Coordinated Expansion Planning of Transmission and Distribution Systems Integrated with Smart Grid Technologies

Integration of smart grid technologies in distribution systems, particularly behind-the-meter initiatives, has a direct impact on transmission network planning. This paper develops a coordinated expansion planning of transmission and active distribution systems via a stochastic multistage mathematical programming model. In the transmission level, in addition to lines, sitting and sizing of utility-scale battery energy storage systems and wind power plants under renewable portfolio standard policy are planned. Switchable feeders and distributed generations are decision variables in the distribution level while the impact of demand response programs as a sort of behind-the-meter technologies is accommodated as well. Expansion of electric vehicle taxi charging stations is included as a feasible option in both transmission and distribution levels. In order to deal with short-term uncertainty of load demand, renewable energy sources output power, and the charging pattern of electric vehicle taxis in each station, a chronological time-period clustering algorithm along with Monte Carlo simulation is utilized. The proposed model is tackled by means of Benders Dual Decomposition (BDD) method. The IEEE RTS test system (as the transmission system) along with four IEEE 33-node test feeders (as distribution test systems) are examined to validate effectiveness of the proposed model.


I. INTRODUCTION
In conventional passive distribution systems, the main focus is on distributing a predetermined amount of power from transmission substations to the medium and low voltage load centers.Accordingly, the operation and planning of transmission and distribution systems have been regularly conducted separately [1].In the wake of distribution system reformation to host high penetration of distributed generation (DG), demand response programs (DRPs), and high shares of electric vehicles (EVs), the local supply of load demands is turning into a reality in the active distribution networks.This fundamental transition enables the distribution system to run as dispatchable sources and dramatically influences the net load demand profiles.In a rare but still feasible scenario, the extra power generated in distribution side can be injected to the main grid under an interactivity between transmission system operator (TSO) and distribution system operator (DSO).This bilateral power exchange, in addition to power and energy quantities, impacts the prices and monetary flows, and the decisions in transmission expansion planning (TEP) should be amended accordingly.Also, high penetration of wind power plants (WPPs) in transmission system and integration of flexible resources like utility-scale battery energy storage (BES) systems, can affect distribution expansion planning (DEP).In this regard, a proper coordination between transmission and distribution systems planning is essential to defer investment and rise the asset utilization [1].
In traditional expansion planning models, the focus is mainly on a particular part of power system, e.g., transmission grid, or distribution system.In [2] the co-planning of transmission grid and ES devices is addressed, and the importance of ES for relieving lines congestion is concluded.Authors of [3] and [4] have developed an expansion model under high penetration of renewable energy sources (RESs) considering power system uncertainties.In [5], a hybrid AC/DC TEP model under high penetration of RESs incorporating BES devices is presented.The research works proposed in [6][7][8] investigate the impact of EVs [6], or DRPs [7,8] on power system operation and planning.An interlink between EV routing and optimal charging strategy in power system is developed in [6].The capability of DRPs for cost and emission reduction in generation and transmission expansion is addressed in [7].A power system expansion framework considering internet data centers load regulation is presented in [8] for facilitating the inclusion of spatial and chronological internet data centers in DRPs.In [9][10][11][12][13][14] the expansion of distribution systems considering some smart technologies is investigated.A mathematical linearization for a reliability-based DEP problem is presented in [9].The co-planning of electric vehicle charging stations (EVCSs), ES devices, and DGs, in a radial distribution network is developed in [10].
Authors of [11] propose a model for expansion planning of distribution and transportation systems, considering ES, DGs, and shared EVCSs, for minimizing investment cost, energy losses, and queue waiting time of EVs.In [12], a stochastic model considering EVs charging demand is utilized for active distribution system reinforcement planning.In [13], optimal expansion of distribution system and EVCSs assuming coordinated power and transportation networks is addressed.In [14] the presented model in [13] is expanded by including ES and fast-charging stations.
Followed by growing penetration of RESs, modern expansion tools, and smart grid technologies it is crucial to further look into the bidirectional interaction and coordination between TSO and DSO, as illustrated in Fig. 1.In this regard, a shortterm study is conducted on sharing energy storage between TSO and DSO in [15] where a coordinated local ES system in distribution level is modeled to relieve transmission system congestions.A coordinated economic dispatch of transmission and distribution systems has been addressed in [16].In [17], the impact of optimal operation of distribution system on TEP problem is investigated ignoring the optimal siting and sizing of BES devices and WPPs.Unlike [16] and [17], an integrated model for TEP and DEP is proposed in [1].The sitting and sizing of utility scale BES devices and WPPs, along with EVCSs in transmission side, also penetration of EVs and applications of DRPs in distribution side are all ignored in [1].In [18] a bi-level framework for coordinated planning of transmission and distribution systems considering the penetration of DGs is presented.The ES devices, WPPs, EVs, and DRPs are not included in [18].A tri-level structure is considered in [19] for TSO, DSO, and independent system operator to coordinate TEP and DEP problems.In [20] a hierarchical collaborative structure for TEP and DEP is addressed considering the allocation of transmission cost.The uncertainties, ES, WPPs, EVs, and DRPs are all ignored in [19] and [20].In [21] an integrated model for planning of power system and fast charging stations under EV diffusion is presented.DRPs impact in distribution systems, and utility scale ES and WPPs, along with EVCS planning in transmission system are not considered in [21].
The EV market in active distribution systems based on the stated policies scenario (STEPS) is targeting 140 million EV penetration by 2030, compared to 7.2 million existing ones in 2020 [22].This rapid growth, which will dominate 7% of the global vehicle fleet, can cause a 550 TWh increase in global electricity demand in the same scenario and time [22].Electric vehicle taxis (EVTs) have a growing penetration in distribution systems.Due to different consumption patterns and long charging time, EVTs need the EVTs-specific charging stations [23].Therefore, EVT charging stations (EVTCSs) introduce a new challenge for the operation and expansion planning of power systems.Although the proposed models in [1,[15][16][17][18][19][20] have incorporated an interaction between transmission and distribution systems, inclusion of EVTs or EVs can give more flexibility to the problem.Moreover, in [21] just the impact of private EVs in distribution systems is investigated.The impacts of EVs charging and solar generated power with respect to TSO and DSO interaction in a short-term horizon is addressed in [24] ignoring ES devices and WPPs in transmission, and DRP in distribution.Furthermore, DRP is an option in active distribution systems for electric energy consumers to contribute in the power system operation.In [25] DRP impacts on DEP problem is investigated.In Table I, the previous papers are briefly reviewed in terms of the planning model description and considered decision variables in transmission and distribution sides.
As shown in Table I, in majority of previous studies (e.g., [2-5, 7-14, 25]), the TEP and DEP problems are conducted separately.Moreover, in previous coordinated TEP and DEP research works (e.g., [1,[18][19][20][21]), the sitting and sizing of utility scale BES devices and WPPs in transmission side and penetration of EVTs and applications of DRPs in distribution side are not considered.In addition, in previous studies (e.g., [10-12, 21, 24]), mainly the impact of private-owned EVs on power system expansion is considered, and the importance of DRPs in [9][10][11][12][13][14][15][16][17][18][19][20][21]24] is ignored.This paper focuses on short-term and long-term impacts of EVTCSs and DRP on the coordinated expansion planning of the transmission and distribution systems.Moreover, in distribution side DGs are planned for dealing with the increasing load and EVTs charging demand which may lead to a highly cost reduction in the transmission system.
Regarding the literature gaps, in what follows, the main contributions of this paper are summarized.
1) A stochastic multistage model is proposed for coordinated expansion planning of transmission and active distribution systems considering operational details.While the investment decisions can be made by public or private sectors in a national or regional levels, the operational management is handled by TSO and DSO.In the  transmission side, in addition to lines, optimal planning of BES devices, and WPPs under renewable portfolio standard (RPS) policy are sought.The expansion of switchable feeders, and DGs are considered as planning options in the distribution side.In both sides the expansion of EVTCSs in several candidate service zones is planned as well.
2) In the proposed coordinated model, with regard to TSO local marginal prices (LMPs) in interface buses, the impact of DRPs implemented by DSO is planned and scheduled.
3) The proposed model is formulated as an MILP problem and is reformulated and solved using a customized Benders Dual Decomposition (BDD) method.
Moreover, to handle the uncertainty of load demand, RESs output power, and EVTs charging pattern in each EVTCS, the chronological time-period clustering (CTPC) algorithm along with Monte Carlo simulation (MCS) are utilized.

II. PROBLEM FORMULATIONS
In the following, the formulations of the proposed coordinated planning model are presented in the integrated and BDD forms.

B.1. Transmission Level Constraints
In power system expansion planning studies the linear DC optimal power flow (OPF) model is the widely used methodology for modeling power system operational details in a long-term planning model.The DC OPF model calculates the power flows of transmission lines with some simplifications and acceptable accuracy.On the other hand, the AC power flow model has a better accuracy, however; the AC power flow equations are nonlinear.
By considering the AC power flow model, the resulted optimization model will be fully non-linear with a large computational burden.In addition, in a non-linear AC power flow the optimality and feasibility of the optimization problem are not guaranteed.Therefore, in this paper the DC OPF model is used for the transmission level constraints.

• Thermal Generation Units
The constraints of (2a)-(2d) are defined to model thermal generation units constraints.
In (2a), the upper and lower limits of thermal units output power are defined.The thermal units generation cost function is linearized in (2b).According to (2b) and (2c), hourly output power of units is considered as the minimum output power plus the summation of all linear segments of generated power.The constraint (2d) is introduced to model the ramping constraints of all thermal units . •

RPS Policy and Wind Curtailment
The generation power capacity bounds of installed WPP are introduced in (3a).It is assumed that a minimum of WPP should be available to supply a determined percentage of the total peak load in each stage of planning.According to the RPS policy, the penetration of WPPs in the last stage of the planning horizon is determined as % of the total peak load, according to (3b).The constraint (3c) ensures the availability of each installed WPP till the end of planning horizon.The limits of wind energy curtailment in each hour are satisfied using (3d).In (3e), the maximum permitted wind energy curtailment in each stage is defined as % of the expected output power of available WPPs.
• Flexible Ramp Reserve Flexible ramp reserve is considered to cover the probable forecast errors and handle the uncertainty of load demand and WPP output power according to (4a)-(4c).The limits of thermal units flexible ramp reserve are bounded by (4a) and (4b).In (4c), the lower bound of total hourly reserve is defined as 3% and 5% of the expected system peak load and WPPs output power, respectively [5].
• Battery Energy Storage Generally, BES devices can be charged during low net-load hours and be discharged during heavy net-load conditions.So, these devices can relieve the transmission congestion and postpone or eliminate the generation and transmission planning investment decisions.Under high penetration of WPPs, to postpone new transmission lines construction, relieve existing transmission lines congestion, and minimize wind curtailment, it is essential to incorporate BES devices.In this regard, to model the sitting and sizing of BES devices in the proposed model the constraints of (5a)-(5g) are introduced [4].The constraints of (5a) and (5b) determine the limits of BES charging and discharging power.In (5c) and (5d), the state of BES charging and discharging is presented.In (5e), the stored energy level in BES devices is defined as the summation of stored energy at the previous hour and the energy exchange at the current hour.The lower and upper bounds of BES stored energy level are considered in (5f).The constraint (5g) ensures the accessibility of each installed BES till the end of planning horizon.• Existing and New Lines The constraint of (7a) defines the limits of existing line flow.In (7b), the power flow of each existing line is determined.The constraints of (7c) and (7d) model the limits and the power flow of new lines, respectively.In (7e), the availability of constructed lines at next stages is guaranteed.

B.2. Distribution Level Constraints
Generally, a linearized DistFlow approach in radial distribution systems makes it possible to calculate the active and reactive power flows considering the voltage drop form the point of common coupling to the node of feeders.Therefore, DistFlow equations are used to model distribution level constraints with a faster computation [27].

• Thermal DGs
To model the operation and expansion of TDGs in distribution systems, the constraints of (9a)-(9f) are presented.The active and reactive output powers of TDGs are bounded in (9a) and (9b), respectively.The linearization of nonlinear cost function of TDGs is considered in (9c) and (9d).To limit TDGs construction in each stage, the tunnel limit constraint is introduced in (9e).In (9f), the availability of constructed TDGs at next stages is guaranteed.

• Wind DGs and RPS Policy
The RPS policy is also considered for WDGs in distribution systems by (10a)-(10c).
The capacity of installed WDGs is bounded in (10a).The minimum penetration of WDGs to supply the distribution system load in each stage, is defined in (10b) according to RPS policy.In (10c) the accessibility of each installed WDGs till the end of planning horizon is ensured.

• Existing and New Feeders
The power flow of existing and new constructed feeders, considering the possibility of operational switching for probable reconfigurations under radiality constraints, is defined in (12a)-(12g).Active and reactive power flows of existing and new feeders are bounded by the maximum apparent power flow in (12a), (12b), (12d), and (12e).The constraints in (12c) and (12f), relate the voltage drop of nodes to active and reactive power flow of existing and new feeders considering their conductance and susceptance, that are stemmed from linearized DistFlow equations [27].In (12g), nodal voltage magnitude is bounded.
• Demand Response The linearized DRP in distribution systems is introduced in (14a)-(14g).In (14a) and (14b), the upper and lower bounds of DRP, that indicate the positive and negative load shifting, are restricted according to the hourly load demand in each responsive load nodes.
The DRP limits are bounded in (14c).In (14d), the summation of DRP in all hours is considered to be zero.The constraint of (14e) ensures that the positive and negative load shifting cannot be activated at the same time.The positive and negative load shifting between hours considering related cross-hour price elasticity and load levels, are defined in (14f) and (14g).
• Power Balance Equation The nodal active and reactive power balance equations in each distribution system are defined in (15) and (16).The active power balance equation in (15) includes the exchange active power between transmission and distribution in interface nodes, the active power of

C. Benders Dual Decomposition
In this subsection the MILP formulations presented in subsections A and B, are reformulated to be solved using the BDD algorithm.The problem is decomposed into a Master Problem (MP), and two Dual Sub-Problems (DSPs), one DSP for transmission level (i.e., TDSP) and one DSP for distribution level (i.e., DDSP).In MP, the integer decision variables are optimized.In TDSP and DDSP the feasibility or optimality of MP solution for transmission and distribution systems, along with optimization of the system operation, WPP and WDG investment costs, as linear continuous variables, are evaluated.
The investment cost of binary decision variables is presented in (27).The optimality cut and feasibility cuts of transmission and distribution systems are introduced using ( 28), (29), and (30), respectively. indicates the iteration number.  and   are the dual variables of the constraints given by (31) as auxiliary constraints for the sub-problems.
• Transmission Dual Sub-Problem In the following, the linear programming formulation of TDSP is presented.
The MP solution determines the integer decision variables (i.e.,   ̅̅̅̅̅ ).According to TDSP solution, if the solution is bounded, the optimality cut (28) is formed; otherwise, the feasibility cut ( 29) is constructed by Modified TDSP (MTDSP).
power [31], and the charging pattern of EVTs [32], in Netherlands at 2019 are considered to extract the representative hours.Moreover, the aggregated historical data are accessible in [33].Due to lack of EVTs charging pattern data in whole hours of a year, MCS method is utilized to extend the available data over a year considering the data probability distribution.The normal probability distribution function is considered for EVTs charging pattern available data.As shown in Fig. 4, by using the CTPC algorithm, the hourly load demand, EVTs charging pattern, and wind power historical data are represented by 96 hours.The extracted representative hours are aggregated across the year using each representative weight.

V. NUMERICAL RESULTS
The performance of the proposed coordinated expansion planning model of transmission and active distribution systems is evaluated over the IEEE 24-bus test system, as transmission system, along with four IEEE 33-node test feeders, as distribution systems.
Four distribution systems are connected to buses 22, 17, 12, and 11 of considered transmission system.The data of these test systems at the beginning of the planning horizon are assumed as input data and extracted from MATPOWER [34].The planning time horizon is divided into 3 stages; each stage contains 2 years.In this paper, the generation expansion planning is not considered.Indeed, it is assumed that enough generation capacity is available in the system until the end of considered planning horizon.
The  for the first, second, and third stages is assumed as 2%, 11%, and 30% [35].All input data and parameters are also accessible in [33].The simulations are run by the CPLEX solver in GAMS software using a PC with an Intel Core i7 CPU, and 32 GB of RAM.
In GWh is curtailed until the end of planning horizon in the proposed model excluding the coordination between transmission and distribution systems.

B. Numerical Results for Coordinated Planning
The numerical results of the proposed model considering the coordination between transmission and four distribution systems connected to buses 11, 12, 17, and 22 are In case I, the proposed coordinated model excluding DRP is executed, while in case II DRP is also incorporated in the proposed model.The numerical results of cases I, and II are reported in Tables III, and IV, respectively.Moreover, the obtained results of case II are illustrated in Fig. 5.As given in Table III, the values of decision variables are just presented for transmission system.In addition, all investment and operation costs are distinguished for both transmission and distribution systems.In case I, the TTIC, TTOC, and total transmission planning cost (TTPC) are 1285.planning and operation costs.As illustrated in Fig. 5, in case II eight new lines, five WPPs, six BES devices, and seven EVTCSs are constructed in transmission system.In addition, six new feeders, three TDGs, five WDGs, and three EVTCSs are constructed in the fourth distribution system, i.e., the system connected to bus 22.In Fig. 6, the total energy balance for all distribution systems in case II, including TDGs and WDGs output energy, energy supply from transmission system, energy demand, and EVT charging demand, is illustrated in each planning stage.Based on Fig. 6, in stages one, two, and three, the share of TSO in suppling DSO energy consumption is 59%, 55%, and 43%, respectively.This result confirms the importance of proposed coordination between transmission and It should be noted that in order to evaluate the effect of forecasting error in the proposed model, it is possible to simulate the considered case studies for different probable scenarios of forecasted parameters.In this paper, some sensitivity analyses can be conducted over load demand and EVT growth factors, the penetration of WPPs in the last stage of the planning horizon, and interest rate.Although the focus of this paper is on modelling the integration of smart grid technologies in active distribution systems planning, and their direct impacts on transmission network planning, flexible ramp reserve of thermal units is incorporated in the proposed model.Indeed, flexible ramp reserve is considered to cover the probable forecast errors and handle the uncertainty of load demand and wind power plants output power as much as possible.

VI. CONCLUSION
This paper proposed a stochastic multistage model to coordinate expansion planning of transmission and active distribution systems, concerning short-term operational details.In the transmission level, lines, BES devices, along with WPPs, and in the distribution level, switchable feeders, TDGs, and WDGs were considered as planning options.The proposed coordinated model will be more impressing with considering the interaction of more distribution systems with transmission system in next studies.In addition, the proposed model in this paper can be discussed in future works considering an electricity market environment.Moreover, in future investigations, the utilized CTPC method in this paper can be improved to capture both temporal chronology and extreme values of input data inside some proper representatives.

Fig. 4 .
Fig. 4. The real historical data and extracted representative hours

Fig. 5 .
Fig. 5.The illustration of the obtained results of case II

Fig. 6 .
Fig. 6.The total energy balance for distribution systems in case II

Table I .
An overview of the previous papers
1     +  2     +      +      +   ̅̅̅̅̅ IEEE 24-bus test system, six WPPs are installed in buses 3, 6, 12, 14, and new buses 25, and 26.The maximum capacity of candidate WPPs in existing buses is assumed as 180 MW, and 300 MW for new buses.The buses 6, 10, 14, 16, 18, 20 and 21 are considered as candidates for three types of BES devices.In this paper, three different types of BES devices are considered as candidates.The maximum power capacity of candidate BES devices is 25, 50, and 100 MW, with a maximum energy capacity of 150, 300, and 600MWh.Four zones are considered for EVTCSs candidate service zones in transmissionIn this subsection, the numerical results of the proposed model excluding the coordination between transmission and distribution systems are presented.In this regard, distribution systems are assumed as a simple bus with/without load demand and generation in interface buses.As reported in TableII, in the first stage, two lines between buses 7-8, and 16-19 are constructed.In this stage, two WPPs in buses 3 and 6, also twelve BES devices are installed in buses 6, 10, 14, 16, 18, and 21, as presented in TableII.Moreover, seven EVTCSs are constructed in buses 6, 8, 9, 11, 22, 15, and 24 in first stage.In second stage, one line in corridor 21-25 is constructed.Additionally, three WPPs are installed in buses 3, 14, and 25.In the last stage of planning, three lines are constructed between buses 9-11, 10-12, 21-25, and two lines between buses 16-25.Two WPPs in buses 25, and 26, along with one BES device in bus10, are installed in third stage.Moreover, one EVTCS is located in bus 12.As presented in TableII, TTIC, TTOC, and total planning cost are obtained as 1292.12,3079.4,and 4371.52 $, respectively.A total wind energy of 56.05

Table II .
Results of The Uncoordinated Planning 1: Investment cost, 2: All costs are in M$, 3: Total transmission investment cost, 4: Total transmission operation cost, 5: Total planning cost presented in this subsection.All the connecting buses contain 12 MW load demand.To illustrate the efficiency of the proposed model, the simulations are conducted for two cases.
5, 3006.5, and 4292 $, respectively.In comparison to the results in Table II, which is an uncoordinated model, TTPC is reduced by 79.52 $.This reduction in TTPC confirms the importance of the proposed coordinated planning model.As shown in Table III, the TDIC, TDOC, and total distribution planning cost (TDPC) are 15.597, 29.153, and 44.75 $, respectively.The Table III.Results of The Proposed Coordinated Planning Excluding DRP Total distribution systems planning cost total planning cost in case I, as the summation of TTPC and TDPC, is 4336.75$ that leads to a 34.77 $ cost saving compared to the obtained result of Table II.The total wind energy curtailment in case I during the planning horizon is 44.18GWh which is 11.87 : 44.75 : 4336.75 1: Transmission system, 2: Stage, 3: Total transmission planning cost, 4: Distribution system, 5: Table IV, by considering DRP in case II, the TTIC, TTOC, and TTPC are 1292.5,2998.65, and 4291.16$, respectively.Moreover, in case II the TDIC, TDOC, and TDPC are 14.89, 24.765, and 39.65 $, respectively.The total planning cost (i.e., ) in case II (i.e., Table IV) is 4330.81$ that includes 4291.16$ as TTPC, and 39.65 $ as TDPC.The total planning cost of case II is 5.94, and 40.71 $ less expensive than case I (i.e., Table III) and the results of uncoordinated model (i.e., Table II), respectively.TTPC in case II is 80.36 $ less expensive than the results of Table II.The obtained results of case II confirm the influence of DRP on reducing both distribution and transmission total

Table IV .
Results of The Proposed Coordinated Planning Including DRP