Smart Service Restoration of Electric Power Systems

Leonardo H. T. Ferreira Neto Electrical Engineering Dept.

Escola de Engenharia de São Carlos - USP São Carlos, Brazil

Benvindo R. Pereira Júnior Electrical Engineering Dept.

Escola de Engenharia de São Carlos - USP São Carlos, Brazil

Geraldo R. M. da Costa Electrical Engineering Dept.

Escola de Engenharia de São Carlos - USP São Carlos, Brazi

Abstract—This paper presents a smart service restoration method for electric power systems. Power system restoration (PSR) is the procedure of restoring the power supply after a power outage. Its objective is to restore the power system rapidly while satisfying all the operation constraints. Although it has been studied and applied most only to electrical distribution systems. The proposed methodology takes account the sub-transmission and distribution systems combined, and considers the objective of minimizing of out-of-service area. The PSR is formulated as a constrained objective optimization problem. Therefore, to solve this problem and obtain feasible solutions of valuable quality, with suitable computational effort, a Tabu Search approach is proposed. Tests were performed on an extended distribution test system, and the results show that the model and methodology are robust and efficient for practical size restoration problem applications.

Index Terms—Electric power systems, heuristic rules, restoration problem, system optimization, Tabu Search.

I. INTRODUCTION Nowadays, along with the development of the Smart Grids

concept, the utilities are focused on attending the increasing customer demand as well as improving the reliability of the power system. Although, in the traditional power industry, power system restoration process was generally designated by a control center, most only based on the operator’s experience. Many researches have been undertaken to solve the service restoration problem, which is extremely important for operation efficiency [1].

The PSR is the process of, after a fault occurrence and isolation of the affected area, transferring as much as possible de-energized loads from out of service areas through the distribution system while satisfying all the operation constraints. The operational configuration target is achieved by switch maneuvers. It is an essential process to utilities in both operation (on-line) and planning (off-line) areas in order to determine the system state and identify schemes to restore/attend the secure system operation, attending the operating constraints. Therefore, determining the feasible load transfer (and load curtail if necessary) solutions represents an important tool to reduce the effects of outages on the power system.

Due to PSR combinatorial nature, complete mathematical models are challenging to establish. A complete mathematical modeling of the restoration problem is presented in [2], where the authors propose the conversion of the original model into a problem of second-order cone programming, solved using tra-

The authors gratefully acknowledge Daimon Engenharia e Sistemas for the support and permitting the use of Interplan® framework.

ditional optimization technique. Although, the results present that for general model, the processing time is considerable for solving the restoration problem.

In order to deal with the processing time, heuristic techniques and expert systems have been developed for hastily determining restoration plans. In [3], the authors present a guided heuristic optimization technique on a binary decision tree using a depth-first search. A genetic algorithm, Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is proposed in [4]. A service restoration problem including a load curtailment heuristic of in-service customers proposed in [5] and [6] and the heuristic proposed embodies procedures based on an operator's experience.

The PSR essential objective is to minimize the of out-of-service area affected by an outages on the power system. Although, other concerns are also introduced to increase the result quality, such as:

i. number of switching operations; ii. type of switches (manual or remote operation);

iii. especial loads prioritization; iv. loss minimization; v. feeders’ load balancing;

vi. distribution system radial topology; vii. power system operational constrains;

viii. service restoration time. As establish in [1] and [2], loss minimization and feeders’

load balancing results minor benefit and may conflict with the essential objectives.

Thereby, this paper presents a smart service restoration method for electric power systems with distributed generation, extending the electric power system, combining sub-transmission and distribution systems, and considers all the essential objectives and constrains.

II. MATHEMATICAL MODEL The service restoration problem is formulated as a mixed

integer non-linear programming problem. The objective is to restore the power supply to the maximum possible out-of-service area and the objective function represents the operational costs . The constraints are related to the power system operational constrains such as source capacity (supply, substations and distributed generation), feeder loading, branch loading, nodal voltage, connectivity of the sub-transmission systems and radiality configuration of the distribution system.

The proposed mathematical model for the PSR is described as follows:

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(1)

subject to:

(2) (3) (4)

(5)

(6)

(7)

(8)

where

Load of section Maneuver operator weight

Decision to maneuver (1) or not (0) distribution switch

Set of sections out-of-service in a system configuration

Set of network buses Set of network branches

Set of lines connected to substation n Set of distribution network sectors

Set of distribution network buses Set of substations Number of distributed generators Minimum voltage level of the feeder

Voltage at bus Maximum voltage level of the feeder

Current of branch

Maximum current allowed through branch

Active power demand at bus Active power generated at bus i Active power demand at bus i

Reactive power injection at bus i Reactive power generated at bus i Reactive power demand at bus i Power output of the n -th DG Nominal capacity of the n -th DG Load at bus i connected to substation n

Losses in branch ij connected to substation n

Capacity of substation n

The objective function considered (1) is to minimize the of out-of-service area (modeled as section ) when an outage occurs in the sub-transmission system, than the search space for this problem is the set of all post-fault network configurations, including the sub-transmission and distribution network configurations.

The operational cost function applies weights, , to each operator applied, as follow:

Distribution system reconfiguration: transference of sections between substations;

Sub-transmission reconfiguration: transference of substations between sub- transmission systems;

Sub-transmission support: closing sub- transmission normally open switches.

The selection of these parameters makes it possible to differentiate between operators and employ preference options of the restoration problem, such as favoring sub-transmission over distribution system operations, or other combination.

The problem constraints are upper and lower voltage limits (2), branch conductors’ capacity (3), the active and reactive node balance equations (4) and (5), distributed generation capacity (6), substation operational capacity (7) and distribution system radiality conditions (4) (5) (8) [7].

III. SOLUTION TECHNIQUE The proposed solution technique is based on [8] enhanced

to solve a broader power system network. The radial distribution system is represented as a forest graph (system switches as graph arcs and the set of loads in between two or more switches as nodes, called section) and modeled using the node depth encoding (NDE) representation [9], where the nodes represent the sectors and the edges connecting the bars represent the switchgear. Figure 1. shows a distribution system with two feeders. Each feeder is represented by a tree formed by solid lines and dashed lines. The edges represented by solid lines symbolize normally closed switches – NC, and dashed edges symbolize normally open switches – NO.

The NDE representation is implemented in a vector containing the nodes, and the corresponding depths, of a graph tree. The order in which the pairs are placed in this list is necessary and can be achieved by a depth-first search algorithm, inserting the pair in the list each time the node is visited by the algorithm.

(a)

(b)

Figure 1. a) Feeders modeled on graphs with two dispersion trees; b) NDE vector of feeders 101 and 104 of Figure 4.

Representing the distribution system by NDE improves the computational efficient of switches maneuvers operations in the distribution system and guarantees the radiality conditions.

Complementing the NDE, the adjacency vector is established for each section of the full electric system. Figure 2. shows the neighborhood of section 8 and its adjacency vector. This representation enables to identify easily the open

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and closed switches during the generation of new network topologies.

(a)

(b)

Figure 2. a) Section 8 sub-graph; b) Section 8 adjacency vector

The proposed model is solved by a tabu search algorithm [10] and the problem is codified with a binary base. The codification structure is illustrated in Figure 3.

Figure 3. Codification structure

Each part of the codification structure represents separately the distribution and sub-transmission systems. All the systems switches are represented in the codification structure along with its status (0 – open, 1 – closed) for each solution generated.

The neighborhood is defined through switches maneuvers operations, considering the connectivity of sectors and radiality of the distribution network.

Therefore, the metaheuristic attempts to change the switches status systematically, generating new solutions by sections transfers between substations, substations transfers between sub-transmission systems and closing loop between sub-transmission systems. The neighborhood generation is defined using a branch exchange technique [11].

The neighborhood is generated from a current solution (seed) and the search starts from the initial network with the faulted section of a sub-transmission line isolated.

In the classical tabu search, the tabu list (TL) stores forbidden (tabu) attributes during k iterations, to prevent the searching processes from cycling (endlessly execution of the same sequence of movements by revisiting the same set of solutions) during the search. The TL proposed stores the last k switches maneuvers operations applied.

It is assumed that the location and capacity of DGs are already in the optimal conditions according to previous planning and the DGs are featured with voltage and frequency controllers (such as co-generation systems).

In order to evaluate the system operation state the Newton Raphson power flow algorithm is applied. The convergence criteria adopted is either a maximum number of iterations or until the best solution found does not modify for a number of iterations.

IV. TESTS AND RESULTS The proposed algorithm has been tested on the power

system network represented in Figure 4. , adapted from [8]. The test system had a distribution system and a sub-transmission system. The distribution system had 53-node, 3 substations, 50 load nodes, active power demand of 45,668.7 kW and a reactive power demand of 22,118.24 kVAr, 4 distributed generation nodes with active power supply of 4 MW, reactive power supply of 2MVAr and nominal voltage was 13.8 kV. The sub-transmission system had 14-node, 8 load nodes, active power demand of 38,55 kW, reactive power demand of 18,27 kVAr and nominal voltage was 69 kV. Its data is presented in TABLE I. and in Appendix A.

TABLE I. NODE DATA

Node Active power (kW)

Reactive Power (kVAr)

Node Active power (kW)

Reactive Power (kVAr)

1 2910.60 1409.64 30 1801.80 872.64 2 1039.50 503.43 31 485.10 234.93 3 485.10 234.93 32 1178.10 570.57 4 762.30 369.22 33 2009.70 973.36 5 1801.80 872.64 34 831.60 402.79 6 485.10 234.93 35 623.70 302.07 7 693.00 335.64 36 207.90 100.72 8 1316.70 637.71 37 1455.30 704.86 9 831.60 402.79 38 762.30 369.21

10 2009.70 973.36 39 693.00 335.64 11 207.90 100.72 40 970.20 469.85 12 1247.40 604.14 41 623.70 302.07 13 762.30 369.22 42 831.60 402.79 14 693.00 335.64 43 900.90 436.36 15 970.20 469.85 44 970.20 469.85 16 1316.70 637.71 45 554.40 268.50 17 485.10 234.93 46 1247.40 604.14 18 831.60 402.79 47 693.00 335.64 19 970.20 469.85 48 554.40 268.50 20 554.40 268.50 49 346.50 167.78 21 1247.40 604.14 50 554.40 268.50 22 762.30 369.22 B169 550.00 270.00 23 693.00 335.64 B176 6000.00 3000.00 24 346.50 167.78 B178 6000.00 3000.00 25 623.70 302.07 B183 5000.00 2000.00 26 831.60 402.78 B192 10000.00 5000.00 27 1039.50 503.42 B193 5000.00 3000.00 28 485.10 234.93 B205 3000.00 1000.00 29 970.20 469.85 B206 3000.00 1000.00

Figure 4. shows the normal operation of the system with a configuration of open (dashed lines) and closed switches (solid lines), forming a radial topology for the distribution system, a radial topology for sub-transmission systems with the sources at bar B177 and B189 and a meshed topology for the sub-transmission system with the source at bar B168. The nominal capacity of the substations at node 101 is 33,400 kVA, 102 is 22,000 kVA, and 104 is 30,000 kVA. The lower and upper voltage limits were 0.95 p.u. and 1.00 p.u., respectively.

For the following tests, any switch could be operated, all of the switches were of the same type and there were no priority loads.

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Figure 4. Topology of the test system

1) Fault at line between B169 and B165: In this case, a fault at line between B169 and B165 was analyzed. As such, the switch between these bars was isolated, disconecting the substation T1 from supply. The operators weights applied where , and , favoring distribution system reconfiguration over sub-transmission support and sub-transmission reconfiguration. The following results were obtained: the switches in circuits B165-B205 where closed restoring the substation, totalizing 21,97MW and 10,31MVAr restored. Despite the fact of operatos weighting, the solution was obtained in the first iteration, when the neighbor created by the sub-transmission support solved the fault, restoring all the out-of-service area.

2) Fault at line between B168 and B169: In this case, a fault at line between B168 and B169 was analyzed. As such, the switch between these bars was isolated, overloadind the branch between bars B186 and B169 to 193.30%. The operators wheights applied where , and

, favoring distribution system reconfiguration over sub-transmission support and sub-transmission reconfiguration. The following results were obtained: the switches in circuits B165-B205, 104-22 where closed and the switches in circuits 9-22 where opend. Restoring 2,42MW and 0,98 MVAr from T1 to T3 and restoring 19,55 MW and 9,33 MVAr from T1 to T2. In this test, the operatos weighting affected the convergence, applying first the distribution reconfiguration and, than, in the second iteration, applying the sub-transmission reconfiguration, restoring all the out-of-service area.

All the study cases, the voltage was above the lower limit, substations and distributed generators operated within their limits.

V. CONCLUSION In this paper PSR is formulated as a constrained objective

optimization problem taking account the electric the sub-transmission and distribution systems combined and considering the minimization of the out-of-service area.

The proposed TS algorithm is very efficient treating the proposed problem, solving the optimization with flexibility of which operation is preferable, allowing the PSR study to be adjustable for the utility needs.

The simulation results show excellent performance with regard to the quality of the solution and demonstrate that the proposed approach is flexible, robust and computationally efficient.

APPENDIX A TEST SYSTEM DATA

TABLE II. CIRCUIT DATA

Initial node

Final node

Resistence (Ω)

Reactance (Ω)

Current limit (A)

101 1 0.0543 0.0675 600 101 3 0.0412 0.0524 600

4 3 0.0603 0.0749 600 7 4 0.0483 0.0600 600 5 4 0.1472 0.1499 250 8 7 0.0603 0.0749 600 6 5 0.1179 0.1201 250 9 1 0.0603 0.0824 600 2 1 0.1472 0.1499 250

10 9 0.3388 0.3449 250 102 14 0.0725 0.0901 600 15 14 0.1769 0.1802 250 16 15 0.1326 0.1350 250

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102 11 0.0543 0.0675 600 12 11 0.0603 0.0749 600 13 12 0.3194 0.2202 150 20 19 0.2281 0.1572 150 19 18 0.1828 0.1260 150 18 17 0.2968 0.2046 150 17 9 0.1256 0.1060 400 21 18 0.1472 0.1499 250

104 21 0.0730 0.0617 400 104 22 0.1769 0.1802 250 22 9 0.2208 0.2248 250 23 22 0.2507 0.1729 150 24 23 0.2054 0.1416 150 25 24 0.1594 0.1099 150 8 25 0.2054 0.1416 150

27 8 0.1769 0.1802 250 26 27 0.2507 0.1729 150 28 27 0.2281 0.1572 150 28 6 0.3655 0.2520 150

104 30 0.0543 0.0675 600 29 30 0.2281 0.1572 150 43 30 0.1916 0.1950 250 37 43 0.1828 0.1260 150 37 43 0.1828 0.1260 150 31 37 0.1367 0.0942 150 10 31 0.2281 0.1572 150 43 13 0.1095 0.0925 400 45 12 0.0483 0.0600 600 44 45 0.0421 0.0524 600 38 44 0.0603 0.0749 600 39 38 0.0809 0.0824 500 32 39 0.2968 0.2046 150 33 39 0.1326 0.1350 250 8 33 0.2208 0.2248 250

33 34 0.1367 0.0942 150 34 35 0.1574 0.1099 150 35 36 0.1594 0.1099 150 40 41 0.2741 0.1890 150 16 40 0.1828 0.1260 150 42 41 0.2741 0.1890 150 48 42 0.1828 0.1260 150 49 48 0.2741 0.1890 150 50 49 0.1594 0.1099 150 47 42 0.0911 0.0769 400 46 47 0.1472 0.1499 250 14 46 0.1002 0.0846 400 35 40 0.1301 0.0897 150 10 38 0.1828 0.1260 150 28 50 0.1126 0.0776 150

B177 B176 0.2280 0.1570 100 B178 B183 0.2280 0.1570 100 B177 B178 0.1400 0.0785 250 B176 B183 0.1400 0.0785 100 B176 B168 0.1400 0.0785 400 B183 B169 0.2280 0.1570 100 B168 B169 0.1400 0.0785 300 B169 B165 0.1400 0.0785 800 B168 B205 0.2280 0.1570 800 B165 B205 0.4560 0.3140 195 B205 B206 0.4560 0.3140 800 B206 B189 0.4560 0.3140 800 B189 B167 0.1400 0.0785 800 B189 B192 0.2736 0.1884 300 B192 B193 0.1824 0.1256 800 B193 B166 0.2280 0.1570 85 B166 B178 0.2280 0.1570 800

TABLE III. DG CAPACITIES

DG Node Capacity (MW)

Power factor

1 7 1.00 0.9 2 17 1.00 0.9 3 44 1.00 0.9 4 77 1.00 0.9

TABLE IV. TRANSFORMERS

Transformers Initial node

Final node

Capacity (MVA)

X (pu)

Voltage (kV)

T1 B165 101 45 0.05 69/13.8 T2 B167 102 40 0.05 69/13.8 T3 B166 104 20 0.05 69/13.8

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