning consists of investment cost, maintenance cost, power losses cost, reliability cost, and technical risk cost. In this paper, appropriate models are proposed to consider the monetary effects of technical risks. The proposed approach is applied to a test system consisting of 52 electric load points and two substations. It is observed that the proposed risk-based method for planning the optimal network structure can properly reduce the cost of extreme events, therefore reducing the concerns of distribution system operators about these possible situations. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Branch exchange method Energy demand Feeder routing Risk Uncertainty
1. Introduction Distribution system planning and the economic and reliable design of distribution networks are important challenges for electrical distribution companies. In an electrical distribution network, a feeder is the group of electrical lines (overhead lines or cables) starting from the supply point (an electrical substation) and connecting a group of loads. Each feeder has a radial topology, and in general multiple feeders start from an electrical substation. For an electrical distribution system, the number of lines existing in the system is larger than the number of loads, in such a way to have a number of redundant lines maintained open in each radial configuration of the network. The lines to maintain open are chosen during the definition of the paths (or routes) with which the loads are served, in such a way to serve all the loads and to maintain the network radial. This selection is indicated as feeder routing in the technical literature. The planning of distribution networks can be divided into two
* Corresponding author. E-mail address: [email protected] (P. Siano).
sub-problems including substation location and feeder routing. Substation location, size and its services are determined in the first problem, while the size of the feeders and their routes are indicated in the second one. In this paper it is assumed that the substations are already positioned, and the optimal feeder routing is discussed. Different approaches for feeder routing have been presented during past years. There are large numbers of discrete variables in distribution system planning and various mathematical programming techniques, such as mixed integer programming [1], branch and bound methods [2], and transportation [3] have been used to solve the problem of feeder routing optimization. However, by using these models, the solution time increases and it is difficult to achieve the optimal solution. In recent years, metaheuristic methods such as particle swarm optimization (PSO) [4], genetic algorithm [5], and teaching learning optimization [6] have been extensively used in distribution network planning. Using these optimization techniques, the nonlinearity of the cost function and constraints can be easily incorporated in the formulation. However, the solution of these methods may be a local optimum. A different approach based on branch-exchange techniques has been applied in deterministic planning of distribution system [7] and in long
http://dx.doi.org/10.1016/j.energy.2016.11.021 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
2
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Nomenclature s CTot CEx CInv s CInt CLs s COM s CTR b;s COC n;s CUOV
t;s CODT
CVaRa OF VaRa Dsn FICb FMCb FPð:Þ Ibrated Ibs s Kel s Kpl
Total cost of planning in Scenario s ($) Expected planning cost over a set of scenarios ($) Investment cost ($) Interruption cost in Scenario s ($) Power losses cost in Scenario s ($) Maintenance cost during in Scenario s ($) Technical risk cost in Scenario s ($) Cost of overcurrent risk in feeder b in Scenario s ($) Cost of undervoltage/overvoltage risk at node n in Scenario s ($) Cost of distribution transformer overload risk for transformer t in Scenario s Conditional VaR with probability level a percent Objective function Value at risk with the probability level a percent Energy demand of node n in Scenario s (kVA) Feeder installation cost ($/km) Feeder maintenance cost ($/km) Penalty function of voltage quality (pu) Thermal rating of feeder b (A) Current of feeder b in Scenario s (A) Electricity price in Scenario s ($/kWh) Economic savings per active power reduction in the peak power for Scenario s ($/kW)
term planning considering uncertainties [8]. This approach is a mathematical method which finds a pseudo-optimal solution in an admissible computational time also for large-scale real distribution networks. The problem of power systems' planning has been traditionally developed using deterministic models. However, in recent decades, new probabilistic models have been introduced to consider uncertainties in power systems. In this approach, the goodness of a solution can be measured through a particular set of scenarios, each one with a given probability. The expected cost over the set of considered scenarios is calculated and the optimal solution is chosen to minimize this expected value. However, this planning approach has encountered several challenges in its generalized adoption [9]. Furthermore, in recent years, a risk analysis approach has been suggested for power system planning and has been well developed in some literature contributions to assess [10] and manage [11] the operational risk of power system. This approach chooses the preferred scheme while considering its cost in extreme events and is well understood by planners who have experienced real and practical problems. The word risk considers both the probability of occurrence of an event that harms or damages people or equipment, and its consequences generally assessed in economic terms. The important issue that should be considered in power system planning is that it is not possible to have a plan without risk. But the risk should be managed and a certain level of risk should be accepted when it is technically and economically admissible. The risk-based planning mainly concentrates on the decision about the admissible level of risk. In electrical distribution networks, the sources of risks are some parameters having probabilistic behaviors. In order to manage these risks, the risk-based planning of distribution networks is used which pays more attention to low-probability and high consequences events. A risk-based allocation of distribution system
Lb LLb ð:Þ
Length of feeder b (km) Loss of feeder b life in Scenario s as a function of feeder current (pu.$) LOLst Loss of life transformer t in scenario s (year) ocn Outage cost for load point n ($/kWh) PNLmax Maximum damage cost to a customer due to undervoltage or overvoltage ($/kW) rb Resistance of the branch b (kU/km) TICt Transformer t installation cost ($) Vns Node voltage in Scenario s (kV) Vmin Minimum allowed voltage (kV) acf Annual cost factor cosf Loads' Power factor DNb Downstream nodes of branch b LF Load factor LSF Load loss factor Nb Number of branches Nn Number of load points Ns Number of scenarios Nt Number of distribution transformers rd Discount rate rs Probability of Scenario s jRf ; jDf ; jEp ; jDl Sets of discrete distributions of failure rate, failure duration, energy price, and load, respectively
maintenance resources is presented in Ref. [12], where a method to allocate maintenance resources to various distribution system assets is proposed. To determine the effects of maintenance, a predictive reliability assessment tool is developed. A risk management method is introduced in Ref. [13] to reduce the negative electrical vehicles (EVs) effects, where stochastic models of EVs, renewable resources, and availability of devices are proposed to evaluate the system reliability comprehensively. It is assumed that the system is at risk when the energy demand is more than the generation capacity. By using the managed charging of EVs, the risk level of smart grid and its adequacy have been improved. In distribution planning, most of papers are not considering the risk concept and its monetary consequences. In this paper, the consequent impacts of risk and probabilistic events on the distribution network are modeled as a monetary term called cost of technical risks. A risk-based method for optimal routing of MV feeders is proposed and the effect of technical risks on the distribution network is investigated. In the presented approach, the probable events, including overcurrent of MV feeders and variations of node voltages more than acceptable values, are considered as technical risks. The feeder routing problem is solved using a customized version of the branch exchange method where the optimal configuration of distribution network is determined in accordance to a predefined objective function including costs of installation, maintenance, power losses, reliability, and technical risks. The novelty of this contribution is the exploitation of the riskbased concept called Conditional Value at Risk (CVaR), used in financial analysis, for optimal planning of a distribution network structure, based on modeling the consequence impacts of probable events (including overcurrents and variations of node voltages beyond acceptable values) by using costs of technical risks. This paper is organized as follows: Section II introduces the proposed feeder routing method. Section III describes the proposed
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
models for the problem. Section IV discusses some numerical results. Finally, Section V concludes the paper. 2. Proposed feeder routing method In this paper, the branch exchange method is used as optimal feeder routing method. In this method, the network configuration is evaluated using a risk-based objective function, determining improvements in the objective function that may be obtained by introducing changes in the network configuration. The specific details are indicated below. 2.1. Branch exchange method The basic branch exchange method is a well-known algorithm, adopted to operate only with radial network configurations in distribution network analysis and planning, thus avoiding the burden of introducing a radiality check in the related solution procedures [14]. This method starts with a feasible radial configuration. Then, by breaking an existing connection between nodes and connecting a new link between two obtained subnets, tries to find a new configuration with better value of the objective function. A dedicated version of this method, suitable for risk-based distribution system planning, is introduced in this paper. The flowchart of the method is presented in Fig. 1. The steps of the flowchart are described in the following paragraphs, considering that a branch to open has been selected among the existing closed branches (i.e., taken from the ordered list of the closed branches). a) Determination the upstream and downstream points: In each configuration of the network, every load point is supplied from a substation or another load point. These energy provider nodes are considered as upstream points. On the other hand, every load point may supply some other load points which are considered as downstream points. If there is more than one substation, those substations which are not connected to a certain load point and also
3
their associated load points are considered as upstream points, in addition to the previous ones, for this certain load point. In this step, for the ending node of the selected branch, the sets of upstream and downstream points are determined. Then, all possible branches between these two sets are determined. b) Branch exchange: In this step, the selected branch is removed and the network is divided in two parts which are upstream and downstream points of ending node of the selected branch. Then, a new possible branch connects these two parts. c) Construction of the network table: In the planning problems, network configurations are continuously changing until the optimal solution is found. Moreover, planning problems need load flow methods that can be used in the planning of multiple-zone distribution systems. A suitable load flow method, called structured power flow, has been introduced in Ref. [7]. In this method, the network connection is represented in tabular form using a very simple and effective way. No special ordering technique is required. Lines are indicated by two end nodes called 'sending' and 'receiving' nodes. The sending end node of a line is entered at the left column and the receiving end node enters at the right column of the network table. In this table, starting from a substation, each load point appears as a receiving node before appearing as a sending node. This ensures that the structure of the network is entered in the network table correctly. To illustrate this method, the network table is constructed for an example configuration in Fig. 2. The advantage of using this table is that traversing from top to the bottom of the table is equivalent to move from root to the leaves of the network in the direction of load flow. Moreover, it is not needed for node and line numbers to be sequential. This is very important in the planning problem where feeders can be connected to different substations. A membership value for nodes and lines are also considered in the network table to indicate their supplying substation. In addition, a column is considered as branch's flag, whose entries indicate whether a branch has been evaluated or not. d) Load flow and optimal conductor selection: A classical load flow algorithm used in distribution system analysis consists of backward
Fig. 1. The flowchart of the used branch exchange method.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
4
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Fig. 2. The network table for an example configuration.
and forward sweeps. Initially, it is assumed that the node voltages are equal to the voltage at the substation node, and the node currents are calculated. Then, the line currents are calculated from bottom to top of table (backward sweep). Then, the node voltages are calculated based on line currents from top to bottom of the table (forward sweep). These two sweeps are repeated until convergence. The convergence criterion is that the absolute value of the difference between node voltages in two consecutive iterations become less than a small certain value. A significant property of the backward/forward sweep algorithm is that it exhibits excellent convergence starting from reasonable initial conditions such as the flat voltage profile (with all voltages equal to unity) [15]. In the adaption of the backward/forward sweep algorithm to distribution planning, after a backward sweep and before starting the forward sweep, the type of branches' conductors and thermal rating are determined. Based on the current flowing through the branch and conductors' cost, the optimal conductor is selected. Then, the branch impedance in U/km is considered for that branch and the load flow is executed. e) Constraints and objective function evaluation: The objective function OF is described in more detail in Section 2.2. The constraints of the problem include the node voltage and line current limits, defined for branch b and node n as:
node voltages. To consider these risks in a single objective function, the technical risk is transformed into an economic risk by considering the damages due to technical risk occurrence. The detailed description of this approach is presented in this section. The uncertainties associated to probabilistic parameters are the sources of risk in distribution system. In order to consider these probabilistic behaviors, some scenarios with specified probability of occurrence are defined. To manage the risk, the distribution system should be designed such that it has sufficient adequacy in extreme events while the total cost is minimized. Extreme events are defined as high consequences and low-probability events. Risk tools that focus on extreme events are used to pay more attention to these events in the decision-making process. To measure the associated risk, this paper applies the CVaR risk indicator used in financial researches. The CVaR indicator is defined by starting from the notion of value at risk (VaR). The VaR with respect to the probability level of a percent (VaRa) is the additional cost, occurring with respect to the expected cost CEx, which will not be exceeded during a percent of all the studied scenarios. It means that the total cost is less than CEx þ VaR in a% of situations. The typical value of a is 95%, however 99% is also frequently used [16]. The CVaRa is associated to those costs that exceed the amount of CEx þ VaRa and defined as the conditional expected cost under this condition. VaRa, CVaRa, and the expected cost are shown in Fig. 3. The expected cost over a set of scenarios is calculated based on the occurrence probability of the scenarios and network's cost in each scenario. The expected cost can be defined as:
CEx ¼
X
s rs CTot
(3)
s2Ns
After calculating the value of CEx using Eq. (3), the value of VaRa can be calculated using the cumulative distribution function as shown in Fig. 3 (b). CVaRa is the expected value that should be paid, in addition to the expected cost, during the (1-a)% of scenarios with the highest costs. By modeling VaRa and CVaRa in the proposed framework for the planning problem, the following formulation is achieved:
X 1 s rs CTot CEx 1 a s2N R
Ib Ibrated
(1)
s s CVaRa CTot ¼ VaRa CTot þ
Vmin Vn Vmax
(2)
s VaRa CTot
If the node voltages or line currents are not within the acceptable limits, an extremely high value is assigned to the objective function. After replacing the selected branch by a new one, the constraints are evaluated using the load flow results to ensure that the constraints are in the acceptable limits. Then, the objective function OF for the minimization problem is calculated. If the obtained value is lower than the minimum objective function OFmin, the replaced branch will be saved, OFmin will be modified, and the flags of the branches will become equal to 0. Otherwise, the next possible branch connecting the upstream and downstream portions of the network is evaluated. When all possible branches are evaluated, the best branch is chosen and the flag of this branch becomes equal to 1. Then, the next branch is evaluated. This procedure should be repeated until the flags of all branches become equal to 1.
(4)
The set of NR is associated to those costs that exceed the amount of CEx þ VaRa and defined as:
s s CTot CEx þ VaRa CTot ; c s2NR
(5)
In the branch exchange method, the optimal configuration of the network is evaluated using an objective function. The objective function in this proposed risk-based planning is network's cost in extreme events, defined as:
s OF ¼ CEx þ CVaRa CTot
(6)
3. Model description 3.1. Scenario generation
2.2. Risk-based planning There are two kinds of risks in planning: technical and economic risks. Economic risks impact on the cost of planning, while technical risks affect technical constraints such as feeder capacity or
The uncertainties considered in this paper are forecasting error of demand and price of energy as well as probabilistic behavior of failure rate and duration. The uncertainties of these parameters can be modeled by some probability distribution. There are some
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
5
Fig. 3. Representation of VaR, CVaR, and expected cost CEx.
literature contributions in this field [17] and appropriate distributions are supposed. Because of heavy burden of calculation, it is difficult to consider a continuous distribution. Thus, as implemented in Ref. [18], discrete probability distribution sets are considered. The combination of these sets generates different operating conditions called scenarios. These discrete sets for energy demand jDl , energy price jEp , failure rates jRf , and failure durations jDf are stated mathematically as follows:
jDl ¼
o n Dl1 ; r1Dl ; Dl2 ; r2Dl ; :::; DlnDl ; rnDl Dl
r1Dl þ r2Dl þ ::: þ rnDl Dl ¼ 1 jRf ¼
n
o Rf 1 ; r1Rf ; Rf 2 ; r2Rf ; :::; Rf nRf ; rnRf Rf
r1Rf þ r2Rf þ ::: þ rnRf ¼1 Rf jDf ¼ r1Df
þ
jEp ¼
n
o nDf Df 1 ; r1Df ; Df 2 ; r2Df ; :::; Df nDf ; rDf
rnDf Df
r2Df
þ ::: þ
n
o nEp Ep1 ; r1Ep ; Ep2 ; r2Ep ; :::; EpnEp ; rEp
¼1
r1Ep þ r2Ep þ ::: þ rnEp Ep ¼ 1 SP¼ jDl ∪jRf ∪jDf ∪jEp rDl rRf rDf rEp ¼ 1
(8) acf ¼ (9)
¼
þ
þ
FICb Lb
(14)
1 ð1 þ rd Þlifetime rd
(15)
The operation and maintenance cost is determined by considering the term FMCb referring to the MV feeder b and expressed in $/km, which includes the cost for inspection as well as the cost for maintenance actions decided upon after inspection, and the length Lb of feeder b (in kilometers). The resulting expression is:
(10) COM ¼
Nb X
FMCb Lb
(16)
b¼1
(11)
The total annual cost includes distribution transformers cost CDT, MV feeders cost CMV and the damage cost of technical risks CTR specifically introduced here. s CTR
Nb X b¼1
3.2. Proposed cost model
s CMV
(13)
The investment cost is determined using the equivalent annual cost of MV feeders. The equivalent annual cost is the cost per year of an asset over its entire life-cycle duration. It is calculated by dividing the NPV of cost by the annual cost factor (acf) which can be found in engineering economy textbooks [20].
CInv ¼ ðacf Þ1
Here, r is the corresponding probability of energy demand, failure rate, failure duration, and energy price. A set of possible scenarios (S) is derived from the union of jDl , jRf , jDf , and jEp .
s CDT
s s CMV ¼ CInv þ COM þ CLs þ CInt
(7)
s2S
s CTot
interruptions. The last two entries depend on the scenario s considered. The total cost of planning is defined as:
(12)
The cost components of distribution transformers are described in detail in Ref. [19] that include investment, maintenance, losses and reliability costs. The annualized value of these costs are considered to constitute distribution transformers cost. The cost of MV feeders consists of operation and maintenance cost COM, the equivalent annual cost of investment CInv, power losses cost CL, reliability cost CInt referring to the service
The cost of the feeder losses includes two parts. One part is the energy loss cost, which is proportional to the cost per kilowatthour. The second part is power loss and related to the worth of loss in peak hours and calculated based on the cost saving due to reduce 1 kW in the peak power [21]. Without loss of generality, in this paper the calculations are made for a single reference hour considering peak load and the load loss factor (LSF) is used to represent the average losses [22]. With reference to the entries indicated in the Nomenclature, the feeder loss cost in scenario s is defined as: Nb X 2 s s CLs ¼ Kpl þ Kel LSF 8760 rb Lb Ibs
(17)
b¼1
In the above equation, the costs of energy and power losses and also the current flowing through the feeders are varied in different scenarios. Therefore, the value of losses cost is varied in different scenarios and indicated by a probability distribution instead of a single value. The reliability cost is determined based on the customer interruption cost. The causes of interruptions are the outages of the MV
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
6
M. Esmaeeli et al. / Energy xxx (2016) 1e10
feeders. The probabilistic behaviors of failure rate and failure duration are considered in scenario generation. Thus, the interruption cost is varied in different scenarios and is defined as: s CInt ¼
Nb X
Rfbs Lb Dfbs
X
LF Dsn cos f ocn
(18)
n2DNb
b¼1
Due to the failure of branch b, all its downstream nodes are interrupted. Thus, the interruption cost is calculated using the demand summation of all nodes downstream branch b. 3.3. Technical risk cost 3.3.1. Components of the technical risk cost The components of the technical risk costs are associated to the constraints of the feeder routing problem. The radiality constraint is addressed by using the branch exchange method (Section 2), which allows the generation of radial configurations only, so that it is not associated to any technical risk cost. The other constraints may be within acceptable limits in deterministic planning, but in some scenarios, the feeder current and voltage drop may exceed the acceptable limits. The exceeding quantities correspond to technical risks for the distribution system. To manage these technical risks in optimal configuration, they should be considered in the planning. In this paper, a single objective function based on economic terms is assumed. Therefore, these technical risks are transformed into economic risks calculating the worth of their damages. In particular, two issues are considered, referring to the risk of overcurrent in the branches and to the risks related to node voltage deviations (undervoltages and overvoltages) from the acceptable range. 3.3.2. Technical risk cost component due to overcurrents The overcurrent through the conductors causes extreme increasing of their temperature, which may have both mechanical and electrical effects. Three main factors should be considered in defining the thermal limit of a power line: loss of strength, overhead line sag, limitation of the conductor fittings. It has been shown that correctly designed and selected fittings are not a restrictive factor for the thermal limit [23]. In addition, the designed safety margin of MV feeders is often specified large enough so that under most conditions, the probability of occurrence for a flashover due to
Fig. 4. Loss of conductor life due to overcurrent.
sag is extremely small. Hence, only the loss of strength is considered in this study. The damages due to loss of strength for MV feeders are analyzed in Ref. [23] where the monetary worth of loss of conductor life due to overcurrent is modeled. The proposed model is represented in Fig. 4, where the overcurrent ratio is defined as the ratio between the actual current and the rated current. The vertical axis of the curve is normalized by the feeder installation cost while the horizontal axis contains multiples of the rated current of the conductor. Therefore, the cost of overcurrent risk in MV feeders can be calculated using the abovementioned curve as a function of feeder current and can be stated as LLb ðIbs Þ. The cost of overcurrent risk in branch b and scenario s can be expressed as: b;s COC ¼
LLb Ibs FICb 0
Ibs > Ibrated otherwise
(19)
When the feeder current is less than its rated value, the overcurrent risk does not occur and its cost is zero. Furthermore, the transformer overload constraint is considered by using a penalty function representing the effect of the overload on the transformer's loss of life [19]. For each scenario, there is a possibility of transformer overload. The corresponding loss of life (LOL) is determined in function of the transformer overload by using the data reported in Ref. [24], and is then converted into a penalty cost considering the annualized cost obtained by dividing the net present value by the annual cost factor acf defined in (15). The penalty cost for the overload of the distribution transformer t in scenario s is expressed as in Ref. [19]: t;s CODT ¼ LOLst
TICt acf
(20)
3.3.3. Technical risk cost component due to voltage deviations There is a growing interest in using performance based regulation (PBR) along with quality regulation for distribution network [25]. In this approach, some penalty and reward mechanisms are defined based on performance of network operators. About voltage deviations, the acceptable range for the node voltage is assumed to be from 0.9 to 1.1 per units; thereby, penalties are adopted for voltages approaching these limits [10]. The penalty will start if the voltage deviation in a load point exceeds 5% of the rated voltage (Fig. 5). The overvoltage may happen only in distribution systems with distributed generation or with electric vehicles injecting power into the grid. In this paper, a penalty function FPðVns Þ is defined as a PBR for the value of undervoltage or overvoltage in the load points. This penalty is determined based on the customer damages because extreme undervoltage or overvoltage could endamage some equipment where electrical motors are most important among them [26]. There are upper and lower caps for the penalty function.
Fig. 5. The voltage penalty function designed as PBR.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Between these caps, the function is assumed linear in accordance to undervoltage severity function presented in Ref. [10]. The cost of voltage deviation risk in node n and scenario s can be expressed (considering the entries defined in the Nomenclature) as:
n;s CUOV ¼ PNLmax Dsn cos f FP Vns
(21)
In this paper, the maximum damage cost to the customer equipment PNLmax is determined based on the worth of electrical motors and their proportion to the customer load while the possible damages of other equipment are ignored. The PNLmax could be defined in any other way while the basis of the proposed approach is not changed. The cost of technical risk is a combination of the abovementioned costs. Thus, this cost is defined as: s CTR ¼
Nb X b¼1
b;s COC þ
Nn X
n;s CUOV þ
n¼1
Nt X t;s CODT
(22)
t¼1
7
The distribution system is generally sized in such a way to have enough adequacy for all load levels, including peak and off-peak hours. The demand of a load point in the worst scenario during off-peak hours is lower than the demand during peak hours. Therefore, the problems related to overcurrent and extreme voltage drop are only considered in peak hours, while overcurrent and undervoltage do not happen in off-peak hours. Conversely, the risk of overvoltage is more likely to appear during off-peak hours with significant presence of local generation. However, the possibility of connecting local generation capacity in the system is limited by the grid connection rules to avoid causing problems to the distribution system. These rules also take into account the limits due to the occurrence of overvoltages. As such, overvoltages could even not appear in the scenario studies. The probabilistic behavior of the system is evaluated by using possible scenarios generated using the discrete probability distributions of the uncertain parameters (the values are shown in the following sections). The proposed technique is developed in MATLAB code and the computational time required was less than 1 min using a computer with 2.53 GHz, Core i5 CPU, and 4 GB of RAM. The optimal network structure with and without considering the proposed risk-based method is investigated in two cases.
3.4. Load and local generation model The load curve related to the peak day is typically used for indicating the yearly load [27]. As implemented in Ref. [28], the daily load curve can be presented by a two-step load cycle. The steps are indicating the average off-peak load and the peak load which is assumed that remains for h hours. In this study, similar to [28], the duration of peak hours is considered 4 h a day. For the purpose of load flow calculations, the relevant entry is the net power demand (that is, load minus local generation) at each node, considering the local generation as a negative load. The feeder parameters are known. In the presence of local generation, the scenarios constructed include both different loading levels and different local generation penetrations. In each scenario, loads and generations are assumed to be exactly defined and are static. Since the local generation is owned and managed by a different entity with respect to the distribution system operator, the costs related to the presence, operation and maintenance of the local generators are not included in the planning analysis. 4. Numerical results The proposed method is applied to a 20-kV distribution network containing 52 distribution transformers (load points) and 2 subtransmission substations. It is assumed that the transformers are sized already in accordance to the method proposed in Ref. [19], therefore distribution transformers can be considered as load points in the feeder routing problem. The positions of substations, load points, and possible feeders are shown in Fig. 6. The data of load points and substations are presented in Tables A1 in the Appendix. Two different types of conductors could be used in the feeders. The characteristics of the available conductors are shown in Table A2 in the Appendix. The load factor and loss factor are assumed respectively 0.6 and 0.35 [29]. The power factor of load points is assumed to be 0.85. The maximum allowable voltage drop is 5% of the rated voltage. The discount rate is 7% and the lifetime of the project is assumed to be 20 years. The outage cost is 4 $/kWh [30]. The value of PNLmax is assumed 112 $/kW [31]. The forecast values of the energy loss cost (Kel) and the peak power cost (Kpl) for horizon year are respectively 0.04 $/kWh and 168 $/kW [20]. Using the model described in Ref. [19], the relevant values of the quantities to be used in each scenario are determined.
4.1. Case 1 e traditional feeder routing In the traditional approach to feeder routing, uncertainties are neglected. This approach is applied to the test service area shown in Fig. 6. In this case, the objective of the planning problem is to minimize the deterministic costs. In this case, technical constraints are always in acceptable margins because the uncertainties are neglected. The results of the optimal routing for MV feeders are shown in Fig. 7. The total deterministic cost of the planning for this test system is $345,800. The corresponding four components of investment, maintenance, losses, and reliability costs are equal to $209,270, $16,628, $48,161, and $71,743, respectively. In this case, the probabilistic behaviors of system's parameters are not considered while they do exist in a real distribution system. To analyze the qualification of the obtained plan in the presence of uncertainties, it is evaluated through different scenarios. Discrete probability distribution sets are used for scenario generation and shown in Table 1. The probabilistic costs associated to this plan are presented in Table 2. 4.2. Case 2 e risk-based feeder routing In risk-based planning, more attention is paid to the extreme events during the decision-making process. The technical risk including overcurrent and voltage deviations are converted into a monetary term using the model indicated in Section 3.3. In this case, the objective of the planning problem is to minimize the cost of the worst possible scenarios. This planning approach is implemented by using CVaR0.95 in calculating the objective function. The proposed method is applied to the test service area. The results of the planning are shown in Fig. 8. The values of the objective function CEx þ CVaR0.95 is equal to $525,380 (while its value was $577,010 in the previous case). In other words, the risk-based planning has improved the results by almost 10% reduction in the cost of worst scenarios. A comprehensive comparison between these two cases is presented in Table 2. As seen in Table 2, the deterministic cost in Case 2 increased in comparison to Case 1 as the investment cost increases. The additional investment cost in Case 2 is due to change in the feeders' costs. In risk based planning, the DSO pays this additional
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
8
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Fig. 6. Available supply routes for 52 load points distribution network.
Table 2 Cost components in various cases ($). Cost component
Case 1 (Traditional)
Case 2 (Risk-based)
Investment Maintenance Losses (worst) Reliability (worst) Technical risk (worst) Deterministic cost Expected cost (CEx) CEx þ CVaR0.95 Worst scenario
209,270 16,628 106,200 401,760 75,900 345,800 382,430 577,010 809,750
222,580 17,685 87,056 375,340 10,980 346,770 371,950 525,380 713,640
cost to decrease the imposed cost in the worst scenarios. Here, the cost of the worst scenario in Case 1 is $809,750 while it is $713,640 in Case 2.
5. Conclusion Fig. 7. Optimal network structure for traditional feeder routing.
The mathematical model of a new risk-based method for optimal feeder routing has been developed to address MV
Table 1 Discrete probability distribution of uncertain parameters. Load
Failure rate
Failure duration
Energy price
Probability
Amount
Probability
Amount
Probability
Amount
Probability
Amount
0.38 0.24 0.24 0.07 0.07
100% 95% 120% 90% 140%
0.40 0.20 0.20 0.10 0.10
100% 70% 150% 50% 200%
0.40 0.20 0.20 0.10 0.10
100% 75% 150% 50% 200%
0.65 0.25 0.10
100% 105% 125%
Amount x% means it is x% of the deterministic value.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
9
Table A1 Load and coordinates of load points and substations.
Fig. 8. Optimal network structure for risk-based feeder routing.
networks exposed to economic and technical risks. The proposed method considers the stochastic behavior of distribution system demand and local generation through a set of scenarios. The problem is solved by using the branch exchange algorithm. The proposed method optimizes the cost of planning for the worst possible scenarios using risk analysis indexes. The decision about optimal configuration is made on the basis of the costs occurring for extreme events. This method is useful for the distribution system operator (DSO) to make decisions about the choice of the planning scheme to be adopted, considering the DSO attitude to accept risks or its risk aversion. The DSO can compare the required additional cost and reduction in worst scenarios to choose the planning scheme. The VaR and CVaR indices make it available more information to the decision maker. The proposed method has been executed on an electrical distribution system with 2 substations and 52 load points. The results show that the proposed risk-based method could reduce the risk of planning due to uncertain parameters. Low-probability events with significant consequences are considered as extreme events. In the risk-based approach, the costs of the extreme events are reduced considerably in comparison to the traditional approach, while the additional required deterministic cost is much lower than this reduction. The main idea of the proposed method can be extended to larger distribution grids with no conceptual changes. On a large scale, the cost reductions could be quantitatively more significant. The optimal structure of the distribution grid is found on the basis of the scenarios identified by the user. Clearly, the definition of many scenarios on a large grid could increase the computation time, but with an accurate choice of the number and type of scenarios done by the user the overall computation time may remain tractable.
Appendix A Test system data The data for the test system are presented in the following tables. The data include load and locational coordinates, to guarantee replicable results.
No.
X (km)
Y (km)
Load (kVA)
No.
X (km)
Y (km)
Load (kVA)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
2.5 4 5 6.5 1.5 3.5 5.5 7.5 1 4 5 8 2 3.5 5.5 7 1 2.5 4 5 6.5 8 3 4.5 6 3.5 5.5
0.6 0.6 0.6 0.6 1.2 1.2 1.2 1.2 1.8 1.8 1.8 1.8 2.4 2.4 2.4 2.4 3 3 3 3 3 3 3.6 3.6 3.6 4.5 4.5
350 630 980 112 210 112 70 112 280 420 350 350 350 630 350 350 280 350 350 140 350 350 630 280 420 420 420
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 100 200
3 4.5 6 1 2.5 4 5 6.5 8 2 3.5 5.5 7 1 4 5 8 1.5 3.5 5.5 7.5 2.5 4 5 6.5 1.5 7.5
5.4 5.4 5.4 6 6 6 6 6 6 6.6 6.6 6.6 6.6 7.2 7.2 7.2 7.2 7.8 7.8 7.8 7.8 8.4 8.4 8.4 8.4 4.5 4.5
420 980 630 350 350 140 350 350 980 630 350 350 350 350 350 420 280 112 70 112 210 112 980 630 350 e e
The substations are indicated as bold.
Table A2 Available conductors' specifications. Capacity Installation (A) cost ($/km)
Maintenance Impedance cost ($/km) (U/km)
80 100
225 270
30,000 36,000
Failure rate (failures/ (km.yr))
1.38 þ j0.39 0.1 0.91 þ j0.38 0.1
Repair duration (h) 4 4
References [1] Wouters C, Fraga ES, James AM. An energy integrated, multi-microgrid, MILP (mixed-integer linear programming) approach for residential distributed energy system planningeA South Australian case-study. Energy 2015;85:30e44. [2] Yokoyama R, Shinano Y, Taniguchi S, Ohkura M, Wakui T. Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation. Energy Convers Manag 2015;92:92e104. [3] Khator SK, Leung LC. Power distribution planning: a review of models and issues. IEEE Trans Power Syst 1997;12(3):1151e9. [4] Aghaeia J, Muttaqi KM, Azizivahed A, Gitizadeh M. Distribution expansion planning considering reliability and security of energy using modified PSO (Particle Swarm Optimization) algorithm. Energy 2014;65:398e411. [5] Sahoo N, Prasad K. A fuzzy genetic approach for network reconfiguration to enhance voltage stability in radial distribution systems. Energy Convers Manag 2006;47(18):3288e306. [6] Abbasi AR, Seifi AR. Considering cost and reliability in electrical and thermal distribution networks reinforcement planning. Energy 2015;84:25e35. [7] Goswami SK. Distribution system planning using branch exchange technique. IEEE Trans Power Syst 1997;12(2):718e23. [8] Salehi J, Haghifam M-R. Long term distribution network planning considering urbanity uncertainties. Int J Electr Power Energy Syst 2012;42(1):321e33. [9] Miranda V, Proença LM. Probabilistic choice vs. risk analysis: conflicts and synthesis in power system planning. IEEE Trans Power Syst 1998;13(3): 1038e43. [10] Fei X, McCalley JD. Power system risk assessment and control in a multiobjective framework. IEEE Trans Power Syst 2009;24(1):78e85. [11] Gitizadeh M, Kaji M, Aghaei J. Risk based multiobjective generation expansion planning considering renewable energy sources. Energy 2013;50:74e82. [12] Yeddanapudi SRK, Li Y, McCalley JD, Chowdhury AA, Jewell WT. Risk-based allocation of distribution system maintenance resources. IEEE Trans Power Syst 2008;23(2):287e95. [13] Hashemi-Dezaki H, Hamzeh M, Askarian-Abyaneh H, Haeri-Khiavi H. Risk management of smart grids based on managed charging of PHEVs and
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
10
[14]
[15]
[16]
[17] [18] [19]
[20] [21]
[22] [23]
M. Esmaeeli et al. / Energy xxx (2016) 1e10 vehicle-to-grid strategy using Monte Carlo simulation. Energy Convers Manag 2015;100:262e76. Chiang H-D, Jean-Jumeau R. Optimal network reconfigurations in distribution systems. II. Solution algorithms and numerical results. IEEE Trans Power Deliv 1990;5(3):1568e74. Bompard E, Carpaneto E, Chicco G, Napoli R. Convergence of the backward/ forward sweep method for the load-flow analysis of radial distribution systems. Int J Electr Power & Energy Syst 2000;22(7):521e30. Alvehag K. Impact of dependencies in risk assessments of power distribution system, Licentiate Thesis, Royal Institute of Technology. School of Electronic and Electrical Engineering, Stockholm; 2008. Billinton R, Allan RN. Reliability evaluation of power systems, vol. 2. New York: Plenum Press; 1996. Saber AY, Venayagamoorthy GK. Resource scheduling under uncertainty in a smart grid with renewables and plug-in vehicles. IEEE Syst J 2012;6(1):103e9. Esmaeeli M, Kazemi A, Shayanfar H, Haghifam M-R, Siano P. Risk-based planning of distribution substation considering technical and economic uncertainties. Electr Power Syst Res 2016;30(135):18e26. Blank L, Tarquin A. Engineering economy. McGraw-Hill Science; 2011. Esmaeeli M, Kazemi A, Shayanfar H, Haghifam M-R. Multistage distribution substations planning considering reliability and growth of energy demand. Energy 2015;84:357e64. Gustafson M, Baylor J. Approximating the system losses equation [power systems]. IEEE Trans Power Syst 1989;4(3):850e5. Wan H, McCalley JD, Vittal V. Increasing thermal rating by risk analysis. IEEE
Trans Power Syst 1999;14(3):815e28. [24] Sen PK. Transformer overloading and assessment of loss-of-life for liquidfilled transformers. Power Systems Engineering Research Center (PSERC); 2011. [25] Alvehag K, Soder L. Risk-based method for distribution system reliability investment decisions under performance-based regulation. IET Gener Transm Distrib 2011;5(10):1062e72. [26] IEC60076e7. Power transformers; part 7: loading guide for oil-immersed power transformers. first ed. 2005-12. [27] Cossi AM, Romero R, Mantovani JRS. Planning of secondary distribution circuits through evolutionary algorithms. IEEE Trans Power Deliv 2005;20(1): 205e13. [28] Esmaeeli M, Kazemi A, Shayanfar H, Haghifam M-R. Sizing and placement of distribution substations considering optimal loading of transformers. Int Trans Electr Energy Syst 2015;25(11):2897e908. [29] Ziari I, Ledwich G, Ghosh A. Optimal integrated planning of MVeLV distribution systems using DPSO. Electr Power Syst Res 2011;81(10):1905e14. [30] Samui A, Singh S, Ghose T, Samantaray SR. A direct approach to optimal feeder routing for radial distribution system. IEEE Trans Power Deliv 2012;27(1): 253e60. [31] De Abreu, JG and Emanuel, A. Induction motor thermal aging caused by voltage distortion and imbalance: loss of useful life and its estimated cost. in Industrial and Commercial Power Systems Technical Conference, 2001. Papers Presented at the 2001 IEEE Annual Meeting.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy Mostafa Esmaeeli a, b, Ahad Kazemi b, Heidarali Shayanfar b, Gianfranco Chicco c, Pierluigi Siano d, * a
Faculty of Industrial and Computer Engineering, Birjand University of Technology, Birjand, Iran Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran Energy Department, Politecnico di Torino, Torino, Italy d Department of Industrial Engineering, University of Salerno, Fisciano, Italy b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2015 Received in revised form 31 October 2016 Accepted 5 November 2016 Available online xxx
Technical and financial uncertainties may put distribution system planning at risk. In this paper, a new risk-based planning method is proposed which pays more attention to low-probability and high consequences events in energy supplying systems. The proposed approach is adopted for determining the optimal structure of a Medium Voltage network where risk-based determination of the radial network structures is implemented through an uncertainty model of the system's variables based on discrete states, called scenarios. The cost of distribution system planning consists of investment cost, maintenance cost, power losses cost, reliability cost, and technical risk cost. In this paper, appropriate models are proposed to consider the monetary effects of technical risks. The proposed approach is applied to a test system consisting of 52 electric load points and two substations. It is observed that the proposed risk-based method for planning the optimal network structure can properly reduce the cost of extreme events, therefore reducing the concerns of distribution system operators about these possible situations. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Branch exchange method Energy demand Feeder routing Risk Uncertainty
1. Introduction Distribution system planning and the economic and reliable design of distribution networks are important challenges for electrical distribution companies. In an electrical distribution network, a feeder is the group of electrical lines (overhead lines or cables) starting from the supply point (an electrical substation) and connecting a group of loads. Each feeder has a radial topology, and in general multiple feeders start from an electrical substation. For an electrical distribution system, the number of lines existing in the system is larger than the number of loads, in such a way to have a number of redundant lines maintained open in each radial configuration of the network. The lines to maintain open are chosen during the definition of the paths (or routes) with which the loads are served, in such a way to serve all the loads and to maintain the network radial. This selection is indicated as feeder routing in the technical literature. The planning of distribution networks can be divided into two
* Corresponding author. E-mail address: [email protected] (P. Siano).
sub-problems including substation location and feeder routing. Substation location, size and its services are determined in the first problem, while the size of the feeders and their routes are indicated in the second one. In this paper it is assumed that the substations are already positioned, and the optimal feeder routing is discussed. Different approaches for feeder routing have been presented during past years. There are large numbers of discrete variables in distribution system planning and various mathematical programming techniques, such as mixed integer programming [1], branch and bound methods [2], and transportation [3] have been used to solve the problem of feeder routing optimization. However, by using these models, the solution time increases and it is difficult to achieve the optimal solution. In recent years, metaheuristic methods such as particle swarm optimization (PSO) [4], genetic algorithm [5], and teaching learning optimization [6] have been extensively used in distribution network planning. Using these optimization techniques, the nonlinearity of the cost function and constraints can be easily incorporated in the formulation. However, the solution of these methods may be a local optimum. A different approach based on branch-exchange techniques has been applied in deterministic planning of distribution system [7] and in long
http://dx.doi.org/10.1016/j.energy.2016.11.021 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
2
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Nomenclature s CTot CEx CInv s CInt CLs s COM s CTR b;s COC n;s CUOV
t;s CODT
CVaRa OF VaRa Dsn FICb FMCb FPð:Þ Ibrated Ibs s Kel s Kpl
Total cost of planning in Scenario s ($) Expected planning cost over a set of scenarios ($) Investment cost ($) Interruption cost in Scenario s ($) Power losses cost in Scenario s ($) Maintenance cost during in Scenario s ($) Technical risk cost in Scenario s ($) Cost of overcurrent risk in feeder b in Scenario s ($) Cost of undervoltage/overvoltage risk at node n in Scenario s ($) Cost of distribution transformer overload risk for transformer t in Scenario s Conditional VaR with probability level a percent Objective function Value at risk with the probability level a percent Energy demand of node n in Scenario s (kVA) Feeder installation cost ($/km) Feeder maintenance cost ($/km) Penalty function of voltage quality (pu) Thermal rating of feeder b (A) Current of feeder b in Scenario s (A) Electricity price in Scenario s ($/kWh) Economic savings per active power reduction in the peak power for Scenario s ($/kW)
term planning considering uncertainties [8]. This approach is a mathematical method which finds a pseudo-optimal solution in an admissible computational time also for large-scale real distribution networks. The problem of power systems' planning has been traditionally developed using deterministic models. However, in recent decades, new probabilistic models have been introduced to consider uncertainties in power systems. In this approach, the goodness of a solution can be measured through a particular set of scenarios, each one with a given probability. The expected cost over the set of considered scenarios is calculated and the optimal solution is chosen to minimize this expected value. However, this planning approach has encountered several challenges in its generalized adoption [9]. Furthermore, in recent years, a risk analysis approach has been suggested for power system planning and has been well developed in some literature contributions to assess [10] and manage [11] the operational risk of power system. This approach chooses the preferred scheme while considering its cost in extreme events and is well understood by planners who have experienced real and practical problems. The word risk considers both the probability of occurrence of an event that harms or damages people or equipment, and its consequences generally assessed in economic terms. The important issue that should be considered in power system planning is that it is not possible to have a plan without risk. But the risk should be managed and a certain level of risk should be accepted when it is technically and economically admissible. The risk-based planning mainly concentrates on the decision about the admissible level of risk. In electrical distribution networks, the sources of risks are some parameters having probabilistic behaviors. In order to manage these risks, the risk-based planning of distribution networks is used which pays more attention to low-probability and high consequences events. A risk-based allocation of distribution system
Lb LLb ð:Þ
Length of feeder b (km) Loss of feeder b life in Scenario s as a function of feeder current (pu.$) LOLst Loss of life transformer t in scenario s (year) ocn Outage cost for load point n ($/kWh) PNLmax Maximum damage cost to a customer due to undervoltage or overvoltage ($/kW) rb Resistance of the branch b (kU/km) TICt Transformer t installation cost ($) Vns Node voltage in Scenario s (kV) Vmin Minimum allowed voltage (kV) acf Annual cost factor cosf Loads' Power factor DNb Downstream nodes of branch b LF Load factor LSF Load loss factor Nb Number of branches Nn Number of load points Ns Number of scenarios Nt Number of distribution transformers rd Discount rate rs Probability of Scenario s jRf ; jDf ; jEp ; jDl Sets of discrete distributions of failure rate, failure duration, energy price, and load, respectively
maintenance resources is presented in Ref. [12], where a method to allocate maintenance resources to various distribution system assets is proposed. To determine the effects of maintenance, a predictive reliability assessment tool is developed. A risk management method is introduced in Ref. [13] to reduce the negative electrical vehicles (EVs) effects, where stochastic models of EVs, renewable resources, and availability of devices are proposed to evaluate the system reliability comprehensively. It is assumed that the system is at risk when the energy demand is more than the generation capacity. By using the managed charging of EVs, the risk level of smart grid and its adequacy have been improved. In distribution planning, most of papers are not considering the risk concept and its monetary consequences. In this paper, the consequent impacts of risk and probabilistic events on the distribution network are modeled as a monetary term called cost of technical risks. A risk-based method for optimal routing of MV feeders is proposed and the effect of technical risks on the distribution network is investigated. In the presented approach, the probable events, including overcurrent of MV feeders and variations of node voltages more than acceptable values, are considered as technical risks. The feeder routing problem is solved using a customized version of the branch exchange method where the optimal configuration of distribution network is determined in accordance to a predefined objective function including costs of installation, maintenance, power losses, reliability, and technical risks. The novelty of this contribution is the exploitation of the riskbased concept called Conditional Value at Risk (CVaR), used in financial analysis, for optimal planning of a distribution network structure, based on modeling the consequence impacts of probable events (including overcurrents and variations of node voltages beyond acceptable values) by using costs of technical risks. This paper is organized as follows: Section II introduces the proposed feeder routing method. Section III describes the proposed
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
models for the problem. Section IV discusses some numerical results. Finally, Section V concludes the paper. 2. Proposed feeder routing method In this paper, the branch exchange method is used as optimal feeder routing method. In this method, the network configuration is evaluated using a risk-based objective function, determining improvements in the objective function that may be obtained by introducing changes in the network configuration. The specific details are indicated below. 2.1. Branch exchange method The basic branch exchange method is a well-known algorithm, adopted to operate only with radial network configurations in distribution network analysis and planning, thus avoiding the burden of introducing a radiality check in the related solution procedures [14]. This method starts with a feasible radial configuration. Then, by breaking an existing connection between nodes and connecting a new link between two obtained subnets, tries to find a new configuration with better value of the objective function. A dedicated version of this method, suitable for risk-based distribution system planning, is introduced in this paper. The flowchart of the method is presented in Fig. 1. The steps of the flowchart are described in the following paragraphs, considering that a branch to open has been selected among the existing closed branches (i.e., taken from the ordered list of the closed branches). a) Determination the upstream and downstream points: In each configuration of the network, every load point is supplied from a substation or another load point. These energy provider nodes are considered as upstream points. On the other hand, every load point may supply some other load points which are considered as downstream points. If there is more than one substation, those substations which are not connected to a certain load point and also
3
their associated load points are considered as upstream points, in addition to the previous ones, for this certain load point. In this step, for the ending node of the selected branch, the sets of upstream and downstream points are determined. Then, all possible branches between these two sets are determined. b) Branch exchange: In this step, the selected branch is removed and the network is divided in two parts which are upstream and downstream points of ending node of the selected branch. Then, a new possible branch connects these two parts. c) Construction of the network table: In the planning problems, network configurations are continuously changing until the optimal solution is found. Moreover, planning problems need load flow methods that can be used in the planning of multiple-zone distribution systems. A suitable load flow method, called structured power flow, has been introduced in Ref. [7]. In this method, the network connection is represented in tabular form using a very simple and effective way. No special ordering technique is required. Lines are indicated by two end nodes called 'sending' and 'receiving' nodes. The sending end node of a line is entered at the left column and the receiving end node enters at the right column of the network table. In this table, starting from a substation, each load point appears as a receiving node before appearing as a sending node. This ensures that the structure of the network is entered in the network table correctly. To illustrate this method, the network table is constructed for an example configuration in Fig. 2. The advantage of using this table is that traversing from top to the bottom of the table is equivalent to move from root to the leaves of the network in the direction of load flow. Moreover, it is not needed for node and line numbers to be sequential. This is very important in the planning problem where feeders can be connected to different substations. A membership value for nodes and lines are also considered in the network table to indicate their supplying substation. In addition, a column is considered as branch's flag, whose entries indicate whether a branch has been evaluated or not. d) Load flow and optimal conductor selection: A classical load flow algorithm used in distribution system analysis consists of backward
Fig. 1. The flowchart of the used branch exchange method.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
4
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Fig. 2. The network table for an example configuration.
and forward sweeps. Initially, it is assumed that the node voltages are equal to the voltage at the substation node, and the node currents are calculated. Then, the line currents are calculated from bottom to top of table (backward sweep). Then, the node voltages are calculated based on line currents from top to bottom of the table (forward sweep). These two sweeps are repeated until convergence. The convergence criterion is that the absolute value of the difference between node voltages in two consecutive iterations become less than a small certain value. A significant property of the backward/forward sweep algorithm is that it exhibits excellent convergence starting from reasonable initial conditions such as the flat voltage profile (with all voltages equal to unity) [15]. In the adaption of the backward/forward sweep algorithm to distribution planning, after a backward sweep and before starting the forward sweep, the type of branches' conductors and thermal rating are determined. Based on the current flowing through the branch and conductors' cost, the optimal conductor is selected. Then, the branch impedance in U/km is considered for that branch and the load flow is executed. e) Constraints and objective function evaluation: The objective function OF is described in more detail in Section 2.2. The constraints of the problem include the node voltage and line current limits, defined for branch b and node n as:
node voltages. To consider these risks in a single objective function, the technical risk is transformed into an economic risk by considering the damages due to technical risk occurrence. The detailed description of this approach is presented in this section. The uncertainties associated to probabilistic parameters are the sources of risk in distribution system. In order to consider these probabilistic behaviors, some scenarios with specified probability of occurrence are defined. To manage the risk, the distribution system should be designed such that it has sufficient adequacy in extreme events while the total cost is minimized. Extreme events are defined as high consequences and low-probability events. Risk tools that focus on extreme events are used to pay more attention to these events in the decision-making process. To measure the associated risk, this paper applies the CVaR risk indicator used in financial researches. The CVaR indicator is defined by starting from the notion of value at risk (VaR). The VaR with respect to the probability level of a percent (VaRa) is the additional cost, occurring with respect to the expected cost CEx, which will not be exceeded during a percent of all the studied scenarios. It means that the total cost is less than CEx þ VaR in a% of situations. The typical value of a is 95%, however 99% is also frequently used [16]. The CVaRa is associated to those costs that exceed the amount of CEx þ VaRa and defined as the conditional expected cost under this condition. VaRa, CVaRa, and the expected cost are shown in Fig. 3. The expected cost over a set of scenarios is calculated based on the occurrence probability of the scenarios and network's cost in each scenario. The expected cost can be defined as:
CEx ¼
X
s rs CTot
(3)
s2Ns
After calculating the value of CEx using Eq. (3), the value of VaRa can be calculated using the cumulative distribution function as shown in Fig. 3 (b). CVaRa is the expected value that should be paid, in addition to the expected cost, during the (1-a)% of scenarios with the highest costs. By modeling VaRa and CVaRa in the proposed framework for the planning problem, the following formulation is achieved:
X 1 s rs CTot CEx 1 a s2N R
Ib Ibrated
(1)
s s CVaRa CTot ¼ VaRa CTot þ
Vmin Vn Vmax
(2)
s VaRa CTot
If the node voltages or line currents are not within the acceptable limits, an extremely high value is assigned to the objective function. After replacing the selected branch by a new one, the constraints are evaluated using the load flow results to ensure that the constraints are in the acceptable limits. Then, the objective function OF for the minimization problem is calculated. If the obtained value is lower than the minimum objective function OFmin, the replaced branch will be saved, OFmin will be modified, and the flags of the branches will become equal to 0. Otherwise, the next possible branch connecting the upstream and downstream portions of the network is evaluated. When all possible branches are evaluated, the best branch is chosen and the flag of this branch becomes equal to 1. Then, the next branch is evaluated. This procedure should be repeated until the flags of all branches become equal to 1.
(4)
The set of NR is associated to those costs that exceed the amount of CEx þ VaRa and defined as:
s s CTot CEx þ VaRa CTot ; c s2NR
(5)
In the branch exchange method, the optimal configuration of the network is evaluated using an objective function. The objective function in this proposed risk-based planning is network's cost in extreme events, defined as:
s OF ¼ CEx þ CVaRa CTot
(6)
3. Model description 3.1. Scenario generation
2.2. Risk-based planning There are two kinds of risks in planning: technical and economic risks. Economic risks impact on the cost of planning, while technical risks affect technical constraints such as feeder capacity or
The uncertainties considered in this paper are forecasting error of demand and price of energy as well as probabilistic behavior of failure rate and duration. The uncertainties of these parameters can be modeled by some probability distribution. There are some
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
5
Fig. 3. Representation of VaR, CVaR, and expected cost CEx.
literature contributions in this field [17] and appropriate distributions are supposed. Because of heavy burden of calculation, it is difficult to consider a continuous distribution. Thus, as implemented in Ref. [18], discrete probability distribution sets are considered. The combination of these sets generates different operating conditions called scenarios. These discrete sets for energy demand jDl , energy price jEp , failure rates jRf , and failure durations jDf are stated mathematically as follows:
jDl ¼
o n Dl1 ; r1Dl ; Dl2 ; r2Dl ; :::; DlnDl ; rnDl Dl
r1Dl þ r2Dl þ ::: þ rnDl Dl ¼ 1 jRf ¼
n
o Rf 1 ; r1Rf ; Rf 2 ; r2Rf ; :::; Rf nRf ; rnRf Rf
r1Rf þ r2Rf þ ::: þ rnRf ¼1 Rf jDf ¼ r1Df
þ
jEp ¼
n
o nDf Df 1 ; r1Df ; Df 2 ; r2Df ; :::; Df nDf ; rDf
rnDf Df
r2Df
þ ::: þ
n
o nEp Ep1 ; r1Ep ; Ep2 ; r2Ep ; :::; EpnEp ; rEp
¼1
r1Ep þ r2Ep þ ::: þ rnEp Ep ¼ 1 SP¼ jDl ∪jRf ∪jDf ∪jEp rDl rRf rDf rEp ¼ 1
(8) acf ¼ (9)
¼
þ
þ
FICb Lb
(14)
1 ð1 þ rd Þlifetime rd
(15)
The operation and maintenance cost is determined by considering the term FMCb referring to the MV feeder b and expressed in $/km, which includes the cost for inspection as well as the cost for maintenance actions decided upon after inspection, and the length Lb of feeder b (in kilometers). The resulting expression is:
(10) COM ¼
Nb X
FMCb Lb
(16)
b¼1
(11)
The total annual cost includes distribution transformers cost CDT, MV feeders cost CMV and the damage cost of technical risks CTR specifically introduced here. s CTR
Nb X b¼1
3.2. Proposed cost model
s CMV
(13)
The investment cost is determined using the equivalent annual cost of MV feeders. The equivalent annual cost is the cost per year of an asset over its entire life-cycle duration. It is calculated by dividing the NPV of cost by the annual cost factor (acf) which can be found in engineering economy textbooks [20].
CInv ¼ ðacf Þ1
Here, r is the corresponding probability of energy demand, failure rate, failure duration, and energy price. A set of possible scenarios (S) is derived from the union of jDl , jRf , jDf , and jEp .
s CDT
s s CMV ¼ CInv þ COM þ CLs þ CInt
(7)
s2S
s CTot
interruptions. The last two entries depend on the scenario s considered. The total cost of planning is defined as:
(12)
The cost components of distribution transformers are described in detail in Ref. [19] that include investment, maintenance, losses and reliability costs. The annualized value of these costs are considered to constitute distribution transformers cost. The cost of MV feeders consists of operation and maintenance cost COM, the equivalent annual cost of investment CInv, power losses cost CL, reliability cost CInt referring to the service
The cost of the feeder losses includes two parts. One part is the energy loss cost, which is proportional to the cost per kilowatthour. The second part is power loss and related to the worth of loss in peak hours and calculated based on the cost saving due to reduce 1 kW in the peak power [21]. Without loss of generality, in this paper the calculations are made for a single reference hour considering peak load and the load loss factor (LSF) is used to represent the average losses [22]. With reference to the entries indicated in the Nomenclature, the feeder loss cost in scenario s is defined as: Nb X 2 s s CLs ¼ Kpl þ Kel LSF 8760 rb Lb Ibs
(17)
b¼1
In the above equation, the costs of energy and power losses and also the current flowing through the feeders are varied in different scenarios. Therefore, the value of losses cost is varied in different scenarios and indicated by a probability distribution instead of a single value. The reliability cost is determined based on the customer interruption cost. The causes of interruptions are the outages of the MV
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
6
M. Esmaeeli et al. / Energy xxx (2016) 1e10
feeders. The probabilistic behaviors of failure rate and failure duration are considered in scenario generation. Thus, the interruption cost is varied in different scenarios and is defined as: s CInt ¼
Nb X
Rfbs Lb Dfbs
X
LF Dsn cos f ocn
(18)
n2DNb
b¼1
Due to the failure of branch b, all its downstream nodes are interrupted. Thus, the interruption cost is calculated using the demand summation of all nodes downstream branch b. 3.3. Technical risk cost 3.3.1. Components of the technical risk cost The components of the technical risk costs are associated to the constraints of the feeder routing problem. The radiality constraint is addressed by using the branch exchange method (Section 2), which allows the generation of radial configurations only, so that it is not associated to any technical risk cost. The other constraints may be within acceptable limits in deterministic planning, but in some scenarios, the feeder current and voltage drop may exceed the acceptable limits. The exceeding quantities correspond to technical risks for the distribution system. To manage these technical risks in optimal configuration, they should be considered in the planning. In this paper, a single objective function based on economic terms is assumed. Therefore, these technical risks are transformed into economic risks calculating the worth of their damages. In particular, two issues are considered, referring to the risk of overcurrent in the branches and to the risks related to node voltage deviations (undervoltages and overvoltages) from the acceptable range. 3.3.2. Technical risk cost component due to overcurrents The overcurrent through the conductors causes extreme increasing of their temperature, which may have both mechanical and electrical effects. Three main factors should be considered in defining the thermal limit of a power line: loss of strength, overhead line sag, limitation of the conductor fittings. It has been shown that correctly designed and selected fittings are not a restrictive factor for the thermal limit [23]. In addition, the designed safety margin of MV feeders is often specified large enough so that under most conditions, the probability of occurrence for a flashover due to
Fig. 4. Loss of conductor life due to overcurrent.
sag is extremely small. Hence, only the loss of strength is considered in this study. The damages due to loss of strength for MV feeders are analyzed in Ref. [23] where the monetary worth of loss of conductor life due to overcurrent is modeled. The proposed model is represented in Fig. 4, where the overcurrent ratio is defined as the ratio between the actual current and the rated current. The vertical axis of the curve is normalized by the feeder installation cost while the horizontal axis contains multiples of the rated current of the conductor. Therefore, the cost of overcurrent risk in MV feeders can be calculated using the abovementioned curve as a function of feeder current and can be stated as LLb ðIbs Þ. The cost of overcurrent risk in branch b and scenario s can be expressed as: b;s COC ¼
LLb Ibs FICb 0
Ibs > Ibrated otherwise
(19)
When the feeder current is less than its rated value, the overcurrent risk does not occur and its cost is zero. Furthermore, the transformer overload constraint is considered by using a penalty function representing the effect of the overload on the transformer's loss of life [19]. For each scenario, there is a possibility of transformer overload. The corresponding loss of life (LOL) is determined in function of the transformer overload by using the data reported in Ref. [24], and is then converted into a penalty cost considering the annualized cost obtained by dividing the net present value by the annual cost factor acf defined in (15). The penalty cost for the overload of the distribution transformer t in scenario s is expressed as in Ref. [19]: t;s CODT ¼ LOLst
TICt acf
(20)
3.3.3. Technical risk cost component due to voltage deviations There is a growing interest in using performance based regulation (PBR) along with quality regulation for distribution network [25]. In this approach, some penalty and reward mechanisms are defined based on performance of network operators. About voltage deviations, the acceptable range for the node voltage is assumed to be from 0.9 to 1.1 per units; thereby, penalties are adopted for voltages approaching these limits [10]. The penalty will start if the voltage deviation in a load point exceeds 5% of the rated voltage (Fig. 5). The overvoltage may happen only in distribution systems with distributed generation or with electric vehicles injecting power into the grid. In this paper, a penalty function FPðVns Þ is defined as a PBR for the value of undervoltage or overvoltage in the load points. This penalty is determined based on the customer damages because extreme undervoltage or overvoltage could endamage some equipment where electrical motors are most important among them [26]. There are upper and lower caps for the penalty function.
Fig. 5. The voltage penalty function designed as PBR.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Between these caps, the function is assumed linear in accordance to undervoltage severity function presented in Ref. [10]. The cost of voltage deviation risk in node n and scenario s can be expressed (considering the entries defined in the Nomenclature) as:
n;s CUOV ¼ PNLmax Dsn cos f FP Vns
(21)
In this paper, the maximum damage cost to the customer equipment PNLmax is determined based on the worth of electrical motors and their proportion to the customer load while the possible damages of other equipment are ignored. The PNLmax could be defined in any other way while the basis of the proposed approach is not changed. The cost of technical risk is a combination of the abovementioned costs. Thus, this cost is defined as: s CTR ¼
Nb X b¼1
b;s COC þ
Nn X
n;s CUOV þ
n¼1
Nt X t;s CODT
(22)
t¼1
7
The distribution system is generally sized in such a way to have enough adequacy for all load levels, including peak and off-peak hours. The demand of a load point in the worst scenario during off-peak hours is lower than the demand during peak hours. Therefore, the problems related to overcurrent and extreme voltage drop are only considered in peak hours, while overcurrent and undervoltage do not happen in off-peak hours. Conversely, the risk of overvoltage is more likely to appear during off-peak hours with significant presence of local generation. However, the possibility of connecting local generation capacity in the system is limited by the grid connection rules to avoid causing problems to the distribution system. These rules also take into account the limits due to the occurrence of overvoltages. As such, overvoltages could even not appear in the scenario studies. The probabilistic behavior of the system is evaluated by using possible scenarios generated using the discrete probability distributions of the uncertain parameters (the values are shown in the following sections). The proposed technique is developed in MATLAB code and the computational time required was less than 1 min using a computer with 2.53 GHz, Core i5 CPU, and 4 GB of RAM. The optimal network structure with and without considering the proposed risk-based method is investigated in two cases.
3.4. Load and local generation model The load curve related to the peak day is typically used for indicating the yearly load [27]. As implemented in Ref. [28], the daily load curve can be presented by a two-step load cycle. The steps are indicating the average off-peak load and the peak load which is assumed that remains for h hours. In this study, similar to [28], the duration of peak hours is considered 4 h a day. For the purpose of load flow calculations, the relevant entry is the net power demand (that is, load minus local generation) at each node, considering the local generation as a negative load. The feeder parameters are known. In the presence of local generation, the scenarios constructed include both different loading levels and different local generation penetrations. In each scenario, loads and generations are assumed to be exactly defined and are static. Since the local generation is owned and managed by a different entity with respect to the distribution system operator, the costs related to the presence, operation and maintenance of the local generators are not included in the planning analysis. 4. Numerical results The proposed method is applied to a 20-kV distribution network containing 52 distribution transformers (load points) and 2 subtransmission substations. It is assumed that the transformers are sized already in accordance to the method proposed in Ref. [19], therefore distribution transformers can be considered as load points in the feeder routing problem. The positions of substations, load points, and possible feeders are shown in Fig. 6. The data of load points and substations are presented in Tables A1 in the Appendix. Two different types of conductors could be used in the feeders. The characteristics of the available conductors are shown in Table A2 in the Appendix. The load factor and loss factor are assumed respectively 0.6 and 0.35 [29]. The power factor of load points is assumed to be 0.85. The maximum allowable voltage drop is 5% of the rated voltage. The discount rate is 7% and the lifetime of the project is assumed to be 20 years. The outage cost is 4 $/kWh [30]. The value of PNLmax is assumed 112 $/kW [31]. The forecast values of the energy loss cost (Kel) and the peak power cost (Kpl) for horizon year are respectively 0.04 $/kWh and 168 $/kW [20]. Using the model described in Ref. [19], the relevant values of the quantities to be used in each scenario are determined.
4.1. Case 1 e traditional feeder routing In the traditional approach to feeder routing, uncertainties are neglected. This approach is applied to the test service area shown in Fig. 6. In this case, the objective of the planning problem is to minimize the deterministic costs. In this case, technical constraints are always in acceptable margins because the uncertainties are neglected. The results of the optimal routing for MV feeders are shown in Fig. 7. The total deterministic cost of the planning for this test system is $345,800. The corresponding four components of investment, maintenance, losses, and reliability costs are equal to $209,270, $16,628, $48,161, and $71,743, respectively. In this case, the probabilistic behaviors of system's parameters are not considered while they do exist in a real distribution system. To analyze the qualification of the obtained plan in the presence of uncertainties, it is evaluated through different scenarios. Discrete probability distribution sets are used for scenario generation and shown in Table 1. The probabilistic costs associated to this plan are presented in Table 2. 4.2. Case 2 e risk-based feeder routing In risk-based planning, more attention is paid to the extreme events during the decision-making process. The technical risk including overcurrent and voltage deviations are converted into a monetary term using the model indicated in Section 3.3. In this case, the objective of the planning problem is to minimize the cost of the worst possible scenarios. This planning approach is implemented by using CVaR0.95 in calculating the objective function. The proposed method is applied to the test service area. The results of the planning are shown in Fig. 8. The values of the objective function CEx þ CVaR0.95 is equal to $525,380 (while its value was $577,010 in the previous case). In other words, the risk-based planning has improved the results by almost 10% reduction in the cost of worst scenarios. A comprehensive comparison between these two cases is presented in Table 2. As seen in Table 2, the deterministic cost in Case 2 increased in comparison to Case 1 as the investment cost increases. The additional investment cost in Case 2 is due to change in the feeders' costs. In risk based planning, the DSO pays this additional
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
8
M. Esmaeeli et al. / Energy xxx (2016) 1e10
Fig. 6. Available supply routes for 52 load points distribution network.
Table 2 Cost components in various cases ($). Cost component
Case 1 (Traditional)
Case 2 (Risk-based)
Investment Maintenance Losses (worst) Reliability (worst) Technical risk (worst) Deterministic cost Expected cost (CEx) CEx þ CVaR0.95 Worst scenario
209,270 16,628 106,200 401,760 75,900 345,800 382,430 577,010 809,750
222,580 17,685 87,056 375,340 10,980 346,770 371,950 525,380 713,640
cost to decrease the imposed cost in the worst scenarios. Here, the cost of the worst scenario in Case 1 is $809,750 while it is $713,640 in Case 2.
5. Conclusion Fig. 7. Optimal network structure for traditional feeder routing.
The mathematical model of a new risk-based method for optimal feeder routing has been developed to address MV
Table 1 Discrete probability distribution of uncertain parameters. Load
Failure rate
Failure duration
Energy price
Probability
Amount
Probability
Amount
Probability
Amount
Probability
Amount
0.38 0.24 0.24 0.07 0.07
100% 95% 120% 90% 140%
0.40 0.20 0.20 0.10 0.10
100% 70% 150% 50% 200%
0.40 0.20 0.20 0.10 0.10
100% 75% 150% 50% 200%
0.65 0.25 0.10
100% 105% 125%
Amount x% means it is x% of the deterministic value.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
M. Esmaeeli et al. / Energy xxx (2016) 1e10
9
Table A1 Load and coordinates of load points and substations.
Fig. 8. Optimal network structure for risk-based feeder routing.
networks exposed to economic and technical risks. The proposed method considers the stochastic behavior of distribution system demand and local generation through a set of scenarios. The problem is solved by using the branch exchange algorithm. The proposed method optimizes the cost of planning for the worst possible scenarios using risk analysis indexes. The decision about optimal configuration is made on the basis of the costs occurring for extreme events. This method is useful for the distribution system operator (DSO) to make decisions about the choice of the planning scheme to be adopted, considering the DSO attitude to accept risks or its risk aversion. The DSO can compare the required additional cost and reduction in worst scenarios to choose the planning scheme. The VaR and CVaR indices make it available more information to the decision maker. The proposed method has been executed on an electrical distribution system with 2 substations and 52 load points. The results show that the proposed risk-based method could reduce the risk of planning due to uncertain parameters. Low-probability events with significant consequences are considered as extreme events. In the risk-based approach, the costs of the extreme events are reduced considerably in comparison to the traditional approach, while the additional required deterministic cost is much lower than this reduction. The main idea of the proposed method can be extended to larger distribution grids with no conceptual changes. On a large scale, the cost reductions could be quantitatively more significant. The optimal structure of the distribution grid is found on the basis of the scenarios identified by the user. Clearly, the definition of many scenarios on a large grid could increase the computation time, but with an accurate choice of the number and type of scenarios done by the user the overall computation time may remain tractable.
Appendix A Test system data The data for the test system are presented in the following tables. The data include load and locational coordinates, to guarantee replicable results.
No.
X (km)
Y (km)
Load (kVA)
No.
X (km)
Y (km)
Load (kVA)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
2.5 4 5 6.5 1.5 3.5 5.5 7.5 1 4 5 8 2 3.5 5.5 7 1 2.5 4 5 6.5 8 3 4.5 6 3.5 5.5
0.6 0.6 0.6 0.6 1.2 1.2 1.2 1.2 1.8 1.8 1.8 1.8 2.4 2.4 2.4 2.4 3 3 3 3 3 3 3.6 3.6 3.6 4.5 4.5
350 630 980 112 210 112 70 112 280 420 350 350 350 630 350 350 280 350 350 140 350 350 630 280 420 420 420
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 100 200
3 4.5 6 1 2.5 4 5 6.5 8 2 3.5 5.5 7 1 4 5 8 1.5 3.5 5.5 7.5 2.5 4 5 6.5 1.5 7.5
5.4 5.4 5.4 6 6 6 6 6 6 6.6 6.6 6.6 6.6 7.2 7.2 7.2 7.2 7.8 7.8 7.8 7.8 8.4 8.4 8.4 8.4 4.5 4.5
420 980 630 350 350 140 350 350 980 630 350 350 350 350 350 420 280 112 70 112 210 112 980 630 350 e e
The substations are indicated as bold.
Table A2 Available conductors' specifications. Capacity Installation (A) cost ($/km)
Maintenance Impedance cost ($/km) (U/km)
80 100
225 270
30,000 36,000
Failure rate (failures/ (km.yr))
1.38 þ j0.39 0.1 0.91 þ j0.38 0.1
Repair duration (h) 4 4
References [1] Wouters C, Fraga ES, James AM. An energy integrated, multi-microgrid, MILP (mixed-integer linear programming) approach for residential distributed energy system planningeA South Australian case-study. Energy 2015;85:30e44. [2] Yokoyama R, Shinano Y, Taniguchi S, Ohkura M, Wakui T. Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation. Energy Convers Manag 2015;92:92e104. [3] Khator SK, Leung LC. Power distribution planning: a review of models and issues. IEEE Trans Power Syst 1997;12(3):1151e9. [4] Aghaeia J, Muttaqi KM, Azizivahed A, Gitizadeh M. Distribution expansion planning considering reliability and security of energy using modified PSO (Particle Swarm Optimization) algorithm. Energy 2014;65:398e411. [5] Sahoo N, Prasad K. A fuzzy genetic approach for network reconfiguration to enhance voltage stability in radial distribution systems. Energy Convers Manag 2006;47(18):3288e306. [6] Abbasi AR, Seifi AR. Considering cost and reliability in electrical and thermal distribution networks reinforcement planning. Energy 2015;84:25e35. [7] Goswami SK. Distribution system planning using branch exchange technique. IEEE Trans Power Syst 1997;12(2):718e23. [8] Salehi J, Haghifam M-R. Long term distribution network planning considering urbanity uncertainties. Int J Electr Power Energy Syst 2012;42(1):321e33. [9] Miranda V, Proença LM. Probabilistic choice vs. risk analysis: conflicts and synthesis in power system planning. IEEE Trans Power Syst 1998;13(3): 1038e43. [10] Fei X, McCalley JD. Power system risk assessment and control in a multiobjective framework. IEEE Trans Power Syst 2009;24(1):78e85. [11] Gitizadeh M, Kaji M, Aghaei J. Risk based multiobjective generation expansion planning considering renewable energy sources. Energy 2013;50:74e82. [12] Yeddanapudi SRK, Li Y, McCalley JD, Chowdhury AA, Jewell WT. Risk-based allocation of distribution system maintenance resources. IEEE Trans Power Syst 2008;23(2):287e95. [13] Hashemi-Dezaki H, Hamzeh M, Askarian-Abyaneh H, Haeri-Khiavi H. Risk management of smart grids based on managed charging of PHEVs and
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021
10
[14]
[15]
[16]
[17] [18] [19]
[20] [21]
[22] [23]
M. Esmaeeli et al. / Energy xxx (2016) 1e10 vehicle-to-grid strategy using Monte Carlo simulation. Energy Convers Manag 2015;100:262e76. Chiang H-D, Jean-Jumeau R. Optimal network reconfigurations in distribution systems. II. Solution algorithms and numerical results. IEEE Trans Power Deliv 1990;5(3):1568e74. Bompard E, Carpaneto E, Chicco G, Napoli R. Convergence of the backward/ forward sweep method for the load-flow analysis of radial distribution systems. Int J Electr Power & Energy Syst 2000;22(7):521e30. Alvehag K. Impact of dependencies in risk assessments of power distribution system, Licentiate Thesis, Royal Institute of Technology. School of Electronic and Electrical Engineering, Stockholm; 2008. Billinton R, Allan RN. Reliability evaluation of power systems, vol. 2. New York: Plenum Press; 1996. Saber AY, Venayagamoorthy GK. Resource scheduling under uncertainty in a smart grid with renewables and plug-in vehicles. IEEE Syst J 2012;6(1):103e9. Esmaeeli M, Kazemi A, Shayanfar H, Haghifam M-R, Siano P. Risk-based planning of distribution substation considering technical and economic uncertainties. Electr Power Syst Res 2016;30(135):18e26. Blank L, Tarquin A. Engineering economy. McGraw-Hill Science; 2011. Esmaeeli M, Kazemi A, Shayanfar H, Haghifam M-R. Multistage distribution substations planning considering reliability and growth of energy demand. Energy 2015;84:357e64. Gustafson M, Baylor J. Approximating the system losses equation [power systems]. IEEE Trans Power Syst 1989;4(3):850e5. Wan H, McCalley JD, Vittal V. Increasing thermal rating by risk analysis. IEEE
Trans Power Syst 1999;14(3):815e28. [24] Sen PK. Transformer overloading and assessment of loss-of-life for liquidfilled transformers. Power Systems Engineering Research Center (PSERC); 2011. [25] Alvehag K, Soder L. Risk-based method for distribution system reliability investment decisions under performance-based regulation. IET Gener Transm Distrib 2011;5(10):1062e72. [26] IEC60076e7. Power transformers; part 7: loading guide for oil-immersed power transformers. first ed. 2005-12. [27] Cossi AM, Romero R, Mantovani JRS. Planning of secondary distribution circuits through evolutionary algorithms. IEEE Trans Power Deliv 2005;20(1): 205e13. [28] Esmaeeli M, Kazemi A, Shayanfar H, Haghifam M-R. Sizing and placement of distribution substations considering optimal loading of transformers. Int Trans Electr Energy Syst 2015;25(11):2897e908. [29] Ziari I, Ledwich G, Ghosh A. Optimal integrated planning of MVeLV distribution systems using DPSO. Electr Power Syst Res 2011;81(10):1905e14. [30] Samui A, Singh S, Ghose T, Samantaray SR. A direct approach to optimal feeder routing for radial distribution system. IEEE Trans Power Deliv 2012;27(1): 253e60. [31] De Abreu, JG and Emanuel, A. Induction motor thermal aging caused by voltage distortion and imbalance: loss of useful life and its estimated cost. in Industrial and Commercial Power Systems Technical Conference, 2001. Papers Presented at the 2001 IEEE Annual Meeting.
Please cite this article in press as: Esmaeeli M, et al., Risk-based planning of the distribution network structure considering uncertainties in demand and cost of energy, Energy (2016), http://dx.doi.org/10.1016/j.energy.2016.11.021