Abstract
The increased deployment of electricity-based hydrogen production strengthens the coupling of power distribution system (PDS) and hydrogen energy system (HES). Considering that power to hydrogen (PtH) has great potential to facilitate the usage of renewable energy sources (RESs), the coordination of PDS and HES is important for planning purposes under high RES penetration. To this end, this paper proposes a multi-stage co-planning model for the PDS and HES. For the PDS, investment decisions on network assets and RES are optimized to supply the growing electric load and PtHs. For the HES, capacities of PtHs and hydrogen storages (HSs) are optimally determined to satisfy hydrogen load considering the hydrogen production, tube trailer transportation, and storage constraints. The overall planning problem is formulated as a multi-stage stochastic optimization model, in which the investment decisions are sequentially made as the uncertainties of electric and hydrogen load growth states are revealed gradually over periods. Case studies validate that the proposed co-planning model can reduce the total planning cost, promote RES consumption, and obtain more flexible decisions under long-term load growth uncertainties.
WITH the global concern for greenhouse gas emissions, clean and low-carbon renewable energy sources (RESs) are gradually replacing traditional fossil energy [
Considering that PDS and HES have significant synergistic effects, several research works have been conducted on the coordinated operation of IPDHS. In [
The above studies prove the significant benefits through the coordinated operation of PDS and HES. However, they mainly focus on the operation level. In view of the above merits, joint optimal planning of IPDHS is urgently needed to benefit both PDS and HES. In general, the planning problems of PDS and HES have been widely studied in the existing literature in a separate manner. For the former, the planning strategies for PDS with high RES penetration have been well investigated such as [
For the HES planning problems, researchers have developed meaningful works. Generally, the HES consists of hydrogen production, transportation, and storage sectors. Considering the scale merit of PtHs, centralized hydrogen generation is widely designed to lower hydrogen production costs, and hydrogen storage (HS) is utilized to increase operational flexibility. In [
As discussed above, little attention has been paid to the joint planning of PDS under high RES penetration and HES with consideration of the production, transportation, and storage sections. There are three main gaps in the existing literature: the coordinated planning of PDS and HES has not been fully considered, and how to take advantage of the synergy between them to reduce the planning cost and facilitate RES consumption has not been explored; the role of HES operation flexibility can be further exploited in the co-planning framework, in which hydrogen production, transportation, and storage can be coordinated with PDS to increase the system operational flexibility; and the IPDHS co-planning is a multi-period problem with long-term planning horizon, and the load growth uncertainties of power and hydrogen deserve to be considered.
This paper proposes a multi-stage stochastic IPDHS co-planning model under long-term load growth uncertainties, and the main contributions are summarized below.
1) A novel multi-stage stochastic IPDHS co-planning model is proposed to optimize the PDS expansion and HES configuration, in which various energy devices can be coordinately deployed to meet the power/hydrogen loads economically.
2) HES including PtH, HS, and HT transportations is coordinated with variable photovoltaics (PVs) and wind turbines (WTs) in PDS, and the flexible operation of HES can effectively promote RES utilization, relieve PDS expansion burden, and reduce the planning cost of the overall system.
3) A multi-stage stochastic model with non-anticipativity constraints is set up for the IPDHS co-planning problem to address long-term load uncertainties, in which the investment decisions are sequentially made as the load growths of power and hydrogen are revealed gradually over periods.
The rest of this paper is organized as follows. Section II illustrates the proposed IPDHS co-planning framework. Section III presents the mathematical formulation of the co-planning model, followed by the solution algorithm in Section IV. Numerical studies are carried on Section V, and Section VI draws the conclusions.
The proposed IPDHS co-planning framework is shown in

Fig. 1 Proposed IPDHS co-planning framework.
In the proposed co-planning framework, substations, power lines, photovoltaics (PVs), and wind turbines (WTs) in the PDS as well as PtHs and HSs in the HES are invested to supply the growing power and hydrogen loads over periods. For the HES, the flexible operation of PtHs with HSs can promote the utilization of variable RES and produce hydrogen with cheaper electricity costs. Besides, by optimizing the locations and capacities of PtHs, the expansion burden of PDS can be potentially relieved.
The proposed co-planning framework is based on the following assumptions and premises: ① the distribution system operator (DSO) serves as the centralized planner and the information of the HES is available to the DSO; ② the planning horizon is divided into stages, and a fixed annual interest rate is considered; ③ typical scenarios in summer, winter and transition seasons are utilized to model the stochastic characteristics of PVs, WTs, and power/hydrogen loads; and ④ the transportation process of HTs is modeled as a vehicle routing problem [
The objective of the proposed co-planning framework is to minimize the present value of total costs over the planning horizon, as shown in (1).
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
1) Investment constraints: constraints of investment decisions are formulated in (7)-(13). Constraints (7)-(9) present the binary nature of investment decisions for substations, transformers, and power lines, respectively. Besides, only one investment of the candidate alternatives is allowed for each device throughout the planning horizon. Constraint (10) ensures that the investment for PVs, WTs, PtHs, and HSs will exist if it has been installed previously, while constraint (11) imposes the upper bounds on them at each planning stage. Constraints (12) and (13) restrict that the transformers and power lines cannot be installed on the attached substations that have not been built.
(7) |
(8) |
(9) |
(10) |
(11) |
(12) |
(13) |
2) PDS constraints: PDS operation constraints are formulated based on the DistFlow model [
(14) |
(15) |
(16) |
(17) |
(18) |
(19) |
(20) |
(21) |
(22) |
(23) |
(24) |
(25) |
(26) |
(27) |
(28) |
The network radiality of PDS is constrained in (29)-(36). Constraint (29) restricts that the power lines cannot operate in two directions simultaneously, while constraint (30) ensures that the uninstalled power lines cannot operate. Constraints (31) and (32) model the PDS operation topology as a tree structure. To be specific, the substation and load nodes are modeled as parent and child nodes, respectively. Furthermore, to avoid the isolated areas formed by the RES, fictitious power flow constraints (33)-(36) are introduced, which ensures that each load node has one substation as the parent node [
(29) |
(30) |
(31) |
(32) |
(33) |
(34) |
(35) |
(36) |
To illustrate the operational constraints for HES, the energy flow in the HES [

Fig. 2 Energy flow in HES.
3) Hydrogen production constraints: constraint (37) defines that the hydrogen productions from PtHs are exported to the HTs, stored in the HS, or provided to the local hydrogen load. Constraint (38) presents the hydrogen balance of HSs within HGSs. Constraint (39) defines the hydrogen export balance from HGS to the HTs. Constraints (40)-(42) present the capacity and operation boundaries of HSs within HGSs. Constraint (43) indicates the exported hydrogen limits of PtHs.
(37) |
(38) |
(39) |
(40) |
(41) |
(42) |
(43) |
4) Hydrogen transportation constraints: the HT-based hydrogen transportation process is modeled as a vehicle routing problem [
(44) |
(45) |
(46) |
(47) |
(48) |
(49) |
(50) |
(51) |
5) Hydrogen refueling station constraints: constraint (52) indicates the hydrogen balance of HSs within HRSs. Constraints (53) and (54) represent the operation boundaries of HSs within HRSs. Hydrogen load and the maximum curtailed hydrogen load at each HRS are restricted in (55).
(52) |
(53) |
(54) |
(55) |
6) Coupling constraints: the PDS is coupled with HES through the PtHs. The power consumed by the PtHs and the compressors is shown in (56) and (57), respectively.
(56) |
(57) |
The overall planning model is an MISOCP problem with objective (1) and subject to constraints (7)-(57).
In this section, the original MISOCP model is firstly converted into an MILP problem to relieve the computation burden by linearizing the second-order cone constraints. Then, a multi-stage stochastic MILP model is formulated to address the long-term power/hydrogen growth uncertainties.
In the original MISOCP model, (17) and (18) are second-order cone constraints. A polyhedral approximation method [
(58) |
(59) |
In general, the mathematical formulation for the proposed planning model can be written as a compact MILP model with the investment variables and the operational variables as follows.
(60) |
s.t.
(61) |
(62) |
where are the coefficient matrices; and is the investment decision.
In practical engineering, the long-term IPDHS co-planning problem will face load growth uncertainties during the planning horizon [
A scenario tree is developed to characterize the load growth uncertainties and describe possible sequential decisions over planning horizons, as shown in

Fig. 3 Scenario tree and sequential decisions with non-anticipativity.
Traditionally, a two-stage stochastic model [
(63) |
s.t.
(64) |
(65) |
The investment decision is the first-stage variable, and the operation decisions are the second-stage variables. In this framework, is determined before the uncertainties are realized, while are made according to different realizations of . The main disadvantage is that the investment decisions cannot be changed during the multi-stage planning process, which sacrifices the flexibility of the decision-making.
To enable a set of flexible decisions in each scenario for both investment and operation variables, a multi-stage stochastic MILP model is formulated as follows.
(66) |
s.t.
(67) |
(68) |
(69) |
where the investment decisions are adjustable to the future realization of load growth uncertainties .
Compared with the two-stage stochastic model in (63)-(65) which obtains a determined planning decision over the planning horizons, the multi-stage stochastic model in (66)-(69) can obtain a more flexible decision tree. As the uncertain load growth state is revealed gradually over stages, the planners can choose planning decisions based on the latest information.
The proposed IPDHS co-planning model is tested on three systems [

Fig. 4 Three typical days in summer, winter, and transition season representing stochastic nature of PVs, WTs, power load, hydrogen load, and electricity price. (a) PV. (b) WT. (c) Power load. (d) Hydrogen load. (e) Electricity price.

Fig. 5 Topology of 8-node PDS with a 7-node hydrogen transportation system. (a) Under 8-node PDS. (b) Under 7-node hydrogen transportation system.
The forecast power and hydrogen load of 8-node PDS are presented in Table I.
Scenario | Power node | Power load (MVA) | Hydrogen node | Hydrogen load (kg) | |
---|---|---|---|---|---|
Cases 1-4 | Case 5 | ||||
Stages 1, 2, 3 | 1 | 4.05, 4.58, 4.74 | 1 | 16, 20, 24 | 8, 12, 16 |
2 | 1.14, 1.50, 1.76 | 4 | 12, 20, 24 | 24, 24, 32 | |
3 | 0.78, 1.50, 1.80 | 6 | 20, 24, 28 | 12, 16, 16 | |
6 | 0.32, 1.00, 1.60 | 7 | 12, 16, 24 | 16, 24, 28 | |
Stages 2, 3 | 4 | 2.05, 2.30 | 2 | 16, 28 | 20, 24 |
Stage 3 | 5 | 1.22 | 3 | 12 | 20 |
7 | 1.68 | 5 | 8 | 12 |
Table II presents the uncertain load growth state and probability at each stage. Candidate power lines and transformer data for 8-node PDS are shown in Tables III and IV. The PV and WT data for 8-node PDS are given in
Parameter | Value |
---|---|
($/km) | 1.3 |
($/km) | 0.7 |
($/km) | 1.3 |
($ per HT) | 100 |
0.5 | |
1.0 | |
0.1, 0.9 | |
, (kg) | 300, 300 |
(kg/kWh) | 52 |
(kWh/kg) | 1.0 |
($/MW) | 1.40 (stage 1), 1.30 (stage 2), 1.20 (stage 3) |
($/kg) | 20 |
Scenario | x (y) | ||
---|---|---|---|
Stage 1 | Stage 2 | Stage 3 | |
ξ1 | 1.0 (100%) | 0.9 (30%) | 0.9 (50%) |
ξ2 | 1.0 (50%) | ||
ξ3 | 1.0 (40%) | 1.0 (100%) | |
ξ4 | 1.15 (30%) | 1.15 (70%) | |
ξ5 | 0.95 (30%) |
Note: x and y in x(y) represent the load growth state and the probability, respectively.
In order to illustrate the effectiveness of the proposed multi-stage stochastic IPDHS co-planning model, five cases are designed and compared.
Case 1: the proposed multi-stage stochastic IPDHS co-planning model.
Case 2: this case is a two-stage stochastic IPDHS co-planning model as in (61)-(63).
Case 3: the multi-stage planning framework is utilized. The PDS expansion and PtHs are firstly optimized, after which the HES capacity is optimized (including hydrogen transportation and HSs).
Case 4: the multi-stage planning framework is utilized. The HES capacity is firstly optimized (including PtHs, hydrogen transportation and HSs), after which the PDS expansion is deployed.
Case 5: this case is similar to Case 1, while the spatial distribution of hydrogen load is varied as listed in Table I.
Table VII presents the cost comparison of five cases. Case 1 and Case 2 are compared to investigate the influence of the multi-stage planning model. It can be observed that the investment costs and the total planning costs of Case 1 are lower than those of Case 2, which shows the merits of multi-stage planning in dealing with long-term load growth uncertainties.
To further illustrate it, planning decisions in Case 1 and Case 2 are given in Table VIII. In Case 1, all the scenarios get the same planning results at stage 1. At stage 2, there are three candidate planning decisions for planners to choose from, which correspond to different load growth states. Similarly, there are five choices to be selected at stage 3. However, in Case 2, only one investment decision can be obtained, and the operation variables can be adjusted to cope with different load growth states. Therefore, the planning decision-making process in Case 1 is more flexible than that in Case 2, which can be adjusted according to the future load growth information.
Type | Resistance (Ω/km) | Reactance (Ω/km) | Capacity (MVA) | Cost ($/km) |
---|---|---|---|---|
1 | 0.614 | 0.399 | 9.38 | 28020 |
2 | 0.507 | 0.480 | 12.80 | 35140 |
Type | Capacity (MVA) | Investment ($) | Maintenance ($) |
---|---|---|---|
1 | 10 | 400000 | 2000 |
2 | 15 | 580000 | 3000 |
Type | Investment for stages 1, 2, 3 ($/MW) | Maintenance cost ($/kW) | Operation cost ($/kWh) | Curtailment cost ($/kWh) |
---|---|---|---|---|
PV | 1.7, 1.6, 1.5 |
4% of investment cost | 0.01 | 0.2 |
WT | 1.3, 1.2, 1.1 | 0.01 | 0.2 |
Cases 1, 3, and 4 are considered for comparison to show the effect of coordinated planning of PDS and HES. Clearly, Case 1 optimizes the IPDHS in a coordinated way and features the lowest total costs among them. In Case 3, the PDS planning is initially optimized, which obtains lower PDS expansion costs and leads to higher planning costs for HES. In contrast, Case 4 firstly optimizes the HES and achieves the cheapest HES planning costs, while the PDS expansion costs increase.
System | Type | Cost ($1 | ||||
---|---|---|---|---|---|---|
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | ||
PDS | Investment | 6.52 | 6.78 | 6.53 | 6.60 | 6.52 |
Maintenance | 3.40 | 3.47 | 3.41 | 3.45 | 3.40 | |
Production | 91.16 | 91.08 | 90.61 | 92.50 | 90.82 | |
Curtailment | 0.54 | 0.59 | 0.57 | 0.85 | 0.54 | |
Total | 101.62 | 101.92 | 101.12 | 103.40 | 101.28 | |
HES | Investment | 7.25 | 7.31 | 8.49 | 5.85 | 7.45 |
Maintenance | 4.49 | 4.50 | 5.30 | 3.52 | 4.53 | |
Production | 23.67 | 23.72 | 22.65 | 24.96 | 23.28 | |
Curtailment | 0 | 0 | 0 | 0 | 0 | |
Total | 35.41 | 35.53 | 36.44 | 34.33 | 35.26 | |
IPDHS | Total | 137.03 | 137.45 | 137.56 | 137.73 | 136.54 |
Case | Scenario (probability) | Planning decision | ||
---|---|---|---|---|
Stage 1 | Stage 2 | Stage 3 | ||
Case 1 |
Scenario 1 (0.15) |
Power line: 2-6(2), 3-8(2); WT: 2(0.16), 3(0.75), 6(0.80); PtH: 6(1.53), 7(1.11); HS: 1(400.0), 2(304.6), 3(115.1), 6(86.4) |
Power line: 1-4(2); WT: 2(0.75), 3(0.75), 6(1.10); PtH: 6(2.85), 7(1.85); HS: 1(400.0), 2(478.8), 3(143.9), 4(341.0), 6(426.3) |
Power line: 3-7(1), 4-5(1), 6-7(1); substation: 8(1); PV: 7(1.19); WT: 2(0.80), 3(1.10), 6(1.55); PtH: 6(2.55), 7(3.56); HS: 1(434.4), 2(600.0), 3(172.7), 4(502.3), 5(238.7), 6(511.5), 7(57.6) |
Scenario 2 (0.15) |
Power line: 3-7(1), 4-5(1), 6-7(1); substation: 8(1); PV: 7(1.39); WT: 2(0.80), 3(1.10), 6(1.80); PtH: 6(2.85), 7(3.14); HS: 1(600.0), 2(580.4), 3(430.6), 4(471.2), 5(86.4), 6(426.3), 7(57.6) | |||
Scenario 3 (0.40) |
Power line: 1-4(2), 3-7(2), 6-7(1); PV: 4(0.56), 7(0.56); WT: 2(0.74), 3(0.82), 6(1.10); PtH: 6(2.89), 7(1.85); HS: 1(453.8), 2(478.8), 3(143.9), 4(287.0), 6(143.9) |
Power line: 4-5(1); substation: 8(1); PV: 4(0.56), 7(0.83); WT: 2(0.80), 3(1.10), 6(1.80); PtH: 6(3.16), 7(2.80); HS: 1(600.0), 2(478.8), 3(430.6), 4(316.8), 5(238.7), 6(172.7), 7(57.6) | ||
Scenario 4 (0.21) |
Power line: 1-4(2), 3-7(2), 6-7(2); PV: 4(0.56), 7(0.56); WT: 2(0.74), 3(1.07), 6(1.20); PtH: 6(3.06), 7(1.76); HS: 1(456.2), 2(456.2), 3(346.7), 4(341.0), 6(426.3) |
Power line: 4-5(2); substation: 8(1); PV: 4(0.66), 7(1.18); WT: 2(0.80), 3(1.20), 6(1.80); PtH: 6(3.06), 7(3.34); HS: 1(600.0), 2(600.0), 3(430.6), 4(341.0), 5(255.8), 6(511.5), 7(57.6) | ||
Scenario 5 (0.09) |
Power line: 4-5(2); substation: 8(1); PV: 4(0.66), 7(0.66); WT: 2(0.80), 3(1.20), 6(1.51); PtH: 6(3.63), 7(2.46); HS: 1(456.2), 2(456.2), 3(511.5), 4(460.4), 5(197.3), 6(426.3), 7(57.6) | |||
Case 2 |
Power line: 2-6(2), 3-8(2); WT: 2(0.45), 3(0.45), 6(0.80); PtH: 6(1.53), 7(1.11);HS: 1(400.0), 2(315.4), 3(115.1), 6(238.7) |
Power line: 1-4(2), 3-7(2), 6-7(2); substation: 8(1) PV: 4(0.66), 7(0.66); WT: 2(0.45), 3(1.06), 6(1.08); PtH: 6(2.97), 7(1.85); HS: 1(500.0), 2(490.3), 3(358.8), 4(341.0), 6(358.8) |
Power line: 4-5(2); PV: 4(0.58), 7(0.76); WT: 2(0.80), 3(1.08), 6(1.80); PtH: 6(3.17), 7(2.79); HS: 1(500.0), 2(600.0), 3(511.5), 4(502.3), 5(255.8), 6(511.5), 7(70.5) |
Note: planning decisions are presented as . For power lines, x and y refer to the line mark and conductor type, respectively. For PV (MW), WT (MW), PtH (MW) and HS (kg), x and y refer to the node mark and installed capacity, respectively. Non-bold nodes and bold nodes represent the PDS and HES nodes, respectively.
Moreover, it can be found that the RES curtailment costs in Case 1 are lower than those in Case 3 and Case 4, which means that the RES utilization rate can be enhanced through coordinated planning.
As the interface between PDS and HES, the capacity allocation of PtHs will influence the planning results of both systems. Among Case 1, Case 3, and Case 4, Case 1 provides a tradeoff between PDS and HES, which can improve the RES consumption rate and achieve the highest economic benefits.
Furthermore, Case 1 and Case 5 are compared to show the influence of hydrogen load spatial distribution on the planning results. It can be observed that the planning costs of PDS and HES are both changed. The reason is that the variations in nodal hydrogen load will influence the transportation process from the HGS to the HRSs, and thus change the PtH allocations and the overall planning decisions.
For further illustration, the planning results for the PDS network in Case 1 in scenario are presented in

Fig. 6 Planning results for PDS in Case 1 in scenario ξ5. (a) Stage 1. (b) Stage 2. (c) Stage 3.
No. | Transportation route of HTs at each stage | ||
---|---|---|---|
Stage 1 | Stage 2 | Stage 3 | |
HT1 | 6-2-6-2-6-1-6 | 6-2-3-6-2-6-2-3-6 | |
HT2 | 6-6-6-2-6 | 6-6-1-6-2-6 | |
HT3 | 7-4-7-4-7-4-7 | 7-4-7-4-7-4-7 | 7-4-7-1-5-7-4-7 |
HT4 | 7-1-7-1-7-1-7 | 7-1-7-1-7-1-7 | 7-1-5-7-4-7-1-7 |
Note: non-bold nodes and bold nodes represent the PDS and HES nodes, respectively.
To validate the scalability of the planning method, a modified 24-node PDS with a 9-node HES is applied. The initial topology is shown in

Fig. 7 Initial topology. (a) Under 24-node PDS. (b) Under 9-node HEs.
Table X presents the uncertain load growth state and probability at each stage in the 24-node PDS. The optimality gap in this system is set as 1.0%, and the computation time is 9.69 hours.
Scenario | x(y) | ||
---|---|---|---|
Stage 1 | Stage 2 | Stage 3 | |
ξ1 | 1.0 (100%) | 0.9 (20%) | 0.9 (20%) |
ξ3 | 1.0 (50%) | 1.0 (50%) | |
ξ3 | 1.15 (30%) | 1.15 (30%) |
Note: x and y in x(y) represent the load growth state and the probability, respectively.
The cost comparison of five cases in the 24-node PDS is presented in Table XI, and the planning decisions of 24-node PDS in Case 1 and Case 2 are presented in Table XII. In the 24-node PDS, similar conclusions can be obtained as in the 8-node PDS. The proposed planning model considers the coordination of PDS and HES, and the investment decisions are determined from a holistic perspective. Two test systems both verify that the planning method provides a tradeoff between the PDS and the HES, which can reduce the total planning cost and promote RES utilization. Besides, the multi-stage stochastic planning model outperforms the two-stage stochastic model, which can provide a decision tree for planners under power and hydrogen load growth uncertainties and make the decision-making process more flexible.
System | Type | Cost ($1 | ||||
---|---|---|---|---|---|---|
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | ||
PDS | Investment | 18.53 | 18.14 | 18.24 | 18.70 | 18.53 |
Maintenance | 8.89 | 8.67 | 8.77 | 8.93 | 8.89 | |
Production | 181.30 | 182.51 | 181.04 | 184.66 | 181.12 | |
Curtailment | 1.42 | 1.47 | 1.48 | 1.75 | 1.42 | |
Total | 210.14 | 210.79 | 209.53 | 214.04 | 209.96 | |
HES | Investment | 15.36 | 15.19 | 16.06 | 14.20 | 15.44 |
Maintenance | 9.38 | 9.35 | 9.85 | 8.71 | 9.61 | |
Production | 34.39 | 34.89 | 34.48 | 35.65 | 34.59 | |
Curtailment | 0 | 0 | 0 | 0 | 0 | |
Total | 59.13 | 59.43 | 60.39 | 58.56 | 59.64 | |
IPDHS | Total | 269.27 | 270.22 | 269.92 | 272.60 | 269.60 |
Case | Scenario (probability) | Planning decision | ||
---|---|---|---|---|
Stage 1 | Stage 2 | Stage 3 | ||
Case 1 |
Scenario 1 (0.2) |
Power line: 4-9, 3-16, 3-23, 7-23, 10-23; substation: 23; PV: 1(0.35), 4(0.86); WT: 2(1.50), 9(1.43); PtH: 8(3.25), 9(1.64); HS: 1(574.1), 4(230.3), 5(172.7), 8(1000.0), 9(630.3) |
Power line: 1-14, 2-12, 6-13, 11-23, 15-17, 17-22;PV: 1(0.44), 4(0.88), 15(0.86); WT: 2(2.50), 9(2.50), 14(0.27); PtH: 8(4.46), 9(6.00); HS: 1(574.1), 3(172.7), 4(287.9), 5(184.7), 6(688.9), 8(1500.0), 9(1500.0) | Power line: 5-24, 7-19, 10-16, 18-24, 20-24; substation: 24; PV: 1(0.44), 4(2.12), 15(0.86); WT: 2(3.50), 9(3.50), 14(1.30), 18(0.79); PtH: 8(6.12), 9(6.28); HS: 1(574.1), 2(230.3), 3(207.3), 4(322.4), 5(209.0),6(688.9), 7(172.7), 8(1500.0), 9(2000.0) |
Scenario 1 (0.5) | Power line: 1-14, 2-12, 6-13, 10-16, 11-23, 15-17,17-22; PV: 1(0.35), 4(1.22), 15(0.85); WT: 2(2.50), 9(2.50), 14(0.86); PtH: 8(4.62), 9(6.00); HS: 1(1023.0), 3(172.7), 4(287.9), 5(230.3), 6(286.1), 8(1425.6), 9(1500.0) | Power line: 2-3, 5-24, 7-19, 18-24, 20-24; substation: 24; PV: 1(0.35), 4(2.71), 15(0.85); WT: 2(3.50), 9(3.50), 14(1.21), 18(1.31), 20(0.39); PtH: 8(6.22), 9(6.61); HS: 1(1023.0), 2(230.3), 3(207.3), 4(322.4), 5(264.8), 6(481.1), 7(172.7), 8(2000.0), 9(2000.0) | ||
Scenario 1 (0.3) | Power line: 1-14, 2-12, 4-15, 6-13, 7-8, 11-23, 15-17, 17-22; PV: 1(0.35), 4(0.86), 15(1.68); WT: 2(2.50), 9(2.50), 14(1.51); PtH: 8(6.00), 9(4.63); HS: 1(723.0), 3(172.7), 4(287.9), 5(574.1), 6(778.4), 8(1305.2), 9(1321.9) | Power line: 4-16, 5-24, 7-19, 10-16, 18-24, 20-24;substation: 24; PV: 1(0.35), 4(2.14), 15(1.68), 19(0.32); WT: 2(3.50), 9(3.50), 14(3.16), 18(1.15), 20(0.09); PtH: 8(6.00), 9(6.69); HS: 1(1004.6), 2(230.3), 3(207.3), 4(322.4), 5(574.1), 6(778.4), 7(430.5), 8(2000.0), 9(2000.0) | ||
Case 2 | Power line: 4-9, 3-23, 7-23, 10-23; PV: 1(0.35), 4(0.87);WT: 2(1.50), 9(1.43); PtH: 8(2.10), 9(2.86); HS: 1(526.2), 4(230.3), 5(477.3), 8(705.0), 9(1000.0) | Power line: 1-14, 2-3, 2-12, 4-15, 6-13, 7-8, 10-16, 11-23, 15-17, 17-22; PV: 1(0.35), 4(1.16), 15(1.01); WT: 2(2.50), 9(2.50), 14(0.63); PtH: 8(4.60), 9(6.00); HS: 1(801.5), 3(172.7), 4(287.9), 5(477.3), 6(718.5), 8(1366.0), 9(1500.0) | Power line: 4-16, 5-24, 7-19, 15-19, 18-24, 20-24; substation: 24; PV: 1(0.35), 4(2.33), 15(1.01); WT: 2(3.50), 9(3.50), 14(1.90), 18(1.11), 20(0.03); PtH: 8(6.08), 9(6.28); HS: 1(801.5), 2(526.2), 3(207.3), 4(322.4), 5(477.3), 6(718.5), 7(172.7), 8(1366.0), 9(2000.0) |
Note: planning decisions for PV (MW), WT (MW), PtH (MW), and HS (kg) are presented as , x and y refer to the node mark and installed capacity, respectively. Non-bold nodes and bold nodes represent the PDS and HES nodes, respectively.
The proposed model is further tested on a modified 54-node PDS with a 9-node HES, which contains 4 substations (35 kV), 50 power load nodes, 17 existing power lines, 46 candidate power lines, 2 HGSs, 7 HRSs, and 13 roads. In HES, 2 HGS nodes 8 and 9 are connected to PDS nodes 9 and 16, respectively. To relieve the computation burden, six time periods are considered for PDS in each day (, hours). Long-term power and hydrogen load growth scenarios are utilized. More data related to the test system can refer to [
Type | Cost ($1 | |||||
---|---|---|---|---|---|---|
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | ||
PDS | Investment | 32.99 | 32.88 | 32.78 | 34.36 | 32.28 |
Maintenance | 19.88 | 19.42 | 19.69 | 19.98 | 19.90 | |
Production | 350.00 | 351.46 | 350.15 | 352.76 | 349.88 | |
Curtailment | 1.17 | 1.55 | 1.14 | 1.36 | 1.16 | |
Total | 404.04 | 405.31 | 403.76 | 408.46 | 403.22 | |
HES | Investment | 20.42 | 21.16 | 20.16 | 17.15 | 20.42 |
Maintenance | 12.26 | 12.79 | 12.09 | 10.08 | 12.17 | |
Production | 54.57 | 53.56 | 56.49 | 58.19 | 54.53 | |
Curtailment | 0 | 0 | 0.08 | 0 | 0 | |
Total | 87.25 | 87.51 | 88.82 | 85.42 | 87.12 | |
IPDHS | Total | 491.29 | 492.82 | 492.58 | 493.88 | 490.34 |
This paper proposes a multi-stage stochastic IPDHS co-planning model under long-term load growth uncertainties. In the planning model, the PDS expansion and the HES including hydrogen production, transportation and storage sectors are comprehensively considered. Wherein, substations, power lines, PVs, WTs, PtHs, and HSs are invested to supply the uncertain power and hydrogen loads over the planning horizon. To achieve a more flexible decision-making process under load growth uncertainties, the multi-stage stochastic planning model is utilized.
Numerical results verify the coordination of PDS, and HES can reduce the total planning cost and achieve more efficient resource allocation. Additionally, the multi-stage stochastic model can provide a flexible planning decision tree and outperform the two-stage stochastic model. In future work, we will investigate more efficient modeling methods and solution techniques to improve the computational performance of the planning model. In addition, more technical features for the hydrogen system such as pipeline transmission and seasonal storage will also be considered. Another direction is to design a decentralized planning framework to preserve the data privacy of different planners.
Nomenclature
Symbol | —— | Definition |
---|---|---|
A. | —— | Indices and Sets |
—— | Index of power distribution system (PDS) scheduling time period | |
—— | Index of hydrogen energy system (HES) scheduling time period | |
—— | Set of head and tail nodes in power lines a | |
—— | Set of uncertain scenarios | |
/ | —— | Set of power lines with node i as head/tail |
—— | Set of planning stages | |
// | —— | Set of hydrogen nodes/hydrogen loads/HTs |
—— | Set of substations/power lines/photovoltaics (PVs)/wind turbines (WTs)/power to hydrogens(PtHs)/hydrogen storages (HSs)/HTs | |
—— | Set of hydrogen nodes corresponding to PtH node i | |
// | —— | Set of power nodes/power loads/transportation paths |
a/(i, j) | —— | Index of power lines |
d | —— | Index of hydrogen tube trailer (HT) |
g | —— | Index of HGS |
i/j | —— | Index of power nodes including generation station (HGS) and hydrogen refueling station (HRS) |
/ | —— | Set of candidate transformers/power line types |
m/n | —— | Index of hydrogen nodes including HGS and HRS |
s | —— | Index of operating scenario |
t/ | —— | Index of planning stages |
B. | —— | Parameters |
—— | Annual interest rate | |
—— | Initial year | |
////// | —— | Capital recovery rate of substation/transformer/power line/PV/WT/PtH/HS |
/ | —— | Duration of time period |
—— | Network loss cost coefficient of PDS | |
—— | Travel cost of HTs per km | |
—— | Fixed dispatch cost for HT d | |
—— | Installed import (export) to capacity ratios of HS | |
—— | The maximum hydrogen export ratio | |
/// | —— | Power factor of substation/power load/PV/WT |
//// | —— | Level of PV/WT/power load/hydrogen load |
—— | The maximum penetration rate of RES | |
—— | Lower/upper capacity level of HSs | |
/ | —— | The maximum curtailed rate of power/hydrogen load |
/ | —— | PtH efficiency/power consumption rate of compressor |
// | —— | Number of hydrogen node/power load node/planning stage |
—— | Investment cost coefficient of substation | |
/ | —— | Investment cost coefficient of transformer/power line in type k |
/// | —— | Investment cost coefficient of PV/WT/PtH/HS |
—— | Maintenance cost coefficient of substations at power node i | |
/ | —— | Maintenance cost coefficient of transformer/power line in type k |
/// | —— | Maintenance cost coefficient of PV/WT/PtH/HS |
—— | Electricity purchase cost from substation | |
/ | —— | Production cost of PV/WT |
—— | Electricity purchase cost of PtHs | |
/ | —— | Unserved cost of power/hydrogen load |
/ | —— | Curtailment cost of PV/WT |
—— | Number of day | |
—— | Hourly/base hydrogen load of m | |
/ | —— | The maximum loading/unloading hydrogen of HT d |
—— | Upper bound for current through the power line | |
—— | Length of power line | |
—— | Distance between m and n | |
M | —— | A large positive number |
—— | Number of time periods within a typical day | |
—— | Hourly/base power load of i | |
—— | Probability of scenario c | |
—— | Resistance/reactance of power line a | |
—— | Capacity of power line/transformer in type k | |
—— | Lower/upper bound for nodal voltage | |
—— | Upper bound for installed PV/WT/PtH/HS | |
C. | —— | Variables |
—— | Binary state variable of HT d between m and n | |
—— | Auxiliary variable of HT d at hydrogen node m | |
/// | —— | Investment/maintenance/operation/unserved energy cost |
—— | Hydrogen level of HS | |
—— | Fictitious power flow through power line a | |
/ | —— | Fictitious power of substation/power load |
/ | —— | Charged/discharged hydrogen of HS |
—— | Hydrogen exported from PtH to HT | |
—— | Hydrogen imported from HT d to HRS m | |
—— | Hydrogen exported to HT d | |
—— | Hydrogen produced by PtH | |
—— | Square of current through power line a | |
// | —— | Active power injected by substation/PV/WT |
/ | —— | Active power consumed by PtH/compressor |
—— | Unserved power/hydrogen load | |
—— | Active/reactive/apparent power flow through power line a | |
/ | —— | Curtailed active power of PV/WT |
// | —— | Reactive power injected by substation/PV/WT |
—— | Square of voltage | |
—— | Binary investment variables for substation/transformer/power line | |
—— | Investment variable for PV/WT | |
—— | Investment variable for PtH/HS | |
/ | —— | Binary forward/backward utilization variable for power line a |
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