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.
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 [
The economy, reliability, and flexibility of ADN can be improved by optimal planning and dispatching of DG [
The impacts of price-based DR programs such as time of use (TOU) program [
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.

Fig. 1 Coordinated optimization of ADN.
In the ADN planning phase, the DR capacity cost is paid by electricity utilities to DR resource providers, i.e.,
(1) |
Based on the characteristics of different DR resources and consumer psychology, the maximum potential coefficient 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 is limited by , which is expressed as:
(2) |
The piecewise linear curve of represented in
(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 is calculated according to the actual usage of DR resources in scenario s, i.e.,
(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).
(5) |
(6) |
(7) |
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.
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 , which includes the energy purchase cost , power loss cost , DR energy cost , and penalty cost for PV curtailment, WT curtailment, and load shedding, and is expressed as:
(8) |
(9) |
(10) |
(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:
(12) |
(13) |
(14) |
(15) |
(16) |
(17) |
(18) |
(19) |
(20) |
(21) |
(22) |
(23) |
(24) |
(25) |
(26) |
(27) |
(28) |
(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 [
The objective of the ADN planning model is to minimize the total cost Ctotal including the investment cost of lines and ESSs and , the capacity cost of DR contract
(30) |
(31) |
(32) |
(33) |
(34) |
(35) |
In (30)-(35), the long-term decision variables include investment variables for the installation and reinforcement of lines , the installation and expansion of ESS , and and the contract amount of DR . The investment constraints are represented as:
(36) |
(37) |
(38) |
(39) |
(40) |
(41) |
(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).
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 [
(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 is defined to describe the restricted degree of scenario and screen out the SRSs, and it can be represented as:
(44) |
The overall scarcity of the ADN resources in operation scenario s is reflected through the scenario impact factor . Unit investment in the scenario with a larger will get better marginal benefits in reducing the operation costs and risks. According to the impact factor , all operation scenarios are evaluated objectively and those with great marginal benefits of investment are selected into the SRS set for ADN planning, which can be represented as:
(45) |
According to (45), the scenarios with larger impact factors than the threshold or the average of all scenario impact factors 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.
(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.
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 [
The flowchart of the proposed bi-level coordinated planning model is presented in

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 and .
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 and .
Step 5: if , turn to Step 6; otherwise, set and return to Step 3.
Step 6: screen out with the proposed SRS screening method.
Step 7: if is an empty set, turn to Step 11; otherwise, return to Step 8.
Step 8: solve the upper-level planning problem considering . The 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 .
Step 11: output the ADN planning result.
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 [
(48) |
(49) |
(50) |
(51) |
(52) |
(53) |
(54) |
(55) |
(56) |
where ||·||2 represents the Euclidean L2-norm.
A 62-node distribution system in Jianshan New District, Zhejiang Province, China, as shown in

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 Typical output curves of WT and PV.
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%.
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 Target distribution network topology of BCP-DR-SRS model.
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
However, scenario 113 is not included in the SRS set at first because it has a low probability () which makes its scenario impact factor () less than those of scenarios 140 () and 139 (). After the first iteration of planning, the impact factors of scenarios 140 and 139 (, ) decrease and are less than that of scenario 113 (). 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 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 Ideal and actual output curves of WT and PV in scenario 109. (a) WT. (b) PV.
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 [
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 Hourly power of load, DR, and nodal injection at bus 39 in scenario 139.
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

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
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.
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 |
—— | Index for iteration | |
, | —— | Sets of existing and loop lines |
, | —— | Sets of nodes with existing energy storage system (ESS) and ESS newly installed |
—— | Set of line | |
—— | Set of load type | |
, | —— | Sets of newly-installed and reinforced candidate lines |
, | —— | Sets of types of newly-installed and reinforced candidate lines |
, | —— | Sets of node and node of load type m |
, | —— | Sets of operation scenarios and severely restricted scenarios (SRSs) |
—— | Set of substation node | |
, | —— | Sets of decision variables of upper-level and lower-level models |
, , | —— | Indices for demand response (DR) provider type |
, , | —— | Indices for nodes |
—— | Index for load type | |
—— | Index for planning stage | |
—— | Index for line type | |
, | —— | Indices for operation and severely-restricted scenarios |
t | —— | Index for time period |
B. | —— | Parameters |
—— | The maximum potential coefficient of DR resource provider at node i of load type m at planning stage n | |
—— | The maximum potential coefficient of load type m at planning stage n | |
, | —— | Charging and discharging efficiencies of ESS |
—— | Duration of time period | |
δ | —— | Conversion coefficient |
ε | —— | Self-discharging rate |
—— | Scenario impact factor of scenario s | |
—— | Threshold of scenario impact factor | |
, | —— | The maximum curtailment rates of photovoltaic (PV) and wind turbine (WT) |
—— | The maximum load shedding rate | |
—— | Lagrange multiplier of the upper limit of DR power constraint at time period t at node i with load type m in scenario s | |
, | —— | Lagrange multipliers of power and stored energy constraints of ESS at node i at time period t in scenario s |
ρ | —— | Discount rate |
—— | Reactance of line ij | |
—— | Shadow price of scenario s | |
, | —— | Lagrange multipliers of line ij power flow constraints at time period t in scenario s |
—— | Total planning cost | |
—— | Total dispatching cost under SRSs | |
—— | DR capacity cost | |
—— | DR energy cost in scenario s | |
, | —— | Investment costs of line and ESS |
, | —— | The upper limit and actual value of investment cost at planning stage n |
—— | Power loss cost in scenario s | |
, | —— | Maintenance costs of line and ESS |
—— | Daily operation cost in scenario s | |
—— | Operation cost in the target year | |
—— | Penalty cost for PV and WT curtailment and load shedding in scenario s | |
—— | Energy purchase cost in scenario s | |
—— | Unit investment cost of line type r | |
—— | Unit DR capacity price at node i of load type m at planning stage n | |
, | —— | Boundary points of the dead and saturated zones of load type m at planning stage n |
—— | Unit DR energy price at node i of load type m | |
, | —— | Unit maintenance costs of line and ESS |
, , | —— | Fixed construction cost, unit rated power cost, and unit capacity cost of ESS at node i |
, , | —— | Unit penalty costs of PV curtailment, WT curtailment, and energy not supplied |
—— | Unit electricity price at time period t | |
—— | The maximum rated capacity of expanded ESS at node i at planning stage n | |
, | —— | The minimum and maximum stored energy limits of ESS at node i |
—— | Sensitivity coefficient of DR resource provider of load type m at planning stage n | |
—— | Length of line ij | |
—— | Sufficiently large positive number | |
—— | Number of lines in the line set with a loop structure | |
—— | Number of operation scenarios | |
—— | Number of planning stages | |
—— | The minimum hourly DR power of DR resource provider of load type m at planning stage n | |
—— | The maximum rated power of expanded ESS at node i at planning stage n | |
—— | The maximum load power at node i of load type m at planning stage n | |
, | —— | The maximum output power of PV and WT at node i at time period t in scenario s |
—— | Probability of scenario s | |
—— | Resistance of line ij | |
—— | The maximum capacity of line ij at planning stage n | |
—— | Number of time periods in a dispatch cycle | |
—— | The maximum duration of DR event period | |
, | —— | Start time and end time of DR event period at node i of load type m |
, | —— | The lower and upper voltage limits at node i |
, | —— | Lifecycles of line and ESS |
C. | —— | Variables |
—— | Rated capacity of expanded ESS at node i at planning stage n | |
—— | State of charge of ESS at node i at time period t in scenario s | |
—— | Current flowing through line ij at time period t in scenario s | |
—— | Square of current flowing through line ij at time period t in scenario s | |
, , | —— | Active nodal injection power, ESS charging power, and ESS discharging power at node j at time period t in scenario s |
—— | Contract capacity signed with the DR resources provider at node i of load type m at planning stage n | |
—— | Active DR power at time period t at node i of load type m in scenario s | |
—— | Rated power of expanded ESS at node i at planning stage n | |
—— | Active power through line ij at time period t in scenario s | |
—— | Power loss of line ij at time period t in scenario s | |
—— | Active power purchased from the upper grid at node i at time period t in scenario s | |
, , | —— | Active power of PV, WT, and load shedding at node i at time period t in scenario s |
, , | —— | Reactive nodal injection power, power purchased from the upper grid and compensation power at node j at time period t in scenario s |
—— | Reactive power through line ij at time period t in scenario s | |
, , | —— | Reactive power of load, WT, and PV at node j at time period t in scenario s |
—— | Nodal voltage at node i at time period t in scenario s | |
—— | Square of nodal voltage at node i at time period t in scenario s | |
, | —— | Binary variables for representing the utilization state of ESS at node i at time period t in scenario s |
—— | Binary variable for representing the investment state of ESS newly installed at node i at planning stage n | |
—— | Binary variable for representing the investment state of line ij at planning stage n | |
—— | Binary variable for representing the utilization state of line ij at planning stage n |
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