Reliability Engineering for Next Generation Electric Power Systems

1. Reliability Engineering forNext Generation Electric Power Systems Alejandro Domínguez-García Department of Electrical and Computer Engineering aledan@ILLINOIS.EDU Power Affiliates Program May 14, 2010 Urbana, IL

2. Outline • Introduction • Existing power system reliability analysis tools • Rethinking power system reliability • Concluding remarks

3. Outline • Introduction • Existing power system reliability analysis tools • Rethinking power system reliability • Concluding remarks

4. Electric Power Systems in Context “I worked on aerospace problems for many years before converting to power systems, and, in my opinion at least, power problems are tougher in many respects. ... The number of variables [in a power system] is huge, and many types of uncertainties are present. ... Few if any aerospace problems yield such a challenging set of conditions.” – Fred. C. Schweppe, 1970 Fred C. Schweppe (1934-1988) Professor of Electrical Engineering, MIT US Power grid

5. Importance of Reliable Operation Impacts of the 2003 blackout (in NYC) • Economic losses estimated in $1 billion • Thousands of people trapped in thesubway system • Large portion of Manhattan without wateras most high-rises need pumps • All three metropolitans airports forcedto close • Major disruptions in hospitals operation Yet it is fair to say that the grid is being fairly reliable... so far • Reliable technologies used in generation and transmission components • Good understanding of the the overall grid operation in the presence ofcomponent outages/contingencies • Good strategies to account for these outages/contingencies

6. Impact of New Technologies • Electric power systems worldwide are undergoing a radical transformation in structure and functionality driven by a quest to increase efficiency and reliability • This added functionality provided by the integration of new technologies comes with side effects • Increasing complexity and the introduction of new sources of uncertainty at all levels in systems that are already inherently complex

7. Impact of New Technology • ≈ • ≈ ≈ Data Concentrator 2 5 1 4 7 StationControl StationControl Control Center P2,V2 P1,V1 8 9 PMU8 PMU9 DataConcentrator DataConcentrator 6 3 P3,V3 StationControl

8. Outline • Introduction • Existing power system reliability analysis tools • Rethinking power system reliability • Concluding remarks

9. Power Systems Reliability • Adequacy.Existence of sufficient facilities within the system to satisfy the consumer load demand or system operational constraints • Mostly focused on generation capacity • Probabilistic analysis • Operational reliability (security). Ability of the system to respond to sudden disturbances within the system • Static security assessment: thermal and voltage limits • Dynamic security assessment small-signal stability (small disturbances), and transient stability (large disturbances) • Deterministic analysis • These two notions have remained separate over the years • Probabilistic vs. deterministic analysis • Wu’s, Bose’s and a few others’ work explored notions of probabilistic security assessment in the early 1980’s

10. Adequacy: Sufficient Facilities? • ≈ • ≈ ≈ Data Concentrator 2 5 1 4 7 StationControl StationControl • Focus is physical components for generation! (and sometimes also for transmission) Control Center P2,V2 P1,V1 8 9 PMU8 PMU9 DataConcentrator DataConcentrator 6 3 P3,V3 StationControl

11. Adequacy outage outage G1 G2 L1 L3 L2 • C=c • C=0 • C=2c • C=3c outage G3 • Model of the total available generation capacity C: • It is assumed they are identical with capacity c • Failure rate is and repair rate is • The simplestmodel: • Transmission lines are assumed 100% reliable and with infinite transfer capacity • A two-state in-service/in-repair model for each unit is assumed, where the failure and repair rate are assumed to be constant • The failures of the units are assumed independent • The total load is modeled as a random variable L • The canonical problem is to compute the probability that the generating unit will not be able to supply the load (Loss-of-Load Probability)

12. Operational Reliability (Security) • Static Security Assessment: • The model is an algebraic nonlinear equation relating bus voltages, power supplied by generators and demanded by loads • The canonical problem is to assess whether or not the system state will violate some static criteria after a disturbance: • Transmission lines are overloaded (thermal limits) or • Bus voltages are outside tolerances • Dynamic Security Assessment: • A nonlinear differential equation must be added to the the algebraic equation for full system characterization • The canonical problem is to assess whether or not the system will remain stable after a disturbance: • Small disturbance: small-signal stability • Large disturbance: transient stability

13. Outline • Introduction • Existing power system reliability analysis tools • Rethinking power system reliability • Concluding remarks

14. Existing Tools in a New Context • Existing tools focus on impact of faults in the physical infrastructure for generation and transmission • Faults in physical componentsgenerators and transmission linesare reasonably well understood • Existing tools are not well equipped to describe the effects of new technology integration: • Impact of faults on the cyber infrastructure that control the physical infrastructure and their coupling are not captured • Component fault behavior and system behavior are assumed to be decoupled • Uncertainty effects associated with renewable-based generation are not properly captured

15. Faults in the Cyber Infrastructure • Motivation. There is no systematic definition and characterization of faults in cyber components: • Need for a taxonomy of faults in cyber components of electric power systems • Need to develop quantitative models for assessing the impact of those faults on system operation • Steady-state stability • Transient stability

16. Example: PMU Intermittent Fault Intermittentfault Data Concentrator PMU7 non-faulty StationControl StationControl P1,V1 Control Center P2,V2 fault on Intermittent fault model PMU9 PMU8 • An intermittent fault in one of the PMUs will cause the system to switch back and forth between two different subsystems • Even if both subsystems are stable, it is well known that the resulting switched system can be unstable: • The system exhibits some emergent behavior not present in the subsystems DataConcentrator DataConcentrator P3,V3 StationControl

17. Example: PMU Intermittent Fault • Quantitative characterization: • If the time structure of the fault is completely unknown • The system is stable despite the presence of this intermittent fault if the two subsystems share a common Lyapunov function • If we know that once the PMU stops sending measurements, it will remain in that state for at least t1 time units, and when the PMU is sending measurements, it will remain in that state for at least t2 time units • The system remains stable under this intermittent fault if the values of the individual Lyapunov functions at the beginning of each time interval for each active subsystem form a decreasing sequence • If the evolution of the fault is described as a random process, then stability statements under this particular fault can be made using stability results of randomly switched systems • Direct connection with previous work on probabilistic security assessment

18. Coupling Between Dynamics and Fault Behavior • Motivation. The concept of operating electrical energy systems with large margins is being challenged • Within the Smart Grid vision, increased communication and control is envisioned as an aid to enable operation closer to system limits • In power system reliability analysis • Component failure mechanisms are modeled as random variables describing the time to occurrence of each particular failure • The time-to-fault is usually characterized by the well-known concept of failure rate, consider usually constant and rarely time-dependent • This failure rate is assumed independent of the system dynamic continuous evolution • These assumptions needs to be revisited in order to understand the effect of system dynamics on individual component reliability, which in turn will affect overall system reliability

19. Example: SHS1-Based Reliability Model contingency fault fault Data Concentrator PMU7 StationControl StationControl P1,V1 Control Center P2,V2 1Stochastic hybrid system PMU9 PMU8 • For each q, the continuous dynamics is modeled by a stochastic DAE, which captures uncertainty in supply (e.g., wind) and demand • Transitions among different modes are triggered by component faults • Very much like the transitions in a Markov chain, but they can be a function of time, the discrete mode and the continuous dynamics • After a transition occurs, a reset map determines the new value of the continuous variable x and y DataConcentrator DataConcentrator P3,V3 StationControl

20. SHS Reliability Modeling Challenges • It is not easy to find the joint probability density function of q, x, and y as the partial differential equations governing their evolution do not usually admit analytical solutions • An alternative method to fully characterize the joint density function of q, x, and y is to: • Obtain the evolution of the discrete mode probability (similarly to calculating the probability distribution in a Markov chain) • To obtain the moments of x, y conditioned on each q • This alternative characterization can be used together with well-know probability inequalities to calculate bounds on system reliability • Scalability might be a showstopper

21. Operational Uncertainty • Another aspect that complicates the planning and operation of power systems is the increased uncertainty in physical components behavior • This uncertainty can be caused by any uncontrolled and unpredictable change (not necessarily a fault) on the demand or on the supply side of an electrical energy system • Generation based on intermittent renewable resources such as solar or wind. • Operational uncertainty is not at all new to electric power systems • Demand variation • Its extension to a significant portion of the generation capacitycaused by the increased penetration of renewable resourcesis a cause of major concern.

22. Uncertainty due to Wind Variability ERCOT Incident02/26/2008 • Day-ahead resource plan for wind • 80% of Wind forecast • Total wind output Output, Plan, and Forecast (MW) Time • Statistical independence might not apply when conducting reliability studies • A weather front might affect several wind farms within the same region at the same time • Wind variability cannot be thought of as small disturbances (small-signal stability) or large (transient stability) • An intermediate approach seems more appropriateReachability

23. Outline • Introduction • Existing power system reliability analysis tools • Rethinking power system reliability • Concluding remarks

24. Summary • Electric power systems worldwide are undergoing a radical transformations in structure and functionality driven by a quest to increase efficiency and reliability • Such transformations are enabled by the introduction of • Advanced communication and control • Integration of new generation sources (wind, photovoltaics) • new loads, such as plug-in hybrid electric vehicles (PHEV) • Advanced power electronics devices for power-flow control • Added functionality provided by the integration of new technologies comes with side effects • Increased complexity and the introduction of new sources of uncertainty at all levels in systems that are already inherently complex

25. Conclusions • Current reliability engineering tools are inadequate to engineer the reliability of future electric power systems • Without adequate tools to address the impact of integrating new technologies • Ad-hoc system designs will likely result, leading to • Deployment of poorly understood, unreliable and unsafe systems, which could have catastrophic consequences. • We need new tools that can properly capture the impact of new technology integration on system reliability of next generation electric power systems