Unit Commitment Model Considering Flexible Scheduling of Demand Response for High Wind Integration
Abstract
:1. Introduction
- (1)
- What is the effect of DR on the system operation flexibility of a power grid with large-scale renewable energy integration?
- (2)
- How can the effectiveness be maximized at minimum cost using the flexible scheduling strategies of DR considering the coupling characteristics of centralized, controlled DR resources?
- (3)
- Which characteristic of DR will affect the flexible schedule performance and what is the turnkey? What are the impacts of the transmission constraints?
2. Problem Definition
2.1. Stochastic Unit Commitment
2.2. Demand Flexibility
- (1)
- Constraints for the first stage:
- minimum onsite hours called once;
- maximum times called during a defined period;
- minimum/maximum responsive capacity.
- (2)
- Constraints for the second stage:
- maximum responsive capacity.
- (3)
- Coupled constraints for both stages:
- maximum capacity of DR of the sum of two stages.
3. Problem Formulation
3.1. Objective Function
3.2. Constraints
3.2.1. Power Balance
3.2.2. Network Constraint
3.2.3. Constraints for Conventional Units
3.2.4. Constraints for DR
3.2.5. Non-Negativity
4. Case Study
4.1. PJM5-Bus System
4.1.1. Data Assumption
Unit | (MW) | (MW) | Incremental Cost ($/MWh) | Scn ($) | MDn/ MUn (h) | / (MW/min) |
---|---|---|---|---|---|---|
G1 | 22 | 110 | 14 | 450 | 6/6 | 0.45 |
G2 | 20 | 100 | 15 | 900 | 6/6 | 0.42 |
G3 | 100 | 500 | 30 | 300 | 4/4 | 2 |
G4 | 60 | 200 | 40 | 150 | 1/1 | 0.8 |
G5 | 120 | 600 | 20 | 1200 | 6/6 | 2.5 |
DR Aggregators | (MW) | (MW) | (h) | / ($/MWh) | ($/MW) |
---|---|---|---|---|---|
1 | 35 | 3.5 | 4 | 8/20 | 15 |
2 | 25 | 2.5 | 4 | 6/25 | 15 |
3 | 25 | 2.5 | 8 | 5/16 | 15 |
4 | 35 | 3.5 | 8 | 2/23 | 15 |
5 | 20 | 2 | 1 | 10/15 | 15 |
4.1.2. Results and Discussion
(1) DR Scheduling Modes Impact on Costs
Mode | ODR | FDR | SDR | F&SDR (Proposed Model) |
---|---|---|---|---|
Total Cost (103$) | Base (597.85) | −5.37 | −60.05 | −62.32 |
Generation Cost (103$) | Base (540.33) | −11.16 | −7.25 | −11.88 |
Start-up Cost (103$) | Base (0.30) | +0 | +0 | +0 |
Wind Curtailment Cost (103$) | Base (0.59) | −0.56 | −0.59 | −0.59 |
Load not served Cost (103$) | Base (56.63) | +0.56 | −56.63 | −56.63 |
DR Capacity Cost (103$) | Base (0) | +1.27 | +0.62 | +1.21 |
DR operating cost (103$) | Base (0) | +4.52 | +3.80 | +5.57 |
(2) DR Allocation among Aggregators with Different Characteristics: no Transmission Constraints
DR Aggregators | First_s a | Second_s1 b | Second_s2 b | Second_s3 b |
---|---|---|---|---|
1 | 0% | 0% | 0% | 7.13% |
2 | 0% | 0% | 0% | 0% |
3 | 26.32% | 11.48% | 18.41% | 17.59% |
4 | 83.33% | 0% | 0% | 0% |
5 | 0% | 16.96% | 22.97% | 26.31% |
DR Aggregators | (MW) | (MW) | (h) | / ($/MWh) | ($/MW) |
---|---|---|---|---|---|
1 | 35 | 3.5 | 4 | 5/14 | 15 |
2 | 25 | 2.5 | 4 | 5/14 | 15 |
3 | 25 | 2.5 | 8 | 6/15 | 15 |
4 | 35 | 3.5 | 8 | 6/15 | 15 |
(3) Results Considering Transmission Constraints
Mode | ODR | FDR | SDR | F&SDR (Proposed Model) |
---|---|---|---|---|
Total Cost (103$) | Base (1141.40) | −508.76 | −525.95 | −556.52 |
Generation Cost (103$) | Base (529.54) | +30.92 | +35.71 | +35.58 |
Start-up Cost (103$) | Base (0.3) | +0 | +0 | +0 |
Wind Curtailment Cost (103$) | Base (2.80) | −2.76 | −2.80 | −2.80 |
Load not Served Cost (103$) | Base (608.79) | −551.54 | −605.67 | −605.67 |
DR Capacity Cost (103$) | Base (0) | +2.1 | +2.1 | +2.1 |
DR Operating Cost (103$) | Base (0) | +12.50 | +44.69 | +14.24 |
Mode | ODR | FDR | SDR | F&SDR (Proposed Model) |
---|---|---|---|---|
Total Cost (103$) | Base (976.590) | −427.33 | −406.55 | −431.16 |
Generation Cost (103$) | Base (492.66) | +29.71 | +30.51 | +29.81 |
Start-up Cost (103$) | Base (0.6) | −0.3 | −0.3 | −0.3 |
Wind Curtailment Cost (103$) | Base (1.14) | −1.14 | −1.14 | −1.14 |
Load not Served Cost (103$) | Base (482.19) | −468.03 | −472.13 | −472.13 |
DR Capacity Cost (103$) | Base (0) | +2.1 | +2.1 | +2.1 |
DR Operating Cost (103$) | Base (0) | +10.34 | +34.41 | +10.51 |
DR Aggregators | First Stage | Second_s1 | Second_s2 | Second_s3 |
---|---|---|---|---|
1 | 49.67% | 5.12% | 1.58% | 9.44% |
2 | 74.27% | 0% | 0% | 0.13% |
3 | 76.67% | 6.67% | 9.17% | 6.67% |
4 | 90.93% | 0% | 0% | 0% |
5 | 21.81% | 16.37% | 24.47% | 32.82% |
DR Aggregators | First_stage | Second_s1 | Second_s2 | Second_s3 | Second_s4 | Second_s5 |
---|---|---|---|---|---|---|
1 | 35.15% | 0.51% | 0.48% | 0.48% | 0.48% | 2.55% |
2 | 59.44% | 0% | 0% | 0% | 0% | 0% |
3 | 70.83% | 4.17% | 6.46% | 4.17% | 5.40% | 4.17% |
4 | 83.33% | 0% | 0% | 0% | 0% | 0% |
5 | 28.65% | 4.84% | 3.21% | 19.19% | 3.96% | 7.25% |
4.2. IEEE 118 Case
4.2.1. Data Assumption
DR Aggregators | (MW) | (MW) | (h) | / ($/MWh) | ($/MW) |
---|---|---|---|---|---|
1 | 42 | 4.2 | 4 | 8/20 | 15 |
2 | 30 | 3.0 | 4 | 6/25 | 15 |
3 | 30 | 3.0 | 8 | 5/16 | 15 |
4 | 42 | 4.2 | 8 | 2/23 | 15 |
5 | 24 | 2.4 | 1 | 10/15 | 15 |
4.2.2. Results and Discussion
DR Aggregators | First_s | Second_s1 | Second_s2 | Second_s3 |
---|---|---|---|---|
1 | 8.75% | 2.08% | 2.08% | 2.41% |
2 | 10.83% | 0% | 0% | 0% |
3 | 15.42% | 2.08% | 3.07% | 6.25% |
4 | 66.67% | 0% | 0% | 0% |
5 | 4.17% | 4.17% | 4.17% | 8.33% |
5. Conclusions
- (1)
- The tight coupling characteristics of specific DR resources on available time and capacity are considered in the proposed stochastic model. Specifically, if sufficient incentives are paid to consumers, some DR resources can be scheduled both in the first stage as resources on a day-ahead basis to integrate the wind power with lower uncertainty and in the second stage as resources on an intra-day basis to integrate the wind power with higher uncertainty. Flexible DR scheduling can achieve the maximal DR values with the minimal cost, combining the cost advantage of DR on a day-ahead basis and the flexibility advantage of DR on an intra-day basis, which is beneficial with high wind power penetration.
- (2)
- The responsive cost rather than the characteristics of flexibility, including “minimum on-site time” and “minimum responsive capacity”, is the most critical factor, but “minimum onsite hours” plays a more important role when only the characteristic of flexibility is considered.
- (3)
- The first stage DR should be dispatched more frequently when transmission congestion is expected to occur.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Indices:
n | Index for thermal units, n = 1–Ng |
t | Index for time interval, t = 1–NT s: Index for scenarios, s = 1–Ns |
d | Index for DR users, d = 1–Nd |
i, j | Index for buses in the grid, i = 1–Nb, j = 1–Nb |
Gi | Index for conventional units connected to ii |
Di | Index for DR users connected to i. |
Parameters:
Prs,ts | Probability of occurrence of scenario s in interval t |
Windω,t,s | Power output, wind farm ω, in t, s (MW) |
Windω | Capacity, wind farm ω (MW) |
Bij | Line susceptance from bus i to j |
Loadi,t | Forecast demand level without effect of demand response, in t, s (MW) |
TRCij | Transmission limit from bus i to j (MW) |
Pnmax | Maximum output when committed, unit n (MW) |
Pnmin | Minimum output when committed, unit n (MW) |
Rnup | Up-ramp limit, unit n, (MW/interval) |
Rndown | Down-ramp limit, unit n, (MW/interval) |
Permissible real power adjustment, unit n (MW) | |
MDn | Minimum off-site time, unit n, (interval) |
MUn | Minimum on-site time, unit n, (interval) |
MUn | Minimum on-site time, unit n, (interval) |
DRdmin | Minimum demand change on a day-ahead basis, user d (MW) |
DRdmax | Maximum demand change on a day-ahead basis, user d (MW) |
MDTd | DR Minimum on-site time on a day-ahead basis, user d (interval) |
Scn | Start-up costs, unit n |
Ccd | DR capacity costs user d ($/MW) |
DR variable operating cost of increasing consumption on a day-ahead basis, user d ($/MWh) | |
DR variable operating cost of decreasing consumption on a day-ahead basis, user d ($/MWh) | |
DR variable operating cost of increasing consumption on an intra-day basis, user d ($/MWh) | |
DR variable operating cost of decreasing consumption on an intra-day basis, user d ($/MWh) | |
Penaω | Wind curtailment cost, wind farm ω ($/MWh) |
Penal | Load not served cost ($/MWh) |
Decision variables:
un,t | Binary on/off variable, unit n, in t |
pn,t,s | Generation (MW) unit n, in t, s |
s_costn,t | Start-up costs ($), unit n, in t |
Voltage angle, bus i, in t, s | |
DR binary on/off variables, users d in t | |
DR capacity, (MW) user d | |
Demand level growth on a day-ahead basis, user d, in t (MW) | |
Demand level reduction on a day-ahead basis, user d, in t (MW) | |
Demand level growth on an intra-day basis, user d, in t, s (MW) | |
Demand level reduction on an intra-day basis, user d, in t, s (MW) | |
Wind power curtailment, wind farm connected to i, in t, s (MW) | |
Load not served at bus i, in t, s (MW) |
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Wang, B.; Liu, X.; Zhu, F.; Hu, X.; Ji, W.; Yang, S.; Wang, K.; Feng, S. Unit Commitment Model Considering Flexible Scheduling of Demand Response for High Wind Integration. Energies 2015, 8, 13688-13709. https://doi.org/10.3390/en81212390
Wang B, Liu X, Zhu F, Hu X, Ji W, Yang S, Wang K, Feng S. Unit Commitment Model Considering Flexible Scheduling of Demand Response for High Wind Integration. Energies. 2015; 8(12):13688-13709. https://doi.org/10.3390/en81212390
Chicago/Turabian StyleWang, Beibei, Xiaocong Liu, Feng Zhu, Xiaoqing Hu, Wenlu Ji, Shengchun Yang, Ke Wang, and Shuhai Feng. 2015. "Unit Commitment Model Considering Flexible Scheduling of Demand Response for High Wind Integration" Energies 8, no. 12: 13688-13709. https://doi.org/10.3390/en81212390