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Multi-Period Coordinated Active-Reactive Scheduling of Active Distribution System Xiangyu Zhao, Student Member, IEEE, Qixin Chen, Member, IEEE, Qing Xia, Senior Member, IEEE, Chongqing Kang, Senior Member, IEEE and Hao Wang Abstract—Distributed energy resources (DERs), including distributed generators (DGs), storage devices (SDs) and controllable loads (CLs), are critical components for active distribution system (ADS). Implementation of DERs components would impose great challenges on traditional distribution system operation. This paper firstly investigates operation characteristics of DERs, including operation flexibility, inter-temporal operation relations and active-reactive power relations. Then, a multiperiod coordinated active-reactive scheduling model is proposed for integrated operation of ADS, in order to minimize overall operation costs over a specific duration of time. The model takes into accounts operation characteristics of various DERs and formulates multi-period operation constraints of ADS. Finally, validity and effectiveness of the proposed model are demonstrated based on case study of a medium-voltage 135-bus distribution system. Index Terms—active distribution system, coordinated activereactive scheduling, distributed generation, storage device, controllable load
A
I. INTRODUCTION
ctive distribution system (ADS) is defined as distribution networks that have systems in place to control a combination of distributed energy resources (DERs), including DGs, SDs and CLs [1]. In recent, high levels of DERs are being integrated into ADS. As most of the DERs are “dispatch-able” units, they could be efficiently scheduled in order to achieve specific operational objectives, for example, costs minimization. Therefore, it would be necessary for the Distribution System Operators (DSOs) to transform from the traditional “passive” uni-directional flow operation approach to novel “active” bi-directional flow operation approach [2]. To this end, a critical challenge is to formulate the operation characteristics of different kinds of DERs and integrate them into the scheduling scheme of ADS. In recent years, many interesting researches related to this topic have been conducted, mainly focusing on active power scheduling problems. Optimal power flow models including DGs and SDs were respectively proposed in [3] and [4]. [5] proposed a disco operation model considering DGs and their goodness factors; with the goodness factors, distribution power This work was jointly supported by the National High-Tech Research and Development Program of China (863 Scheme, No. 2011AA05A118), and National Natural Science Foundation of China (No 51107059). Xiangyu Zhao, Qixin Chen, Qing Xia and Chongqing Kang are with State Key Lab of Power Systems; Dept. of Electrical Engineering; Tsinghua University; Beijing, 100084. (E-mail:
[email protected]). Hao Wang is with Power Dispatch and Control Center, China Southern Power Grid.
978-1-4799-1303-9/13/$31.00 ©2013 IEEE
losses could be simply expressed. A two-stage scheduling model was proposed in [1], which synchronously took DGs and SDs into accounts; the proposed approach integrated a centralized day-ahead and an intra-day schedulers; the dayahead scheduler was based on DC power flow model, ignoring bus voltage constraints and reactive power outputs of DERs, while the intra-day scheduler solved single-period scheduling problem. Inter-temporal operation relations of DERs were not considered. [6] formulated energy resource scheduling problem in ADS with DERs aggregated as virtual power players. Moreover, [7], [8] and [9] discussed the use of DERs in ancillary market, as DERs could become reactive power suppliers in distribution system. A model remarrying active and reactive power dispatching was proposed in [6], however, it failed to integrate and formulate active-reactive power relations of DERs. In fact, as active and reactive power were coupled in ADS dispatching, scheduling of reactive power of DERs could not be ignored or simply taken independent with their active power outputs. Based on the above analysis, this paper is focus on multiperiod coordinated active-reactive scheduling of ADS. Firstly, operation characteristics of various DERs are investigated, including operation flexibility, inter-temporal operation relations and active-reactive power relations. Then, a novel multi-period active-reactive coordinated scheduling model is proposed for integrated operation of ADS, in order to minimize overall operation costs over a specific duration of time. The model takes into accounts operation characteristics of various DERs and formulates multi-period operation of ADS. Finally, validity and effectiveness of the proposed model are demonstrated based on case study of a medium-voltage 135-bus distribution system. II. OPERATION CHARACTERISTICS OF DERS This section is focus on analyzing operation characteristics of various DERs, including DGs, SDs and CLs. The analyzed characteristics include operation flexibility, inter-temporal operation relations and active-reactive power output relations. A. Distributed Generator DGs within ADS are mainly in the form of wind turbine (WT), photovoltaic (PV) and gas turbine (GT). 1) Operation flexibility Generally, active power output of WT and PV would be fully utilized in ADS except for the case of curtailment. For GT, its power output could be adjusted within its generation
2
capacity limitation. These relations could be expressed as:
⎧P ≤ P ⎪⎪ P P _ avl ⎨ Pi , j ≤ Pi , j ⎪ G G G ⎪⎩ P j ≤ Pi , j ≤ P j W i, j
W
P
discharge and non-use state. Operation flexibility of SDs could be expressed as:
W _ avl i, j
⎧ ai , j , bi , j ∈ {0,1} ⎪ ⎪⎪ ai , j + bi , j ≤ 1 sC ⎨ sC sC ⎪ ai , j ⋅ P j ≤ Pi , j ≤ ai , j ⋅ P j sD ⎪ sD sD ⎪⎩bi , j ⋅ P j ≤ Pi , j ≤ bi , j ⋅ P j
(1)
G
where Pi , j , Pi , j and Pi , j denote active power output of WT, W _ avl i, j
PV and GT j at time interval i , P
P _ avl i, j
and P
denote the G
G
maximum available output of WT and PV; P j and P j
denote upper and lower bound of GT j. 2) Inter-temporal operation relations Inter-temporal operation constraints would be imposed on GTs, which could be expressed in the form of ramping constraints. Compared to general coal-fired based generation unit, ramping ability of GT is much better.
PjG , RD ≤ Pi +G1, j -Pi ,Gj ≤ PjG , RU G , RD
where Pj
G , RU
and Pj
(2)
indicate ramping up and down limits
of GT j. 3) Relations on active-reactive power output Reactive power outputs of DGs are critical in ADS operation, especially for bus voltage control. Reactive power outputs of DGs are also closely related to their active power outputs. Hence, relations on active-reactive power output should be considered in scheduling scheme of ADS. DGs are always connected to distributed systems through power electronics equipment. Relations on active-reactive power output are mainly decided by types and control strategies of the equipment. There are mainly two kinds of control strategies: constant voltage control (CVC) and constant power factor control (CPFC) [7]. For CVC, DGs individually control reactive their power outputs to keep bus voltage stable, while for CPFC, reactive power outputs are determined by their active power outputs in certain proportions. These relations could be formulated as:
⎧Q d ≤ Q d ≤ Q d j i, j ⎪ j ⎪ d d , Pset d ⎨CPFC : Qi , j =C j ⋅ Pi , j ⎪ V =V jd ,Vset ⎪⎩CVC :
(4)
where ai , j and bi , j jointly denote operation state of SD j at time interval i : (1,0) indicates discharge, (0,1) indicates sC
sD
charge and (0,0) indicates non-use state. Pi , j and Pi , j sC
respectively denote its active power input and output; P j and sC
sD
P j are upper and lower bounds in charge state, while P j sD
and P j are related to discharge state. 2) Inter-temporal operation relations It must be insured that the stored energy is within the storage capacity limitation, which is: i
(
)
P j ≤ Pjs , I + ∑ PnsC, j − PnsD ≤ Pj ,j s
n =1
s,I
where Pj
s
s
(5)
s
is the initial storage level. P j and P j are upper
and lower bounds of storage capacity. The summary term indicates accumulated storages (charges minus discharges) from the initial time interval to the current time interval i. 3) Relations on active-reactive power output For charge process (CP), as half control elements are always utilized, there is no reactive power exchange between SDs and ADS; however, for discharge process (DP), with full control elements, SDs could export reactive power into the ADS. Moreover, relations on active-reactive power are decided by the control strategies. Like DGs, CVC and CPFC are two major control strategies for SDs. The relations could be formulated as:
⎧CP : QisC, j =0 ⎪ ⎧Q sD ≤ Q sD ≤ Q sD ⎪ j i, j ⎪ ⎪ j ⎨ ⎪ sD sD sD ⎪ DP : ⎨CPFC : Pi , j = C j ⋅ Qi , j ⎪ ⎪ s ,Vset ⎪⎩CVC : V = V j ⎪⎩
(3)
d
where Qi , j denotes reactive power output of DG j at the time sC
sD
sD
and Q j
(6)
interval i , while Q and Q j are upper and lower bounds.
where Qi , j and Qi , j are reactive power input and output of
P is active power output and Cdj , Pset is the controlled power
SD j, Q
d
d
j
d i, j
d ,Vset
factor. V j
d
indicates the controlled voltage level, which is
related to Qi , j .
j
sD
sD
are upper and lower bounds. Pi , j is sD
active power output of storage discharge process and C j is s ,Vset
the controlled power factor. V j
voltage level. B. Storage Device C. Controllable Load 1) Operation flexibility 1) Operation flexibility SDs are generally operated separately at three states: charge,
indicates the controlled
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In this paper, controllable loads (CLs) are defined as power loads directly controlled by DSOs. Generally, DSOs control active power loads of the consumers by changing operation levels of the targeted electric facilities. For the sake of simplicity, we assume that the load levels could be changed continuously. Obviously, CLs could impose either positive or negative impacts on the consumed power loads: c
c
P j ≤ Pi ,cj ≤ P j
(7)
c
where Pi , j is active power load adjustment of CL j at time c
c
interval i ; P j and P j indicate upper and lower bounds of the adjustment. 2) Inter-temporal operation relations CLs always sign contracts with DSOs to set specific control rules, mainly including maximum capacity, available periods, cumulative time and allowable dispatch times. Dispatch of CLs should follow these specific terms, thus imposing strict intertemporal period constraints. These constraints could be expressed as: ⎧ci , j , d i , j , ei , j ∈ {0,1}
⎪ c c ⎪ci , j = 0, i ∈ [0, T j ] ∪ [T j , T ] ⎪ ⎪ci , j − ci −1, j − d i , j − ei , j = 0 ⎪T ⎪ P c ≤ P c , set j ⎨∑ i , j ⎪ i =1 ⎪T c , set ⎪∑ ci , j ≤ Tj ⎪ i =1 ⎪T d i , j ≤ N cj , set ⎪⎩∑ i =1
(8)
where ci , j denotes the dispatch state of CL j at time interval i,
d i , j and ei , j are slack variables, indicating changes on dispatch states over sequenced periods. When CL j is initially dispatched from period i, the value of ci , j would be assigned as one; when CL j ends its dispatching state from period i, d i , j would be assigned as one as well; Otherwise, the two variables would be assigned as zero. The above relations could be formulated by the third sub-formula in (8). It’s assumed that c
c
CL j could only be dispatched from T j to T j , as shown in the second sub-formula. Pjc , set , T jc , set and N cj , set respectively
III. MULTI-PERIOD COORDINATED SCHEDULING MODEL A. Decision variables The decision variables include continuous ones for active and reactive power of source bus, DGs, SDs as well as CLs, and “0-1” binary integer ones for operation states of SDs and CLs. Noted that there are two operation processes for SDs, discharge and charge, two sets of decision variables would be assigned for each process. 1) Continues decision variables include: sD c c Pi s , Qis , Pi ,dj , Qid, j , Pi ,sCj , Pi ,sDj , QisC , j , Qi , j , Pi , j , Qi , j
where Pi s and Qi s denote active and reactive power of source bus at time interval i. Considering the radiation property of distribution system, it would be reasonable to just consider one source bus for each distribution system. It should be noted that network reconfiguration issue is beyond the scope of this paper. 2) “0-1” binary integer decision variables include:
ai , j , bi , j , ci , j , d i , j , ei , j B. Object function The object is to minimize overall operation costs of ADS over a specific duration of time, including power generation/ operation costs from source bus, DGs, SDs and CLs.
⎧ T s , P s s ,Q s T NG d , P d d ,Q d ⎫ (λi Pi +λi Qi )+∑∑ (λi , j Pi , j +λi , j Qi , j )+ ⎪ ⎪∑ i =1 j =1 ⎪ i =1 ⎪ (10) Min ⎨ T NS ⎬ T NC ⎪∑∑ (λ sD , P P sD +λ sD ,Q Q sD )+∑∑ (λ c , P | P c |) ⎪ i, j i, j i, j i, j i, j i, j i =1 j =1 ⎩⎪ i =1 j =1 ⎭⎪ Where λ denotes cost coefficients. The superscripts of the variables and parameters in (10) are used to distinguish different kinds of DERs (s, d, sD and c) and active and reactive power output (P, Q). T denotes the number of included time periods; NG , NS and NC respectively denote sets of DGs, SDs and CLs. In (10), generation costs of the source bus are related to its active and reactive power. The costs of reactive power might come from contracts or auxiliary markets, these two mechanisms could both be reflected by cost coefficients. The same situation would be implemented to DGs and SDs. Regardless of storage losses, we use discharge power (or charge power) to indicate operation costs of SDs. Operation costs of CLs are related to the changes of load levels incurred by direct control, which could be reflected by absolute value
indicate constraints on maximum capacity, cumulative time and allowable dispatch times. c 3) Relations on active-reactive power of Pi , j . Relations on active-reactive power of CLs are mainly decided by the controlled facilities. Generally, for specific CLs, C. Constraints their power factors are always constant, which is: Constraints mainly consist of two categories, respectively Qic, j = C cj ⋅ Pi ,cj (9) related to system operation and various DERs. 1) System operation constraints: c where Qi , j is reactive power adjustment of CL j at time Power balance constraint on source bus is expressed as: c
interval i and C j indicates the specific power factor.
4
⎧⎪ Pi s − Pi ,ls = F1 (Vi ,θ i ) ⎨ s l ⎪⎩Qi − Qi , s = F2 (Vi ,θ i )
(11)
Power balance constraints on other buses are expressed as:
⎧ NG d NS sD NS sC NC c l ⎪ ∑ Pi ,m + ∑ Pi , m - ∑ Pi , m + ∑ Pi , m − Pi , j = F1 (Vi ,θ i ) ⎪ DG =1 SD =1 SD =1 CL =1 ⎨ NG NS NS NC ⎪ Q d + Q sD - Q sC + Q c − Q l = F (V ,θ ) (12) ∑ ∑ ∑ i ,m i,m ∑ i,m i,m i, j i i 2 ⎪⎩ DG =1 SD =1 SD =1 CL =1 j
j
j
j
j
j
j
j
j = 1L NB where NB denotes the number of buses in distributed system; NG j , NS j and NC j indicate the number of DGs, SDs and
hour as basic time interval. Eight DGs are added, including five GTs, two WTs and one PV; one SD and one CL are added as well. Detailed operation data and parameters of the test system could be found in the Appendix file. The model is solved by Lingo and the results are as follow: 1) Schedules of the source bus The curve with crosses in fig 1 shows active power schedules of the source bus; while the one with triangles denotes the total load demand. The trends of the two curves are roughly consistent, with deviations reflecting power outputs from various DERs.
CLs connected to bus j. Pi l, j and Qil, j are active and reactive load of bus j at time interval i . F1 and F2 are active and reactive power flow functions. Vi is vector of bus voltage magnitude and θ i is vector of bus voltage angle. Constraints on transmission power flow are expressed as: f2
f 2
S j ≤ Pi ,fj 2 + Qi ,f j 2 ≤ S i , j
(13)
where NL denotes the number of lines. Pi ,fj and Qi f, j indicate active and reactive power flow of line j at time interval i, S
f j
f
and S j are upper and lower capacity limitations of line j. Constraints on bus voltage are expressed as:
⎧V b ≤ V ≤ V bj ⎪ j i ,j ⎪⎪θ b ≤ θ ≤ θ bj ⎨ j i ,j ⎪ Vi s =V s , set ⎪ s ⎪⎩ θ i =0
Fig 1. Active power schedules of the source bus
2) Schedules of the DGs Fig 2 shows active and reactive power schedules of the DGs. The curves with crosses denote active power schedules; while the ones with triangles denote reactive power schedules. DG 1 and 2 are WTs, DG 8 is PV, and the rest are GTs.
(14)
where Vi s and θis denote voltage magnitude and angle of b
b
b
b
source bus. V j , V j , θ j and θ j respectively denote upper and lower limitation of voltage magnitude and angle of bus j. 2) DER operation constraints: Operation constraints on DGs, SDs and CLs are established based on their operation characteristics, including operation flexibility, inter-temporal operation relations and activereactive power relations. As discussed in Section II, operation constraints on DGs are formulated by (1)-(3); operation constraints on SDs are formulated by (4)-(6); operation constraints on CLs are formulated by (7)-(9). Conclusively, the formulated multi-period coordinated scheduling model is essentially a typical nonlinear mixed integer programming problem. Effective algorithms have been developed to solve this type of problem, for example, genetic algorithm (GA) [12], particle swarm algorithm (PSA) [13], etc. Fig 2. Active-reactive power schedules of the DGs
IV. CASE STUDY The proposed model is implemented on the tested REDS (REpository of Distribution Systems) 135-bus distribution system. The test system has been extended from single-period to multi-period, with one day as the scheduled duration and 1
No curtailments are observed for WTs and PV, as their capacities are relatively low in this tested system; therefore, the fluctuations could be easily offset by the source bus and the GTs. Reactive power schedules of DG 3, 5 and 7 are appropriately adjusted to keep the bus voltages at the set range,
5
as they adopt CVC control strategy. Therefore, schedules of reactive power are independent of that of active power. However, For DG 4 and 6, as they adopt CPFC strategy, reactive power schedules are proportional to that of active output. 3) Schedules of the SD
output relations various DERs are respectively discussed and formulated. Then, a multi-period coordinated active-reactive scheduling model is proposed for integrated operation of ADS, with the object of costs minimizing. A tested case is studied, which is based on a 135-bus distribution system with eight DGs, one SD and one CL connected. Solution of the proposed model includes optimal schedules of the DERs, which help to smooth bus load and cut distribution losses in the premise of secure operation constraints. VI. REFERENCES
Fig. 3. Active power schedule of the SD
Fig 3 shows active power schedule of the SD. Positive values indicate charge state while negative indicate discharge. It could be observed that operation state of the SD is well scheduled, which is in charge state during valley load periods and in discharge state during peak load periods. This schedule could smooth bus load curve and thus might be helpful to reduce overall distribution power losses to some extent. 4) Schedules of the CL
Fig. 4. Active power schedule of the CLs
Fig 4 shows active power schedule of the CL. Positive values indicate load cutting, while negative values indicate load promoting. Recovery of the loads being cut is simply assumed to take place all over the scheduled duration in an average sense. Discussions on load recovery patterns would not be included in this paper. It could be observed that the CL is mostly implemented in peak load periods. The reason for such scheduling is to smooth the bus load curve as well, with the object of cutting operation costs of the whole system. V. CONCLUSIONS Implementation of DERs imposes great challenges on traditional distribution system operation. And scheduling of ADS has become an important research topic, which imposes remarkable impacts on system economics and secutiry. This paper firstly investigates operation characteristics of various DERs, including DGs, SDs and CLs. Operation flexibility, inter-temporal operation relations and active-reactive power
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