1. Introduction
The development of new technologies in power systems has led to more flexible and robust networks; nevertheless, the risk of a total power system blackout is still present. There are many situations that may cause power system blackouts such as transmission line tripping and overloading, failure of protection or control systems, voltage collapse and cyber attacks, among others [
1]. Power system blackouts around the world, such as the 2003 North American blackout [
2], 2006 European blackout [
3], 2007 Colombian blackout [
4], and 2013 Indian blackout [
5] bring about great economic losses and may even endanger human lives [
6]. Despite all efforts to prevent their occurrence, the risk of blackouts is inherent in complex power systems; therefore, counting with proper methodologies for system restoration is of paramount importance for power system planners and operators.
Electric power generation units are divided in two groups based on the required power to start up: BS units that can start with their own internal resources (which include hydro, diesel, and gas turbine units [
7]), and NBS units that require external power sources for starting up [
8]. The restoration of a power system begins with BS units, which provide the initial power necessary to start up the NBS units. At the same time, as new units are started up increasing the availability of power generation, the loads are reconnected to maintain the stability of the power system [
9].
Power system restoration following a blackout is one of the most important tasks of power system operators at control centers. It is a complex process aimed at setting the system back to normal operation after an extensive outage. The experience learned from historical blackouts has demonstrated that an efficient power system restoration plan is of utmost importance [
10]. Generally, a common approach to the restoration process consists of three phases: the start-up of generators, the re-energizing of the network, and the restoration of load. The common thread linking each of these stages is the generation availability at each restorative stage.
Researchers have worked towards new models and solutions to solve the optimal generation start-up sequence, which is the most important feature of the restoration problem. In [
11], an ant colony optimization algorithm is proposed to determine the optimal generation start-up sequence during bulk power system restoration. In this case, the authors intend to maximize the system generation capacity over the restoration period considering the characteristics of different types of generation units and system constraints. In [
12], a firefly optimization algorithm is implemented to find the optimal starting generation sequence that minimizes the overall restoration time of a power system. In [
13], a genetic algorithm is used to obtain the optimal unit restoration sequence taking into account a decreasing trend of unit start-up efficiency. In [
14], a backtracking algorithm is adopted to determine the best unit restarting sequence considering a two-layer restoration process. The aforementioned heuristic methods provide good solutions to the restoration problem; nonetheless, their computational complexity require more time than the available during the restoration process; also, the achievement of a global optimal solution is not guaranteed. On the other hand, knowledge-based system approaches such as the ones presented in [
15,
16] require special software tools for which the maintenance and support are often impractical for the power industry. Some conventional optimization methods have also been proposed to provide more accurate solutions to the optimal restoration problem of power systems. In [
17], the authors solve the generation start-up sequence and load pick up through a branch-and-bound and interior point method to provide an optimal skeleton-network restoration. In [
18], the authors propose the integration of microgrids within the back-start optimization problem. In this case, the uncertainties of the microgrid black-start resources are modeled by discretizing the probability distribution of the forecast errors. A mixed integer linear programming model is implemented to solve the generator start-up sequence. In [
19], the authors propose a distributed black-start optimization method for global transmission and distribution networks. In this case, the global black-start optimization problem is divided in several sub-problems in transmission and distribution networks taking advantage of distributed generation. Other methodologies to solve the optimal stat-up sequence for system restoration include bilevel optimization [
9], dynamic programming [
20], mixed-integer linear programming [
21], Lagrangian relaxation [
22], and Benders decomposition [
23].
Depending on the structure and characteristics of the power system, its restoration process may be different. On the one hand, in power systems with a high number of BS units, the power system is restored quickly due to the availability of sufficient initial power resources. On the other hand, in power systems with a limited number of BS units, the system restoration results are more complicated and time consuming. In this research, the restoration of power systems with a limited number of BS resources and available renewable power plants is discussed. The main contributions of this paper are twofold: (i) it provides a novel mixed integer linear programming approach to solve the optimal generation start-up power system restoration problem, and (ii) it considers the effect of non-conventional renewable energy sources (NCRES) within the restoration process.
Table 1 presents a brief account of several methodologies applied to the optimal generation start-up problem, where CG and MIQP stand for conventional generation and mixed integer quadratic programming, respectively. Note that the proposed approach is the only one that simultaneously considers CG, NCERS, and BESS. It is worth mentioning that BESS have already been considered in start-up methodologies such as in [
24,
25]; nonetheless, in these works the authors integrate BESS in the black-start problem from the standpoint of the expansion planning aimed at improving the system resiliency, and not from an operative perspective, as carried out in this paper.
This paper is organized as follows:
Section 1 provides an introduction and literature review regarding the power system restoration problem.
Section 2 describes the conventional and non-conventional generation start-up strategy.
Section 3 displays the proposed mathematical formulation for the generation start-up problem.
Section 4 offers the test and results performed on the IEEE-39 RTS test system evidencing the impact of considering NCRES and battery energy storage systems (BESS) in the restoration process; finally,
Section 5 presents the conclusions.
2. Conventional and Non-Conventional Generation Start-Up Strategies
NCRES have significantly increased their presence in electric power systems; therefore, such technologies are more frequently integrated into power system planning and operation studies [
28]. This section presents the main guidelines that must be considered when integrating NCRES into a restoration process.
The objective of the methodology is to maximize the generation capacity of the system and minimize the non supplied energy in a blackout.
Before starting the restoration process, a preliminary analysis should be carried out to identify the cause of the event as well as available and unavailable resources. Knowing this before starting the system restoration will make the process more effective.
BS units are the first ones to enter the system. For these units, a start-up time equal to zero is considered in the model.
BESS will serve as BS units and will aim at bringing cranking power to NBS units to accelerate their start-up. They will also contribute to the normalization of priority loads.
A priority order must be considered when performing the service restoration. There are priority loads that must be attended first such as control centers, aqueducts, hospitals, and substations.
NCRES are considered in this methodology as NBS units; however, due to the benefits of their control systems; their power rise time is considered to be much less than that of conventional generators. With this fact, it will be assumed that the start-up of renewable resources are of the step type.
Conventional NBS units can be started if they meet minimum or maximum start-up times, depending on the technical characteristics of the unit. Further, they require minimum starting power; that is to say, generation units will only be able to start until there is a power in the system equal to or greater than their declared starting power.
NBS units based on NCRES can start if they meet the following conditions:
- -
Minimum starting power.
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Frequency stability to events in the restoration process. The starting of NCRES takes place when there is minimal inertia in the system. This inertia value is determined by the system operator through planning studies such as TMR (transmission must run). TMR is an indicator that determines the minimum generation required that must be online and operating at specific levels. This generation compensates for the lack of transmission networks in relation to the demand that is being restored.
- -
Minimum firm generation. To comply with this condition, it is necessary to have adjusted historical and forecast data for both wind and solar generation production and the primary resource associated with these generation sources. These data serve as input to the proposed methodology to calculate average values and generation probabilities from the data series.
PV and wind NCRES will have as their main function within the restoration process to accelerate the demand meeting process and compensate the load-generation imbalances while gaining stability in the system.
A MILP model is built based on the proposed methodology as illustrated in
Figure 1. At first glance, it might be inferred that NCRES units should be the first ones to be started, prioritizing the fastest units to speed up the restoration process; however, there are more factors that affect the start-up process such as the stochastic characteristics of solar and wind resources and also the lack of inertia of the system. In consequence, an optimization process is required to find the best solution that ensures a fast but secure restoration. As illustrated in
Figure 2, prioritizing the connection of a NCRES unit with maximum power output does not guarantee to achieve an optimal solution to the restoration problem [
20]. With the generation profiles available in
Figure 2 and assuming that at
it is determined which unit should be connected to the system; it can be thought that
should be the first unit to be connected, because it has the maximum power output; however, at
, the power output of
drops drastically. In this case, the sudden decrease in
output will limit the ability to restore demand at later stages of the process; therefore, another unit must be considered to begin the restoration process even if it features lower power output.
This research work opens a new field in the modeling of the restorative state of electric power systems with NCRES and BESS. Among the areas that can be covered in order to continue with this research and overcome current limitations, the following have been identified:
The restoration process is a complex problem that must be observed from different aspects: generation, transmission, distribution, and demand. This research work covers directly the generation and indirectly the demand aspects. In this sense, this research work presents a methodology that provides the first signal or iteration of the restoration route, but does not provide the full route, which must also include the transmission network.
To make the problem more complete, transmission and distribution networks should be added to the methodology. This research takes into account only the generation part and although it provides a good starting point, it is not the definitive scenario. Within the restoration process, constraints associated with the normalization of the network must be taken into account, such as the number of maneuvers to be performed and the conditions of voltage and frequency stability. For example, the following constraints can be considered: the Ferranti effect when long lines are to be normalized, the normalization of radial networks in the first instance, not energizing lines in parallel until a certain degree of network robustness is reached, energizing transformers in parallel only when 50 % of the chargeability of one of the transformers is reached, etc.
The behavior of the variability and uncertainty of the primary FERNC generation resource should be further analyzed. It is recommended to model these variables in an optimization problem under uncertainty.
New constraints may be included in the methodology if the full network model is used. Voltage, stability, and operation problems of transformer tap changers, as well as system losses, could also be considered from this approach.
4. Tests and Results
Several tests were performed with the IEEE-39 RTS system for validating the proposed model. In the specialized literature, this test case does not present renewable generation; however, in [
33] it is proposed to include six NCRES generators located at nodes 3, 5, 7, 16, 21, and 23. A laptop with an Intel (R) core (TM) i5-4200U @ 1.6 GHz 2.3 GHz processor, 6.00 GB of RAM, and a 64-bit operating system was used in all tests.
Although the system chosen to demonstrate the applicability of the proposed approach is relatively small, the scalability of the problem is straightforward. This is due to the fact that the model was implemented in GAMS (general algebraic modeling system) software. On the other hand, to reduce the computation time in real applications, several strategies can be explored such as parallelization or the use of computation equipment with higher performance.
4.1. Input Data
The IEEE-39 RTS system has 10 generators whose characteristics are presented in
Table 2. An evaluation period of four hours with a granularity of 5 min is considered, which is equivalent to 55 periods of time.
Table 3 shows the loads associated with the test system; the evaluated scenario considers a total blackout. For this case study, three solar and three wind-type generators were chosen, whose parameters are shown in
Table 4.
The historical and forecast statistical data used to perform simulations were taken from different wind and PV generators operated by the TSO of Netherlands Elia Group [
34]. The information selected to carry out the experimental tests corresponds to both the historical data series of 8 March 2020 from 00:00 to 08:30 h of 22 March 2020 with a granularity of 15 min; as well as the solar and PV generation prediction series for 22 March from 08:30 a.m. to 1:00 p.m. with a granularity of 5 min. These data are the input to the model illustrated in
Figure 7. The parameters of BESS are presented in
Table 5, where
b stands for battery.
The proposed optimization model was implemented under three scenarios: (1) only conventional generation, (2) NCRES and conventional generation, and (3) all technologies (conventional generation, NCRES, and BESS).
4.2. General Results
Table 6 presents the general results for the analyzed scenarios. After running the optimization model with the first scenario, an objective function of 227278.4 [MW/h] was obtained in a time of 27.16 [s]. In the second scenario, that considers the effect of NCRES, the objective function decreased 10.37% compared to the first scenario. When all available resources are integrated (third scenario), the objective function decreases by 27.4% compared to the first scenario. Note that including all technologies (NCRES and BESS apart from conventional generation) require more computing time and a higher number of iterations; nonetheless a better objective function is obtained.
Figure 8 shows the added generation profiles of the system for each of the three scenarios under consideration. As new types of resources are included, the total value of energy available in the system increases. Note that the greatest benefit is achieved when all technologies are involved in the restoration process.
4.3. Comparison with Other Methodologies
A comparison of the optimization model developed in this paper with other methodologies presented in the specialized literature is presented in this section.
Table 7 shows, for different optimization techniques, the computational time and whether or not the global optimum was reached in the restoration process of the IEEE-39 RST test system with conventional generation. It can be observed that the methodology developed in this paper allows achieving a global optimal solution with a satisfactory computational time. It is worth mentioning that a comparison of the complete methodology integrating NCRES and BESS is not possible to carry out since to the best of the authors knowledge there are no other methodologies that simultaneously integrate this two resources within the optimal restoration process (see
Table 1). On the other hand, a comparison regarding the execution time would not be fare, since the results were obtained with different computers. The enumeration algorithm was processed on a Core i3 computer @ 2.53 GHz. The two-step algorithm does not refer to the characteristics of the test computer, and the proposed methodology was performed on a computer with Intel(R) core(TM) i5-4200U @ 1.6 GHz 2.3 GHz.
4.4. Progression of Unserved Energy in the System
Figure 9 shows that as NCRES and BESS resources are integrated; the unserved demand decreases. Despite the fact that NCRES do not participate directly in the starting of NBS units, they allow speeding up the process of restoring demand guaranteeing a faster response for the load-generation balance.
Figure 9 shows that with the integration of NCRES the demand recovery time decreases in 45 min (it would take up to 4 h 15 min if only conventional generation is used), which is equivalent to 17.6% of the total time used in scenario 1. By implementing all the resources in the system, this time decreases 1 h, which is equivalent to 23.52% of the total time in scenario 1. The unserved energy is correlated proportionally to the reestablishment times of unserved demand. This means that the unserved energy decreases as the demand recovery times shorten.
Figure 10 shows the demand restoration progression times in the system where the advantage of having a mixed of NCRES and BESS is also evident.
4.5. Start-Up Times of Generation Units
Regarding the start-up times of the generation units,
Figure 11 shows that scenarios 1 and 2 present the same time. This is because in the proposed approach NCRES are considered as NBS resources whose main function is to restore demand and guarantee the load-generation balance.
Nonetheless, an evident improvement in the start-up process occurs when BESS units are added.
Figure 12 shows the discharge power of the batteries considered in the test system. Note that there are two slopes in the discharge of these resources. According to
Table 5, the first slope, until 01:45 [Hrs], represents the discharge of battery
; while the second slope, until 04:19 [Hrs], represents the discharge of battery
.
Note that two relatively small storage resources of 50 [MW] each with a discharge rate of 1 and 0.5 [MW/h], respectively, accelerate the restoration times for both non-conventional and NCRES resources. This acceleration in the start-up of generation resources translates into a reduction in the time to reestablish the non-attended demand.
4.6. Inertia of the System
Figure 13 shows the accumulated inertia due to the number of synchronized generation units in the system. It is observed that the accumulated inertia curves for the first two scenarios are the same; this is because in both cases generators are synchronized at the same time. Likewise, due to the fact that starting times are accelerated with the integration of BESS, the inertia of the system increases in a shorter time, which allows the NCRES units a faster synchronization and therefore the non-served load decreases in less time.
Figure 13 also shows that after 5 min, the minimum inertia criterion is already met and NCRES units can participate in the restoration process.