Design of a simulation process to fit a power network behavior

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Network theory approaches

The dynamics of cascading are related to statistical topological properties of networks inspired by the Internet. The cascading failure has similar features to a power system grid, but the models usually differ. The importance of links or nodes is measured by betweenness, which is proportional to the number of least distance paths through the link or node. Several graph analysis techniques have been applied to power grid vulnerability assessment, including small-world networks, scale-free networks, and centrality (Dobson, et al., 2008).
The small-world network model was first proposed by Watts and Strogatz in 1998. It is a breakthrough in the study of complex networks, (Mei, et al., 2011). The small-world network concept has the properties of a relative big clustering coefficient and relative small characteristic length path. The theory reveals that a few remote connections greatly decrease the path length. The loss of those remote connections will increase the characteristic path length, decrease the transfer capacity of power grid, cause partial power shortage and ultimately lead to cascading failures. The model assumes that a node will fail if a given fraction of its neighbors have failed. Starting with initial failures on a few isolated nodes, the process will become cascading when these initial failures lead to subsequent failures due to exceeding the fraction . Those lines with remote connections would have the initial failures and are the vulnerable lines according to the small-world network theory (Huang, et al., 2009).
The scale-free network model was proposed by Barabasi and Albert in 1999 (Huang, et al., 2009). They incorporated two critical notions in the formation of scale-free networks, growth and preferential attachment. Growth means that new nodes are added sequentially to the existing network, and preferential attachment means that a newly added node has a tendency to be linked to the nodes in the network with higher degrees preferential (Mei, et al., 2011). Scale -free networks have important properties such as that the degree of distribution follows the power-law distribution and a few nodes have a large number of links but most nodes have only a few links. Simultaneity scale-free networks have other properties, like resistant to accidental attacks but are extremely vulnerable to coordinated ones. Power networks have a number of highly-connected hub buses and can have important implications for the reliability and security of power networks (Huang, et al., 2009).
The centrality of a vertex is used to determine the relative importance of a vertex within the network. A network may have a set of center nodes. Then centrality is a property determined by each vertex’s topological position. The distribution of centrality reflects the level of centralization in the whole network. Some of these include degree centrality, closeness centrality and betweenness centrality (Freeman, 1977). A degree centrality is the degrees of nodes that are related to the importance of the node in the network. A node with a higher degree is connected to more nodes (only immediate links). A closeness centrality, is concerned with the shortest distance between a node and all other nodes that are reachable from it. Here, distance can be defined differently and once a definition is picked, the distance between any two nodes can be calculated. Then the distance distribution shows the centrality of the network (Mei, et al., 2011). A betweenness centrality indicates the topological importance and capability of this node. If the node is often located in the shortest paths of other node pairs, then it is highly influential on information propagation in the network (Freeman, 1977). The betweenness approach is further improved by the introduction of an efficiency index.

Critical components and high risk multiple contingencies

The identification of critical components and high risk multiple contingencies can be used to estimate the vulnerability of the network. Dynamic decision trees and fast simulation are used in the Practical estimation of high-risk N-k contingencies (Chen & McCalley, 2005). Several methods for the identification of critical multiple contingencies have been proposed to identify vulnerabilities to deliberate attack or worst-case scenarios (Dobson, et al., 2008).

Recognizing patterns

Recognizing patterns in major blackouts and then studying how they combine into cascading sequences of events (including line tripping, overloading of other lines, malfunctions of protection devices, power oscillations and voltage instability, and system splitting and collapse) can give key information to the operator to use to manage the blackout risk. Common characteristics of blackouts are clarified by analyzing the cascaded events of the major blackouts (Yamashita, et al., 2009).

Conventional reliability methods

There is extensive literature and assessment tools on power system reliability (Cepin, 2011) , including component reliability and maintenance, generation adequacy and assessments of transmission system reliability, the effects of weather, and common cause failure. These methods are useful and commonly used in the electrical industry, but they are based on underlying assumptions of independent events and do not apply to cascading failure because the successive weakening of the system as the cascade proceeds makes the cascading events dependent (Dobson, et al., 2008).
Severe power outages let us realize that the single-contingency criterion (the N-1 principle) that has been used for many years in the power industry may not be sufficient to preserve a reasonable system reliability level. However, it is also commonly recognized that no utility can financially justify the N-2 or N-3 principle in power system planning. Obviously, one alternative is to bring risk management into the practice of planning, design, operation, and maintenance, keeping system risk within an acceptable range (Wenyuan, 2006).

Risk approach

A comprehensive risk analysis should contain a combination of probability and consequences (technical, business, and social costs). The risk evaluation of power systems should recognize the likelihood of failure events and the severity and degree of their consequences. Utilities have dealt with system risks for a long time. The criteria and methods first used in practical applications were all deterministically based, such as the reserve percentage in generation capacity planning and the single-contingency principle in transmission planning.
Suppressing all blackouts is not possible. But think about joint solutions for the risk of small, medium, and large blackouts, allows tradeoffs between small and large blackouts to be assessed (Dobson, et al., 2007; Carreras, et al., 2003).
Large cascading blackouts, although rare due to industry efforts, are a challenge to analyze and simulate in a predictive way due to the huge number of possible rare interactions and the diversity and complexity of these interactions. Analyses of blackout records in a number of countries show that although large blackouts are rarer than small blackouts, blackouts of all sizes can occur, and there is a substantial risk of large cascading blackouts. A catastrophic failure, defined as one that results in the outage of a sizable amount of load, may be caused by dynamic instabilities in the system or exhaustion of the reserves in transmission due to a sequence of line tripping leading to voltage collapse. Therefore one cannot dismiss large cascading blackouts as so unlikely that they should be neglected. At the same time it should be recognized that the current methods for directly understanding and mitigating cascading failure are not well developed.
Vulnerability is a measure of the system’s weakness with respect to a sequence of cascading events that may include line or generator outages, malfunctions or undesirable operations of protection relays, information or communication system failures, and human errors.
In most cases the power failure is not caused by a single event (it has been covered by the criteria of reliability in the operation of the electrical power system) and are caused by a series of events related to each other. After the first event a sequence of other related events producing a cascade occurs that often result in non-supply demand for end-users of EPS. In more general terms, it can be said that a number of factors cause cascading failures that cause a blackout as a result.
Electrical systems maintain a good level of robustness and reliability due to the implementation of multiple control systems and protection. These systems include risk management measures for the risk of a blackout, and influence the system’s response to internal or external disturbance to which it is subjected to some time scale.
When electric power systems fail they greatly impact the final consumers and the supply chain of the electricity market, and indirectly impact the welfare of the citizens due to the inconvenience in transportation, security, communications, system health and the country’s productivity chain.
The network impacts caused by blackouts can be complex and the risks should be analyzed using a more systemic approach. This approach allows for optimization and prioritization of network investments and operating policies that reduce the likelihood and impact of a blackout to society.

Emerging technologies

Some additional elements that could increase the likelihood or severity of cascading failures are: the interconnection function to facilitate large electrical energy trades across wide areas, increased difficulty in building new overhead lines (ambient difficulties, or stakeholder), increased dependency in power system operation on a greater number of individual independent actors (difficulties of information), limited flexibility of new generations plants (solar and wind plants, or combines cycle gas turbine), decreased clarity of responsibility in disaggregate industries and between different interconnected systems, increased size of interconnected grids and additional difficulties in the operation coordination of different industries of transmission and generations (Bell, et al., 2010).
For electric power systems the impact of some emerging technologies can help estimate the vulnerability of the network. These include phasor technology, advanced visualization, high-performance computing (HPC), and how data mining in cascading failure analysis influence the evaluation of the vulnerability of the electric power system (Huang Z. et al. IEEE PES CAMS Task Force on Understanding, 2009).
New trends in the development of electrical systems are bringing more complexity to the operation. Developments in smart grid as demand response, distributed generation or inclusion of large batteries in the generation or transmission systems will be a challenge in terms of predicting the behavior of these new system agents. Large variability in variables such as demand and power generation is expected, requiring many more real- time systems. This trends increase the chances of a blackout, especially when the system is limited by a lack of network expansion.

Risk quantification approach

This proposed methodology is based on the complex behaviour of the power system as demonstrated in several theoretical works (Carreras B. A, 2004) and applied to some actual power systems (watts & Ayala, 2014). First, the consolidation and analysis of the databases of electric power systems failures are carried out. Next, a statistical model of behavioural data is performed using SOC models. Then an electrical model is developed using a DC power flow for networks. Finally, the results for a real power system with databases of daily operation of the Colombian electrical system (day ahead market) are calculated comparing the use of the deterministic criterion N-1 with the probabilistic model simulations result.
The deterministic criteria N-1, is frequently applied to help to suppress cascades from the initial event. There are a range of industry practices devoted to analyzing and mitigating failures caused by a variety of processes, such as overloads and various types of instabilities, as well as efforts to improve the reliability of individual components. Indeed there are analysis and simulation tools that apply separately for each of these processes.
It would be too restrictive to plan or operate the system generally beyond conventional N-1 or N-D security. However, it is important that the tools are available such that high impact/low probability events can be managed in the control room and in planning to reduce the system’s exposure to risk. It is beneficial to have a real-time view of risk in power systems to alert the user to the occurrence and characteristics of a particular risk issue. It is also useful to quantify risk in relation to the operational planning timeframe to aid decision making by highlighting critical system states and elements in the power system that are vulnerable. With this information, targeted guidance reports enable operators to move away from high-risk states. A measurement-based approach can be used to validate the operational action and provide notifications to operators that the system has moved to a lower risk state as a result of the action.
This proposal manages the risks of widespread disturbance in electrical power systems for decision-making in a day-ahead market. International literature on blackouts, as well as research on the Colombian power system, shows that large-scale disturbances occur much more frequently than deterministic reliability criteria suggest. The use of conventional N-1 or N-D contingency analyses does not address high impact events adequately. Furthermore, it is noted that the more congested a power system becomes the more likely it is for hidden weaknesses to be exposed and wide area collapse is increasingly likely.

Table of contents :

1. Power system and blackout risk
1.1 Complexity of the electric power system
1.2 A cascading failure
1.3 Industry practice
1.4 Methods of analysis
1.4.1. Power flow based analysis
1.4.2. The hidden failure
1.4.3. Resilience
1.4.4. High-level probabilistic models
1.4.4.1. CASCADE model
1.4.4.2. Network theory approaches
1.4.5. Critical components and high risk multiple contingencies
1.4.6. Recognizing patterns
1.4.7. Conventional reliability methods
1.5 Risk approach
1.5.1. Emerging technologies
1.5.2. Risk quantification approach
2. Design power network model based in Self Organized Criticality
2.1 Self-Organized Criticality
2.1.1. In power systems
2.1.2. In Colombian power systems.
2.1.2.1. Colombian power system description
2.1.2.2. Colombian database
2.2 Statistical analysis
2.2.1. α -stable Laws Properties
2.2.2. Particle Swarm Optimization for estimation of α -stable laws
2.2.3. α-stable distribution for Colombian power system data
2.3 Estimation of VaR of demand not supplied in electric power systems
3. Design of a simulation process to fit a power network behavior
3.1 Model general structure
3.2 Slow dynamics: Power network evolution
3.2.1. Power demand and generation power evolution
3.2.2. Network improvement strategy
3.2.2.1. Immediate strategy approach
3.2.2.2. Delayed strategy approach
3.2.3. Generation economic dispatch (OPF eco)
3.2.4. Final load power demand shedding and/or generation power re-dispatching 54
3.2.5. Identification of “power demand shedding” event
3.3 Fast dynamics: Cascade phenomena
3.3.1. Line trip initial occurrence
3.3.1.1. Overloaded line condition
3.3.1.2. Overloaded line trip occurrence
3.3.2. Power demand load shedding and/or generation power re-dispatching process
3.4 DC SPFM inputs and outputs summarize
3.4.1. DC SPFM input parameters summarize
3.4.2. DC SPFM outputs summarize
3.5 DC SPFM inputs from Colombian system
3.5.1. Parameter for Transmission DC SPFM Model:
3.5.2. Parameter for Demand DC SPFM Model:
3.5.3. Parameter for generation DC SPFM Model:
3.5.4. Parameter for line fault DC SPFM Model:
3.6 SOC Conditions Settings
3.6.1. Cellular automata
3.6.1.1. Local Phase
3.6.1.2. Accumulation phase
3.6.1.3. Transmission evolution capacity
3.6.1.4. Determination of coefficient (local phase and accumulation phase) with respect to the observable (historical data)
3.6.2. Parameter associated with SOC conditions setting
3.6.2.1. Physical point of view of SOC for power grid
3.6.2.2. Assumptions from the Colombian power system
4. Applications in day-ahead market in real power system. N-1 criteria.
4.1 General results
4.2 Reliability criteria model
4.3 Other interesting results
4.3.1 Critical lines
4.3.2 Probability of fault on particular line
4.3.3 Sequence of events
5. Conclusions

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