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Energy-saving scheduling optimization under up-peak traffic for group elevator system in building
Energy and Buildings 66 (2013) 495–504
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Energy-saving scheduling optimization under up-peak traffic for group elevator system in building Jinglong Zhang ∗ , Qun Zong College of Electric Engineering and Automation, Tianjin University, Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 13 December 2012 Received in revised form 27 May 2013 Accepted 26 July 2013 Keywords: Group elevator system Energy-saving Scheduling optimization Up-peak
a b s t r a c t Energy-saving group scheduling is a significant challenge for multi-elevator system in building. Among various traffic patterns in building, most energy is consumed under up-peak traffic pattern. To save unnecessary energy consumption and realize optimal scheduling, an energy-saving scheduling optimization method for up-peak pattern is proposed. The optimization objective is minimizing the scheduling energy price of the group system. The up-peak energy price function is defined first, both of picking and traveling energy are considered in it. Based on that, scheduling Robust Optimization model is built to handle elevator scheduling under uncertain up-peak traffic flow. The key point of optimization is a dual energy-saving mechanism. One is adaptive configuration, choosing fewer but enough number’s elevator to transport waiting passengers on the lobby floor. Another is optimization selection, choosing which elevators to serve according to minimum energy price after the number of dispatched elevators is decided. In practice, elevators in group system are dispatched by scheduling decision of the optimization to realize system energy-saving operation under up-peak pattern. In simulation, compared with the scheduling performances of other algorithms under different up-peak flows in several buildings, effectiveness of the method proposed is verified. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Scheduling operation of building transportation systems has profound societal impact such as in improving efficiency and reducing costs [1]. Scheduling of a group of elevators in a building has long been recognized as an important issue, since elevator service ranks second after heating, ventilation and air conditioning (HVAC) as the main complaints of building tenants [2]. For group elevator system in building, a major challenge is developing a scheduling optimization algorithm for deciding which one or more elevators should be dispatched to carry waiting passengers on different calling floors based on specified scheduling criteria [3,4]. Effective elevator scheduling algorithms must meet certain scheduling performances [5]. In elevator scheduling, passenger waiting time is the prevalent performance. This is the time from when a passenger enters the system (hallway) until that passenger can board an elevator. Many scheduling algorithms have been developed to minimize the time performance, e.g., minimizing waiting time algorithm [3], exact calculation of expected waiting time algorithm [6], group elevator scheduling with advance information [7]. Currently, we have paid more attention to energy-saving elevator
∗ Corresponding author. Tel.: +86 15002219242. E-mail addresses: [email protected] (J. Zhang), [email protected] (Q. Zong). 0378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.enbuild.2013.07.069
scheduling in building. Recent statistics suggest that the global energy use contributed by buildings is about 40% [8], and the overall electricity consumption of a building contributed by elevators is about 3–8% and rising [9,10]. How to reduce the energy consumption of the whole elevator system effectively is a challenging issue. The energy performance which indicates the quality of elevator system in energy use should be considered in scheduling algorithms [11]. Elevator energy costs are different under different traffic patterns. There are three traffic patterns in building, peak, inter-floor and idle pattern. Most energy is consumed under uppeak pattern because of the numerous passengers during up-peak. The up-peak traffic pattern occurs during the morning rush hour at a typical office building, when hall calls occur at the lobby only and result in car calls to all floors [5]. Energy-saving dispatching of group elevator system is not handled by most peak scheduling algorithms [12–15]. The ideal way of optimal scheduling is balancing the trade-off between energy performance and time performance. In this paper we propose an energy-saving scheduling optimization method for up-peak traffic pattern for minimizing elevator system dispatching energy and keeping time performance acceptable. Elevator group scheduling is a typical combinational optimization problem [16], we can solve energy-saving elevator scheduling by optimization approaches. Recent studies on multi-elevator energy conservation algorithms yield limited success. Yu [17] proposed an energy consumption group control method based on Genetic Network Programming (GNP), considered energy in the
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fitness function of GNP, but mathematical expression of energy cost was not given. And our previous work, Zhang [18] developed an energy-saving scheduling strategy based on Ant Colony Optimization (ACO), the optimization object is minimizing multi-elevator system consumption. However, only picking energy (energy consumed by elevator from current position to calling floor) was studied in its energy price function, traveling energy (energy consumed by elevator from calling floor to destination floor) was neglected in it. Precise objective function of scheduling energy price is important for scheduling optimization, we can design energysaving scheduling algorithms with the optimization objective of minimizing the energy price function. In this paper, we make two improvements on the basis of work in [18] to handle up-peak dispatching. First, both of picking and traveling energy are considered in the energy price function, the two energy constitute the whole energy consumption of group elevators. Second, the energy function in [18] is a general one for all traffic patterns in building, here the new function is built specially for up-peak pattern, and applied to peak scheduling. Based on the energy price objective function, Robust Optimization (RO) scheduling model is built in this paper. RO theory provides a framework to handle uncertain programming [19,20], and has been applied in scheduling optimization areas [21–23]. Here RO method is introduced to handle uncertain energy-saving dispatching optimization. Scheduling under uncertain traffic flows is always a challenging issue in group elevator system, passenger flows uncertainty influences scheduling seriously, unnecessary energy is consumed by unreasonable dispatching. Recent studies on uncertain group scheduling focus on elevator traffic flow recognition by increasing hardware, e.g., dispatching based on video monitoring scanner/camera [24,25] or destination registration device [26–28]. However, it is not realistic to upgrade all existing multi-elevator system by hardware. The goal of our work is to explore a novel energy-saving elevator scheduling optimization method which is immune to the traffic flows uncertainty, and we only change the scheduling algorithm in the group scheduling controller without new hardware investments. Besides, we consider adaptive adjustment of operating elevator number in the RO up-peak scheduling model. In most cases of up-peak scheduling, it is no need to dispatch all elevators in group to take and carry passengers, dispatching fewer elevators to serve can save energy to some extent. And during up-peak, the waiting time of lobby waiting passengers has close relationship with the number of elevators dispatched. Because more operating elevators lead to more carrying capacity, less round-trip time for elevators and less waiting time for passengers, but more electricity consumption. It is feasible to choose a proper operating elevator number to balance the trade-off between energy and time performance. The pioneer research was proposed by Nagatani [29]. However, there is an ideal assumption in [29], all passengers get in elevators in the lobby and get off on the top floor of the building. Thus it is no need to determine which cars to move after the decision of operating cars number in scheduling, because the states of all dispatched elevators are same. Nevertheless in practice, scheduling algorithms have to decide, not only dispatching how many cars to move, but also dispatching which cars to move, and the ideal condition does not exist. To handle the two-stage optimization, a dual energy-saving mechanism is proposed in our RO model. On one hand, adaptive configuration, choosing how many cars need to be scheduled according to up-peak traffic, commanding dispatched elevators to be active and un-dispatched ones to be dead. Active and dead are two states defined for each elevator. On the other hand, optimization selection, choosing which cars to be dispatched. During up-peak, elevator state changes between active and dead according to optimal energy-saving dispatching solution.
The remainder of this paper is organized as follows. In Section 2, basic idea of energy-saving up-peak scheduling problem is shown. In Section 3, scheduling energy price function is derived, with consideration of picking and traveling energy. In Section 4, up-peak energy-saving scheduling RO model with dual energysaving mechanism is built to minimize the scheduling energy price, up-peak energy-saving strategy is proposed. Section 5 gives performance results to demonstrate the efficacy of our algorithm. Finally, conclusion is drawn in Section 6.
2. Problem formulation The passenger flow of up-peak traffic pattern is called up-peak flow. During up-peak, all passengers arrive only at the first floor and move up from the first floor to their requested destinations [12]. More energy is consumed under up-peak pattern than other traffic patterns because of the numerous upwards passengers. Research on up-peak energy-saving scheduling has great significance for group system energy-saving operation. In fact, there is always a contradiction between system energy consumption and passengers waiting time. We cannot only emphasize the energy and neglect passengers feeling. How to reduce the energy consumption effectively and keep acceptable time performance is a challenging issue. The pioneer work studied the coupling relationship between energy and time in group elevator scheduling [29]. We can save elevator system energy and keep passengers waiting time not to exceed some specified value, by choosing an optimal number of operating cars in up-peak dispatching. After deciding the number of dispatched cars, we further determine which cars to be chosen by minimum scheduling energy criteria. This is the basic idea of dual energy-saving mechanism proposed in the following scheduling optimization model. First, adaptive configuration, choosing the number of operating cars as few as possible to serve waiting passengers in the lobby to save energy costs, commanding dispatched cars to be active and un-dispatched cars dead, for making full use of every car’s loading capability, avoiding the situation passengers aboard all elevators in the lobby dispersedly, and keeping passenger waiting time acceptable. Second, optimization decision, choosing which cars to be dispatched according to minimum scheduling energy. In this paper, the energy price contains not only picking energy, but also traveling energy, considers not only “energy from waiting to loading”, but also “energy from loading to unloading”. For illustration, Fig. 1 is given. In the system with three cars installed, in a scheduling during up-peak, if dispatched two elevators is enough to satisfy waiting time performance, and dispatching one elevator cannot meet the time demand, for the purpose of system energy-efficient operation, the scheduling algorithm will dispatch two cars to serve the waiting people on the first floor. After choosing the number of dispatched cars, the algorithm will decide which two cars to be scheduled. From the example, car number 2 is static now, car number 1 and 3 are moving towards, and the current position of car 1 is higher, its final top destination is lower. It is assumed, present people number inside car 1 and 3 are same, there is only one destination floor of car 1 and 3, and the waiting passengers on the first floor will be distributed to each dispatched car uniformly. Based on minimum scheduling energy (picking and traveling energy) criteria, car 1 and 2 will be dispatched to take the waiting passengers on the lobby floor. Moreover, according to the above scheduling decision, three elevators’ running states will be different and typical. Car 1 (Active Before Active After) is loading passengers upwards before this scheduling and dispatched this scheduling, thus the car will transport the passengers inside to their destinations first, and return to lobby to transport new waiting people. Car 2 (Dead Before Active After) is stopping and a dead car now, after receiving the scheduling
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For elevator ri , uniform running energy consumption of picking Ep−2 (ri ), is computed by working for resisting gravitational potential energy in (2). Because the car’s load is changed by inside people unloading or outside waiting people loading when start–stop occurs, we update the number of passengers aboard in real time to count running cost precisely. During up-peak, passenger number in a car decreases gradually when the car is moving upwards, we describe it by initial people number minus leaving number continuously.
t−1 Ep−2 (ri ) = np (ri , s) × m + mcar − mcwt np0 (ri ) − t=1 s=1 p (ri )
× g × hp (ri , t)
(2)
Declarations of other parameters:
Fig. 1. Up-peak elevator scheduling.
command, its state will be changed from dead to active, and the car will move to lobby to serve now. Car 3 (Active Before Dead After), it is running upwards with passengers due to last scheduling decision, the car will finish current transporting task first, then turn to be dead, stopping and waiting for later commands, because it is not dispatched this scheduling. 3. Scheduling energy price function The goal of energy-saving optimization is minimizing scheduling energy consumption of the elevator system. Scheduling energy price function is defined first. The scheduling energy price refers to all active (dispatched) elevators’ energy costs. And in the total scheduling energy, picking and traveling energy are both considered. The energy spent from one dispatched car’s current position to the lobby to take waiting passengers is called picking energy, and the energy consumed to transport the passengers to their destinations is called traveling energy. Both of picking and traveling energy consist of start–stop and running energy respectively. Start–stop energy is consumed when an elevator accelerates and decelerates, while running energy is spent when a car runs with uniform speed [18,30]. Moreover, the former one is calculated by, once start–stop energy constant times start–stop counts, the latter one is computed by working for resisting gravitational potential energy. Picking energy price function is derived first. The following parameter ri stands for the ith dispatched car in a scheduling during up-peak, indicates the serial numbers of dispatched elevators. For elevator ri , its start–stop energy consumption of picking Ep−1 (ri ), is computed in (1) by the product between Ec and p (ri ), they are once start–stop energy constant, and start–stop counts needed by the car to response to the lobby floor call respectively. The counts equal to inside-choose floor numbers unfinished last scheduling of elevator ri plus one, the additional one indicates that the empty car return to the lobby downstairs to take waiting passengers. Ep−1 (ri ) = p (ri ) × Ec
(1)
np0 (ri ): initial passenger number of elevator ri when picking passengers, i.e., last scheduling remaining people in the car np (ri , s): leaving passenger number from elevator ri when it moves to the lobby floor at the sth startup m: passenger average mass mcar : elevator empty car mass mcwt : elevator counter weight mass g: acceleration of gravity hp (ri , t): floors displacement between the tth startup and its stop when picking passengers
Picking start–stop and running energy constitute the whole picking consumption of a car. And total picking energy of all elevators dispatched in system Ep , is obtained by (3), where M stands for the number of elevators dispatched.
Ep =
M i=1
Ep−1 (ri ) + Ep−2 (ri )
t−1 = pp (ri ) × Ec + np (ri , s) × m np0 (ri ) − t=1 s=1 i=1 + mcar − mcwt × g × hp (ri , t) M
p (ri )
(3)
Similarly, traveling energy includes traveling start–stop and running energy. And there exists a strong duality between the calculation of picking and traveling energy, traveling energy is counted as below. Traveling accelerate–decelerate energy of elevator ri , Et−1 (ri ), is expressed by (4), t (ri ) means start–stop counts needed by the elevator ri to deliver people in the car to their destinations, i.e., total inside-choose floor numbers of the elevator ri this scheduling. Et−1 (ri ) = t (ri ) × Ec
(4)
And traveling uniform-speed energy of elevator ri , Et−2 (ri ), is computed by (5). Where nt0 (ri ) is initial passenger number of elevator ri when traveling, nt (ri , s) stands for leaving passenger number from the elevator ri when it delivers the upwards passengers at the sth startup, ht (ri , t) means floors displacement between thetth
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startup and its stop when traveling.
t (ri ) t−1 Et−2 (ri ) = nt (ri , s) × m + mcar − mcwt nt0 (ri ) − t=1 s=1 × g × ht (ri , t)
(5)
System traveling energy Et , consists of traveling start-up and running energy of each dispatched elevator by (6). Et =
M i=1
=
M i=1
Et−1 (ri ) + Et−2 (ri )
pt (ri ) × Ec +
t (ri )
|
nt0 (ri ) −
t=1
+mcar − mcwt | × g × ht (ri , t)]
t−1
nt (ri , s)
×m
s=1
(6)
Finally, total scheduling energy of elevator system E, includes picking and traveling energy of all dispatched elevators in scheduling, E = Ep + Et . And the following up-peak scheduling optimization model for group elevators is built with the goal of minimizing the total scheduling energy E. 4. Up-peak energy-saving scheduling optimization In group elevator system, different scheduling performances are always contradictive with each other, how to balance the tradeoff between energy performance and others has been a significant challenge in energy-saving scheduling. During up-peak, a feasible way to realize energy-saving elevator operation is choosing fewer but enough elevators to transport calling people from lobby floor to their destinations. Dispatching fewer cars will be beneficial to reduce the whole system consumption and harmful to the time performance. In our work, both of energy and time performances are considered, the basic idea of scheduling optimization is saving system energy cost and keeping passenger waiting time acceptable. The up-peak energy-saving scheduling strategy proposed is realized based on scheduling optimization model below. A dual energy-saving mechanism is presented in our model. On one hand, adaptive configuration, choosing fewer but enough number’s elevator to transport waiting passengers on the lobby floor, based t(n + 1) = (+)t(n) +
t(n + 1) =
( + ˇ)t(n) +
( + ˇ)t(n) +
( + ˇ)t(n) +
t(n + 1) =
( + ˇ)t(n) t(n + 1) = + M +
Ts
2
(2Lri ,max (n)/V ) + Ts i=1
2
M
(2Lri ,max (n)/V ) + Ts i=1
M
(2Lri ,max (n)/V ) + Ts i=1
on the coupling relationship between energy cost of elevator system and average waiting time of passengers. On the other hand, optimization selection, choosing which cars to serve after the operating car number is decided. The selection decision is made with the objective, minimizing the system scheduling energy price derived above.
(2Lri ,max (n)/V ) M
M
(7)
Mo
t1,2 ≤ t(n) < t2,3
(n) i=1 ri
M
Mo
i=1
(n) i=1 ri
(n) i=1 ri
2
Mo
M
M
The new passenger waiting time could be predicted according to three terms, loading and unloading time of passengers last scheduling, average uniform speed running time of dispatched elevators, and average start–stop total time of dispatched elevators when accelerating and decelerating. First, we describe new passengers arriving rate by parameter , then t(n) means the number of all waiting passengers last scheduling, and it is assumed that, the passengers are distributed uniformly to all dispatched cars, all waiting people are transported in one scheduling (which is always satisfied by the criteria of group elevators designing), system carrying capacity is sufficient to serve all calling requests during up-peak, thus we can obtain and unloading time of each dispatched ele the loading vator by + ˇ t(n)/M, and ˇ represent the time spent by one people boarding and leaving car; secondly, we define Lri ,max (n) as max arriving floor of elevator ri , consider average moving time of M every dispatched car by i=1 2Lri ,max (n)/V /M; thirdly, we introduce Ts to indicate once acceleration-deceleration time, and ri (n) to represent total start–stop counts of elevator ri at trip n, thus we M use Ts i=1 ri (n)/M to compute elevator average total start–stop time. The predictive passenger waiting time is obtained by adding the three terms by (7).
2Lr1 ,max (n) + Ts r1 (n) t(n) < t1,2 V
t(n + 1) =
The pioneer work of energy-saving adaptive configuration has been studied in [29]. The coupling relationship between the optimal operating car number and waiting time is introduced. However, the result of optimal elevator configuration in [29] is based on an assumption, passengers enter the building on the lobby floor, board the elevators, and only get off the elevators on the top floor of building. And an improved coupling model is presented on the basis of the pre-research ideal problem, more practical situation is considered in this paper. Average passengers waiting time, the time interval between the average arrival moment of elevators at the lobby floor at this trip and previous one, can be predicted according to the former waiting time. Define t(n + 1) as predictive average waiting time of new coming passengers, which equals to the average tour time of cars this scheduling, and t(n) as the true value of average waiting time last scheduling, we have the following expression by (7), which reflects the coupling between the waiting time and the operating car number:
(8) tM−1,M ≤ t(n) < tM,M+1
(n) i=1 ri
tM o −1,M o ≤ t(n)
In practice, when t(n) of last scheduling is longer, there will be more waiting people gathering in the lobby this scheduling, more time will be spent in loading and unloading the passengers, and more counts start–stop will occur, finally, new waiting time performance will become longer. More elevators need to be dispatched to serve to shorter the time performance. Though more energy is saved by dispatching fewer elevators, the time performance should
J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
be guaranteed within acceptable range. Here in (8) we balance the trade-off between energy consumption and time performance, by dividing an optimal denominator (operating elevator number), from 1 to Mo , Mo means the number of total elevators in group system. In scheduling optimization, the key parameter, actual passenger arriving rate is difficult to be obtained because of the uncertainty of up-peak passenger flows, while we can predict the traffic flows by elevator flow forecasting method [31]. Because RO handles bounded uncertainty optimization, wedefine the uncertain passen ˆ − , ˆ + , where , , ˆ ger arriving rate by close interval, ∈ represent new passengers arriving rate’s actual value, predictive value, disturbance limit, and the predictive values obey up-peak traffic flows’ statistical laws. The Robust Optimization scheduling model for up-peak pattern is listed as follows: minimize E s.t. X=
M
Xi
The structure of the up-peak scheduling solution is described by (9) and (10). Total up-peak scheduling solution X, consists of M partial solutions Xi , and each partial solution stands for a specific elevator which will be dispatched. The dimension of Xi is 1 × Mo , corresponding to all elevators in group. In addition, the serial number of the dispatched car represented by Xi could be extracted by (10). Elevator adaptive configuration mechanism is described by (11) and (12). The number of cars dispatched M, is decided by the coupling relationship between energy and time performance in (11). By (12) the predictive value of average passengers waiting time cannot exceed the long time constant, tl . We reduce more energy consumption of elevator system with a precondition, not influencing time performance seriously. The optimization selection is described from (13) to (17). The total scheduling energy E, consists of picking energy Ep and traveling energy Et by (13). (14) and (15) calculate the two energy separately. For the two alterable initial values, np0 (ri ) and nt0 (ri ) are obtained by (16) and (17). It is assumed, all waiting passengers in the lobby are distributed uniformly to each dispatched car, thus the initial people number of elevator ri of picking np0 (ri ), equals to that, the last average people number distributed to each dispatched car
(9)
i=1 T
M o ] )(M o ×1)
ri = Xi(1×M o ) ([1 2 · · ·
( + ˇ)t(n) +
i = 1, · · ·, M
(10)
M
(2Lri ,max (n)/V ) + Ts i=1
t(n + 1) =
i=1
Et =
M
tM−1,M ≤ t(n) < tM,M+1
(11)
(12)
E = Ep + Et Ep =
(n) i=1 ri
M
t(n + 1) ≤ tl
M
M
499
p (ri )
pp (ri ) × Ec +
|
t=1
t (ri )
pt (ri ) × Ec +
np0 (ri ) −
|
nt0 (ri ) −
t=1
i=1
t−1 s=1
t−1
np (ri , s)
(13)
× m + mcar − mcwt | × g × hp (ri , t)
nt (ri , s)
(14)
× m + mcar − mcwt | × g × ht (ri , t)
(15)
s=1
Zr
B(n − 1) n (ri , s ) − M(n − 1) p i
np0 (ri ) =
(16)
s =1
p
B(n) [t(n) − t(n − 1)] nt0 (ri ) = = M M Xi · q = {0, 1} i = 1, · · ·, M
Xi(1×M o ) [1 1 · · ·
1]
T
B(n − 1) minus total leaving people number before this Zscheduling ri n (ri , s ), by (16). The leaving people number is computed by s =1
q = 1, 2, · · ·, M o
(M o ×1)
=1
ri < ri+1
(17) (18) (19) (20)
Model parameter declarations: tl : long waiting time constant X: total up-peak scheduling solution Xi : partial solution ri : serial number of the dispatched elevator expressed by partial solution Xi np (ri , s ): leaving passenger number of the elevator ri at the s th startup from lobby before scheduling Zri : start–stop counts of the rth elevator from the lobby floor last scheduling to current position Xi·q : the qth element in Xi After model simplification, this model has a certain optimization object, minimizing elevator system energy costs, subjects to some conditions. The conditions consist of three parts, expressions of scheduling solution, dual energy-saving mechanism and scheduling constraints.
where Zri means the start–stop counts finished, np (ri , s ) stands for each time’s leaving passenger number. Moreover, total waiting person number B(n) divided by the number of dispatched cars equals the initial value of traveling nt0 (ri ) by (17). And new passengers arriving rate times the time interval equals the total waiting people number. Finally, scheduling constraints are listed from (18) to (20). Each element in Xi needs to be one or zero only, represents dispatching a car or not by (18). We convert classical group scheduling decision into 0–1 integer programming in this paper. Every partial solution represents only one dispatched elevator by (19). Serial number of every dispatched elevator should be in ascending order in partial solutions by (20). Because there are uncertain parameters in the RO scheduling model, we cannot solve it directly. It is necessary to transform uncertain optimization into certain one for solving by robust counterparts [20]. The following robust counterparts are introduced, (17) and (18) in the initial RO model, are transformed to (21) and (22) because of the uncertain parameter in them.
t(n + 1) =
+ˇ
ˆ +
M
M 2
+
L i=1 ri ,max
t(n)
/V + T
M
M
(r ) i=1 p i
(21)
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Fig. 2. Flow chart of up-peak energy-saving scheduling strategy.
B(n) nt0 (ri ) = = M
ˆ + [t(n) − t(n − 1)] M
(22)
The uncertain parameter is amplified to the possible max value, corresponding to maximum passengers flows which lead to maximum energy consumption. If group elevator system consumes less energy when elevators are scheduled based on RO scheduling solutions that are obtained in the worst case, the system will save more energy consumption in more general cases under up-peak pattern. After robust counterpart transformation, the uncertain optimization has become certain optimization. We can solve it by different optimization solving algorithms, finally up-peak energysaving optimal scheduling solution is obtained, and all elevators are scheduling based on the solution. In real application, total up-peak energy-saving scheduling strategy is described below. Fig. 2 shows the flow chart of the strategy. In every scheduling, the group controller with the algorithm proposed loads every elevator’s current state, all call signals and average waiting time last scheduling separately. Then, the group controller decides to dispatch how many elevators to serve the waiting passengers based on the energy-time piecewise function. Next, the group controller chooses which cars to serve based on RO scheduling solution for minimizing the energy consumption under up-peak pattern. After the optimization solving iterations, the optimal scheduling plan is obtained and all elevators are scheduled based on the plan. When elevators are scheduled based on the optimal plan, the scheduling algorithm judges each elevator is dispatched or not in this scheduling, each elevator operation is controller by running logics for active and dead elevator, and there are four running logics in Fig. 2.
(a) Active Before Active After, if the car is dispatched and moving upwards with passengers inside, the car will finish current transporting task first and return to the lobby floor to transport new waiting passengers; (b) Dead Before Active After, if the car is dispatched and stopping now, the car will change the state from dead to active, and move to the lobby to serve directly;
(c) Active Before Dead After, if the car is not dispatched and transporting passengers now, the car will finish current task first, stay where it is, and wait for new task next scheduling; (d) Dead Before Dead After, if the car is not dispatched last scheduling and this scheduling, the car will maintain the dead state. 5. Simulation This section presents simulation results to illustrate the validity of our strategy based on the virtual elevator environment of our lab [32]. The software can simulate each elevator’s actual movements, realize group system’s scheduling operation under different algorithms, display the dispatching process by real-time animation, and validate various performances of scheduling algorithms. Fig. 3 shows the interface of the simulation environment. Table 1 shows the specifications of the simulation system. Three simulation experiments are implemented based on three typical up-peak traffic flows. Simulation 1: floors of building A, 20, number of elevators, 3, up-flow passengers, 600 Simulation 2: floors of building B, 26, number of elevators, 4, up-flow passengers, 800 Simulation 3: floors of building C, 32, number of elevators, 5, up-flow passengers, 1000 The duration time of each flow is 60 min, and the peak point time is 30 min. Fig. 4 shows the three curves of new passengers arriving rate varied with time, blue line for up-flow A, green line for up-flow B, and red line for up-flow C. Similar variation trends of the three curves conform to the characteristic of up-peak traffic flow. Before Table 1 Specifications of simulation. Items
Value
Floor distance [m] Velocity [m/s] Acceleration [m/s/s] Jerk [m/s/s/s] Car capacity [person] Time of opening and closing door [s] Time of passenger’s loading and unloading [s/person]
3 2.5 1 1.8 10 4 1
J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
501
Fig. 3. Interface of elevator group scheduling simulation environment.
the peak point of up-peak, the arriving rate of calling passengers increases gradually. The arriving rate of flow A, B, C are 0.24, 0.32 and 0.40 people per second separately, and flow C rate ranks the first. Moreover, the area of region bounded by each curve and the horizontal axis stands for the total arriving passenger number
during up-peak, the total passenger numbers of up-flow A, B, and C are 600, 800, 1000 persons respectively. Fig. 5 indicates that the dispatched elevator number varies with time under three different conditions of simulation 1, 2 and 3. The line charts of dispatched numbers match the curves in Fig. 4 with
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J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
Table 2 Quantitative analysis of dispatched and un-dispatched elevator number. Simulation
Parameter
Avg. dispatched cars
Avg. un-dispatched cars
Avg. utilization rate
1 2 3
Building A, up-flow A Building B, up-flow B Building C, up-flow C
1.67 2.17 3.06
1.33 1.83 1.94
55.7% 54.3% 61.2%
colors, blue, green and red. From Fig. 5, the number of dispatched elevators increases with the increasing of passengers arriving rate, and decreases as the rates decreases. In our adaptive elevator scheduling strategy, we use optimal and necessary cars to transport waiting passengers during up-peak for reducing elevator system energy consumption. Quantitative analysis results of adaptive elevator number adjustments are listed in Table 2. In simulation 1, 3 elevators serve a 20 floors building, average numbers of dispatched and undispatched cars are 1.67 and 1.33, and average utilization rate of all elevators is 55.7%. In simulation 2, 4 elevators serve a 26 floors building, the numbers of dispatched and un-dispatched elevators are 2.17 and 1.83, the elevator utilization rate is 54.3%. In simulation 3, 5 elevators serve a 32 floors building, the numbers of dispatched and un-dispatched elevators are 3.06 and 1.94, the elevator utilization rate is 61.2%. From the three simulations, only about half 0.45 up−flow A up−flow B up−flow C
max =0.40 p/s
new passengers arriving rate (p/s)
0.4 0.35
max =0.32 p/s
0.3 max =0.24 p/s
0.25 0.2 0.15 0.1 0.05 0
0
600
1200
1800 time (s)
2400
3000
3600
3 simulation 1 2 1
No. of active cars
0
4 3 2 1
No. of active cars
No. of active cars
Fig. 4. Curves of up-peak new passengers arriving rate.
5 4 3 2 1
600
1200
1800 time (s)
2400
3000
3600
simulation 2
0
600
1200
1800 time (s)
2400
3000
3600
simulation 3
0
600
1200
1800 time (s)
2400
3000
Fig. 5. Line charts of up-peak dispatched elevator number.
3600
of the elevators are dispatched during up-peak by our strategy, it is beneficial to energy-saving operation of group elevator system. In fact, the elevator utilizations of most commonly used up-peak scheduling algorithms are greater than our strategy. The system energy is wasted by unnecessary elevators, and in some cases, passenger waiting time may be longer because of the unreasonable scheduling. For comparison, another three scheduling algorithms are chosen, including minimizing waiting time algorithm, destination zoning algorithm and ACO scheduling algorithm [18]. Min-waiting algorithm minimizes all calling passengers’ waiting time. Destination zoning algorithm separates floors into different zones according to passenger destinations and dispatches each car to serve every fixed zone. ACO algorithm minimizes system picking energy and considers time performance by a long waiting time threshold [18]. Table 3 displays comparison of scheduling performances. In simulation 1, 3 elevators serve 600 passengers in a 20 floors building, the start–stop and running energy of energy-saving algorithm are 24,031.29 kJ and 16,105.23 kJ, they are less than energy costs of other three algorithms, because elevator unnecessary start–stop and running counts are reduced effectively by our algorithm. Total energy consumption of our algorithm is 40,136.52 kJ. Total energy savings by our algorithm are 21,212.25 kJ than min-waiting algorithm, 12,765.83 kJ than zoning algorithm, 4996.9 kJ than ACO algorithm. The time performance of our algorithm ranks the third, 24.27 s. Coupling relationship between energy and time is considered in our algorithm, thus elevator system energy consumption is saved effectively, and the time performance is kept in acceptable range. For performances of other algorithms, min-waiting algorithm only emphasizes average passenger waiting time, its time performance is less than others, 18.05 s. However, the better time is acquired by sacrificing more system energy, its total energy performance is 61,348.77 kJ. Destination zoning algorithm is a classical non-optimization scheduling strategy, both of its total energy and time performance are not outstanding, 52,902.35 kJ and 22.16 s. ACO algorithm minimizes system picking passengers’ energy, total energy consumption of ACO is 45,133.42 kJ, worse than energysaving algorithm, because our algorithm considers not only picking energy, but also traveling energy in up-peak scheduling optimization. The waiting time of ACO is worst, 25.91 s, because the time is considered by long waiting time threshold, thus the time performance is always close to the threshold. In simulation 2, 4 elevators serve 800 passengers in a 26 floors building, total energy savings by our algorithm are 28,997.88 kJ than min-waiting algorithm, 16,474.13 kJ than zoning algorithm, 4734.44 kJ than ACO algorithm. In simulation 3, 5 elevators serve 1000 passengers in a 32 floors building, total energy savings by our algorithm are 63,825.31 kJ than min-waiting algorithm, 19,653.92 kJ than zoning algorithm, 6959.19 kJ than ACO algorithm. Table 4 displays the energy-saving results of our up-peak energy-saving scheduling optimization. In simulation 1, for elevator system, our algorithm saves 34.58% energy than min-waiting algorithm, 24.13% than zoning algorithm, 11.07% than ACO algorithm. The overall electricity consumption of a building contributed by elevators is about 3–8% [10], if we take an average 5.5%, for building, compared with other algorithms, the saving ratios of our algorithm are 1.90%, 1.33% and 0.61%. An elevator system
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Table 3 Comparison of scheduling performances. Parameter
Start–stop energy (kJ)
Running energy (kJ)
18.05 22.16 25.91 24.27
33,274.25 29,535.08 28,440.93 24,031.29
28,074.52 23,367.27 16,692.49 16,105.23
61,348.77 52,902.35 45,133.42 40,136.52
21,212.25 12,765.83 4996.9
Min-Waiting Zoning ACO Energy-saving
25.47 30.31 37.22 34.85
40,177.25 36,871.16 32,902.37 31,084.93
47,337.10 38,119.44 30,348.54 27,431.54
87,514.35 74,990.60 63,250.91 58,516.47
28,997.88 16,474.13 4734.44
Min-Waiting Zoning ACO Energy-saving
35.68 39.52 46.96 40.13
61,552.39 49,473.38 45,994.10 38,251.97
76,954.85 44,862.47 35,647.02 36,429.96
13,8507.24 94,335.85 81,641.12 74,681.93
63,825.31 19,653.92 6959.19
Algorithm
Avg. wait-time (s)
Min-waiting Zoning ACO Energy-saving
Total energy consumption (kJ)
Total energy saving (kJ)
Simulation 1 Building A Up-flow A Simulation 2 Building B Up-Flow B Simulation 3 Building C Up-Flow C
Table 4 Energy-saving results of up-peak energy-saving scheduling optimization. Parameter
Algorithm
Saving ratio for elevator system
Saving ratio for building
Min-waiting Zoning ACO
34.58% 24.13% 11.07%
1.90% 1.33% 0.61%
Min-waiting Zoning ACO
33.14% 21.97% 7.49%
Min-waiting Zoning ACO
46.08% 20.83% 8.52%
Saving energy per day (kW/h)
Saving energy per year (kW/h)
Financial saving per year (D )
5.8923 3.5461 1.3880
2150.69 1294.33 506.62
251.63 151.44 59.27
1.82% 1.21% 0.41%
8.0550 4.5761 1.3151
2940.08 1670.28 480.01
343.99 195.42 56.16
2.53% 1.15% 0.47%
17.7293 5.4594 1.9331
6471.19 1992.68 705.58
757.13 233.14 82.55
Simulation 1 Building A Up-flow A Simulation 2 Building B Up-flow B Simulation 3 Building C Up-flow C
scheduled by energy-saving algorithm can save energy 5.8923 kW/h, 3.5461 kW/h, 1.3880 kW/h than other algorithms per day, and save 2150.69 kW/h, 1294.33 kW/h, 506.62 kW/h energy per year. According to the average electricity price for office building in EU27 provided by Eurostat [33], 0.117 Euro per kW/h, compared with other three scheduling algorithms, financial savings for one building of our algorithm are 251.63 Euro, 151.44 Euro and 59.27 Euro per year. In simulation 2, compared with other algorithms, financial savings for one building of our algorithm are 343.99 Euro, 195.42 Euro and 56.16 Euro per year. In simulation 3, compared with other algorithms, financial savings for one building of our algorithm are 757.13 Euro, 233.14 Euro and 82.55 Euro per year. And enormous economic benefits will be made by our energy-saving scheduling optimization method, because there are millions of buildings with group elevator system in the world. 6. Conclusion Scheduling operation of building transportation systems has profound societal impact. Scheduling of group elevators in building has long been recognized as an important issue, and energy-saving elevator scheduling has been a significant challenge recently. The energy-saving scheduling of up-peak pattern is more important than other traffic patterns, because more energy is consumed during up-peak. Up-peak energy-saving scheduling has a great significance for multi-elevator system efficient operation, and offers useful guidance to optimal scheduling under other traffic pattern in building. In this paper, an energy-saving elevator scheduling optimization method under up-peak traffic is proposed. Robust Optimization is applied to solve up-peak elevator scheduling under uncertain
passenger flows. The optimization objective is minimizing the scheduling energy price of elevator system, and keeping the passengers waiting time performance acceptable. The energy price function is built first, including picking and traveling energy costs. Based on that, up-peak RO scheduling model and energy-saving scheduling strategy are presented, a dual energy-saving mechanism is realized by the optimization. One is adaptive configuration, choosing fewer but enough number’s elevators to run transport waiting passengers on the first floor. Another is optimization selection, choosing which elevators to serve after the number of dispatched elevators is decided. Simulation tests are implemented under the conditions of three up-peak traffic flows, different floors high-rise buildings and diverse sizes of elevator group. Results indicate that the energy performance of elevators in building is significantly improved by the energy-saving scheduling method during up-peak, and the time performance is acceptable as well.
Acknowledgements This work is supported by National Nature Foundation of China under Grant #91016018, #61273092, Key Project of Chinese Ministry of Education #311012, Tianjin Basic Study Key Foundation #11JCZDJC25100.
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Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Energy-saving scheduling optimization under up-peak traffic for group elevator system in building Jinglong Zhang ∗ , Qun Zong College of Electric Engineering and Automation, Tianjin University, Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 13 December 2012 Received in revised form 27 May 2013 Accepted 26 July 2013 Keywords: Group elevator system Energy-saving Scheduling optimization Up-peak
a b s t r a c t Energy-saving group scheduling is a significant challenge for multi-elevator system in building. Among various traffic patterns in building, most energy is consumed under up-peak traffic pattern. To save unnecessary energy consumption and realize optimal scheduling, an energy-saving scheduling optimization method for up-peak pattern is proposed. The optimization objective is minimizing the scheduling energy price of the group system. The up-peak energy price function is defined first, both of picking and traveling energy are considered in it. Based on that, scheduling Robust Optimization model is built to handle elevator scheduling under uncertain up-peak traffic flow. The key point of optimization is a dual energy-saving mechanism. One is adaptive configuration, choosing fewer but enough number’s elevator to transport waiting passengers on the lobby floor. Another is optimization selection, choosing which elevators to serve according to minimum energy price after the number of dispatched elevators is decided. In practice, elevators in group system are dispatched by scheduling decision of the optimization to realize system energy-saving operation under up-peak pattern. In simulation, compared with the scheduling performances of other algorithms under different up-peak flows in several buildings, effectiveness of the method proposed is verified. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Scheduling operation of building transportation systems has profound societal impact such as in improving efficiency and reducing costs [1]. Scheduling of a group of elevators in a building has long been recognized as an important issue, since elevator service ranks second after heating, ventilation and air conditioning (HVAC) as the main complaints of building tenants [2]. For group elevator system in building, a major challenge is developing a scheduling optimization algorithm for deciding which one or more elevators should be dispatched to carry waiting passengers on different calling floors based on specified scheduling criteria [3,4]. Effective elevator scheduling algorithms must meet certain scheduling performances [5]. In elevator scheduling, passenger waiting time is the prevalent performance. This is the time from when a passenger enters the system (hallway) until that passenger can board an elevator. Many scheduling algorithms have been developed to minimize the time performance, e.g., minimizing waiting time algorithm [3], exact calculation of expected waiting time algorithm [6], group elevator scheduling with advance information [7]. Currently, we have paid more attention to energy-saving elevator
∗ Corresponding author. Tel.: +86 15002219242. E-mail addresses: [email protected] (J. Zhang), [email protected] (Q. Zong). 0378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.enbuild.2013.07.069
scheduling in building. Recent statistics suggest that the global energy use contributed by buildings is about 40% [8], and the overall electricity consumption of a building contributed by elevators is about 3–8% and rising [9,10]. How to reduce the energy consumption of the whole elevator system effectively is a challenging issue. The energy performance which indicates the quality of elevator system in energy use should be considered in scheduling algorithms [11]. Elevator energy costs are different under different traffic patterns. There are three traffic patterns in building, peak, inter-floor and idle pattern. Most energy is consumed under uppeak pattern because of the numerous passengers during up-peak. The up-peak traffic pattern occurs during the morning rush hour at a typical office building, when hall calls occur at the lobby only and result in car calls to all floors [5]. Energy-saving dispatching of group elevator system is not handled by most peak scheduling algorithms [12–15]. The ideal way of optimal scheduling is balancing the trade-off between energy performance and time performance. In this paper we propose an energy-saving scheduling optimization method for up-peak traffic pattern for minimizing elevator system dispatching energy and keeping time performance acceptable. Elevator group scheduling is a typical combinational optimization problem [16], we can solve energy-saving elevator scheduling by optimization approaches. Recent studies on multi-elevator energy conservation algorithms yield limited success. Yu [17] proposed an energy consumption group control method based on Genetic Network Programming (GNP), considered energy in the
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fitness function of GNP, but mathematical expression of energy cost was not given. And our previous work, Zhang [18] developed an energy-saving scheduling strategy based on Ant Colony Optimization (ACO), the optimization object is minimizing multi-elevator system consumption. However, only picking energy (energy consumed by elevator from current position to calling floor) was studied in its energy price function, traveling energy (energy consumed by elevator from calling floor to destination floor) was neglected in it. Precise objective function of scheduling energy price is important for scheduling optimization, we can design energysaving scheduling algorithms with the optimization objective of minimizing the energy price function. In this paper, we make two improvements on the basis of work in [18] to handle up-peak dispatching. First, both of picking and traveling energy are considered in the energy price function, the two energy constitute the whole energy consumption of group elevators. Second, the energy function in [18] is a general one for all traffic patterns in building, here the new function is built specially for up-peak pattern, and applied to peak scheduling. Based on the energy price objective function, Robust Optimization (RO) scheduling model is built in this paper. RO theory provides a framework to handle uncertain programming [19,20], and has been applied in scheduling optimization areas [21–23]. Here RO method is introduced to handle uncertain energy-saving dispatching optimization. Scheduling under uncertain traffic flows is always a challenging issue in group elevator system, passenger flows uncertainty influences scheduling seriously, unnecessary energy is consumed by unreasonable dispatching. Recent studies on uncertain group scheduling focus on elevator traffic flow recognition by increasing hardware, e.g., dispatching based on video monitoring scanner/camera [24,25] or destination registration device [26–28]. However, it is not realistic to upgrade all existing multi-elevator system by hardware. The goal of our work is to explore a novel energy-saving elevator scheduling optimization method which is immune to the traffic flows uncertainty, and we only change the scheduling algorithm in the group scheduling controller without new hardware investments. Besides, we consider adaptive adjustment of operating elevator number in the RO up-peak scheduling model. In most cases of up-peak scheduling, it is no need to dispatch all elevators in group to take and carry passengers, dispatching fewer elevators to serve can save energy to some extent. And during up-peak, the waiting time of lobby waiting passengers has close relationship with the number of elevators dispatched. Because more operating elevators lead to more carrying capacity, less round-trip time for elevators and less waiting time for passengers, but more electricity consumption. It is feasible to choose a proper operating elevator number to balance the trade-off between energy and time performance. The pioneer research was proposed by Nagatani [29]. However, there is an ideal assumption in [29], all passengers get in elevators in the lobby and get off on the top floor of the building. Thus it is no need to determine which cars to move after the decision of operating cars number in scheduling, because the states of all dispatched elevators are same. Nevertheless in practice, scheduling algorithms have to decide, not only dispatching how many cars to move, but also dispatching which cars to move, and the ideal condition does not exist. To handle the two-stage optimization, a dual energy-saving mechanism is proposed in our RO model. On one hand, adaptive configuration, choosing how many cars need to be scheduled according to up-peak traffic, commanding dispatched elevators to be active and un-dispatched ones to be dead. Active and dead are two states defined for each elevator. On the other hand, optimization selection, choosing which cars to be dispatched. During up-peak, elevator state changes between active and dead according to optimal energy-saving dispatching solution.
The remainder of this paper is organized as follows. In Section 2, basic idea of energy-saving up-peak scheduling problem is shown. In Section 3, scheduling energy price function is derived, with consideration of picking and traveling energy. In Section 4, up-peak energy-saving scheduling RO model with dual energysaving mechanism is built to minimize the scheduling energy price, up-peak energy-saving strategy is proposed. Section 5 gives performance results to demonstrate the efficacy of our algorithm. Finally, conclusion is drawn in Section 6.
2. Problem formulation The passenger flow of up-peak traffic pattern is called up-peak flow. During up-peak, all passengers arrive only at the first floor and move up from the first floor to their requested destinations [12]. More energy is consumed under up-peak pattern than other traffic patterns because of the numerous upwards passengers. Research on up-peak energy-saving scheduling has great significance for group system energy-saving operation. In fact, there is always a contradiction between system energy consumption and passengers waiting time. We cannot only emphasize the energy and neglect passengers feeling. How to reduce the energy consumption effectively and keep acceptable time performance is a challenging issue. The pioneer work studied the coupling relationship between energy and time in group elevator scheduling [29]. We can save elevator system energy and keep passengers waiting time not to exceed some specified value, by choosing an optimal number of operating cars in up-peak dispatching. After deciding the number of dispatched cars, we further determine which cars to be chosen by minimum scheduling energy criteria. This is the basic idea of dual energy-saving mechanism proposed in the following scheduling optimization model. First, adaptive configuration, choosing the number of operating cars as few as possible to serve waiting passengers in the lobby to save energy costs, commanding dispatched cars to be active and un-dispatched cars dead, for making full use of every car’s loading capability, avoiding the situation passengers aboard all elevators in the lobby dispersedly, and keeping passenger waiting time acceptable. Second, optimization decision, choosing which cars to be dispatched according to minimum scheduling energy. In this paper, the energy price contains not only picking energy, but also traveling energy, considers not only “energy from waiting to loading”, but also “energy from loading to unloading”. For illustration, Fig. 1 is given. In the system with three cars installed, in a scheduling during up-peak, if dispatched two elevators is enough to satisfy waiting time performance, and dispatching one elevator cannot meet the time demand, for the purpose of system energy-efficient operation, the scheduling algorithm will dispatch two cars to serve the waiting people on the first floor. After choosing the number of dispatched cars, the algorithm will decide which two cars to be scheduled. From the example, car number 2 is static now, car number 1 and 3 are moving towards, and the current position of car 1 is higher, its final top destination is lower. It is assumed, present people number inside car 1 and 3 are same, there is only one destination floor of car 1 and 3, and the waiting passengers on the first floor will be distributed to each dispatched car uniformly. Based on minimum scheduling energy (picking and traveling energy) criteria, car 1 and 2 will be dispatched to take the waiting passengers on the lobby floor. Moreover, according to the above scheduling decision, three elevators’ running states will be different and typical. Car 1 (Active Before Active After) is loading passengers upwards before this scheduling and dispatched this scheduling, thus the car will transport the passengers inside to their destinations first, and return to lobby to transport new waiting people. Car 2 (Dead Before Active After) is stopping and a dead car now, after receiving the scheduling
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For elevator ri , uniform running energy consumption of picking Ep−2 (ri ), is computed by working for resisting gravitational potential energy in (2). Because the car’s load is changed by inside people unloading or outside waiting people loading when start–stop occurs, we update the number of passengers aboard in real time to count running cost precisely. During up-peak, passenger number in a car decreases gradually when the car is moving upwards, we describe it by initial people number minus leaving number continuously.
t−1 Ep−2 (ri ) = np (ri , s) × m + mcar − mcwt np0 (ri ) − t=1 s=1 p (ri )
× g × hp (ri , t)
(2)
Declarations of other parameters:
Fig. 1. Up-peak elevator scheduling.
command, its state will be changed from dead to active, and the car will move to lobby to serve now. Car 3 (Active Before Dead After), it is running upwards with passengers due to last scheduling decision, the car will finish current transporting task first, then turn to be dead, stopping and waiting for later commands, because it is not dispatched this scheduling. 3. Scheduling energy price function The goal of energy-saving optimization is minimizing scheduling energy consumption of the elevator system. Scheduling energy price function is defined first. The scheduling energy price refers to all active (dispatched) elevators’ energy costs. And in the total scheduling energy, picking and traveling energy are both considered. The energy spent from one dispatched car’s current position to the lobby to take waiting passengers is called picking energy, and the energy consumed to transport the passengers to their destinations is called traveling energy. Both of picking and traveling energy consist of start–stop and running energy respectively. Start–stop energy is consumed when an elevator accelerates and decelerates, while running energy is spent when a car runs with uniform speed [18,30]. Moreover, the former one is calculated by, once start–stop energy constant times start–stop counts, the latter one is computed by working for resisting gravitational potential energy. Picking energy price function is derived first. The following parameter ri stands for the ith dispatched car in a scheduling during up-peak, indicates the serial numbers of dispatched elevators. For elevator ri , its start–stop energy consumption of picking Ep−1 (ri ), is computed in (1) by the product between Ec and p (ri ), they are once start–stop energy constant, and start–stop counts needed by the car to response to the lobby floor call respectively. The counts equal to inside-choose floor numbers unfinished last scheduling of elevator ri plus one, the additional one indicates that the empty car return to the lobby downstairs to take waiting passengers. Ep−1 (ri ) = p (ri ) × Ec
(1)
np0 (ri ): initial passenger number of elevator ri when picking passengers, i.e., last scheduling remaining people in the car np (ri , s): leaving passenger number from elevator ri when it moves to the lobby floor at the sth startup m: passenger average mass mcar : elevator empty car mass mcwt : elevator counter weight mass g: acceleration of gravity hp (ri , t): floors displacement between the tth startup and its stop when picking passengers
Picking start–stop and running energy constitute the whole picking consumption of a car. And total picking energy of all elevators dispatched in system Ep , is obtained by (3), where M stands for the number of elevators dispatched.
Ep =
M i=1
Ep−1 (ri ) + Ep−2 (ri )
t−1 = pp (ri ) × Ec + np (ri , s) × m np0 (ri ) − t=1 s=1 i=1 + mcar − mcwt × g × hp (ri , t) M
p (ri )
(3)
Similarly, traveling energy includes traveling start–stop and running energy. And there exists a strong duality between the calculation of picking and traveling energy, traveling energy is counted as below. Traveling accelerate–decelerate energy of elevator ri , Et−1 (ri ), is expressed by (4), t (ri ) means start–stop counts needed by the elevator ri to deliver people in the car to their destinations, i.e., total inside-choose floor numbers of the elevator ri this scheduling. Et−1 (ri ) = t (ri ) × Ec
(4)
And traveling uniform-speed energy of elevator ri , Et−2 (ri ), is computed by (5). Where nt0 (ri ) is initial passenger number of elevator ri when traveling, nt (ri , s) stands for leaving passenger number from the elevator ri when it delivers the upwards passengers at the sth startup, ht (ri , t) means floors displacement between thetth
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startup and its stop when traveling.
t (ri ) t−1 Et−2 (ri ) = nt (ri , s) × m + mcar − mcwt nt0 (ri ) − t=1 s=1 × g × ht (ri , t)
(5)
System traveling energy Et , consists of traveling start-up and running energy of each dispatched elevator by (6). Et =
M i=1
=
M i=1
Et−1 (ri ) + Et−2 (ri )
pt (ri ) × Ec +
t (ri )
|
nt0 (ri ) −
t=1
+mcar − mcwt | × g × ht (ri , t)]
t−1
nt (ri , s)
×m
s=1
(6)
Finally, total scheduling energy of elevator system E, includes picking and traveling energy of all dispatched elevators in scheduling, E = Ep + Et . And the following up-peak scheduling optimization model for group elevators is built with the goal of minimizing the total scheduling energy E. 4. Up-peak energy-saving scheduling optimization In group elevator system, different scheduling performances are always contradictive with each other, how to balance the tradeoff between energy performance and others has been a significant challenge in energy-saving scheduling. During up-peak, a feasible way to realize energy-saving elevator operation is choosing fewer but enough elevators to transport calling people from lobby floor to their destinations. Dispatching fewer cars will be beneficial to reduce the whole system consumption and harmful to the time performance. In our work, both of energy and time performances are considered, the basic idea of scheduling optimization is saving system energy cost and keeping passenger waiting time acceptable. The up-peak energy-saving scheduling strategy proposed is realized based on scheduling optimization model below. A dual energy-saving mechanism is presented in our model. On one hand, adaptive configuration, choosing fewer but enough number’s elevator to transport waiting passengers on the lobby floor, based t(n + 1) = (+)t(n) +
t(n + 1) =
( + ˇ)t(n) +
( + ˇ)t(n) +
( + ˇ)t(n) +
t(n + 1) =
( + ˇ)t(n) t(n + 1) = + M +
Ts
2
(2Lri ,max (n)/V ) + Ts i=1
2
M
(2Lri ,max (n)/V ) + Ts i=1
M
(2Lri ,max (n)/V ) + Ts i=1
on the coupling relationship between energy cost of elevator system and average waiting time of passengers. On the other hand, optimization selection, choosing which cars to serve after the operating car number is decided. The selection decision is made with the objective, minimizing the system scheduling energy price derived above.
(2Lri ,max (n)/V ) M
M
(7)
Mo
t1,2 ≤ t(n) < t2,3
(n) i=1 ri
M
Mo
i=1
(n) i=1 ri
(n) i=1 ri
2
Mo
M
M
The new passenger waiting time could be predicted according to three terms, loading and unloading time of passengers last scheduling, average uniform speed running time of dispatched elevators, and average start–stop total time of dispatched elevators when accelerating and decelerating. First, we describe new passengers arriving rate by parameter , then t(n) means the number of all waiting passengers last scheduling, and it is assumed that, the passengers are distributed uniformly to all dispatched cars, all waiting people are transported in one scheduling (which is always satisfied by the criteria of group elevators designing), system carrying capacity is sufficient to serve all calling requests during up-peak, thus we can obtain and unloading time of each dispatched ele the loading vator by + ˇ t(n)/M, and ˇ represent the time spent by one people boarding and leaving car; secondly, we define Lri ,max (n) as max arriving floor of elevator ri , consider average moving time of M every dispatched car by i=1 2Lri ,max (n)/V /M; thirdly, we introduce Ts to indicate once acceleration-deceleration time, and ri (n) to represent total start–stop counts of elevator ri at trip n, thus we M use Ts i=1 ri (n)/M to compute elevator average total start–stop time. The predictive passenger waiting time is obtained by adding the three terms by (7).
2Lr1 ,max (n) + Ts r1 (n) t(n) < t1,2 V
t(n + 1) =
The pioneer work of energy-saving adaptive configuration has been studied in [29]. The coupling relationship between the optimal operating car number and waiting time is introduced. However, the result of optimal elevator configuration in [29] is based on an assumption, passengers enter the building on the lobby floor, board the elevators, and only get off the elevators on the top floor of building. And an improved coupling model is presented on the basis of the pre-research ideal problem, more practical situation is considered in this paper. Average passengers waiting time, the time interval between the average arrival moment of elevators at the lobby floor at this trip and previous one, can be predicted according to the former waiting time. Define t(n + 1) as predictive average waiting time of new coming passengers, which equals to the average tour time of cars this scheduling, and t(n) as the true value of average waiting time last scheduling, we have the following expression by (7), which reflects the coupling between the waiting time and the operating car number:
(8) tM−1,M ≤ t(n) < tM,M+1
(n) i=1 ri
tM o −1,M o ≤ t(n)
In practice, when t(n) of last scheduling is longer, there will be more waiting people gathering in the lobby this scheduling, more time will be spent in loading and unloading the passengers, and more counts start–stop will occur, finally, new waiting time performance will become longer. More elevators need to be dispatched to serve to shorter the time performance. Though more energy is saved by dispatching fewer elevators, the time performance should
J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
be guaranteed within acceptable range. Here in (8) we balance the trade-off between energy consumption and time performance, by dividing an optimal denominator (operating elevator number), from 1 to Mo , Mo means the number of total elevators in group system. In scheduling optimization, the key parameter, actual passenger arriving rate is difficult to be obtained because of the uncertainty of up-peak passenger flows, while we can predict the traffic flows by elevator flow forecasting method [31]. Because RO handles bounded uncertainty optimization, wedefine the uncertain passen ˆ − , ˆ + , where , , ˆ ger arriving rate by close interval, ∈ represent new passengers arriving rate’s actual value, predictive value, disturbance limit, and the predictive values obey up-peak traffic flows’ statistical laws. The Robust Optimization scheduling model for up-peak pattern is listed as follows: minimize E s.t. X=
M
Xi
The structure of the up-peak scheduling solution is described by (9) and (10). Total up-peak scheduling solution X, consists of M partial solutions Xi , and each partial solution stands for a specific elevator which will be dispatched. The dimension of Xi is 1 × Mo , corresponding to all elevators in group. In addition, the serial number of the dispatched car represented by Xi could be extracted by (10). Elevator adaptive configuration mechanism is described by (11) and (12). The number of cars dispatched M, is decided by the coupling relationship between energy and time performance in (11). By (12) the predictive value of average passengers waiting time cannot exceed the long time constant, tl . We reduce more energy consumption of elevator system with a precondition, not influencing time performance seriously. The optimization selection is described from (13) to (17). The total scheduling energy E, consists of picking energy Ep and traveling energy Et by (13). (14) and (15) calculate the two energy separately. For the two alterable initial values, np0 (ri ) and nt0 (ri ) are obtained by (16) and (17). It is assumed, all waiting passengers in the lobby are distributed uniformly to each dispatched car, thus the initial people number of elevator ri of picking np0 (ri ), equals to that, the last average people number distributed to each dispatched car
(9)
i=1 T
M o ] )(M o ×1)
ri = Xi(1×M o ) ([1 2 · · ·
( + ˇ)t(n) +
i = 1, · · ·, M
(10)
M
(2Lri ,max (n)/V ) + Ts i=1
t(n + 1) =
i=1
Et =
M
tM−1,M ≤ t(n) < tM,M+1
(11)
(12)
E = Ep + Et Ep =
(n) i=1 ri
M
t(n + 1) ≤ tl
M
M
499
p (ri )
pp (ri ) × Ec +
|
t=1
t (ri )
pt (ri ) × Ec +
np0 (ri ) −
|
nt0 (ri ) −
t=1
i=1
t−1 s=1
t−1
np (ri , s)
(13)
× m + mcar − mcwt | × g × hp (ri , t)
nt (ri , s)
(14)
× m + mcar − mcwt | × g × ht (ri , t)
(15)
s=1
Zr
B(n − 1) n (ri , s ) − M(n − 1) p i
np0 (ri ) =
(16)
s =1
p
B(n) [t(n) − t(n − 1)] nt0 (ri ) = = M M Xi · q = {0, 1} i = 1, · · ·, M
Xi(1×M o ) [1 1 · · ·
1]
T
B(n − 1) minus total leaving people number before this Zscheduling ri n (ri , s ), by (16). The leaving people number is computed by s =1
q = 1, 2, · · ·, M o
(M o ×1)
=1
ri < ri+1
(17) (18) (19) (20)
Model parameter declarations: tl : long waiting time constant X: total up-peak scheduling solution Xi : partial solution ri : serial number of the dispatched elevator expressed by partial solution Xi np (ri , s ): leaving passenger number of the elevator ri at the s th startup from lobby before scheduling Zri : start–stop counts of the rth elevator from the lobby floor last scheduling to current position Xi·q : the qth element in Xi After model simplification, this model has a certain optimization object, minimizing elevator system energy costs, subjects to some conditions. The conditions consist of three parts, expressions of scheduling solution, dual energy-saving mechanism and scheduling constraints.
where Zri means the start–stop counts finished, np (ri , s ) stands for each time’s leaving passenger number. Moreover, total waiting person number B(n) divided by the number of dispatched cars equals the initial value of traveling nt0 (ri ) by (17). And new passengers arriving rate times the time interval equals the total waiting people number. Finally, scheduling constraints are listed from (18) to (20). Each element in Xi needs to be one or zero only, represents dispatching a car or not by (18). We convert classical group scheduling decision into 0–1 integer programming in this paper. Every partial solution represents only one dispatched elevator by (19). Serial number of every dispatched elevator should be in ascending order in partial solutions by (20). Because there are uncertain parameters in the RO scheduling model, we cannot solve it directly. It is necessary to transform uncertain optimization into certain one for solving by robust counterparts [20]. The following robust counterparts are introduced, (17) and (18) in the initial RO model, are transformed to (21) and (22) because of the uncertain parameter in them.
t(n + 1) =
+ˇ
ˆ +
M
M 2
+
L i=1 ri ,max
t(n)
/V + T
M
M
(r ) i=1 p i
(21)
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J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
Fig. 2. Flow chart of up-peak energy-saving scheduling strategy.
B(n) nt0 (ri ) = = M
ˆ + [t(n) − t(n − 1)] M
(22)
The uncertain parameter is amplified to the possible max value, corresponding to maximum passengers flows which lead to maximum energy consumption. If group elevator system consumes less energy when elevators are scheduled based on RO scheduling solutions that are obtained in the worst case, the system will save more energy consumption in more general cases under up-peak pattern. After robust counterpart transformation, the uncertain optimization has become certain optimization. We can solve it by different optimization solving algorithms, finally up-peak energysaving optimal scheduling solution is obtained, and all elevators are scheduling based on the solution. In real application, total up-peak energy-saving scheduling strategy is described below. Fig. 2 shows the flow chart of the strategy. In every scheduling, the group controller with the algorithm proposed loads every elevator’s current state, all call signals and average waiting time last scheduling separately. Then, the group controller decides to dispatch how many elevators to serve the waiting passengers based on the energy-time piecewise function. Next, the group controller chooses which cars to serve based on RO scheduling solution for minimizing the energy consumption under up-peak pattern. After the optimization solving iterations, the optimal scheduling plan is obtained and all elevators are scheduled based on the plan. When elevators are scheduled based on the optimal plan, the scheduling algorithm judges each elevator is dispatched or not in this scheduling, each elevator operation is controller by running logics for active and dead elevator, and there are four running logics in Fig. 2.
(a) Active Before Active After, if the car is dispatched and moving upwards with passengers inside, the car will finish current transporting task first and return to the lobby floor to transport new waiting passengers; (b) Dead Before Active After, if the car is dispatched and stopping now, the car will change the state from dead to active, and move to the lobby to serve directly;
(c) Active Before Dead After, if the car is not dispatched and transporting passengers now, the car will finish current task first, stay where it is, and wait for new task next scheduling; (d) Dead Before Dead After, if the car is not dispatched last scheduling and this scheduling, the car will maintain the dead state. 5. Simulation This section presents simulation results to illustrate the validity of our strategy based on the virtual elevator environment of our lab [32]. The software can simulate each elevator’s actual movements, realize group system’s scheduling operation under different algorithms, display the dispatching process by real-time animation, and validate various performances of scheduling algorithms. Fig. 3 shows the interface of the simulation environment. Table 1 shows the specifications of the simulation system. Three simulation experiments are implemented based on three typical up-peak traffic flows. Simulation 1: floors of building A, 20, number of elevators, 3, up-flow passengers, 600 Simulation 2: floors of building B, 26, number of elevators, 4, up-flow passengers, 800 Simulation 3: floors of building C, 32, number of elevators, 5, up-flow passengers, 1000 The duration time of each flow is 60 min, and the peak point time is 30 min. Fig. 4 shows the three curves of new passengers arriving rate varied with time, blue line for up-flow A, green line for up-flow B, and red line for up-flow C. Similar variation trends of the three curves conform to the characteristic of up-peak traffic flow. Before Table 1 Specifications of simulation. Items
Value
Floor distance [m] Velocity [m/s] Acceleration [m/s/s] Jerk [m/s/s/s] Car capacity [person] Time of opening and closing door [s] Time of passenger’s loading and unloading [s/person]
3 2.5 1 1.8 10 4 1
J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
501
Fig. 3. Interface of elevator group scheduling simulation environment.
the peak point of up-peak, the arriving rate of calling passengers increases gradually. The arriving rate of flow A, B, C are 0.24, 0.32 and 0.40 people per second separately, and flow C rate ranks the first. Moreover, the area of region bounded by each curve and the horizontal axis stands for the total arriving passenger number
during up-peak, the total passenger numbers of up-flow A, B, and C are 600, 800, 1000 persons respectively. Fig. 5 indicates that the dispatched elevator number varies with time under three different conditions of simulation 1, 2 and 3. The line charts of dispatched numbers match the curves in Fig. 4 with
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J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
Table 2 Quantitative analysis of dispatched and un-dispatched elevator number. Simulation
Parameter
Avg. dispatched cars
Avg. un-dispatched cars
Avg. utilization rate
1 2 3
Building A, up-flow A Building B, up-flow B Building C, up-flow C
1.67 2.17 3.06
1.33 1.83 1.94
55.7% 54.3% 61.2%
colors, blue, green and red. From Fig. 5, the number of dispatched elevators increases with the increasing of passengers arriving rate, and decreases as the rates decreases. In our adaptive elevator scheduling strategy, we use optimal and necessary cars to transport waiting passengers during up-peak for reducing elevator system energy consumption. Quantitative analysis results of adaptive elevator number adjustments are listed in Table 2. In simulation 1, 3 elevators serve a 20 floors building, average numbers of dispatched and undispatched cars are 1.67 and 1.33, and average utilization rate of all elevators is 55.7%. In simulation 2, 4 elevators serve a 26 floors building, the numbers of dispatched and un-dispatched elevators are 2.17 and 1.83, the elevator utilization rate is 54.3%. In simulation 3, 5 elevators serve a 32 floors building, the numbers of dispatched and un-dispatched elevators are 3.06 and 1.94, the elevator utilization rate is 61.2%. From the three simulations, only about half 0.45 up−flow A up−flow B up−flow C
max =0.40 p/s
new passengers arriving rate (p/s)
0.4 0.35
max =0.32 p/s
0.3 max =0.24 p/s
0.25 0.2 0.15 0.1 0.05 0
0
600
1200
1800 time (s)
2400
3000
3600
3 simulation 1 2 1
No. of active cars
0
4 3 2 1
No. of active cars
No. of active cars
Fig. 4. Curves of up-peak new passengers arriving rate.
5 4 3 2 1
600
1200
1800 time (s)
2400
3000
3600
simulation 2
0
600
1200
1800 time (s)
2400
3000
3600
simulation 3
0
600
1200
1800 time (s)
2400
3000
Fig. 5. Line charts of up-peak dispatched elevator number.
3600
of the elevators are dispatched during up-peak by our strategy, it is beneficial to energy-saving operation of group elevator system. In fact, the elevator utilizations of most commonly used up-peak scheduling algorithms are greater than our strategy. The system energy is wasted by unnecessary elevators, and in some cases, passenger waiting time may be longer because of the unreasonable scheduling. For comparison, another three scheduling algorithms are chosen, including minimizing waiting time algorithm, destination zoning algorithm and ACO scheduling algorithm [18]. Min-waiting algorithm minimizes all calling passengers’ waiting time. Destination zoning algorithm separates floors into different zones according to passenger destinations and dispatches each car to serve every fixed zone. ACO algorithm minimizes system picking energy and considers time performance by a long waiting time threshold [18]. Table 3 displays comparison of scheduling performances. In simulation 1, 3 elevators serve 600 passengers in a 20 floors building, the start–stop and running energy of energy-saving algorithm are 24,031.29 kJ and 16,105.23 kJ, they are less than energy costs of other three algorithms, because elevator unnecessary start–stop and running counts are reduced effectively by our algorithm. Total energy consumption of our algorithm is 40,136.52 kJ. Total energy savings by our algorithm are 21,212.25 kJ than min-waiting algorithm, 12,765.83 kJ than zoning algorithm, 4996.9 kJ than ACO algorithm. The time performance of our algorithm ranks the third, 24.27 s. Coupling relationship between energy and time is considered in our algorithm, thus elevator system energy consumption is saved effectively, and the time performance is kept in acceptable range. For performances of other algorithms, min-waiting algorithm only emphasizes average passenger waiting time, its time performance is less than others, 18.05 s. However, the better time is acquired by sacrificing more system energy, its total energy performance is 61,348.77 kJ. Destination zoning algorithm is a classical non-optimization scheduling strategy, both of its total energy and time performance are not outstanding, 52,902.35 kJ and 22.16 s. ACO algorithm minimizes system picking passengers’ energy, total energy consumption of ACO is 45,133.42 kJ, worse than energysaving algorithm, because our algorithm considers not only picking energy, but also traveling energy in up-peak scheduling optimization. The waiting time of ACO is worst, 25.91 s, because the time is considered by long waiting time threshold, thus the time performance is always close to the threshold. In simulation 2, 4 elevators serve 800 passengers in a 26 floors building, total energy savings by our algorithm are 28,997.88 kJ than min-waiting algorithm, 16,474.13 kJ than zoning algorithm, 4734.44 kJ than ACO algorithm. In simulation 3, 5 elevators serve 1000 passengers in a 32 floors building, total energy savings by our algorithm are 63,825.31 kJ than min-waiting algorithm, 19,653.92 kJ than zoning algorithm, 6959.19 kJ than ACO algorithm. Table 4 displays the energy-saving results of our up-peak energy-saving scheduling optimization. In simulation 1, for elevator system, our algorithm saves 34.58% energy than min-waiting algorithm, 24.13% than zoning algorithm, 11.07% than ACO algorithm. The overall electricity consumption of a building contributed by elevators is about 3–8% [10], if we take an average 5.5%, for building, compared with other algorithms, the saving ratios of our algorithm are 1.90%, 1.33% and 0.61%. An elevator system
J. Zhang, Q. Zong / Energy and Buildings 66 (2013) 495–504
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Table 3 Comparison of scheduling performances. Parameter
Start–stop energy (kJ)
Running energy (kJ)
18.05 22.16 25.91 24.27
33,274.25 29,535.08 28,440.93 24,031.29
28,074.52 23,367.27 16,692.49 16,105.23
61,348.77 52,902.35 45,133.42 40,136.52
21,212.25 12,765.83 4996.9
Min-Waiting Zoning ACO Energy-saving
25.47 30.31 37.22 34.85
40,177.25 36,871.16 32,902.37 31,084.93
47,337.10 38,119.44 30,348.54 27,431.54
87,514.35 74,990.60 63,250.91 58,516.47
28,997.88 16,474.13 4734.44
Min-Waiting Zoning ACO Energy-saving
35.68 39.52 46.96 40.13
61,552.39 49,473.38 45,994.10 38,251.97
76,954.85 44,862.47 35,647.02 36,429.96
13,8507.24 94,335.85 81,641.12 74,681.93
63,825.31 19,653.92 6959.19
Algorithm
Avg. wait-time (s)
Min-waiting Zoning ACO Energy-saving
Total energy consumption (kJ)
Total energy saving (kJ)
Simulation 1 Building A Up-flow A Simulation 2 Building B Up-Flow B Simulation 3 Building C Up-Flow C
Table 4 Energy-saving results of up-peak energy-saving scheduling optimization. Parameter
Algorithm
Saving ratio for elevator system
Saving ratio for building
Min-waiting Zoning ACO
34.58% 24.13% 11.07%
1.90% 1.33% 0.61%
Min-waiting Zoning ACO
33.14% 21.97% 7.49%
Min-waiting Zoning ACO
46.08% 20.83% 8.52%
Saving energy per day (kW/h)
Saving energy per year (kW/h)
Financial saving per year (D )
5.8923 3.5461 1.3880
2150.69 1294.33 506.62
251.63 151.44 59.27
1.82% 1.21% 0.41%
8.0550 4.5761 1.3151
2940.08 1670.28 480.01
343.99 195.42 56.16
2.53% 1.15% 0.47%
17.7293 5.4594 1.9331
6471.19 1992.68 705.58
757.13 233.14 82.55
Simulation 1 Building A Up-flow A Simulation 2 Building B Up-flow B Simulation 3 Building C Up-flow C
scheduled by energy-saving algorithm can save energy 5.8923 kW/h, 3.5461 kW/h, 1.3880 kW/h than other algorithms per day, and save 2150.69 kW/h, 1294.33 kW/h, 506.62 kW/h energy per year. According to the average electricity price for office building in EU27 provided by Eurostat [33], 0.117 Euro per kW/h, compared with other three scheduling algorithms, financial savings for one building of our algorithm are 251.63 Euro, 151.44 Euro and 59.27 Euro per year. In simulation 2, compared with other algorithms, financial savings for one building of our algorithm are 343.99 Euro, 195.42 Euro and 56.16 Euro per year. In simulation 3, compared with other algorithms, financial savings for one building of our algorithm are 757.13 Euro, 233.14 Euro and 82.55 Euro per year. And enormous economic benefits will be made by our energy-saving scheduling optimization method, because there are millions of buildings with group elevator system in the world. 6. Conclusion Scheduling operation of building transportation systems has profound societal impact. Scheduling of group elevators in building has long been recognized as an important issue, and energy-saving elevator scheduling has been a significant challenge recently. The energy-saving scheduling of up-peak pattern is more important than other traffic patterns, because more energy is consumed during up-peak. Up-peak energy-saving scheduling has a great significance for multi-elevator system efficient operation, and offers useful guidance to optimal scheduling under other traffic pattern in building. In this paper, an energy-saving elevator scheduling optimization method under up-peak traffic is proposed. Robust Optimization is applied to solve up-peak elevator scheduling under uncertain
passenger flows. The optimization objective is minimizing the scheduling energy price of elevator system, and keeping the passengers waiting time performance acceptable. The energy price function is built first, including picking and traveling energy costs. Based on that, up-peak RO scheduling model and energy-saving scheduling strategy are presented, a dual energy-saving mechanism is realized by the optimization. One is adaptive configuration, choosing fewer but enough number’s elevators to run transport waiting passengers on the first floor. Another is optimization selection, choosing which elevators to serve after the number of dispatched elevators is decided. Simulation tests are implemented under the conditions of three up-peak traffic flows, different floors high-rise buildings and diverse sizes of elevator group. Results indicate that the energy performance of elevators in building is significantly improved by the energy-saving scheduling method during up-peak, and the time performance is acceptable as well.
Acknowledgements This work is supported by National Nature Foundation of China under Grant #91016018, #61273092, Key Project of Chinese Ministry of Education #311012, Tianjin Basic Study Key Foundation #11JCZDJC25100.
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