Bart W. Tuinema1, Nikoleta Kandalepa2 and José Luis Rueda-Torres3
1Researcher of Intelligent Electrical Power Grids, Department of Electrical Sustainable Energy, Delft University of Technology, The Netherlands
2Grid Strategist, Asset Management, TenneT TSO B.V., Arnhem, The Netherlands
3Assistant professor of Intelligent Electrical Power Grids, Department of Electrical Sustainable Energy, Delft University of Technology, The Netherlands
Current developments in the power system put increasing stresses on the transmission network. The transition towards a renewable energy supply, the integration of large-scale renewable energy sources (RES) and the liberalisation of the electricity market are some of the challenges for the transmission network. At the same time, the lowest cost of an ageing transmission network is strived for. To prevent large blackouts, reliability analysis and reliability management are of the utmost importance. While deterministic approaches and criteria have been used effectively in the past, probabilistic methods will be increasingly applied in the future as these provide more insight into the reliability of the transmission network.
This chapter describes how probabilistic reliability analysis is used to study the reliability of large transmission networks. We discuss how probabilistic reliability analysis is related to deterministic criteria and risk categories. Two common approaches for probabilistic reliability analysis will be presented, that is, state enumeration and Monte Carlo simulation. In a case study of the Dutch extra-high voltage (EHV) transmission network, these methods are applied to analyse the reliability impact of EHV underground cables.
The organisation of this chapter is as follows. In Section 3.2, the concept of time horizons in the planning and operation of a power system is introduced. Several reliability indicators that are commonly used in probabilistic reliability analysis are discussed in Section 3.3. In Section 3.4, two methods for reliability analysis are described: state enumeration and Monte Carlo simulation. Section 3.5 describes a case study of the Dutch transmission network. General conclusions are discussed in Section 3.6.
In the planning and operation of power systems, Transmission System Operator (TSO) actions are performed in different processes and time horizons [1]. The main objective is to maintain a high level of reliability. Basically, three main processes can be distinguished: grid development, asset management and system operation. TSO actions are taken in time horizons ranging from long-term, mid-term and short-term to real-time. Table 3.1 shows some typical activities for each of the main TSO processes and for different time horizons. As can be seen, TSO actions range from long-term grid development (with a timescale of decades) to real-time system operation (with a timescale up to real-time).
Table 3.1 Actions taken during different time horizons [1]
There is always some overlap between the three main TSO processes. For example, the installation of new assets can be a grid development activity or an asset management activity. In asset management, maintenance activities are scheduled, but these could be cancelled in system operation during critical situations. Traditionally, TSO activities were mostly performed sequentially, as shown in Figure 3.1. An example is the Dutch 380 kV-ring, which was designed to be n-2 redundant (n-1 redundant during maintenance). This gave enough room to plan maintenance activities in asset management while still providing n-1 redundancy during system operation. As can be seen in Figure 3.1, in the sequential approach there is only a small overlap between the TSO processes.
In the future, the developments as mentioned in the introduction of this chapter are expected to put more stress on the transmission network. The transmission network will become more heavily loaded, and the room to plan TSO activities will decrease. Consequently, the overlap between the processes will increase and the planning of TSO activities will be more interacted, as illustrated in Figure 3.1. A typical example is the development of offshore grids. Other studies showed that it is often not economical to apply full n-1 redundancy in offshore networks. However, if there is no redundancy, maintenance activities will have more consequences for the availability of the offshore grid and therefore maintenance planning can become challenging. Moreover, without offshore redundancy, failures of offshore networks can have a large impact on the onshore power system during system operation as it becomes more likely that a substantial amount of wind capacity is interrupted. Here, the interaction of grid development (n-1 redundancy), asset management (maintenance planning) and operational planning (remedial actions) can be clearly seen.
As there is always interaction and overlap between the three main TSO processes, it is important to model this in the reliability analysis as well. In the application example described in this chapter, the focus is on long-term grid development decisions and the consequences for (short-term and real-time) system operation. It will be discussed how the application of new underground cable connections in grid development is related to remedial actions like generation redispatch and load curtailment in system operation.
Remedial actions are operational interventions performed by the TSO to avoid/relieve overload of the network during critical situations. Typical remedial actions are: application of PSTs (Phase-Shifting Transformers), network reconfiguration, cancelling maintenance, local generation redispatch, cross-border-redispatch and load/wind curtailment [2]. With PSTs, the phase shift of the voltage can be varied such that the magnitude and direction of the power flow can be controlled. The network can be reconfigured by performing switching actions to reduce the loading of overloaded connections. This is mainly applied in the high voltage (HV) and lower voltage networks. If a connection is under maintenance in an overloaded part of the network, it can be decided to cancel this maintenance to relieve the loading of other connections. By performing local (or national) generator redispatch, the production of some generators is increased while it is decreased for other generators to reduce the loading of connections in overloaded parts of the network. If local generator redispatch is not sufficient, cross-border (or international) redispatch can be performed. Wind curtailment can also be used to relieve the overloading of the network. The last resort to relieve overloading is to disconnect load by load curtailment (or load shedding).
In system operation, a risk framework is often used in which the current risk status of the network is indicated. The reliability (measured as the level of redundancy) can be related to the risk categories of this risk framework [3]. Remedial actions can be related to these risk categories as well. Table 3.2 shows that remedial actions like PSTs and maintenance cancellation are often applied first, while load curtailment is the last resort. Although Table 3.2 shows how remedial actions are related to the risk categories and redundancy levels, the choice for a certain remedial action always depends on the situation.
Table 3.2 Risk categories, redundancy levels and remedial actions
The main function of a power system is to supply the load. If the power system is not able to supply its load, it is considered as unreliable. Therefore, the reliability indicator security-of-supply is often regarded as the most important Key Performance Indicator (KPI) of power system reliability. Several reliability indicators exist that are directly related to security-of-supply. Some reliability indicators are specially defined to measure the reliability of a part of the power system, while others are developed for combined generation/ transmission/distribution systems.
Reliability indicators developed to measure the reliability of the generation system [4, 5]:
Other reliability indicators are developed to measure the reliability of combined (generation)/transmission/distribution networks [2, 4, 5]. A few of these are:
Traditionally, power system reliability studies concentrate on these security-of-supply related indicators. Often, it is assumed that there is one TSO that can take any remedial action to secure the load supply. The liberalisation of the electricity market has, however, led to several new actors such as producers, consumers, service providers and system operators. All of these actors have their own vision on power system reliability. For example, consumers wish to have a reliable power supply, while producers wish to be connected to the grid and sell their electricity. For a TSO, the transmission network is reliable if the customers (i.e. producers and consumers) are able to trade in electricity, while the network should also be maintainable.
In this sense, the reliability of a power system is not only reflected by the security-of-supply, but also related to indicators like the probability of wind curtailment, the probability of generation redispatch and the maintenance possibilities. These aspects can be included in reliability analysis by calculating several reliability indicators instead of one. As remedial actions are related to the risk states (see Table 3.2), calculating the probability of these states can provide more insight as well. Possible additional reliability indicators are then [2]:
The application example in Section 3.5 of this chapter will illustrate how a combination of reliability indicators provides more insight into the reliability of the power system.
Based on various input information (such as load/generation scenarios and network parameters), the reliability of the transmission network can be calculated. Figure 3.2 shows an overview of this process. The different parts of the calculation process are discussed in the following sections.
The following input information is needed to perform the reliability analysis:
The input information is now pre-processed in order to be used in the reliability analysis. The following calculations/analyses are performed:
Based on the input information and the results of the pre-calculations (i.e. the load flow scenario, the network information and the contingency lists), the reliability of the network can now be analysed. There are two main approaches to probabilistic power system reliability analysis: state enumeration and Monte Carlo simulation [4, 5]. The first is a structured analytical study of possible contingencies, the second is a computer simulation. Both approaches are discussed in this section.
The results of the reliability analysis are various reliability indicators. As described in Section 3.3, these reliability indicators can be directly related to security-of-supply, but can also be additional reliability indicators. Together, these reliability indicators give a more complete understanding of the reliability of the studied transmission network.
The reliability analysis as described in the previous section was applied to a case study of the Dutch extra-high voltage (EHV) transmission network. Currently, underground cables are installed in the backbone of the Dutch 380 kV network in the Randstad380 project [6]. So far, 380 kV Underground Cables (UGCs) have been installed in the Randstad380 South ring and another 380 kV cable project (Randstad380 North) is expected to come into operation in the near future. After the operation of both projects, around 20 kilometres will be underground in an entire route of approximately 80 km across the Randstad region. Figure 3.5 shows the Dutch EHV (380/220 kV) transmission network.
As not much is known about the behaviour of EHV underground cables, various aspects like resonance behaviour, transient performance and reliability are being studied [7]–[10]. Regarding the reliability, previous research studied the reliability of cable components [7, 10] and the reliability of transmission links consisting of overhead lines and underground cables [9]. As underground cables will have an impact on the reliability of large transmission networks, the risk of further cabling of the EHV transmission network is also considered [2].
The application example examines how the installation of more EHV underground cables (UGC) in the Dutch transmission grid affects the overall reliability level. Although the cable failure frequency is very close to that of overhead lines (OHL), the additional components of UGC (joints and terminations) reduce the reliability of the whole system [13]. Therefore, the unavailability of a connection is higher when it is partially or fully cabled than when it is completely an overhead line. Moreover, underground cables have a lower characteristic impedance. This is why it is important to study how the increased unavailability and the reduced impedance of the connection affect the overall reliability level.
As already described in Section 3.4, the reliability analysis consists of four major parts: contingency definition, load flow analysis, application of remedial actions if necessary and calculation of KPIs. A state enumeration is performed for the contingency types: independent single circuit failures, dependent double circuit failures, dependent triple circuit failures. All these contingencies refer to OHL and UGC failures. In addition, combinations of two of these contingency types are considered. In this way, 2nd-order contingencies can occur with two single circuit failures or with one double circuit failure and 6th-order contingencies are (only) reached by the combination of two triple circuit failures. Moreover, in this example three corrective actions are used with the following priority: national generator re-dispatch, cross-border re-dispatch and load curtailment. Taking these remedial actions into account, the state enumeration algorithm as shown in Figure 3.3 now becomes as shown in Figure 3.6.
In order to examine how further 380 kV cabling in the Dutch transmission network will impact the overall reliability level, simulations are performed by installing UGCs in three different connections (named Con1, Con2 and Con3). The PLC, the probability of overload and expected redispatch costs are calculated. The network topology and the required data are determined according to TenneT's scenario2020. It provides hourly data regarding generation (conventional/wind), load and export/import for the specific year. It is also important to describe the configuration of UGCs which is used in this study. As shown in Figure 3.7a, the UGCs consist of two circuits, and each circuit phase consists of two separate cables. In this configuration, a failure of a separate cable leads to a failure of one circuit, as operation with only one cable per circuit phase is undesirable in system operation.
In the case study, the cable length in the considered connections varies from 0% to 100% cabling with steps of 25%. The percentage refers to the transmission length of the connection and 0% means purely OHLs while 100% means a fully-cabled connection (as shown in Figure 3.7a). For example, in Figure 3.7b, 50% of the connection is cabled. The number of cable sections per connection can vary as well. For example, in Figure 3.7c there are two cable sections in the connection. Figure 3.7d shows the standard OHL connection configuration.
Due to the limited experience with EHV UGCs, there are no accurate values for their failure frequency and repair time. An earlier survey among European TSOs is used where a high and a low estimation of the failure frequencies are given, as shown in Tables 3.3 and 3.4 [7]. The repair time of UGCs is estimated as 730 h (1 month), which could be reduced to 336 h (2 weeks) if the repair process becomes more optimised in future [9]. For OHL, long experience has given more insight into failure statistics. The values are derived from actual failure statistics of the Dutch network [11].
Table 3.3 Failure frequency of EHV overhead lines and underground cables
Failure frequency | ||
OHL | 0.00220 [/cctkm·y] | |
TSOs high | TSOs low | |
Cable | 0.00120 [/cctkm·y] | 0.00079 [/cctkm·y] |
Joint | 0.00035 [/comp·y] | 0.00016 [/comp·y] |
Termination | 0.00168 [/comp·y] | 0.00092 [/comp·y] |
Table 3.4 Repair time of EHV overhead lines and underground cables
Repair time | ||
OHL | 8 h | |
high | low | |
UGC | 730 h | 336 h |
The reliability analysis algorithm developed (Figure 3.6) is used to execute a number of simulation sets, and both categories of KPIs (directly linked to loss of load and not directly linked to loss of load) are calculated. Fig. 3.8 shows how the PLC changes when varying cable length is installed in the three considered connections. While one of these connections includes UGCs, the others are full OHLs. There are three curves, each devoted to a specific connection. The y-axis represents the PLC in h/y, while in the x-axis the cable length is presented as percentage of the connection length. The point 0% indicates that the three connections are OHLs, and this is the starting point for all curves.
The installation of UGC in Con1 has no impact on the PLC, while the other two curves illustrate an upward trend as cable length increases. However, while 50% cabling in Con2 causes a 5% increase in PLC, the same percentage of cabling in Con3 leads to a 70 times higher probability. In order to explain this phenomenon, the relative loadings of these connections were studied, and it was observed that the maximum loadings present similar behaviour with the amount of increase of the indicator, namely very small loading for Con1, larger for Con2 and even more considerable for Con3. It seems that the loading of the connection where UGCs are installed influences the impact on the reliability level.
Fig. 3.9 examines the probability of overload when UGCs are installed in each of the three connections. By comparing Fig. 3.8 with Fig. 3.9, it can be seen that the probability of overload in Con1 shows a very small upward trend as cable length increases (and is not constant like the PLC). The other two connections are characterised by an increasing trend as well. It is also clear that the values of the probability of overload are orders of magnitude larger than those of the PLC.
Fig. 3.10 illustrates the expected redispatch costs when UGCs are installed in each of the three connections. By considering a specific percentage of cabling, the three points of the connections are depicted next to each other. This occurs for each cabling percentage. The diagram is normalised (logarithmic), where the base 1 represents the starting point (0% cabling, three connections as OHL). The expected redispatch costs confirm the remarks made so far. They show a growing trend with rising cable length, and the installation of UGCs in Con3 seems the most expensive option (from redispatch costs point of view). Con3 is a heavily-loaded connection, and its failure appears several times in the contingencies which lead to generator redispatch. On the other hand, Con1 appears to be the most economical solution, since even at 100% cabling, the increase of the indicator is less than 10% from the starting point.
The results were verified using a Monte Carlo simulation as shown in Figure 3.11.
To sum up, the installation of UGC in specific connections might not influence the reliability indicators related to load curtailment, compared to the starting point. However, this does not mean that the level of reliability remains the same. It was shown in the results that in these cases, the reliability indicators which are not directly related to security-of-supply might demonstrate significant change leading to a lower reliability level. Therefore, it can be concluded that indicators not directly linked to load curtailment should be used as well.
This chapter discussed the probabilistic reliability analysis of transmission networks. It described how the planning and operation of power systems will change in future and what challenges can be expected. The most common probabilistic reliability indicators were presented and we discussed how these are related to deterministic criteria and risk categories and how these indicators can provide more insight into the reliability of power systems. The two probabilistic reliability analysis approaches, state enumeration and Monte Carlo simulation, were explained. In a case study of the Dutch EHV transmission network, these approaches were applied to study the reliability impact of EHV underground cables.
The case study clearly showed that multiple reliability indicators provide more insight into the reliability of the transmission network than one single reliability indicator. In some cases, a reliability indicator such as the Probability of Load Curtailment does not show any difference whereas other reliability indicators such as the probability of redispatch can show a difference. For a TSO, both load curtailment and generation redispatch can be risks in the liberalised electricity market. Decisions on future developments, such as the installation of underground cables in the EHV transmission network, should be based on a combination of reliability indicators as presented in this chapter.
For future work, it is of interest to study further on how the results of probabilistic reliability analysis must be interpreted. Also, the development of fast probabilistic reliability analysis and decision making would be beneficial, such that probabilistic reliability analysis can effectively be applied in system operation as well. Clear and intuitive deterministic criteria have been used for a long time; it should be studied how probabilistic reliability analysis can best complement deterministic criteria and approaches.