In this paper, the green port consists of gas turbines (GTs), wind generators (WGs), photovoltaics (PVs), BESs, QCs, and ships. The aforementioned devices are connected to the AC and DC ports of the proposed multiport PET system, which reduces the steps of energy conversion and improves energy efficiency. The structure of the green port with multiport PET system is shown in Figure 1.

Figure 1 shows that the proposed multiport PET system is simplified and equivalent to a three-port power electronic device: high-voltage alternating current (HVAC), low-voltage alternating current (LVAC), and low-voltage direct current (LVDC) ports. Specifically, WGs, GTs, and QCs in the AC area are connected to the LVAV port through the AC bus. PVs, BESs, and ships in the DC area are connected to the LVDV port through the DC bus. Moreover, the MVAV port is connected to the main grid for participating in day-ahead markets.

The multiport PET system can manage the power flow direction according to the power surplus or deficit of each port, ensuring the power balance of each area and the whole green port. Notably, the reactive power of the AC area is left out of consideration due to the reactive compensation function of PET. The power balance of the green port with a multiport PET system is as follows: p m a , t o u t − p m a , t i n = η A C p A C , t , k i n − p A C , t , k o u t + η D C p D C , t , k i n − p D C , t , k o u t (1) ∑ s = 1 N s p G T , s , t , k + ∑ w = 1 N w p W G , w , t , k + p A C , t , k o u t − p A C , t , k i n − ∑ l = 1 N l P l , t = 0 (2) ∑ p = 1 N p p P V , p , t , k + ∑ e = 1 N e p B E S , e , t , k d i s − p B E S , e , t , k c h + p D C , t , k o u t − p D C , t , k i n − ∑ d = 1 N d P d , t = 0 (3) Eqs 1–3 represent the energy balance model of the MVAC, LVAC, and LVDC ports, respectively. t is the index of time periods; k is the index of scenarios; and s, e, p, w, l, and d are the indices of GTs, BESs, PVs, WGs, QCs, and ships, respectively. p m a , t o u t and p m a , t i n are energy purchased and sold by the green port by the MVAV port of PET in the energy market, respectively. p A C , t , k i n , p A C , t , k o u t , p D C , t , k i n , and p D C , t , k o u t represent output and input energy in the LVAV and LVDC ports, respectively. p G T , s , t , k , p W G , w , t , k , and p P V , p , t , k represent power generation of GTs, WGs, and PVs at time t under scenario k, respectively. p B E S , e , t , k d i s and p B E S , e , t , k c h represent discharging and charging power of BESs at time t under scenario k. P l , t and P d , t are loads of QCs and ships, respectively. η A C and η D C are efficiencies of PET’s LVAC and LVDC ports, respectively.

The key to the logistics system in green port is dispatching the QCs for the efficient loading and unloading of ships. In other words, the number of QCs is directly related to the duration of the ship in the port and then affects the status of the ship in the port.

The rule of dispatching in the port requires that the ships must leave before the latest time of departure within a certain range, as shown in Eq. 4. During the scheduling cycle, ships arrive at the port only once and do not return after leaving the port, as modeled in Eq. 5: t d l e a v e − t d a r r i v e ⩽ ∑ t u d , t s h i p ⩽ t d − l e a v e − t d a r r i v e , (4) u d , t s h i p ⩾ u d , t + 1 s h i p , (5) where t d l e a v e and t d − l e a v e denote the earliest and latest time of departure of ships, respectively. t d a r r i v e denotes the time of arrival of ships. u d , t s h i p is the binary variable that defines the status of the ship in the port.

Due to the limitation to ship length and cargoes loaded and unloaded, the numbers of QCs allocated cannot exceed the minimum and maximum QC demands of ships, as shown in Eq. 6. Meanwhile, the number of QCs in operation at some point should be limited to the total number of QCs in the port and defined in Eq. 7. Eq. 8 indicates that containers can be unloaded at one time within the specified time: u d , t s h i p Q C d min ⩽ Q C d , t ⩽ u d , t s h i p Q C d max , (6) ∑ d Q C d , t ⩽ Q C max , (7) η Q C ∑ t Q C d , t ⩾ C O d , (8) where Q C d , t is the number of QCs allocated, C O d is the number of containers loaded and unloaded by ships, and η Q C is the efficiency of the loading and unloading of QCs.

In this paper, the green port is considered an aggregator that can purchase or sell energy in the energy market, providing reserves in the reserve market and trading carbon credit in the carbon market. Generation companies (Gencos) are the other participants of the multiple markets. The framework of multiple markets in the green port is shown in Figure 2.

To be specific, the green port and Gencos provide energy and reserve to meet the requirements of the main grid in the day-ahead market. In the inner carbon market, a carbon credit is set as a commodity to participate in market transactions. Units with high carbon emissions may have to pay high costs to buy carbon credits in the carbon market; units with low carbon emissions may purchase additional carbon credits from the carbon market as a means of reducing their carbon footprint.

In other words, the green port can trade and obtain carbon credit in the process of GT, WG, and PV generation. Whenever the green port dispatches GTs to generation, it also has to purchase carbon credits for itself. The dispatch of WT and PV can result in corresponding carbon credits, which can be sold on the carbon trading market to gain economic benefits.

In the perspective of the proposed bi-level stochastic optimization model, which considers the uncertainties, the operation scheme of the green port is modeled in the upper-level problem, and the lower-level problem consists of clearing the energy (problem Ⅰ) and reserve market (problem Ⅱ), as shown in Figure 3. The behavior of other participants (Genco and consumers) is not strategic, and their bids are only modeled in the lower-level problem.

Before solving the problem, the uncertainties of stochastic parameters are described as stochastic processes, and the Monte Carlo simulation (MCS) (Chin et al., 2003) approach is used to generate scenarios. Uncertainties in PVs, WGs, and loads in the main grid are considered in this work. With each parameter obtained, the sets of generated scenarios are joined to form a scenario tree. Because the number of created scenarios directly impacts the complexity of the optimization problem’s computation, it must be reduced to a smaller number of scenarios that adequately represent the uncertainties. In order to lessen the stochastic procedure’s computational overhead, the simultaneous backward reduction (SBR) (Heitsch and Romisch, 2003) algorithm is employed as a proper scenario-reduction strategy to reduce the scenario tree to a reasonable level of possibilities.

In the upper-level problem, the green port system aims to minimize the operation cost and profit from the energy market, reserve market, and carbon trade, as presented in Eqs 9–13. Eq. 9 presents the objective function of the green port’s operation problem consisting of seven terms. C G T and C B E S represent the operation cost of GTs and BESs. C P V and C W G describe the generating cost of PVs and WGs. C E N and C R S describe the profit from energy and reserve settlements in the day-ahead market. C C indicates revenue from carbon trade: min C G T + C B E S + C P V + C W G − C E N − C R S − C C , (9) C G T = ∑ t = 1 N t ∑ s = 1 N s γ G T ∑ k = 1 K Π k p G T , s , t , k , (10) C B E S = ∑ t = 1 N t ∑ e = 1 N e γ B E S ∑ k = 1 K Π k ( p B E S , e , t , k d i s + p B E S , e , t , k c h ) , (11) C P V = ∑ t = 1 N t ∑ p = 1 N p γ P V ∑ k = 1 K Π k p P V , p , t , k , (12) C W G = ∑ t = 1 N t ∑ w = 1 N w γ W G ∑ k = 1 K Π k p W G , w , t , k , (13) C E N = ∑ t = 1 N t ρ t E N p m a , t o u t − ρ t E N p m a , t i n , (14) C R S = ∑ t = 1 N t ρ t U P ⋅ r P E T , t i n , U P + r P E T , t o u t , U P + ρ t D N ⋅ r P E T , t i n , D N + r P E T , t o u t , D N , (15) C C = ∑ t = 1 N t ρ t C T ∑ k = 1 K Π k ( ∑ p = 1 N p p P V , p , t , k + ∑ w = 1 N w p W G , w , t , k − ∑ s = 1 N s p G T , s , t , k , (16) where γ G T , γ B E S , γ P V , and γ W G are unit costs of GTs, BESs, PVs, and WGs, respectively. Π k is the probability of scenario k. ρ t E N is the energy market-clearing price at time t. ρ t U P and ρ t D N are upward reserve and downward reserve market-clearing prices at time t, respectively. r P E T , t i n , U P , r P E T , t o u t , U P , r P E T , t i n , D N , and r P E T , t o u t , D N represent upward and downward reserves provided by the green port in the reserve market at time t, respectively.

In the first lower-level problem, the green port participates in the energy market. The objective function of the energy market clearing model is shown in Eqs 47–49. C G E N and C P E T E N describe the cost of purchasing electricity capacity from generators and the green port by the upper-layer grid, respectively. The power balance equation is expressed in Eq. 50, and the energy price is provided by its corresponding dual variable. The constraint (Eq. 51) restricts the energy production of Gencos: min C G E N + C P E T E N , (47) C G E N = ∑ t = 1 N t ∑ n = 1 N n γ G , t E N p G , n , t , (48) C P E T E N = ∑ t = 1 N t ( v P E T , t o u t , E N p m a o u t − v P E T , t i n , E N p m a i n ) , (49)

subject to ∑ m = 1 N m P m , t − p m a , t o u t − p m a , t i n − ∑ n = 1 N n p G , n , t = 0 : ρ t E N , (50) 0 ≤ p G , n , t ≤ P G , n max : μ _ G , n , t , μ ¯ G , n , t , (51) where γ G , t E N is the offer price of Gencos in the energy market. P G , n max is the maximum output of Gencos. p G , n , t is the power generation of Gencos n at time t. P m , t is forecasted load demand m in the main grid. μ _ G , n , t and μ ¯ G , n , t are dual variables.

The reserve market is cleared as the second lower-level problem given by Eq. 52, which consists of two terms. C G R S and C P E T R S represent the cost of purchasing reserve capacity from Gencos and the green port, respectively. Constraints (Eqs. 55, 56) indicate that the market’s upward and downward reserve requirements are met by Gencos and the green port, and the upward and downward reserve capacity commitment prices are determined by their associated dual variables. Constraints (Eqs. 57–60) show the upward and downward reserve commitment limit provided by Gencos: min C G R S + C P E T R S , (52) C G R S = ∑ t = 1 N t ∑ n = 1 N n γ G , t R S ( r G , n , t U P + r G , n , t D N ) , (53) C P E T R S = ∑ t = 1 N t v P E T , t U P , R S ⋅ r P E T i n , U P + r P E T o u t , U P + v P E T , t D N , R S ⋅ r P E T i n , D N + r P E T o u t , D N , (54) subject to ∑ n = 1 N n r G , n , t U P + r m a , t i n , U P + r m a , t o u t , U P = R t U P : ρ t R S , U P , (55) ∑ n = 1 N n r G , n , t D N + r m a , t i n , D N + r m a , t o u t , D N = R t D N : ρ t R S , D N , (56) 0 ≤ r G , n , t U P ≤ R G , n U P : μ _ G , n , t U P , μ ¯ G , n , t U P , (57) 0 ≤ r G , n , t D N ≤ R G , n D N : μ _ G , n , t D N , μ ¯ G , n , t D N , (58) p G , n , t + r G , n , t U P < P G , n max : μ G , n , t , U P (59) r G , n , t D N − p G , n , t ≤ 0 : μ G , n , t D N , (60) where γ G , t R S is the offer price of Genco in the reserve market. R t U P and R t D N are upward and downward reserve requirements for the market at time t, respectively. r G , n , t U P and r G , n , t D N are upward and downward reserves provided by Genco n in the reserve market at time t, respectively. R G , n U P and R G , n D N are maximum upward and downward reserve capacities of Genco. ρ t R S , U P and ρ t R S , D N are associated with dual variables as upward and downward reserve capacity commitment prices at time t, respectively. μ _ G , n , t U P , μ ¯ G , n , t U P , μ _ G , n , t D N , μ ¯ G , n , t D N , μ G , n , t U P , and μ G , n , t D N are dual variables corresponding to inequality constraints, respectively.

In this paper, the decision-making process of the green port is modeled as a bi-level stochastic optimization model, which is considered a Stackelberg game, where the upper level is given by Eqs 1–46, the first lower level by Eqs 47–51, and the second lower level by Eqs 52–60. The whole process of the solution method is described in Figure 4.

First, because the decision variables of the upper-level problem are considered parameters in the lower-level problem, the lower-level problem can be transformed into a convex and linear one and replaced with its KKT optimality conditions by the Lagrangian method (Bahramara et al., 2015) as follows: L i = f i x i + μ i T h i x i + ρ i T g i x i , (61) γ G , t E N − ρ t E N − μ _ G , n , t + μ ¯ G , n , t + μ G , n , t U P − μ G , n , t D N = 0 , (62) γ G , t R S − ρ t U P − μ _ G , n , t U P + μ ¯ G , n , t U P + μ G , n , t U P = 0 , (63) γ G , t R S − ρ t D N − μ _ G , n , t D N + μ ¯ G , n , t D N + μ G , n , t D N = 0 , (64) v P E T , t o u t , E N − ρ t E N = 0 , (65) − v P E T , t i n , E N + ρ t E N = 0 , (66) v P E T , t U P , R S − ρ t U P = 0 , (67) v P E T , t D N , R S − ρ t D N = 0 , (68) 0 ≤ μ _ G , n , t ⊥ p G , n , t ≥ 0 , (69) 0 < μ ¯ G , n , t ⊥ P G , n max − p G , n , t > 0 , (70) 0 ≤ μ _ G , n , t U P ⊥ r G , n , t U P ≥ 0 , (71) 0 ≤ μ ¯ G , n , t U P ⊥ R G , n U P − r G , n , t U P ≥ 0 , (72) 0 < μ _ G , n , t D N ⊥ r G , n , t D N > 0 , (73) 0 ≤ μ ¯ G , n , t U P ⊥ R G , n U P − r G , n , t U P ≥ 0 , (74) 0 ≤ μ G , n , t U P ⊥ P G , n max − p G , n , t − r G , n , t U P ≥ 0 , (75) 0 ≤ μ G , n , t D N ⊥ p G , n , t − r G , n , t D N ≥ 0 . (76)

Then, the Big-M method (Talbi, 2013) is used to linearize the complementarity requirement, transforming Eqs 69–76 into Eqs 77–92. Note that θ i is an auxiliary binary variable and M is a large enough positive constant: 0 ≤ μ _ G , n , t ≤ M θ G L , (77) 0 < p G , n , t < M 1 − θ G L , (78) 0 ≤ μ ¯ G , n , t ≤ M θ G U , (79) 0 ≤ P G , n max − p G , n , t ≤ M 1 − θ G U , (80) 0 < μ _ G , n , t U P < M θ U P L , (81) 0 ≤ r G , n , t U P ≤ M 1 − θ U P L , (82) 0 ≤ μ ¯ G , n , t U P ≤ M θ U P U , (83) 0 ≤ R G , n U P − r G , n , t U P ≤ M 1 − θ U P U , (84) 0 < μ _ G , n , t D N < M θ D N L , (85) 0 ≤ r G , n , t D N ≤ M 1 − θ D N L , (86) 0 ≤ μ ¯ G , n , t D N ≤ M θ D N U , (87) 0 < R G , n D N − r G , n , t D N < M 1 − θ D N U , (88) 0 ≤ μ G , n , t U P ≤ M θ U P , (89) 0 ≤ P G , n max − p G , n , t − r G , n , t U P ≤ M 1 − θ U P , (90) 0 < μ G , n , t D N < M θ D N , (91) 0 ≤ p G , n , t − r G , n , t D N ≤ M 1 − θ D N . (92)

Therefore, the bi-level problem is transformed into a single-level problem generating a mathematical program with equilibrium constraints (MPECs). Furthermore, the nonlinear terms of the upper-level objective function need to be linearized based on the strong duality theorem (Kazempour et al., 2011), as described in detail in Eq. 93, which is a mixed-integer linear programming (MILP) model: Min ∑ t = 1 N t ∑ s = 1 N s γ G T ∑ k = 1 K Π k p G T , s , t , k + ∑ w = 1 N w γ W P ∑ k = 1 K Π k p W P , w , t , k + ∑ e = 1 N e γ E E S ∑ k = 1 K Π k ( p E E S , e , t , k d i s + p E E S , e , t , k c h + ∑ p = 1 N p γ P V ∑ k = 1 K Π k p P V , p , t , k + ∑ e = 1 N e γ E E S ∑ k = 1 K Π k ( p E E S , e , t , k d i s + p E E S , e , t , k c h + ρ t C T ∑ k = 1 K Π k ( ∑ p = 1 N p p P V , p , t , k + ∑ w = 1 N w p W G , w , t , k − ∑ s = 1 N s p G T , s , t , k ) + ∑ n = 1 N n γ G , t E N p G , n , t + γ G , t R S r G , n , t U P + r G , n , t D N + ∑ n = 1 N n ( μ ¯ G , n , t P G , n max + μ ¯ G , n , t U P R G , n U P + μ ¯ G , n , t D N R G , n D N + μ G , n , t U P P G , n max ) − ( ρ t R S , U P R t U P + ρ t R S , D N R t D N ) − ∑ m = 1 N m ρ t E N P m , t . (93)

The constraints of the MPEC include 1) the constraints of the upper-level problem (Eqs 1–46), 2) the KKT optimality conditions of lower-level problems (Eqs 61–76), and 3) the complementarity conditions (Eqs 77–92).

A hypothetical marketing structure is established in this test green port system, composed of the operator of the green port system and three Gencos that participate in the energy, reserve, and carbon market. In the simulation, the time step is 1 h, and the dispatching cycle is 24 h. This test green port system contains a multiport PET, PVs, WGs, BESs, and QCs and is connected to the main grid. The forecasted values for the power generation of WGs, PVs, and the load demand in the main grid are shown in Figure 5. Based on the forecasted values, 2,000 scenarios are generated using the MCS approach. Then, the SBR algorithm is adopted to reduce the scenario to a reasonable level of possibilities. The corresponding probabilities are 0.305, 0.155, 0.23, 0.115, and 0.195, respectively.

The operational characteristics of the green port system are listed in Table 1. In Table 2, the relevant parameters of Gencos are reported. The relevant parameters of the port logistics system are shown in Table 3.

The carbon trading price in the carbon market is assumed as $0.0013/kW. The hourly maximum upward and downward reserve requirements in the main grid are considered to be 20% of its load. In order to demonstrate the effectiveness of the proposed strategy, the operation results are shown in the following section.

Based on the proposed bi-level stochastic optimization strategy, this section analyzes the operation of each power generation equipment, energy storage equipment, and port logistics equipment in the green port, considering intimal carbon trading as described in the upper level. Furthermore, the operator of the green port participates in external markets, including energy and reserve markets; then, the corresponding market clearing results are discussed in the following paragraphs.

In the aspect of the operation scheduling of the green port, the dispatching results of GT, PV, WG, BES, and loads are shown in Figure 6. The positive values in the figure represent the supplied power, and the negative values represent the consumed power.

Figure 6 shows that GTs barely run due to their high operation cost. BESs are in the charging mode in hours 9–18 due to the abundant power generation of PVs. Moreover, energy consumption on ships approaching and berthing and containers loading and unloading by QCs is the main load source in the green port. It is assumed that the energy consumption of ships during berthing is provided by the port.

The operation results of port logistics are shown in Figures 7, 8. More specifically, Figure 7 presents details of each ship’s berthing schedule. Compared to Table 3, each ship can leave the port before the latest departure time, arrive only once, and do not return after leaving. Furthermore, containers’ loading and unloading are finished by dispatching the QCs, as shown in Figure 8. The numbers of QCs assigned to each ship at each time period do not exceed the maximum QCs required of each ship. Moreover, the numbers of the operating QCs in each hour are within the range of the total quantity of QCs in the port.

In terms of marketing activities, the clearing results in the energy market are shown in Figure 9, in which the negative value represents the green port purchasing energy from the main grid and the positive value represents the green port selling energy to the main grid. The clearing results in the reserve market are shown in Figure 10, in which the negative/positive values correspond to the downward/upward reserve. The clearing prices in the energy and reserve markets are shown in Figure 11.

The data in Figure 9 show that the green port sells energy to the main grid in hours 1 and 9–24 on account of a reduction in local load or an increase in local renewable energy power generation. In hours 10, 12, 13, 16, and 24, Genco 3 is involved with the energy market separately among the three-generation companies, thus resulting in the lowest energy trading prices equivalent to the offer price of Genco 3, as shown in Figure 11. In hours 2–7, 11, 14, 15, 17–19, 22, and 13, Genco 2 is added to the market to meet the growing load demand in the main grid. At these times, the energy price is the same as the price of Genco 2. Furthermore, the clearing prices in the energy market are the highest in hours 8, 9, 20, and 21, equal to the offer price of Genco 1, as presented in Figure 11.

As shown in Figure 10, the upward reserve and downward reserve requirements are met by Genco 3 and the green port system. Note that the reserve prices are identical to the reserve offer price of Genco 3, as presented in Figure 11.

In order to evaluate the effectiveness of the proposed market strategy in this study, the following different strategies are compared in this section.

1) Case 1: Strategy for the single energy market,

The green port system’s operation cost and expected market profits in different strategies are shown in Table 4.

Table 4 shows that compared to the different strategies with a combination of different markets, the proposed strategy results in a lower total cost for the operation of the green port system and gains more profit from the day-ahead energy market, day-ahead reserve market, and carbon trading market.

Moreover, in case 1, the strategy for the single energy market only gains profit from the day-ahead energy market, and the revenue is less than the operation cost. In case 3, the revenue from the energy market is the lowest because the requirements for less GT generation in carbon trading lead to a decrease in green port participation in the energy market.

Generally, the aforementioned results indicate that the green port system participating in multiple markets can generate more revenue to cover the system operation cost.