Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

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Bi-level Coordinated Planning of Active Distribution Network Considering Demand Response Resources and Severely Restricted Scenarios  PDF

  • Yixin Huang
  • Zhenzhi Lin
  • Xinyi Liu
  • Li Yang
  • Yangqing Dan
  • Yanwei Zhu
  • Yi Ding
  • Qin Wang
College of Electrical Engineering, Zhejiang University, Hangzhou, China; State Grid Zhejiang Economic Research Institute, Hangzhou, China; State Grid Ningbo Power Supply Company, Hangzhou, China; Electric Power Research Institute, Palo Alto, USA

Updated:2021-09-28

DOI:10.35833/MPCE.2020.000335

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Abstract

Due to the uncertainty and fluctuation of distributed generation (DG) and load, the operation of active distribution network (ADN) is affected by multi-dimension factors which are described by massive operation scenarios. Efficient and accurate screening of severely restricted scenarios (SRSs) has become a new challenge in ADN planning. In this paper, a novel bi-level coordinated planning model which combines the short-time-scale operation problem with the long-time-scale planning problem is proposed. At the upper level, the demand response (DR) resource, an effective non-component planning resource characterized by low capacity price, high energy price, and short contract term, is co-optimized with the configuration of lines and energy storage systems (ESSs) to achieve the economic trade-off between the investment cost and the operation cost under SRSs. At the lower level, with the planning scheme obtained from the upper level, massive operation problems are optimized to minimize the daily operation cost; and the SRSs are provided to the upper level through a shadow-price-based scenario screening method, which simulates the planning information (i.e., the restricted degrees of operation scenarios) feedback process from ADN operators to ADN planners. Case studies on a 62-node distribution system in Jianshan New District, Zhejiang Province, China, illustrate the effectiveness of the proposed bi-level coordinated planning model considering DR resources and SRSs.

I. Introduction

NOWADAYS, more distributed generations (DGs) such as photovoltaic (PV) and wind turbine (WT) are connected to the distribution network due to their advantages of low carbon emissions, high efficiency, and high flexibility [

1], which brings in numerous operation scenarios with high risks but low probabilities [2], [3]. In some of these operation scenarios, the inadequate ability of the distribution network to consume renewable energy raises requirements for expensive additional investments [4]. The optimal dispatching of energy storage system (ESS) [5], [6], electric vehicle (EV) [7], combined heat and power (CHP) unit [8], and demand response (DR) [9] is considered in active distribution network (ADN) operation and planning, which not only reduces the operation risks caused by the mass connection of DGs, but also improves the economic performance of the distribution network planning scheme.

The economy, reliability, and flexibility of ADN can be improved by optimal planning and dispatching of DG [

10], [11]. Considering the active management of DG, a multistage ADN planning model is proposed in [12] to decide the installation location, capacity and time of substations, lines, capacitors, and voltage regulators. In [13], the DG investment is integrated with a multi-stage planning model of lines and substations to reduce the investment cost. To handle the uncertainties caused by DG and load [14], [15], the stochastic theory [16]-[19] and robust theory [20]-[22] are widely applied in ADN planning models. In [21] and [22], robust distribution network planning models are proposed considering the uncertainty of the demands of load and EV. Based on the stochastic theory, the uncertain characteristics of loads and DGs are modeled with probability distribution functions. In [23], the uncertain forecasting errors of DGs are described with Gaussian distribution to obtain the confidence intervals of the forecasting load. With the development of the multi-scenario technique, the uncertainties of ADN planning are described as probabilistic scenarios. Based on the multi-load scenarios obtained from the forecasting data, an ADN planning model is presented in [16] to obtain the optimal reconfiguration of lines and DGs for power system planners, as well as the economic dispatching of DG and the topology reconfiguration for grid companies. In [17], based on several representative scenarios describing the uncertainty of DG and load, a bi-level ADN planning model is proposed to determine the distribution network frame at the upper level and the DG optimal configuration at the lower level. The correlated uncertainty of DG and load is represented with equiprobable scenarios in the stochastic programming model proposed in [18]. To avoid the computational burden [24], only several predetermined scenarios rather than massive scenarios are considered in [16]-[18]. It is difficult for ADN operator to identify all scenarios which should be considered in ADN planning based on experience. In power system economics, the shadow prices of active constraints reflect the marginal values of an optimal operation cost [25], [26]. The scarcity of an ADN planning resource in an operation scenario is quantitatively assessed by the shadow price, which further reflects the restricted degree of the scenario, i.e., the value and necessary level to be considered in the ADN planning. In this paper, a shadow price-based scenario screening method is proposed to screen out the necessary scenarios for ADN planning.

The impacts of price-based DR programs such as time of use (TOU) program [

27] and real-time pricing (RTP) program [28], [29] are investigated in existing ADN planning models. The load adjustment can be achieved based during different TOU pricing strategies at different time periods [30]. In [31], different TOU pricing strategies at different time periods are incorporated in the ADN planning model to postpone the investment. In [32], the influences of different TOU-based DR policies and penetration rates on possible benefits and overcharges are considered in the proposed ADN planning model with the minimum investment and operation costs. In [33], the RTP-based DR is integrated with the planning model to balance load and electricity supply in the ADN with high penetration of DG. In [34], [35], the planning models considering the own-price and cross-price elasticities of RTP-based DR are established to determine the investment of ADN components. It can be seen that the DR is considered in the short-term operation problems in the ADN planning scheme only, rather than as a long-term non-component planning resource directly in [30]-[35]. In fact, the management risk and the overall cost of electricity utilities can be reduced with the capacity cost prepaid to the long-term DR resource procured in the ADN planning phase [36]. For example, both PJM capacity market, called the reliability pricing model, and ISO-NE forward capacity market (FCM) procure DR resources to meet anticipated demands on a rolling three-year schedule [37]. In this paper, both the short-time-scale dispatching of DR and the long-time-scale procurement of DR resources are considered in the ADN planning to improve the benefits of electricity utilities.

In this paper, a novel bi-level coordinated ADN planning model is presented, considering DR resources and severely restricted scenarios (SRSs) screened out by a shadow-price-based scenario screening method. The main contributions of this paper are as follows.

1) The DR resource is regarded as a non-component planning resource and integrated into the proposed bi-level coordinated ADN planning model, considering both the capacity cost prepaid in the planning phase and the energy cost calculated in the operation phase. A better trade-off between long-term investment cost and short-term operation cost is achieved by the proposed model with DR resources than the models without DR resources.

2) Based on the shadow price theory in power system economics, the scenario impact factor is presented to evaluate the economic benefits of ADN resource planning in each scenario, which effectively reflects the influence of the ADN operation scenario on the ADN planning. The screening of massive scenarios for ADN planning is efficiently achieved to select out the important SRSs to be planned, which helps obtain better planning results than the methods with experiential predetermined scenarios.

II. DR in ADN Planning and Operation

Figure 1 illustrates the coordinated optimization of ADN. Generally, the long-term and ultra-short-term load demands in ADN are met with the investment and the economic dispatch of component resources such as lines and ESSs, respectively. Due to the high penetration of DG, ADN planners need to consider the short-term or even ultra-short-term load demands under various operation scenarios and achieve a coordinated optimization of the ADN planning and operation. The short time-scale operation cost can be reduced by avoiding load curtailment and consuming more renewable energy through the dispatch of ESS. However, due to its long lifecycle and high construction cost, the ESS configuration cannot be changed flexibly. As a non-component planning resource, the DR contract is signed by power consumers with electricity utilities, which is characterized by low capacity price, high energy price and short contract term [

38]. For example, the ISO-NE annual capacity auction prices are only 4.63  $/(kWmonth) and 3.80  $/(kWmonth), in 2018 and 2019, respectively. Within the DR contract period, customers participating in capacity market receive payments for the load (e.g., air conditioners [39], water heaters [40], and ice-storage air-conditioners [41]) reductions, which are made to satisfy the short-term dispatch demand [42], effectively delaying the construction of lines and ESSs. When the contract expires, the DR contract will not be renewed if the controllable load is no longer required for the economic dispatch. Consequently, less long-term impacts on the ADN and better economic benefits to deal with the short-term dispatch demand are achieved through the procurement of DR resources compared with the construction of component planning resources such as lines and ESSs in some situations.

Fig. 1 Coordinated optimization of ADN.

In the ADN planning phase, the DR capacity cost Ccap is paid by electricity utilities to DR resource providers, i.e.,

Ccap=n=1NT(1+ρ)-n+1mΩmiΩnodemcn,m,icapPn,m,icap (1)

Based on the characteristics of different DR resources and consumer psychology, the maximum potential coefficient αn,m,iDR reflects the largest incentive-based response capacity of the DR resource provider at node i of load type m at planning stage n. The contract capacity Pn,m,icap is limited by αn,m,iDR, which is expressed as:

0Pn,m,icapP¯n,m,iloadαn,m,iDR (2)

The piecewise linear curve of αn,m,iDR represented in Fig. 2 is expressed as:

αn,m,iDR=00cn,m,icapcn,m,deadcapKn,mDR(cn,m,icap-cn,m,deadcap)cn,m,deadcap<cn,m,icap<cn,m,satcapαn,m,maxDRcn,m,icapcn,m,satcap (3)

Fig. 2 Piecewise linear curves of the maximum potential coefficient.

In the ADN operation phase, the procured DR resources can be dispatched for economic operation in all scenarios. The DR energy cost Csene is calculated according to the actual usage of DR resources in scenario s, i.e.,

Csene=mΩmiΩnodemt=tm,istarttm,iendcn,m,ienePs,m,i,tDRΔt (4)

For each operation scenario s, the hourly DR power is constrained by the minimum limit and the contract capacity during the DR event period, as shown in (5); and the hourly DR power is zero beyond the DR event period, as shown in (6); and the duration of each DR event period cannot exceed the maximum limit, as shown in (7).

Pn,m,minDRPs,m,i,tDRPn,m,icap    ttm,istart,tm,iend (5)
Ps,m,i,tDR=0    ttm,istart,tm,iend (6)
tm,iend-tm,istartTmaxDR (7)

III. Bi-level Coordinated ADN Planning Model Considering DR Resource and SRS

Generally, the best economics of the ADN planning scheme is guaranteed in the planning model based on a universal operation scenario set. However, the number of decision variables and constraints is too large to be solved within an acceptable time. A planning scenario set with finite predetermined scenarios may lead to incorrect planning decisions. Ignoring some representative scenarios could lead to the inadequate investment cost and high operation cost; and over-evaluating the risks of some scenarios might lead to low utilization for the newly installed components and high investment cost. To reach an acceptable optimization time and achieve a trade-off between the investment cost and the operation cost during the whole planning period, an SRS set is built through scenario screening for the bi-level coordinated ADN planning model in this paper. The non-network solution, including the economic dispatch strategies and the restricted degrees of scenarios, is obtained in the lower level of the proposed model. Then, the SRSs are screened out and fed back to the upper level of the model to obtain the network solution. The approximately optimal solution is obtained after several iterations between the two levels.

A. Economic Dispatch Problem of ADN Considering DR in Lower Level

As discussed in Section II, the ability of ADN to deal with short-term operation risks caused by the mass connection of DG can be enhanced by DR, which is considered in the economic dispatch problem in the lower level of the model.

In the lower level of the proposed model, the decision variables include the hourly power of ESS, DR, WT, PV, and load shedding. The economic dispatch problem is to minimize the daily operation cost Csope, which includes the energy purchase cost Cspur, power loss cost Csloss, DR energy cost Csene, and penalty cost Cspenalty for PV curtailment, WT curtailment, and load shedding, and is expressed as:

minCsope=Cspur+Csloss+Csene+Cspenalty (8)
Cspur=iΩsubt=1TPs,i,tpurctpurΔt (9)
Csloss=ijΩlinet=1TctpurPs,ij,tlossΔt=ijΩlinet=1TctpurIs,ij,t2rijΔt (10)
Cspenalty=iΩnodet=1TcPVP(P¯s,i,tPV-Ps,i,tPV)Δt+cWTP(P¯s,i,tWT-Ps,i,tWT)Δt+cshedPs,i,tshedΔt (11)

The decision variables of the economic dispatch problem are constrained by the DR constraints (5)-(7) and the operation constraints. The operation constraints are represented as:

(1-θWT)P¯s,i,tWTPs,i,tWTP¯s,i,tWT (12)
(1-θPV)P¯s,i,tPVPs,i,tPVP¯s,i,tPV (13)
jkΩlinePs,jk,tline=ijΩline(Ps,ij,tline-Is,ij,t2rij)-Ps,j,t (14)
jkΩlineQs,jk,tline=ijΩline(Qs,ij,tline-Is,ij,t2σij)-Qs,j,t (15)
Ps,j,t=P¯s,j,tload-Ps,j,tpur-Ps,j,tWT-Ps,j,tPV-Ps,j,tshed-Ps,j,tDR-Ps,j,tdis+Ps,j,tchar (16)
Qs,j,t=Qs,j,tload-Qs,j,tpur-Qs,j,tWT-Qs,j,tPV+Qs,j,tCB (17)
Vs,i,t2Is,ij,t2=(Ps,ij,tline)2+(Qs,ij,tline)2 (18)
Ps,ij,tlineSn,ijline (19)
Ps,j,tpur0 (20)
Vs,j,t2Vs,i,t2-2(rijPs,ij,tline+σijQs,ij,tline)+Is,ij,t2(rij2+σij2)+M(1-yn,ijline) (21)
Vs,j,t2Vs,i,t2-2(rijPs,ij,tline+σijQs,ij,tline)+Is,ij,t2(rij2+σij2)-M(1-yn,ijline) (22)
Vi,minVs,i,tVi,max (23)
0Ps,i,tshedλP¯s,i,tload (24)
0xs,i,tdis+xs,i,tchar1 (25)
xs,i,tdisPs,i,tdis-xs,i,tcharPs,i,tcharPiESS (26)
Ei,minSOCEs,i,tSOCEi,maxSOC (27)
Es,i,tSOC=(1-ε)Es,i,t-1SOC-1γdisPs,i,tdisΔt+γchPs,i,tchΔt (28)
Es,i,1SOC=Es,i,TSOC (29)

The hourly output power of DGs is constrained in (12) and (13). The nodal power balance equations are represented in (14)-(17). The square of the current magnitude of line ij is computed in (18). The power flow constraint considering the bidirectional power flow is formulated in (19). Constraint (20) prevents power from being injected into the upper power grid. The big-M method is used in (21) and (22) to deal with the nonlinear terms when considering the radial topology distribution network [

43], [44]. The nodal voltage is limited in (23). The load shedding power of every node is constrained in (24). The constraints for discharging and charging status and hourly power of ESS are defined in (25) and (26), respectively. The stored energy of ESS is constrained in (27). The ESS power balance constraint is shown in (28). Constraint (29) guarantees the conservation of daily charging and discharging energy.

B. ADN Planning Considering DR Resource in Upper Level

The objective of the ADN planning model is to minimize the total cost Ctotal including the investment cost of lines and ESSs Clineinv and CESSinv, the capacity cost of DR contract Ccap, the maintenance costs of lines and ESSs Clinem and CESSm, and the daily economic dispatching cost under SRSs Cs*, which is formulated as:

minCtotal=Clineinv+CESSinv+Ccap+Clinem+CESSm+Cs* (30)
Clineinv=n=1NT(1+ρ)-nρρ(1+ρ)Yline(1+ρ)Yline-1ijΩNlinerΩNlrxn,ijlinecrLij+ijΩRlinerΩRlrxn,ijlinecrLij (31)
CESSinv=n=1NT(1+ρ)-nρρ(1+ρ)YESS(1+ρ)YESS-1iΩNESSxn,iNESScS,iNESS+iΩEESSΩNESScP,iESSPn,iESS+cE,iESSEn,iESS (32)
Clinem=n=1NT(1+ρ)-nijΩElineclinemLij+ijΩNlinexn,ijlineclinemLij (33)
CESSm=n=1NT(1+ρ)-niΩEESSΩNESScESSmEn,iESS (34)
Cs*=sΩs*δ(1+ρ)-npsCsope (35)

In (30)-(35), the long-term decision variables include investment variables for the installation and reinforcement of lines xn,ijline, the installation and expansion of ESS xn,iNESS, Pn,iESS and En,iESS and the contract amount of DR Pn,m,icap. The investment constraints are represented as:

n=1NTxn,ijline1 (36)
n=1NTxn,iNESS1 (37)
0Pn,iESSPi,maxESS   (38)
0En,iESSEi,maxESS   (39)
yn,ijline=1              ijΩElinen=1NTxn,ijline    ijΩNline (40)
ijΩLlineΩElineyn,ijline+ijΩLlineΩNlineyn,ijlineNLS-1 (41)
CninvCmaxinv (42)

Throughout the entire planning horizon, each line and ESS are allowed to be constructed once at most, as constrained in (36) and (37), respectively. The maximum power and stored energy limit of ESS are constrained in (38) and (39), respectively. The construction state of line is constrained in (40). The radiality of the distribution network is constrained in (41). As discussed in Section II, DR potential capability is constrained in (2). The investment cost constraint at every planning stage is represented in (42).

The constraints associated with the ADN operation should be satisfied at each time period in all planning scenarios, which are listed in (12)-(29).

C. Shadow-price-based SRS Screening Method

The uncertainty and fluctuation levels of the ADN are enhanced by the development of DG and load, which generates a variety of restricted scenarios. The restricted scenarios represent those with congestion and high operation cost due to the insufficiency capacity of power grid resources. The best planning scheme can be achieved with the planning model considering all operation scenarios but is time-consuming and difficult to be solved. There are unrestricted scenarios and some restricted scenarios that do not need to be considered in the planning phase because of their low restricted degrees or probabilities. The operation risks in these scenarios may be reduced when the network solution is made for other scenarios with more severely restricted degrees. In this paper, a novel shadow-price-based SRS screening method is proposed to screen out the correct scenarios, which should be considered in ADN planning in the massive operation scenarios.

The shadow price, i.e., Lagrange multiplier, is the additional product when using the primal-dual interior-point method based on Karush-Kuhn-Tucker (KKT) conditions, which evaluates the worth of increment for additional unit capacity quantitatively [

45]. In the ADN planning model, the limits of some constraints are decided by the capacities of power system resources. The Lagrange multipliers of the upper limit of DR power constraint, the upper and lower limits of power flow constraint, and the upper limits of ESS power and stored energy constraints (i.e., μs,m,i,t, νs,ij,tu, νs,ij,td, πs,j,t, and τs,j,t) correspond to the shadow prices of DR resources, lines and ESSs, respectively. Based on these Lagrange multipliers, a new factor named as the shadow price of scenario Ψs is defined to evaluate the restricted degree of scenario, which is represented as:

Ψs=mΩmiΩnodemt=1Tμs,m,i,tcmcap+ijΩNlineΩElinet=1Tνs,ij,tu+νs,ij,tdcr+iΩEESSΩNESSt=1Tπs,i,tcP,iESS+τs,i,tcE,iESS (43)

It is noted that the scenario probability is independent of the shadow price of scenario, which is important to evaluate the restricted degree of scenario. The scenario impact factor ζs is defined to describe the restricted degree of scenario and screen out the SRSs, and it can be represented as:

ζs=Ψsps (44)

The overall scarcity of the ADN resources in operation scenario s is reflected through the scenario impact factor ζs. Unit investment in the scenario with a larger ζs will get better marginal benefits in reducing the operation costs and risks. According to the impact factor ζs, all operation scenarios are evaluated objectively and those with great marginal benefits of investment are selected into the SRS set Ωs* for ADN planning, which can be represented as:

Ωs*=s*ζs*maxζ0,1NssΩsζs,s*Ωs (45)

According to (45), the scenarios with larger impact factors than the threshold or the average of all scenario impact factors ζ0 are included in the SRS set (i.e., the planning scenario set). The SRS set simulates the information transmitted from system operators to ADN planners.

D. Bi-Level Coordinated ADN Planning Model

1) Upper-level Model

minΩuCtotal=Clineinv+Clineinv+Ccap+Clinem+CESSm+Cs*s.t.  (2), (5)-(7), (12)-(29), (36)-(42)         sΩs*,mΩnodem,iΩnode,jΩnode,kΩnode,        ijΩline,jkΩline,n=1,2,...,NT,t=1,2,...,T (46)

2) Lower-level Model

minΩlCsope=Cspur+Csloss+Csene+Cspenaltys.t.  (5)-(7), (12)-(29)        sΩs,mΩnodem,iΩnode,jΩnode,kΩnode,        ijΩline,jkΩline,t=1,2,...,T (47)

The proposed bi-level planning model consists of a master problem of ADN planning and a set of sub-problems of ADN operation. The intermediate variables between the upper- and lower-level models are the SRSs screened out based on the simulation result of ADN operation and the ADN planning solution, which reflects the interaction between ADN planning and operation.

IV. Iterative Solving Process of Bi-level Coordinated Planning Model

With the SRS screening method introduced in Section III-C, the planning scenario sets are built for the planning model to obtain the network solutions in every iteration until the approximately optimal solution is obtained. In the solving process, the second-order cone relaxation is applied to simplify the non-convex nonlinear planning model in the lower level to the convex linear planning model [

46]-[48].

A. Iterative Solving Process of Bi-level Optimization Model

The flowchart of the proposed bi-level coordinated planning model is presented in Fig. 3. The iterative solving steps are summarized as follows.

Fig. 3 Flowchart of proposed bi-level coordinated planning model.

Step 1:  input the initial distribution network information (network solution) and the parameters for ADN planning.

Step 2:   set τ=0 and s=1.

Step 3:   solve the lower-level economic dispatch in scenario s. The non-network solution including the economic daily dispatch strategy and the Lagrange multipliers (i.e., shadow prices) of DGs, ESSs, and DR contracts is obtained.

Step 4:   calculate Ψs and ζs.

Step 5:   if s>Ns, turn to Step 6; otherwise, set s=s+1 and return to Step 3.

Step 6:  screen out Ωs* with the proposed SRS screening method.

Step 7:   if Ωs* is an empty set, turn to Step 11; otherwise, return to Step 8.

Step 8:   solve the upper-level planning problem considering Ωs*. The τth network solution including the line and ESS investment and the DR contract signing decisions is obtained.

Step 9:   if the planning result is changed, turn to Step 10; otherwise, turn to Step 11.

Step 10:   update the distribution network scheme with the network solution and set τ=τ+1.

Step 11:   output the ADN planning result.

B. Conversion Method of Constraint Based on Second-order Cone Relaxation

The proposed economic dispatch problem is a non-convex nonlinear programming problem which is difficult to solve. The second-order cone relaxation can guarantee the accuracy of the solution algorithm and meet the computational speed requirement [

49]. Using the conversion equations (48) and (49), (14), (15), (18), and (21)-(23) are reformulated to (50)-(55). Then, (52) is converted to (56) by using second-order cone relaxation. In the upper level, the mixed-integer conic quadratic (MICQ) model is converted to the mixed-integer linear planning (MILP) model. The approximately optimal solutions of the upper-level and lower-level models are obtained by the commercial solver CPLEX [50]-[52].

Is,ij,tφ=Is,ij,t2 (48)
Vs,i,tφ=Vs,i,t2 (49)
jkΩlinePs,jk,tline=ijΩline(Ps,ij,tline-Is,ij,tφrij)-Ps,j,t (50)
jkΩlineQs,jk,tline=ijΩline(Qs,ij,tline-Is,ij,tφσij)-Qs,j,t (51)
Vs,i,tφIs,ij,tφ=(Ps,ij,tline)2+(Qs,ij,tline)2 (52)
Vs,j,tφ<Vs,i,tφ-2(rijPs,ij,tline+σijQs,ij,tline)+Is,ij,tφ(rij2+σij2)+M(1-yn,ijline) (53)
Vs,j,tφVs,i,tφ-2(rijPs,ij,tline+σijQs,ij,tline)+Is,ij,tφ(rij2+σij2)-M(1-yn,ijline) (54)
Vi,min2Vs,i,tφVi,max2 (55)
2Ps,ij,tline2Qs,ij,tlineIs,ij,tφ-Vs,i,tφ2Is,ij,tφ+Vs,i,tφ (56)

where ||·||2 represents the Euclidean L2-norm.

V. Case Study

A 62-node distribution system in Jianshan New District, Zhejiang Province, China, as shown in Fig. 4, is used to illustrate the effectiveness of the proposed model.

Fig. 4 Initial network topology of an actual 62-node distribution system.

The distribution system comprises two substation nodes, 55 industrial load nodes, five commercial load nodes, and 62 lines. The planning problem is divided into four planning stages, and each stage represents a period of one year. The candidate nodes for ESS and DR contract, the location and capacity information of DGs, and the parameters of the planning model are shown in Tables I-III, respectively. The PV and WF scenarios are clusted into six and three scenarios, respectively,and shown in Fig. 5. A universal operation scenario set with 144 joint scenarios is considered for scenario screening. The probability of the joint scenario is the product of the probabilities of PV, WT, and load.

Fig. 5 Typical output curves of WT and PV.

TABLE I Candidate Nodes For ESS and DR Contract
TypeNo. of node
ESS 5, 8, 9, 10, 12, 13, 14, 23, 33, 34, 35, 39, 40, 41, 54, 55, 56
DR contract 5, 6, 8, 9, 12, 13, 14, 39, 41, 51, 55
TABLE II Location and Capacity Information of DG
TypeNo. of nodeMaximum output power (MW)
PV 4 1.3
23 2.0
29 2.7
35 2.7
43 1.8
50 1.2
WT 5 3.6
12 2.1
55 4.6
TABLE III Parameters of Planning Model
TypeParameterValue
ESS Fixed construction cost ¥10000
Unit rated power cost 300000 ¥/MW
Unit capacity cost 300000 ¥/MWh
Maintenance cost 10000 ¥/(MWh·year)
Lifecycle 15 year
Line Maintenance cost 2000 ¥/(km·year)
Lifecycle 20 year
Unit investment cost (JKLYJ-20-240) ¥700000
Impedance (JKLYJ-20-240) (0.13+j0.34)Ω/km
Maximum capacity (JKLYJ-20-240) 8.6 MW
Unit investment cost (JKLYJ-20-300) ¥800000
Impedance (JKLYJ-20-300) (0.16+j0.29)Ω/km
Maximum capacity (JKLYJ-20-300) 10.6 MW
Operation Unit penalty for load shedding 8000 ¥/MWh
Unit penalty for PV and WT curtailment 4000 ¥/MWh
Operation time of DSM 10:00 to 16:00
Limit for nodal voltage [0.95VB,1.05VB]
Planning Discount rate 8%
Load growth rate 5%
DG growth rate 7%
Investment limit ¥3000000

Simulations have been implemented on a PC with an Intel Core i5 CPU at 1.8 GHz and 8 GB of RAM using the YALMIP tool in MATLAB and calculated with CPLEX 12.6. The termination for the branch-and-cut algorithm of CPLEX is set at an optimal gap tolerance equal to 0.01%.

A. Result of Proposed Bi-level Coordinated Planning

The final planning scheme and target distribution network topology of the proposed bi-level coordinated planning model considering DR resources and SRSs (BCP-DR-SRS model) are presented in Fig. 6 and Table IV, respectively. In Fig. 6 and Table IV, to meet the periodic growth of load in the ADN, L1-56, L60-57, L53-61, and L53-60 are newly installed; L53-14, L1-43, L1-8, L53-26, and L43-44 are reinforced; ESSs with different rated power and capacities are newly installed at nodes 5, 10, 23, and 39; and DR contracts are signed with users at nodes 9 (i.e., 45 kW) at planning stage 1, at nodes 38 and 39 (i.e., 80 kW and 14 kW, respectively) at planning stage 2, and at nodes 38 and 39 (i.e., 170 kW and 152 kW, respectively) at planning stage 3.

Fig. 6 Target distribution network topology of BCP-DR-SRS model.

TABLE IV Planning Scheme of BCP-DR-SRS Model
Planning stageLineNewly installed ESSRated power of ESS (MW)Rated capacity of ESS(MWh)DRCapacity of DR(kW)
1 L53-14R,L1-43R,L1-56A,L60-57A,L53-61A,L53-60B ESS5 0.4 0.7 DR9 45
ESS10 0.8 1.5
ESS23 1.4 2.8
ESS39 1.2 2.4
2 L1-8R ESS5 0.4 0.8
ESS10 0.5 1.0
ESS23 0.6 2.5
ESS39 0.8 1.6
3 L53-26R,L43-44R DR38 80
DR39 14
4 DR38 170
DR39 152

Note:   the superscript “R” represents newly reinforced parallel lines; the superscripts “A” and “B” represent two types of newly built lines, i.e., JKLYJ-20-240 and JKLYJ-20-300.

In order to demonstrate the effectiveness of the proposed SRS screening method, the restricted degrees of six scenarios out of all SRSs are presented in Table V. Both the typical scenarios (e.g., scenarios 103, 104, 139, and 140) with probabilities larger than 7.0% and the extreme scenarios (e.g., scenarios 109 and 113) with probabilities less than 2% are included in the SRS set. Under these SRSs, the loads at nodes 9, 12, 23, 39, and 46 are shed for the power flowing through L1-8, L53-14, L53-26, L1-38, and L1-44, which exceeds the maximum capacity limits. On the other hand, the shadow price of scenario 113 (Ψ113) is 2064.2, which is higher than those of scenarios 140 and 139 (Ψ140=483.9, Ψ139=474.8).

TABLE V Restricted Degrees of SRSS Before and After Planning
Scenario (planning stage)Scenario probabilityps (%)Shadow price of scenario ΨsScenario impact factor ζs
Before planningAfter planningBefore planningAfter planning
140 (4) 8.0 483.9 113.6 38.7 9.1
139 (4) 8.0 474.8 113.6 38.0 9.1
104 (3) 8.0 432.2 84.0 34.6 6.7
103 (3) 8.0 413.2 84.0 33.1 6.7
109 (4) 1.5 1753.9 1129.6 26.3 16.9
113 (4) 1.2 2064.2 1883.0 24.8 22.6

However, scenario 113 is not included in the SRS set at first because it has a low probability (p113=1.2%) which makes its scenario impact factor (ζ113=24.8) less than those of scenarios 140 (ζ140=38.7) and 139 (ζ139=38.0). After the first iteration of planning, the impact factors of scenarios 140 and 139 (ζ140=8.78, ζ139=8.79) decrease and are less than that of scenario 113 (ζ113=23.4). Then, scenario 113 is included in the SRS set which influences the planning result in the second iteration. The original and final scenario impact factors of all operation scenarios are presented in Fig. 7, where all scenario impact factors decrease after planning, indicating that the shortages of network resources in all operation scenarios are alleviated. The scenario impact factors of scenarios 140, 139, 109, and 113 decrease by 76.5%, 76.1%, 35.6%, and 8.8%, respectively, indicating that the ADN operation risks are effectively reduced through the proposed BCP-DR-SRS model. In sum, the restricted degrees of scenarios are objectively quantized by the scenario impact factors to effectively solve various restricted operation problems in the ADN planning.

Fig. 7 Scenario impact factors before and after planning.

To demonstrate the DG consumption ability of the ADN optimized by BCP-DR-SRS model, the DG consumption before and after planning is compared in Fig. 8. In Fig. 8, the actual output curves of WT and PV after planning are higher than those before planning, indicating a higher renewable energy consumption in the target ADN. Considering all scenarios, the average WT and PV consumption rates increase from 80.3% and 95.7% to 96.1% and 99.2%, respectively.

Fig. 8 Ideal and actual output curves of WT and PV in scenario 109. (a) WT. (b) PV.

B. Comparison with Other Models

To illustrate the advantages of the proposed BCP-DR-SRS model, other models are presented for comparison, i.e., bi-level coordinated planning model considering SRSs (BCP-SRS model), single-level planning model considering multi-scenario technique [

53] (SP-MT model) and single-level planning model considering DR resources and multi-scenario technique (SP-DR-MT model). According to [53], the planning scenarios consist of four kinds of typical scenarios and one kind of extreme scenario at each planning stage provided by system operators, which are described with scenarios 24, 27, 31, 32, 35, 60, 63, 67, 68, 71, 96, 99, 103, 104, 107, 132, 135, 139, 140, and 143 in SP-MT and SP-DR-MT models. The planning schemes of BCP-STS, SP-MT and SP-DR-MT models are presented in Table VI.

TABLE VI Planning Schemes of BCP-SRS, SP-MT and SP-DR-MT Models
Planning stageBCP-SRSLine in SP-MT[53]SP-DR-MT
LineNewly installed ESSRated power of ESS (MW)Rated capacity of ESS (MWh)LineDRCapacity of DR (kW)
1 L1-8R, L53-14R, L1-43R, L1-56A,L53-61A, L53-60B ESS5 0.4 0.7 L1-8R, L53-14R, L1-43R,L1-57A, L53-59A, L58-62A, L53-14R

L53-14R, L1-43R,

L1-57A, L53-59A,

L58-62A, L53-62B

DR9 36
ESS23 1.4 2.8
ESS39 0.9 1.7
ESS54 1.1 2.2
2 ESS5 0.4 0.8 L1-8R
ESS23 0.6 2.5
ESS39 0.4 0.8
ESS54 0.9 1.8
3 L53-26R, L43-44R L53-26R, L1-38R, L43-44R L53-26R, L43-44R DR39 74
4 L1-38R DR39 258

1) Effect of DR on ADN Considering Multi-time-scales

The hourly power of load, DRs, and nodal injection at bus 39 in scenario 139 in SP-DR-MT model is shown in Fig. 9. In the short time-scale, the peak load is controlled through DR, which reduces the annual operation cost. The investment costs of the four models are presented in Table VII. It can be seen that the operation cost in the target year (Ctargetope) of SP-DR-MT model is ¥1155000 less than that of SP-MT model, which proves the effectiveness of DR resources in avoiding load shedding in some short-term scenarios through dispatching the controlled load flexibly. In the long time-scale, the reinforcement of L1-8 is delayed for one year and that of L1-38 is canceled when comparing the planning scheme of SP-MT model with that of SP-DR-MT model in Table VI. In Table VII, the investment cost of lines and the total investment cost Cinv of SP-DR-MT model are ¥1773500 and ¥1742200 less than those of SP-MT model, respectively, which indicates the performance of DR resources in saving the investment cost. In sum, the better economic dispatch in the short time-scale and reduction of the investment cost in the long time-scale can be realized with DR resources effectively.

Fig. 9 Hourly power of load, DR, and nodal injection at bus 39 in scenario 139.

TABLE VII Comparison of Investment Costs of Four Models
ModelClineinv (¥107)CESSinv (¥107)Ccap (¥104)Clinem (¥105)CESSm (¥105)Ctargetope (¥108)Cinv (¥107)
BCP-DR-SRS 1.22422 1.97789 4.56 1.068 4.217 1.092845 3.25952
BCP-SRS 1.38893 1.97789 1.153 4.217 1.092885 3.42052
SP-MT[53] 1.34468 1.165 1.361647 1.35633
SP-DR-MT 1.16733 4.56 1.022 1.350097 1.18211

2) Effect of SRS Screening Method on Cost and DG Consumption

The planning schemes of BCP-DR-SRS and SP-DR-MT models are compared to illustrate the effect of the proposed SRS screening method on investment and operation costs. It can be seen from Tables IV and VI that new ESSs at nodes 5, 23, 33, and 40 are not installed in the planning scheme of SP-DR-MT model because some scenarios with high risks (e.g., scenarios 109 and 113) are not considered in the planning phase. As shown in Table VII, the investment cost of SP-DR-MT model is ¥20774100 less than that of BCP-DR-SRS model; but the operation cost in the target year of SP-DR-MT model is ¥25725200 more than that of BCP-DR-SRS model. The different planning results of BCP-DR-SRS and SP-DR-MT models indicate that the determination of the planning scenario set has an obvious impact on the planning result, which further influences the operation cost of the ADN. As a result, the proposed SRS screening method can screen out the correct scenarios to achieve a better trade-off between the investment cost and the operation cost.

Figure 10 illustrates the operation cost difference between BCP-DR-SRS model and SP-DR-MT model in scenarios 1-6, 10-12, and 16, 17. In Fig. 10, the difference in scenario 17 is small and does not change much at planning stages. However, taking scenario 5 as an example, the difference of the operation cost increases stage by stage and reaches ¥54816 in the target year. BCP-DR-SRS model illustrates a better adaptability to the operation scenarios varying with the planning stages than the SP-DR-MT model.

Fig. 10 Operation cost difference between BCP-DR-SRS model and SP-DR-MT model.

In order to illustrate the effect of the SRS screening method on improving the DG consumption ability of the ADN, the penalty cost for WT and PV curtailment of four models are presented in Table VIII. In Table VIII, the penalty cost for WT and PV curtailment of BCP-SRS model is 3337300 less than that of SP-MT model during the whole planning period, which indicates that more renewable energy is efficiently consumed in the planned distribution network considering the scenarios screened out by the proposed SRS screening method.

TABLE VIII Penalty Cost for WT and PV Curtailment of Four Models
ModelPenalty cost (¥)
Planning stage 1Planning stage 2Planning stage 3Planning stage 4
BCP-DR-SRS 612500 527500 808200 1108500
BCP-SRS 614900 527500 813500 1126800
SP-MT 1128200 1367200 1758500 2166100
SP-DR-MT 1125400 1367200 1750900 2137600

In terms of computational burden, it is time-consuming to solve the planning model with the universal operation scenario set. The calculation time of the planning problem with BCP-DR-SRS model is 3 hours, which is acceptable for the distribution network planner in practice. In conclusion, the economic planning scheme can be achieved by the proposed BCP-DR-SRS model with the SRS screening method under an acceptable computation burden.

VI. Conclusion

In this paper, a bi-level coordinated planning model integrated with DR resources procurement and ESS/line configuration is proposed to deal with the increasing operation risks of the ADN. A shadow-price-based screening method is proposed to screen out the SRSs for ADN planning. With the coordinated optimization of the ADN operation and planning, the proposed model not only meets the long-term development demand of the distribution network, but also provides specific strategies for the short-term dispatch problem. Finally, the effectiveness of the proposed model is validated by the comparison between different ADN planning models based on an actual distribution system. The main conclusions are summarized as follows.

1) The proposed bi-level coordinated planning model, which regards DR as a new non-component means, can reduce the operation cost of the distribution network by dispatching the controllable load under SRSs in the short time-scale and delay the investment of the component planning resource by signing DR contracts in the long time-scale. Compared with component planning resources such as lines and ESSs, the non-component resource DR is configured more flexibly because of its low capacity price and short contract term. A better trade-off between the long-term investment cost and the short-term operation cost is obtained by the proposed model with DR resources in the ADN planning.

2) The proposed shadow price-based screening method effectively screens out SRSs for the ADN planning from a universal operation scenario set within an acceptable time. The DG consumption level of the distribution network is effectively improved by the proposed planning model considering the SRSs. Consequently, a balance between the network solutions and non-network solutions at multiple stages is achieved through iterations between the upper level and lower level, which simulates the information interaction process between planners and operators of ADN.

Nomenclature

Symbol —— Definition
A. —— Indices and Sets
τ —— Index for iteration
ΩEline, ΩLline —— Sets of existing and loop lines
ΩEESS, ΩNESS —— Sets of nodes with existing energy storage system (ESS) and ESS newly installed
Ωline —— Set of line
Ωm —— Set of load type
ΩNline, ΩRline —— Sets of newly-installed and reinforced candidate lines
ΩNlr, ΩRlr —— Sets of types of newly-installed and reinforced candidate lines
Ωnode, Ωnodem —— Sets of node and node of load type m
Ωs, Ωs* —— Sets of operation scenarios and severely restricted scenarios (SRSs)
Ωsub —— Set of substation node
Ωu, Ωl —— Sets of decision variables of upper-level and lower-level models
a, b, c —— Indices for demand response (DR) provider type
i, j, k —— Indices for nodes
m —— Index for load type
n —— Index for planning stage
r —— Index for line type
s, s* —— Indices for operation and severely-restricted scenarios
t —— Index for time period
B. —— Parameters
αn,m,iDR —— The maximum potential coefficient of DR resource provider at node i of load type m at planning stage n
αn,m,maxDR —— The maximum potential coefficient of load type m at planning stage n
γch, γdis —— Charging and discharging efficiencies of ESS
Δt —— Duration of time period
δ —— Conversion coefficient
ε —— Self-discharging rate
ζs —— Scenario impact factor of scenario s
ζ0 —— Threshold of scenario impact factor
θPV, θWT —— The maximum curtailment rates of photovoltaic (PV) and wind turbine (WT)
λ —— The maximum load shedding rate
μs,m,i,t —— Lagrange multiplier of the upper limit of DR power constraint at time period t at node i with load type m in scenario s
πs,j,t, τs,j,t —— Lagrange multipliers of power and stored energy constraints of ESS at node i at time period t in scenario s
ρ —— Discount rate
σij —— Reactance of line ij
Ψs —— Shadow price of scenario s
νs,ij,tu, νs,ij,td —— Lagrange multipliers of line ij power flow constraints at time period t in scenario s
Ctotal —— Total planning cost
Cs* —— Total dispatching cost under SRSs
Ccap —— DR capacity cost
Csene —— DR energy cost in scenario s
Clineinv, CESSinv —— Investment costs of line and ESS
Cmaxinv, Cninv —— The upper limit and actual value of investment cost at planning stage n
Csloss —— Power loss cost in scenario s
Clinem, CESSm —— Maintenance costs of line and ESS
Csope —— Daily operation cost in scenario s
Ctargetope —— Operation cost in the target year
Cspenalty —— Penalty cost for PV and WT curtailment and load shedding in scenario s
Cspur —— Energy purchase cost in scenario s
cr —— Unit investment cost of line type r
cn,m,icap —— Unit DR capacity price at node i of load type m at planning stage n
cn,m,deadcap, cn,m,satcap —— Boundary points of the dead and saturated zones of load type m at planning stage n
cm,iene —— Unit DR energy price at node i of load type m
clinem, cESSm —— Unit maintenance costs of line and ESS
cS,iNESS, cP,iESS, cE,iESS —— Fixed construction cost, unit rated power cost, and unit capacity cost of ESS at node i
cPVP, cWTP, cshed —— Unit penalty costs of PV curtailment, WT curtailment, and energy not supplied
ctpur —— Unit electricity price at time period t
Ei,maxESS —— The maximum rated capacity of expanded ESS at node i at planning stage n
Ei,minSOC, Ei,maxSOC —— The minimum and maximum stored energy limits of ESS at node i
Kn,mDR —— Sensitivity coefficient of DR resource provider of load type m at planning stage n
Lij —— Length of line ij
M —— Sufficiently large positive number
NLS —— Number of lines in the line set with a loop structure
Ns —— Number of operation scenarios
NT —— Number of planning stages
Pn,m,minDR —— The minimum hourly DR power of DR resource provider of load type m at planning stage n
Pi,maxESS —— The maximum rated power of expanded ESS at node i at planning stage n
P¯n,m,iload —— The maximum load power at node i of load type m at planning stage n
P¯s,i,tPV, P¯s,i,tWT —— The maximum output power of PV and WT at node i at time period t in scenario s
ps —— Probability of scenario s
rij —— Resistance of line ij
Sn,ijline —— The maximum capacity of line ij at planning stage n
T —— Number of time periods in a dispatch cycle
TmaxDR —— The maximum duration of DR event period
tm,istart, tm,iend —— Start time and end time of DR event period at node i of load type m
Vi,min, Vi,max —— The lower and upper voltage limits at node i
Yline, YESS —— Lifecycles of line and ESS
C. —— Variables
En,iESS —— Rated capacity of expanded ESS at node i at planning stage n
Es,i,tSOC —— State of charge of ESS at node i at time period t in scenario s
Is,ij,t —— Current flowing through line ij at time period t in scenario s
Is,ij,tφ —— Square of current flowing through line ij at time period t in scenario s
Ps,j,t, Ps,j,tchar, Ps,j,tdis —— Active nodal injection power, ESS charging power, and ESS discharging power at node j at time period t in scenario s
Pn,m,icap —— Contract capacity signed with the DR resources provider at node i of load type m at planning stage n
Ps,m,i,tDR —— Active DR power at time period t at node i of load type m in scenario s
Pn,iESS —— Rated power of expanded ESS at node i at planning stage n
Ps,ij,tline —— Active power through line ij at time period t in scenario s
Ps,ij,tloss —— Power loss of line ij at time period t in scenario s
Ps,i,tpur —— Active power purchased from the upper grid at node i at time period t in scenario s
Ps,i,tPV, Ps,i,tWT, Ps,i,tshed —— Active power of PV, WT, and load shedding at node i at time period t in scenario s
Qs,j,t, Qs,j,tpur, Qs,j,tCB —— Reactive nodal injection power, power purchased from the upper grid and compensation power at node j at time period t in scenario s
Qs,ij,tline —— Reactive power through line ij at time period t in scenario s
Qs,j,tload, Qs,j,tPV, Qs,j,tWT —— Reactive power of load, WT, and PV at node j at time period t in scenario s
Vs,i,t —— Nodal voltage at node i at time period t in scenario s
Vs,ij,tφ —— Square of nodal voltage at node i at time period t in scenario s
xs,i,tdis, xs,i,tchar —— Binary variables for representing the utilization state of ESS at node i at time period t in scenario s
xs,iNESS —— Binary variable for representing the investment state of ESS newly installed at node i at planning stage n
xn,ijline —— Binary variable for representing the investment state of line ij at planning stage n
yn,ijline —— Binary variable for representing the utilization state of line ij at planning stage n

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