1. Electrical and Computer Engineering Mississippi State University
5th Southeast Symposium on Contemporary Engineering Topics (SSCET), 2014
A Parallel Solution to Stochastic Power System Operation with Renewable Energy
Yong Fu, Ph.D.
Associate Professor
Electrical and Computer Engineering
Mississippi State University
New Orleans, LA
September 19th, 2014

2. Parallel Computing
With development of high performance computing technique, parallel computing technique can significantly improve computational efficiency of optimization problem with utilization of multi-processors and multi-threads.
These improvements cannot be achieved by the architectures of the machines alone, it is equally important to develop suitable mathematical algorithms and proper decomposition & coordination technique in order to effectively utilize parallel architectures

3. Large Scale, Non-Convex, Mixed Integer Nonlinear Problem
A Typical Power System Operation Problem
– Security Constrained Unit Commitment
Objective Function – Minimize
Generation and startup/shutdown costs
Generating Unit Constraints
Unit 1
Unit 2
Unit 3
Generation capacity
Minimum ON/OFF time limits
Ramping UP/DOWN limits
Must-on and area protection constraints
Forbidden operating region of generating units
System Operation Constraints
Power balance
System reserve requirements
Power flow equations
Transmission flow and bus voltage limits
Limits on control variables
Limits on corrective controls for contingencies
Large Scale, Non-Convex, Mixed Integer Nonlinear Problem

4. Security-Constrained
Who Use SCUC and How?
ISOs: PJM, MISO, ISO New England, California ISO, New York ISO and ERCOT
Day Ahead Market (DAM) determines the 24-hourly status of the generating units for the following day based on financial bidding information such as generation offers and demand bids.
Day Ahead UC for Reliability (RUC), which focuses on physical system security based on forecasted system load, is implemented daily to ensure sufficient hourly generation capacity at the proper locations.
Look-Ahead UC (LAUC), as a bridge between day-ahead and real-time scheduling, constantly adjusts the hourly status of fast start generating units to be ready to meet the system changes usually within the coming 3-6 hours.
Real-Time Market (RTM) further recommits the very fast start generating units based on actual system operating conditions usually within the coming two hours in 15-minute intervals.
GENCOs
TRANSCOs
ISO
Security-Constrained
Unit Commitment
DISTCOs
ISO (SCUC) and Market Participants

5. Stochastic SCUC
In stochastic programming, the decision on certain variables has to be made before the stochastic solution is disclosed, whereas others could be made after.
The set of decisions is then divided into two groups:
A number of decisions are made before performing experiments. Such decisions are called first-stage decisions and the period when these decisions are made is called the first stage.
A number of second-stage decisions are made after the experiments in the second stage.
Stochastic models containing above two groups of variables, first-stage and second-stage decision variables, are called two-stage stochastic programming.

6. Stochastic SCUC --- Example
Cases
Equipment Outage
Wind
(WM)
Load (MW)
Base case - 20
100
Scenario 1 G3 15
105
Scenario 2 L2 23 95 G1
13 $/MWh
40MW~80MW 1 2 G3
16 $/MWh
10MW~40MW
L1 75MW G2
42 $/MWh
15MW~ 40MW
L2 75MW
Load
G3 can adjust dispatches by 5 MW
G2 is quick-start unit with 30 MW QSC W
System
Base Case Scenario Scenario 2
80 MW
75 MW
? MW
0 MW
0 MW
0 MW
Solution 1
50 MW
52.5 MW
75 MW
0 MW
15 MW
? MW
50 MW
100 MW
52.5 MW
105 MW
95 MW
20 MW
15 MW
23 MW
Base Case Scenario Scenario 2
65 MW
60 MW
52 MW
20 MW
15 MW
0 MW
42.5 MW
52.5 MW
75 MW
Solution 2
0 MW
30 MW
0 MW
42.5 MW
100 MW
52.5 MW
105 MW
95 MW
20 MW
15 MW
23 MW

7. Current Work
Amdahl’s law: an upper bound on the relative speedup achieved on a system with multi-processors is decided by the execution time of the application operating sequentially.

8. Proposed Approach
Structure of Algorithm: Scenario-based stochastic model is adopted to analyze the uncertainties of load and wind energy in this paper. Instead of master-and-slave structure, UC and OPF subproblems are solved simultaneously in the proposed parallel calculation method.
Convergence performance: In an iterative solution process, the number of iterations affects the overall computational time. Several convergence acceleration options, including initialization and update of penalty multipliers, truncated auxiliary problem principle and trust region technique, are used to improve the convergence performance and efficiency in a scenario-based study.

9. Decomposition Strategy
Mathematically, the stochastic SCUC can be formulated as a mixed integer programming (MIP) problem as shown in
Variable Duplication Technique
Augmented Lagrangian Method

10. Algorithms for Parallel Solutions
Auxiliary Problem Principle (APP) Method
Diagonal Quadratic Approximation (DQA) Method
Alternating Direction Method of Multipliers (ADMM)
Analytical Target Cascading (ATC) Method

11. Iterative Solution Procedure
Decomposition structure:
Two separated auxiliary problem:
Given values
from the previous iteration
Decision variables for the current iteration

12. Case Study – IEEE 118-bus Testing System
Case 1: Deterministic case
Case 2: Stochastic case with 3 scenarios
54 thermal units
3 wind farms
118 buses
186 branches

13. Deterministic Case Study
The converged result is obtained after 39 iterations.
Unit 36 at Hour 5
Unit 45 at Hour 5
Unit 36 at Hour 21
Unit 45 at Hour 21

14. Deterministic Case Study
Items
Centralized
SCUC
Parallel
Changes
Total Cost ($)
1,583,700
1,584,997
+0.08%
Time (Seconds) 19 8
-58%

15. Stochastic Case Study (3 scenarios)
Items
Centralized SCUC
Parallel SCUC
Changes
Cost ($)
1,582,840
1,583,565
+0.046%
Time (Seconds)
1,083 20
-96%

16. Case Study – A 1168-bus Power System
A practical 1168-bus power system with 169 thermal units, 10 wind farms, 1474 branches, and 568 demand sides.
It could be nearly impossible to get a near-optimal stochastic SCUC solution for this system by applying a traditional centralized SCUC algorithm.
However, the proposed parallel stochastic SCUC algorithm provides solutions.
Unit 8 at Hour 1

17. Case Study – A 1168-bus Power System
# of Scenarios
# of Iteration
Total Time (sec.)
315
109.55 1
330
146.06 2
299
139.31 3
327
163.47 4
277
142.28 5
278
140.28 6
248
139.52 7
243
130.94 8
242
133.25 9
237
148.33 10
231
131.95

18. Conclusions
The proposed stochastic SCUC approach minimizes the operation cost of system by possibility expectation of each scenarios, which can adaptively and robustly adjust generation dispatch in response to constraints in different scenarios.
In comparison with traditional stochastic SCUC, optimal power flow problem does not have to wait for unit commitment decision, both problems can be solved simultaneously, which is more computational efficient in both day-head and real-time power markets.
The ideas can be applied to various power system applications: state estimation, economic dispatch, and planning.

19. Thanks !