Optimal Virtual Power Plant Operation for Promoting Energy Efficiency of Distribution Systems Ya-Chin Chang *1, Rung-Fang Chang2 Department of Electrical Engineering, Cheng Shiu University, Kaohsiung, 833, Taiwan
1
Department of Electrical Engineering, Kao Yuan University, Kaohsiung, 821, Taiwan
2
*1ycchang@csu.edu.tw; 2rfchang@cc.kyu.edu.tw Abstract In this paper, an optimal virtual power plant (VPP) operational method is proposed to maximize the benefit obtained with respect to the power supply limit of the distribution transformers and the system security constraints. In the method, an iterative dynamic programming optimal BESS schedule approach and a PSO-based DR scheme optimization approach are executed alternatively until the maximum benefit reached. With the TOU rate each hour, test results had confirmed the validity of the proposed method with obviously decreased power supply needed on peak-load hours and largely reduced electricity cost or maximum benefit accordingly. Keywords Virtual Power Plant; Battery Energy Storage System; Distributed Energy Resource; Demand Response
Introduction The VPP with the regulable loads participating in DR action can optimize the DR scheme by suitably regulating the demand powers of the loads over the 24 hours to help improve system security of a whole day. The definition of DR in the Federal Energy Regulation Commission (FERC) is: changes in electric usage by demand-side resources from their normal consumption patterns in response to changes in the price of electricity over time (TOU, dynamic pricing, critical peak pricing, peak-time rebate, etc.), or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized [1]. Recently, many DR strategies have been introduced to solve peak-load shedding and shifting problems. In [2], as a load shaping tool, a DR strategy is proposed to alleviate the potential new load peaks with minimal infrastructure investments. While in [3], with price uncertainty modeled through robust optimization techniques, a real-time DR model with a linear programming algorithm is used to adjust the hourly load level of a given consumer in response to hourly electricity prices. Energy storage systems (ESSs) are increasingly drawing more attention from utility engineers and regulators for its potential to address a variety of technical challenges in the management of electric power [4-8]. Utilities face the need to economically serve uncertain peak load growth at substations, the desire to provide enhanced reliability and resilience in adaptive smart grids, and the need to use highly variable and unpredictable renewable energy sources. All these matters could potentially be addressed using storage technologies. In this study, the objective of the proposed method is to maximize the benefit (or minimize the electricity cost) of the supply powers from the distribution transformers over the 24 hours under the VPP operation by optimizing the charging/discharging schedules of each BESS and the DR scheme simultaneously. Composed of an iterative dynamic programming optimal BESS schedule approach and a PSO-based DR scheme optimization approach, the proposed optimal VPP operating is achieved by respecting the power supply limit of each distribution transformer and the system security constraints.. International Journal of Automation and Control Engineering, Vol. 4, No. 1—April 2015 2325-7407/15/01 045-6 Š 2015 DEStech Publications, Inc. doi:10.12783/ijace.2015.0401.11
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Ya-Chin Chang, Rung-Fang Chang
Problem Formulation The real and reactive powers balance equations at each bus of the network are shown in (1) and (2) respectively: N
PB ,i ,t + = PDG ,i ,t − Pd ,i ,t ∑ Vi ,tV j ,t Yij cos(θij + δ j ,t − δ i ,t ) ∀i, j , t j =1
N
QB ,i ,t + Q= ∑ Vi ,tV j ,t Yij sin(θij + δ j ,t − δ i ,t ) ∀i, j , t DG ,i ,t − Qd ,i ,t j =1
(1) (2)
The system security considering the thermal rating of each line and the voltage magnitudes at each node are shown in (3) and (4) respectively: Yij [Vi ,2t + V j2,t − 2Vi ,tV j ,t cos(δ j ,t − δ i ,t )]1/ 2 ≤ I ij ,cap ∀i, j , t
(3)
Vmin ≤ Vi,t ≤ Vmax ∀i ≠ 1,t
(4)
The limits of total real power each hour, PGSP ,t , access to the main transformers or the grip supply point (GSP) are :
ω Psub,cap ≤ PGSP ,t ≤ Psub,cap ∀t
(5)
where Psub,cap is the capacity of the substation and scaling factor −1 ≤ ω ≤ 0 is used to enforce the reverse power, if allowable, for the substation. The problem to optimize the DR scheme and each BESS schedule at the same time is formulated below: ∑ ( ∑ Pd ,i ,t − PGSP ,t ) ⋅ TOURt
Max
∀t∈T ∀i∈R
s.t.
(6) (1)-(5)
Start with the SOC of the each BESS and the DR contract and without any scheduled BESS
No
Execute the PSO Based DR Scheme Optimization Approach with the present BESS schedules
Convergence ? Yes
Execute the Iterative Dynamic Programming Optimal BESS Schedule Approach with the present DR scheme Output the optimum DR scheme and each BESS schedule
FIGURE 1. FLOWCHART OF THE PROPOSED METHOD
Proposed Method The two approaches included in the proposed approach shown in Figure 1 are introduced below. PSO-Based DR Scheme Optimization Algorithm The steps of the PSO algorithm used to evaluate the settings of the control variables, α t ∀t ∈ T , to optimize the DR scheme are as follows: 1) Set the iteration number. 2) Narrow down the control variable adjustment ranges and generate a swarm with NP particles. 3) A load flow computation is conducted for each element of each particle with X i (k ) = [α1 α 2 α 24 ]T . If no available particle exists, return to step 2. Otherwise, set pbest and fitness for each particle. For the particle
Optimal Virtual Power Plant Operation for Promoting Energy Efficiency of Distribution Systems
47
with a converged load flow solution, fitness = ψ / (1 + pene _ v) , and for the particles without a load flow solution, fitness = −10 , where pene_v is a penalty that is proportional to the severity of security constraint violation and ψ is the current benefit obtained from the VPP operation. Set Ite_num = 0 and go to step 4. 4) Ite_num = Ite_num+1, gbest = the pbest of the particle with maximum fitness. Restore the control variable adjustment range to the original problem. 5) Execute load flow for each particle and check security constraints. Update particle fitness ( fitness = ψ / (1 + pene _ v) ). If Ite_num is lower than the maximum iteration number specified, go to step 4, otherwise, go to step 6. Record the present settings of α t ∀t ∈ T , utility benefit and optimized DR scheme. Input benefit cost and BESS number = NE i=1
Execute the dynamic programming algorithm for BESS i with the other BESS known schedules
Renew benefit cost No i=i+1
i=NE ? Yes
Yes
Benefit increased? No
Output the schedule of each BESS
FIGURE 2. ITERATIVE DP OPTIMAL BESS SCHEDULING METHOD
Iterative Dynamic Programming Optimal BESS Scheduling Algorithm As shown in Figure 2, in the iterative dynamic programming optimal BESS scheduling algorithm, with the other BESSs operated at each stage (namely, time interval) according to the presently recorded charging and discharging schedules, the charging and discharging schedule of each BESS i is determined by the forward DP method. Test Results and Discussions The proposed method to optimize the VPP operation is tested on the distribution network shown in Figure 3. The capacity rating summed up for all transformers is 60 MVA, the nominal voltage is 22.8 kV, and the current capacity and apparent power rating of each feeder are 437 A and 17.26 MVA respectively. As seen that there are three feeders used to supply power to the commercial, industrial and residential areas respectively with three BESS at buses 5, 10 and 16 and PV plant at bus 3. Without use of DR scheme and BESS, the original daily load curves of the three areas, the total system loads and the supplied powers are shown in Figure 5. As seen that the peak load about 37 MW happening at hour 14:00 while the system off-peak load about 25 MW appearing around hour 3:00. Obviously, the VPP should be able to remove some system demand from the peak-load hours to the off-peak load hours. The TOU rates ($/MWh) used are shown in Table 1. The benefits obtained from the optimal VPP operations under 0~ ±50% demands regulable based DR schemes versus different capacities of each BESS are shown in Figure 4. It is seen in Figure 4(a) that the maximum benefit being 228.6 USD/day under the optimal VPP operation would happen as each BESS is operated at capacity 2 MWh and DR scheme is executed at ±50% demands regularly. When the capacity of each BESS is 2 MWh, based on ±10% and ±50% demands regulable respectively, the daily benefits of the VPP obtained by optimizing the BESS schedules and DR scheme are shown in Figure 4(b). As can be seen that the maximum cumulated benefits of both
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Ya-Chin Chang, Rung-Fang Chang
cases all happen at about hour 22:00. After then, due to the demand increases in hours 20:00~24:00 that are removed from the demands within the peak-load hours, the electricity cost increases and thus the benefit decreases accordingly. Commercial Area
Residential Area
Industrial Area
Feeder 1
Feeder 2
1
Feeder 3
2
3
BESS 2 2
8
BESS 1
10
1
9
4
11
5
PV
13
14
12
BESS 3 6
15
3
7
16
FIGURE 3. THREE FEEDERS DISTRIBUTION NETWORK BASED VPP TABLE 1. RATES FOR TIME OF USE
Time of Use Energy price ($/MWh)
Peak (09-20) 36.34
Off-peak1 (01-08) 21.00
Off-peak2(21-24) 27.48
X: 0.5 Y: 2 Z: 228.6
250
Benefit (USD/Per-day)
200 150 100 X: 0.5 Y: 0 Z: 121.9
50 0
X: 0 Y: 2 Z: 37.5
-50 -100 2 1.5 1
Capacity of BESS (MWh)
0.5 0
0.05
0
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Regulable Percentage of System Load
(A) 300 250 DR with 10% system load regulable DR with 50% system load regulable
Benefit (USD)
200 150 100 50 0 -50 -100
0
5
10
15
20
25
Hour
(B) FIGURE 4. (A)BENEFITS OBTAINED FROM DIFFERENT DEMANDS REGULABLE PERCENTAGES BASED DR VS. DIFFERENT CAPACITIES OF BESS AND (B) UNDER THE CAPACITY OF EACH BESS BEING 2 MWH, THE BENEFITS OBTAINED WITH ±10% AND ±50% DEMANDS REGULABLE FOR DR SCHEMES RESPECTIVELY
40
40
35
35
30
30
Power (MW)
Power (MW)
Optimal Virtual Power Plant Operation for Promoting Energy Efficiency of Distribution Systems
25 20 15
49
25 Original System Load PV Generation Regulated System Load Supplied Power
20 15
Original System Load
10
PV Generation
10
Regulated System Load
0
5
Supplied Power
5
0 0
5
10
15
20
25
0
5
10
15
20
25
Hour
Hour
(B) (A) FIGURE 5. THE LOAD PROFILES FOR THE OPTIMAL VPP OPERATIONS UNDER THE CAPACITY OF EACH BESS BEING 2 MWH CORRESPONDING TO (A) ±50% (B) ±10% DEMANDS REGULABLE FOR DR SCHEME 2 1.8
0.2
BESS1 BESS2 BESS3
1.6 0.1
Energy (MWh)
Charging/Discharging Power (MW)
0.3
0
-0.1
BESS1 BESS2 BESS3
-0.2
1.4 1.2 1 0.8 0.6
-0.3
-0.4
0.4 0
5
10
15
Hour
(A)
20
25
0.2
0
5
10
15
20
25
Hour
(B)
FIGURE 6. UNDER THE CAPACITY OF EACH BESS BEING 2 MWH AND ±50% DEMANDS REGULABLE FOR DR SCHEME, (A) CHARGING/ DISCHARGING SCHEDULE OF EACH BESS AND (B) VARIATION OF THE ENERGY SHORED IN EACH BESS
Under the capacity of each BESS being 2 MWh, the load profiles resulted from the optimal VPP operations with ±50% and ±10% demands regulable based DR schemes respectively are shown in Figure 5. With the optimal charging process of the three BESS between hours 01:00 to 08:00 and the discharging process after hour 08:00, it can be found that, comparing Figure 5(a) and Figure 5(b), the maximum difference between the results by optimizing the DR schemes based on ±50% and ±10% respectively is that the the levels of decreased system loads and the supplied powers. Besides, under the VPP optimally operated with ±50% demands regulable based DR scheme and the capacity of each BESS being 2 MWh, the charging/discharging schedules of each BESS and the variations of the energy stored in each BESS can be found in Figure 6(a) and Figure 6(b) respectively. Conclusions In order to maximize the benefit of the power supply of the distribution system, an optimal VPP operation approach is proposed in this paper to determine the best charging/discharging schedule of each BESS and the DR scheme at the same time. The validity of the proposed method is confirmed with the results that the VPP is able to bring about the maximum benefit to the system owner by removing certain amount of demand power from the loads that participates in DR contract and, at the same time, charging BESSs during the times with lower TOU rates and discharging BESSs during the times with higher TOU rates. ACKNOWLEDGMENT
The authors gratefully acknowledge the financial supports for this work from National Science Council of Taiwan under contract MOST 103-2221-E-230-010.
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