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Generators startup sequence plays a significant role in achieving a suitable and effective restoration strategy. This paper outlines an ant colony search algorithm in order to determine the generator starting times during the bulk power system restoration. The algorithm attempts to maximize the system generation capability over a restoration period, where the dynamic characteristics of different types of units and system constraints are considered. Applying this method for the 39-bus New England test system, and comparing the results with backtracking-search and P/t methods, it is found that proposed algorithm improved generation capability.

In recent years, power systems are operated fairly close to their limits primarily due to economic competition and deregulation. At the same time, they have increased in size and complexity. Both factors increase the risk of major power outages [

In the case of a total system outage, system restoration must begin from the black-start unit(s). Black-start units are units that do not require off-site power to start, such as: diesel generator sets and hydroelectric units [

A number of studies have been carried out to determine generators start-up sequence [

The goal of the proposed method is to maximize the total system generation capability over a restoration period whilst considering the corresponding static and dynamic constraints including the cranking power, critical maximum interval, and critical minimum interval constraints.

In the following sections, first the problem formulation is presented. The proposed ACS algorithm is then described. Finally, the simulation results for a 39-bus New England test system are illustrated and compared with those obtained by backtracking search and p/t methods.

During total blackout, the initial power source to crank non-black-start generators must be found. The initial source of power is provided by starting black-start generator quickly. For non-black-start generators, different physical characteristics and the starting requirements in each power station need to be considered. Table

Startup characteristics of different types of units.

Unit type | Crank power | Critical maximum interval | Critical minimum interval |
---|---|---|---|

Black-start (CT or Hydro) | No | No | No |

Drum | Yes | Yes | No |

SCOT | Yes | No | Yes |

Figure

restartup time,

synchronization time,

time to reach minimum load,

time to reach maximum load.

Startup timing for a typical unit.

Finding proper cranking priorities for non-black-start units can increase the system MW output. The goal is to maximize

The constraints to be considered in this problem are as follows:

maximum MW output of units,

reactive power over and under excitation limits (from generator capability curve),

start-up times,

start-up and house-load MW requirement,

ramping rates.

To deliver cranking power from black-start to non-black-start units, it is necessary to build transmission paths between them. The number of required switching as well as limitations of the units MVAR are the two most important issues in path selection. Wherever units MVAR limitations permit, the shortest path (i.e., the path requiring the minimal number of switching action) between the supplying unit and the non-black-start unit is selected. A heuristic algorithm, called

Load restoration and power supply must coincide with each other to guarantee the stability of system frequency and voltage, because the restoration of power plants and that of loads are synchronous.

Ant Colony Optimization (ACO) method handles successfully various combinatorial complex problems. Dorigo, inspired by the behavior of real ant colonies, proposed ACO method for the first time in his Ph. D. thesis [

Recently a large number of different ACO algorithms have become available. All of these algorithms contain a strong exploitation of the best solutions found during the search; the most successful of which add explicit features to the search in order to avoid premature stagnation. The main differences between the various ant system extensions consist of the techniques used to control the search process. ACS is reported to be the most aggressive of the ACO algorithms [

In power systems, the ACO has been applied to solve the optimum generation scheduling problems [

Once the search space of generators start-up problem is established using multi-process decision making concept, the ACS algorithm can be applied to problems such as traveling salesman problem (TSP). TSP defines the task of finding a tour of minimal total cost given a set of fully connected nodes and costs associated with each pair of nodes. The tour must be closed and contain each node exactly once. This can be represented as a sequence of

The sequence in which generators are started up during system restoration is important since different sequences yield different MWH outputs. Figure _{k}

Search space of ant sequence determination.

The two main phases of the ACS algorithm constitute the ants’ solution construction and the pheromone update.

In this algorithm, ants find solutions starting from a start node and move to feasible neighbor nodes in the process of ants’ generation and activity. During the process, information collected by ants is stored in the so-called pheromone trails. During the process, ants can also release pheromone while building the solution (local pheromone trail update) or after the solution is built (global pheromone trail update). An ant-decision rule, made up of the pheromone and heuristic information, governs ants’ search toward neighbor nodes stochastically. Pheromone evaporation is a process of decreasing the intensities of pheromone trails over time. This process is used to avoid local convergence and explore more search areas.

Sequences are constructed by applying the following simple constructive procedure to each ant: _{0}

In ACS, following each iteration, only one ant (the best-so-far ant) is allowed to add pheromone such that the new pheromone trail becomes a weighted average between the old pheromone value and the amount of pheromone deposited. Thus, the update in ACS is implemented by the following equation:

where

In addition to the global pheromone trail updating rule, in ACS the ants use a local pheromone update rule that they apply immediately after having crossed a sequence

The flowchart of the ACS algorithm for optimal generators start-up is shown in Figure

The flowchart of the ACS algorithm for optimal generators start-up.

Good convergence behavior of ACS algorithm can be achieved by suitable selection of parameters. The parameters that affect the computation of ACS algorithm directly or indirectly include ant number,

The settings are done for 39-bus New England system whose characteristics are given in next section. They are tested for each parameter taking several values within a boundary limit, all others being constant. More than 10 simulations for each setting are performed in order to achieve some statistical information about the average evolution. The range of interval considered for each parameters are

The initial trail level is set as

In this section, the proposed method is used for restoration of 39-bus New England system (see Figure

One line diagram of 39 bus New England test system.

The results of proposed method are compared with results of P/t and backtracking search method. In P/t method, the priority for generators start-up is determined based on the ratio of MW capability and the time required for the plant to be synchronized with the system, whose, the generator that its P/t is greater than others has priority for start-up [

Figure

Performances of ACS algorithm during starting sequence optimization.

Tables

Generator start-up sequence and selected path with the proposed method.

Unit no. | Bus no. | Cranking unit | Start time | Selected path for energization |
---|---|---|---|---|

1 | 30 | Black start | 0 : 00 | — |

6 | 35 | Black start | 0 : 00 | — |

4 | 33 | 6 | 0 : 10 | (35-22), (22-21), (21-16), (16-19), (19-33) |

10 | 39 | 1 | 0 : 15 | |

7 | 36 | 6 | 0 : 20 | (22-23), (23-36) |

2 | 31 | 6 | 0 : 30 | (16-15), (15-14), (14-4), (4-5), (5-6), (6-31) |

3 | 32 | 4 | 0 : 40 | (33-19), (14-13), (13-10), (10-32) |

5 | 34 | 4 | 0 : 45 | (19-20), (20-34) |

8 | 37 | 10 | 2 : 00 | (2-25), (25-37) |

9 | 38 | 10 | 3 : 20 | (1-27), (27-26), (26-29), (29-38) |

Generator start-up sequence and selected path with the backtracking search method.

Unit no. | Bus no. | Cranking unit | Start time | Selected path for energization |
---|---|---|---|---|

1 | 30 | Black start | 0 : 00 | — |

6 | 35 | Black start | 0 : 00 | — |

4 | 33 | 6 | 0 : 10 | (35-22), (22-21), (21-16), (16-19), (19-33) |

7 | 36 | 6 | 0 : 20 | (35-22), (22-23), (23-36) |

8 | 37 | 1 | 0 : 20 | (30-2), (2-25), (25-37) |

5 | 34 | 4 | 0 : 40 | (19-20), (20-34) |

3 | 32 | 4 | 0 : 50 | (16-15), (15-14), (14-13), (13-10), (10-32) |

2 | 31 | 4 | 0 : 50 | (10-11), (11-6), (6-31) |

10 | 39 | 8 | 1 : 40 | (2-1), (1-39) |

9 | 38 | 8 | 3 : 30 | (25-26), (26-29), (29-38) |

Generator start-up sequence and selected path with the P/T method.

Unit no. | Bus no. | Cranking unit | Start time | Selected path for energization |
---|---|---|---|---|

1 | 30 | Black start | 0 : 00 | |

6 | 35 | Black start | 0 : 00 | |

7 | 36 | 6 | 0 : 20 | (35-22), (22-23), (23-36) |

8 | 37 | 1 | 0 : 20 | |

5 | 34 | 6 | 0 : 30 | (22-21), (21-16), (16-19), (19-20), (20-34) |

4 | 33 | 7 | 1 : 10 | (19-33) |

2 | 31 | 7 | 1 : 10 | (16-15), (15-14), (14-4), (4-5), (5-6), (6-32) |

3 | 32 | 7 | 1 : 20 | (14-13), (13-10), (10-32) |

10 | 39 | 8 | 1 : 40 | (2-1), (1-39) |

9 | 38 | 8 | 3 : 30 | (25-26), (26-29), (29-38) |

Figure

Generation capability of 39-bus New England system.

During the first 800 minutes of system restoration, the system generation capability for the proposed method, backtracking search method, and P/t method are 51402, 48535, and 46946 MWH, respectively. This indicates that determination of optimal sequence for start-up can increase generation capability of the system during system restoration.

These simulation results and other test cases show the improved effectiveness and accuracy of the proposed method in identifying the optimal generator’s start-up sequence.

During restoration of large power system, it is advantageous in most cases to split the power system into subsystems in order to allow parallel restoration of islands, and to reduce the overall restoration time. Within each subsystem, the proposed method can be used to determine optimal starting sequence. Then the subsystems are interconnected and remaining loads are picked up and the system performs its transition to the normal state.

A method for unit start-up sequence determination during system restoration is described in this article. Once the search space of generators start-up problem is established using multiprocess decision-making concept, the ACS algorithm is used to determine the units starting times to maximize the generation capability dispatch during restoration period. The dynamic characteristics of different types of units and system constraints are also considered. The proposed method has been tested on the 39-bus New England test system in order to determine the optimal start-up sequence. The results are then compared with those obtained by the backtracking search method and P/t method, which indicated improved effectiveness and accuracy of the proposed method.