Scalable and flat controls for reliable power grid operation with high renewable penetration April 2011 Annual Report

Transcription

1 Scalable and flat controls for reliable power grid operation with high renewable penetration April 2011 Annual Report Research Institutions University of Tennessee (lead) University of Illinois Northeastern/Tufts University Rensselaer Polytechnic Institute

2 Investigators University of Tennessee Fran Li, Asst. Professor, Electrical Engineering and Computer Science Leon Tolbert, Professor, Electrical Engineering and Computer Science Kevin Tomsovic (Lead PI), Professor, Electrical Engineering and Computer Science Guodong Liu, Ph.D. student, Electrical Engineering and Computer Science Alex Melhorn, M.S. student, Electrical Engineering and Computer Science Maryam Variani, Ph.D. student, Electrical Engineering and Computer Science Bailu Xiao, Ph.D. student, Electrical Engineering and Computer Science Yao Xu, Ph.D. student, Electrical Engineering and Computer Science University of Illinois Alejandro Dominguez-Garcia, Asst. Professor, Electrical and Computer Engineering George Gross, Professor, Electrical and Computer Engineering Philip Krein, Professor, Electrical and Computer Engineering Thomas Overbye (UI lead PI), Professor, Electrical and Computer Engineering Pete Sauer, Professor, Electrical and Computer Engineering Dimitra Apostolopoulou, Ph.D. student, Electrical and Computer Engineering Yannick Degeilh, Ph.D. student, Electrical and Computer Engineering McDavis Fasugba, Ph.D. student, Electrical and Computer Engineering Justin Hughes, Ph.D. student, Electrical and Computer Engineering Northeastern University Ali Abur, Professor, Electrical and Computer Engineering Hanoch Lev-Ari, Professor (NEU lead PI), Electrical and Computer Engineering Aleksandar M. Stankovic (now at Tufts University), Professor, Electrical and Computer Engineering Paraskevas Argyropoulos, Ph.D. student, Electrical and Computer Engineering Mert Korkali, Ph.D. student, Electrical and Computer Engineering Ronald Hernandez, Ph.D. student, Electrical and Computer Engineering Bei Yan, Ph.D. student, Electrical and Computer Engineering Rensselaer Polytechnic University Joe Chow (RPI lead PI), Professor, Electrical, Computer and Systems Engineering Daniel Shawhan, Asst. Professor, Economics Jian Sun, Assoc. Professor, Electrical, Computer and Systems Engineering Scott Ghiocel, PhD student, Electrical Computer and Systems Engineering Andrew Kindle, PhD student, Economics Hanchao Liu, PhD student, Electrical Computer and Systems Engineering 2

3 Abstract The main challenges of operating a power grid with a high proportion of generation based on renewable resources include that these resources: (1) are less predictable than traditional fuel-based power plants, (2) may be far from load centers so power may have to flow through congested transmission paths, (3) do not generally match the daily cycle of load variation, (4) suffer from unusual operating constraints, such as, rapid variation or complicated weather dependence, and (5) need to be tightly coupled to storage, which may be mobile. To respond to this challenge, this work envisions a fundamental shift in the approach to the electric power infrastructure with both a broadening of the electric grid to consider overall end energy use and a flattening of the control structure at all levels of the power grid the traditional control strategies. The proposed project focuses on the grid control and communication structure to facilitate coordination. Coordination is critical to ensuring that the future grid can enable efficient, low cost and reliable integration of renewables. As such, the work is a system development investigating several areas of control and communications, device technologies as well as electricity market structures. Commonalities arising across these diverse research tasks include the importance of new measurement technologies, increased functionality at the device level and managing uncertainty in both control systems and markets. More specifically, new phasor measurements are being used in this work to enable wide area control of the power grid and understand system limits more precisely. New power electronic functionality, both at the source and load, allow improved stability and voltage control. These functions mean that alternative sources can provide services to the grid that will support their costs. Investigations into incorporating reliability and risk considerations into market structures will properly allocate costs and better define contributions of renewables and controllable load to system performance. Managing uncertainty in the control systems, as for example we do with the proposed delay-cancelling approach, improves reliability and thus, allows greater penetration of renewables. 1. Introduction Frequently overlooked in discussions on energy problems is the central role that the electric power system infrastructure must play in any viable solution. Power generation plants are among the largest sources of greenhouse gas (GHG) emissions and in addition, many of the proposed solutions for minimizing emission wind farms, solar roof-tops, plug-in hybrid cars, even the hydrogen economy must rely heavily on the grid. Historically, energy systems have been engineered according to the separate industry sectors, i.e., transportation, heating, electric delivery, and thus, represent frozen accidents. Today, a comprehensive solution to the reduction of GHG requires a more general approach. This is not only to avoid shifting problems between sectors but also to take advantage of efficiencies that can only be realized through interaction among the subsystems. The electric power grid must function centrally to this system of systems. Global warming concerns, rising fossil fuel costs, and management of a carbonconstrained economy will require the development of a different type of electric power system infrastructure while electric energy resources based on renewable resources and storage are expected to be pervasive. Overall, energy delivery by electricity has great 3

4 advantages in terms of ease of energy transformation, precise control capability and flexibility for end use i.e., heating, cooling, lighting, consumer electronics, heavy industry, and so on. The modern electric power grid is extremely reliable and efficient in delivering bulk energy from large-scale sources to load distribution centers. At a high level, the interconnected power grid is reliable because system operators can depend on controllable equipment, e.g., generators, to supply power to meet relatively predictable loads. Unfortunately, many of the renewable technologies pose great operational difficulties because the present system is a centralized control structure with a limited amount of storage and control options that requires a precise balance between load and generation to be maintained at all times. The main challenges of operating a power grid with a high proportion of generation based on renewable resources include that these resources: (1) are less predictable than traditional fuel-based power plants, (2) may be far from load centers so power may have to flow through congested transmission paths, (3) do not generally match the daily cycle of load variation, (4) suffer from unusual operating constraints, such as, rapid variation or complicated weather dependence, and (5) need to be tightly coupled to storage, which may be mobile. To respond to this challenge, this research envisions two fundamental shifts in the approach to the electric power infrastructure, namely A broadening of the electric grid to consider overall end energy use, so that electric power generation and delivery does not merely respond to load demand but actively controls energy delivery for plug-in vehicles, the production of fuels (e.g., hydrogen), production of power versus commercially sold steam at thermal plants, energy storage, and end demand as needed. A flattening of the control structure that fully changes, at all levels of the power grid, the traditional control strategies. Existing energy systems today are characterized by multiple, largely autarchic control systems, including such systems as transient stability control, load frequency control, voltage control, power quality control, and distribution protection. These need to be replaced by a simpler, flatter structure with a local control operating within a more global context for the system. 1.1 A systems approach centered on the electric grid As illustrated in Figure 1, the PIs believe that a broad integrated energy systems approach is crucial to achieving goals of reduced GHG, adequate performance and low economic cost. Some researchers have suggested a highly distributed approach with, for example at one extreme, extensive roof-top solar and wind units with local storage [1]. This concept is attractive in that it does not rely on the existing infrastructure and allows innovations to be driven at the consumer level. Still, it is not clear that this approach can achieve desired reliability or low economic costs without major technological breakthroughs. The viewpoint taken in this work does not preclude such an eventuality, but does not assume these breakthroughs will materialize. A more pragmatic version of the highly distributed system would rely on some networking and sharing of resources in the distribution system, so-called microgrids, or variations of the different Smart Grid 4

5 ideas [e.g., 2]. Again, it is not clear that one can capture the needed reliability and benefits of source diversity by such a structure. At the other extreme, one can envision an extension of the traditional centralized power system operation with say, massive wind farms requiring major new transmission infrastructure, or perhaps large clean coal plants with CO 2 sequestration. The uncertainty of the wind output would likely require over building of transmission to take advantage of high power output time periods. Some large scale generation will certainly be built but the economies of scale tend not to hold well for alternative energy units where some smaller installations will certainly be built. Clean technologies for burning fuels are still unavailable. Moreover, the costs and difficulty of siting major new transmission hinder such an approach. Again, this work does not preclude new transmission, and in fact the PIs suggest strongly that new transmission must be added, but depending entirely on extensive new transmission is risky and costly. Finally, while there are certainly potential efficiency gains within the electric power grid to be obtained, these are not as large, and more difficult to achieve, as those from the broader energy system and delivery of services related to overall energy consumption (electric, thermal, HVAC, transportation). Thus, our vision of an expanded electric delivery system is one with greater load and expanded control tools available to operators. Figure 1: Power system of the future with large penetration of renewable energy and highly responsive distribution Underlying this new framework for reliable power system operation is our proposed concept of flat control. Existing energy systems today are characterized by multiple, largely autarchic control systems, including such systems for control of transient stability, load frequency, voltage, power quality, and protection. Within each control system, coordination is achieved through a multi-layered hierarchy at substations, power plants, independent system operators (ISOs), and regional power pools. Such control systems 5

6 are often myopic with regard to system needs and emphasize protection of individual components rather than protection of energy delivery and are already stretched to their practical limits. We envision a simpler, flatter structure that consists of only two levels at each scale: Local control in which individual components and individual loads operate in a manner that tends to support the best interests of the overall system, for reliability, speed, and robustness of control actions. Contextual control in which larger-scale controllers select one of a finite number of system-level control goals, such as efficiency maximization, cost minimization, stabilization, network recovery, or other goals that best reflect needs based on overall system status at a given moment. An example might be a plug-in hybrid car, for which the owner has set the controls to allow limited use as a grid storage resource in exchange for preferential electricity rates. Given a contextual controller goal, the car s local power electronics might charge the batteries at night and deliver energy back to the grid for a short time during system load peaks or wind/solar sags. The vehicle could also provide reactive power to the system for local voltage regulation even while charging the battery. However, this context must change with conditions as they arise. There may be, to continue this simplified example, a lull in winds that creates a shortage of supply. The plug-in vehicle should stop, or limit, charging under these conditions. Price signals will convey this to obtain some response, but a simple pricing signal does not provide sufficient granularity for overall system control. The research issue here is how to provide the proper context signal and constraints on local controls to ensure consumption needs are adequately met without jeopardizing overall system operation. Flat control approaches would be implemented at many different scales, given the multi-scale nature of the overall energy system. For example, a roof-top solar installation would have a local control that might alter its energy behavior in response to local frequency or voltage variation. A shopping center would have a contextual controller to serve the many local controllers within its domain. Each version requires support through information exchange and a communication layer that support this exchange. Flat control supports concepts of aggregation, in which a new type of business offers sophisticated contextual control that serves the power grid operator while supporting local control and its economic benefits down to the customer level. Individual aspects of flat control have been broached in recent work [3, 4], but the overall system-level issues and methods are a key issue for this research. Suitable economic incentives for local control of individual loads do not exist at present. Together, these needs suggest research across several levels to form an appropriate framework. An electric power system is an extremely complex dynamic system that relies on regular patterns of operation. Even though system characteristics cannot be completely understood, high performance can be assured as long as system limits are respected. A power system with strong renewable energy penetration would be far more dynamic and subject to greater uncertainties than the present system. Successful 6

7 operation cannot be realized following current design and decision-making paradigms. The control system and communication methodologies to realize a flat control framework have not been established in a large-scale practical system. Once a framework is established, with published rules and standards, all participants can contribute to the overall goal of employing high levels of renewables. Moreover, this work seeks to establish a structure where capabilities can be added incrementally at various levels and by different technologies, players, and localities. The remainder of the report breaks down the results to date and plans for the current year by the different research tasks. 2. Research Developments and Plans This project consists of the following primary five research thrusts: 1. Flat control and communication framework 2. Intelligent device interfaces 3. Optimization with multi-scale energy sources and demands 4. Transmission grid management and operation 5. Test and verification Work and plans on each of these areas will be addressed in sequence. 2.1 Flat control and information system methodologies This task seeks to develop the fundamental theories and methodologies to establish the foundation for system wide flat controls. The key issues relate to identifying the measured variables that must be monitored for effective control and integrating communication systems (and their inherent delays) into the control structure. In this vein, we have developed: a new control approach for load balancing using phase angle measurements, a concept for delay canceling to improve estimation and control over communication networks, sensitivity methods to understand power flow limits and improved grid models based on phase measurements. A common thread through these developments is the importance of new measurement technology using synchronized time stamping to allow coordinated operation over wide areas. AGC based on a flat control framework Automatic generation control (AGC) is the name given to a control system having three major objectives: 1. hold system frequency at or very close to a specified nominal value (e.g., 60Hz); 2. maintain correct value of interchange real power between control areas.; and 3. dispatch each unit's generation at the most economic value [5]. In conventional AGC, these objectives are achieved through primary and secondary control actions. Primary control is fast and automatically occurs within the seconds following a disturbance to stabilize the interconnection. Secondary control takes place in the minute time frame and manages the deployment of resources to ensure reliable and economic generation. Wind power plants presently installed in the USA are not 7

8 responsive to grid frequency or to load frequency control commands, therefore the presence of wind power plants in the system narrows the range of choice available to the system operator in assigning primary and secondary control duty and we need to consider the effect of these units on AGC to allow a high penetration of wind energy [6]. Primary Control relates to the governor and load response that stabilizes interconnection frequency whenever there is a change in load-resource balance. This control is provided in the first few seconds following a frequency change and is maintained until it is replaced by AGC action. Frequency Response (or Beta) is the more common term for Primary Control. Frequency response depends on the combined effect of the droop of all generator speed governors and the frequency characteristics of all the loads in the system. If the generators start to slow with the frequency decline, their governors supply more energy to the generators' prime mover; On the other hand, a given portion of interconnection demand is composed of motor load, which draws less energy when the motors slow down due to the lower frequency. Figure 2 illustrates the effects of governor speed droop and the frequency sensitivity of load on the net frequency change. In this diagram D is the load-damping constant which characterizes the load response to frequency deviation and R is referred to as speed regulation or droop [7]. We investigated this basic frequency control loop using flat control concepts. Figure 2: Composite governor and load characteristic When a system is flat it is an indication that the nonlinear structure of the system is well characterized and one can exploit that structure in designing control algorithms for motion planning, trajectory generation, and stabilization. Flatness was first defined by Fliess [8] using the formalism of differential algebra. The system is said to be flat if one can find a set of variables, called the flat outputs, such that the system is algebraic over the differential field generated by the set of flat outputs. Roughly speaking, a system is flat if we can find a set of flat outputs (equal in number to the number of inputs) such that all states and inputs can be determined from these outputs without integration. One major property of differential flatness is that, the state and input variables can be directly expressed, without integrating any differential equation, in terms of the flat output and a finite number of its derivatives [9]. 8

9 We have these derived necessary conditions on a third order generator model in a multi-area system, which satisfy the flat-based control method criteria and uses standard control design to set the parameters [10]. In this formulation, the bus voltage phase angles [δ 1,..., δ i,..., δ n ] as the flat outputs, the algebraic relationships between the state variables of the generators and [δ 1,..., δ i,..., δ n ] with its derivatives can be found. The resulting control logic is depicted in Figure 3. The importance of the structure is the simplicity of the primary control loop given the phase angles as the outputs and the introduction of trajectories for each generator to track. Figure 3: Flatness-based control block diagram for AGC Figure 4: Wind generation in areas one and two Details can be found in [10] but here we present a few simulation results on a threearea system [11] for the proposed control. The simulation investigates the impact of wind generation on frequency response and performance of the flatness-based control strategy relative to conventional AGC. Figure 4 shows the wind generation in areas one and two. As observed in Figure 5 and Figure 6, the flatness-based control tracks frequency as does the conventional AGC but with some reduced variation. Moreover, this control strategy is significantly easier to implement compared to conventional AGC given the phase angle measurement and requires only the coordination of the trajectory 9

10 planning. Finally a NERC Balancing Standard, CPS1, is calculated for the system under flatness-based control as well as the conventional AGC. The results shows that this value is about 200 for both cases, which means that frequency is on schedule or ACE is zero [12]. Figure 5: Frequency deviations (pu) Figure 6: Mechanical power deviations (pu) 10

11 Estimation and control over networks Communication delay is one of the unavoidable side-effects of using a computer network to interconnect sensors, actuators and control centers/nodes. In general, increased delay in a feedback control system often results in instability or reduced performance [13]. In [14], we have proposed a delay compensation approach based on time-stamping of transmitted signals, which can successfully mitigate the destabilizing effects of delay. By time-stamping we mean that every signal sample x(t) is transmitted over the network as an ordered triplet (x, t, k), consisting of the sample value x, the corresponding sampling time instant t, and the identity of the source of the signal x(t) (e.g., which sensor). Time stamping is enabled by the availability of precise time signals derived from the Global Positioning System (GPS) in various nodes of the power system. Such signals are part of Phasor Measurement Units (PMUs) that are increasingly being deployed as a key ingredient of system-wide monitoring and control. For illustration, we show the performance of our robust estimation scheme for the case of a 2.5 kw induction motor with an uncertain model. Figure 7 shows the signal to estimation error ratio as a function of the network delay for the accurate model (top trace) and for two models with parametric uncertainties (1% and 5%, two lower traces). In comparison, we note that the system without delay compensation becomes unstable for a 50 ms delay. Figure 7: Networked estimation/control configuration Time-stamping of transmitted information can also be used to overcome random, time-variant, delays in the observation path between sensors and estimation/control centers. It can be used with any state-estimation method and any feedback-control strategy, not just Kalman filtering and LQG state-feedback control. In particular, robust 11

12 estimation and control methods (see, e.g., [15]) may be required to accommodate significant uncertainty in system parameters (and models). Endowing such robust estimation and control techniques with delay mitigation capability will be the key to successful implementation in spatially-extended power systems. Previous analysis of the effects of observation intermittency have mostly addressed the problem of dropped communication packets [16], which result in an irregular (random) inter-sample interval with a Bernoulli (i.e., geometric) probability distribution. We have recently extended these results to the case of arbitrary (non-bernoulli) sensor sampling patterns [17]. In contrast to the formulation in [18], our results do not rely on coordination between the individual sensors, since we assume the cyber-physical power system to be geographically-distributed over a wide area. Uncoordinated (i.e., statistically independent) sampling and transmission of sensor observations result in enhanced resilience to communication packet loss and cyber-security attacks. In particular, we have demonstrated that staggered sampling - i.e., displacing the sampling instants of individual sensors with respect to each other so as to reduce the variation of the combined multi-sensor inter-sample intervals - results in a reduction of the average estimation error covariance [19]. We established a necessary condition for stability of a continuous-discrete Kalman filter with irregularly sampled observations [17]. Our stability condition extends [18] and relates the location of system poles to the region of convergence of the characteristic function (a.k.a. moment generating function) associated with the random inter-sample interval. We have also shown that estimation performance depends primarily on the average length of the sampling interval, with a very minor dependence on the variance and a negligible dependence on higher order moments of the (time-varying) sampling interval (see Figure 8, where ξ is the normalized variance of the random sampling interval and λ controls kurtosis). These observations lead to a simple design rule: the average sampling interval T av can be adjusted to achieve an acceptable level of state estimation error. Further research is needed to extend these findings to the multi-sensor case, with special focus on estimator stability conditions and on the explicit relation between the average and variance of the signal-to-estimation-error-ratio (SEER) and the average sampling rates of the individual sensors. 12

13 Figure 8: Effect of statistics of sampling interval on SEER (top) and zoom-in (bottom) PMU measurements for voltage sensitivities at transfer interface Voltage stability analysis is normally based on analytical models and data and requires a significant amount of computation [20], [21], [22] using complex analysis tools. In addition to steady-state analysis, some longer term simulation programs would also provide information on various system component responses as the power system evolves through a voltage stability scenario [23]. Recently the US Department of Energy (DOE) has provided awards to install a large number of phasor measurement units (PMUs), to supplement those PMUs that are already operational [24]. These measured data from these PMUs will be synchronized via GPS signal, allowing wide-area dynamic analysis. With a good coverage of PMUs in some operating regions, it is of interest to develop on-line tools using synchrophasor data to assess voltage stability along power 13

14 transfer paths. An investigation of using PMU data for voltage stability analysis is found in [25]. In [25], the disturbance event data of a loss of generation were used to develop a Thevenin equivalent circuit model [26]. There is, however, quite a bit of complexity in the load area because it is supplied by several in-feed paths. Hence the Thevenin equivalent parameters are highly dependent on the load model used. In addition, no analytical model analysis using system model data was performed to support the PMU data analysis. In this work, we extended the method proposed in [25] to a transfer path in the EI, where the PMU data of a loss- of-generation event at a nearby location is available. This particular transfer path is one of several possible paths to supply generation to the affected areas. Results are reported in [27] Dynamic data source measurements Dynamic data source measurements, such as PMUs and digital fault recorders (DFRs), are needed to improve power system dynamic models. In particular, research over the last decade or two has made it clear that the load models used in a transient stability study can have a significant impact on the results, particularly with respect to voltage stability. As a result, transient stability packages such as PSS/E, GE, and PowerWorld include dynamic load models that include a mix of loads including induction motors, discharge lighting, and electronic load. Also, the current draft of NERC Standard TPL (Transmission System Planning Performance Requirements) requires that dynamic load models, which include the behavior of induction motor models, be used in system studies. Hence the focus on our initial work has been to determine the most appropriate load models for use in positive sequence transient stability studies (that is, studies with a time frame on the order of several to several dozen seconds). Of course, for many locations on a power system the load composition has a substantial time variation, with factors such as time-of-day and weather conditions having a significant impact. For example, during a hot summer afternoon the load in residential locations would have a high percentage of single-phase air-conditioners, whereas during a winter evening it would have more lighting and resistive heating. However, regardless of the time of day, a significant percentage of the load will need to be modeled using dynamic induction machine models. The goal of this work is to use actual system measurements to determine the appropriate load models, recognizing that this might require several different models to represent different operating conditions. We plan continue to focus on the application of dynamic data source measurements, for the development of improved power system dynamic models. We are in the process of getting NDAs in place with utilities in order to get access to actual system information. Work will continue on developing appropriate load models, and will also expand to the development of better models for wind turbines. Modeling and control via dynamic phasors Dynamic phasors are finding increasing use in analysis and control of electric energy components and systems. Applications of the dynamic phasor framework are numerous, and include power systems (analysis of unbalanced faults and protection), electric drives 14

15 (analysis of unbalanced electric machines and of position-dependent loads, torque ripple minimization) and power electronics (model reduction in DC/DC converters, analysis of resonant and high-power converters, control of active filters). While dynamic phasors are intended for near-to-periodic operation, they have a number of useful features: (i) models are time-invariant (autonomous); (ii) inputs and consequently states tend to vary slowly compared to the driving frequencies; (iii) they achieve "simultaneous demodulation" in that all variables are constant (``dc") in a steady state; (iv) they are very effective in revealing dynamic couplings between various quantities, as shown in derivation of novel equivalent circuits for unbalanced ac machines [28]. Recently we have shown that such dynamic phasor expressions are a special case of a broader family of customizable signal transforms that we called Phasor Banks [29]. The need for compact dynamic phasor representations that can be efficiently communicated across a spatially distributed cyber-physical energy system mandates customization that focuses on frequency selectivity. Similarly, dynamic phasors for fault detection and location applications require a customization focused on time selectivity. In this project, we will explore advantages of matching the phasor bank to different applications such as fault detection and location, power decomposition, adaptive compensation and networked estimation. We will also explore the use of such descriptions in model-based detection and neutralization of cyber intrusions [30]. Dynamic power analysis and control One well-known approach to dynamic characterization of power, proposed in [31], relies on the observed instantaneous (polyphase) voltage and current. Instantaneous quantities are convenient in real-time control implementations, especially when minimization of memory requirements and online calculations is of key importance. This is much less important for modern discrete controllers whose memory and computational capabilities are often driven by very demanding applications (such as video), and typically much surpass control requirements in electronic and electromechanical systems. Instantaneous quantities are extremely sensitive to noise and processing delays, and thus are often filtered in an ad-hoc way in implementations. They are often used in straightforward control schemes that rely on integral action (at an appropriate frequency) to drive the error signals (e.g., the instantaneous reactive power as defined by Akagi- Nabae [31]) to acceptably low levels. We propose an alternative approach, motivated by our steady-state decomposition, to construct a novel dynamic (i.e., time-variant) 7-component power decomposition [32]. Our approach is based on dynamic phasors, and offers an interesting alternative. It relies on the fundamental, cyclic mode of operation of all energy conversion systems (periodic in the idealized steady-state) and applies naturally to any number of phases. It includes explicit models of components, and reduces to well-known quantities (such as harmonics) in steady state. Such quantities are often the subject of binding regulations (e.g., the power factor or the harmonic content). The quantities that we define dynamically can be used both in simple integral controllers and in more ambitious model-based control schemes. In addition, dynamic phasors can be customized to optimize specific properties 15

16 in transients (e.g., frequency separation), as shown in [29]. decomposition, viz., Our dynamic power S 2 (t) = P 2 (t) + N s 2 (t) + N u 2 (t) + Q B 2 (t) + Q s 2 (t) + Q u 2 (t) + S 2 (t)) captures transient behavior, while reducing to the standard (constant phasor) characterization in steady-state [31]. Here, P denotes the real (active) power, Q B is the reactive (Budeanu) power, N s (respectively Q s ) is the co-active (resp. co-reactive) power due to the spread of (incremental) conductances (resp. susceptances) in various phases over frequency, N u (respectively Q u ) is the co-active (resp. co-reactive) power due to the spread of (incremental) conductances (resp. susceptances) in various phases across phases, and S denotes a component due to system responses (typically currents) at frequencies or phases when there is no driving term (caused by circuit nonlinearity). For instance, Figure 9 shows the time-evolution of our seven power components, determined from data recorded in a paper plant during an outage described in [33] (the data was graciously provided to us by the authors). Figure 9: Dynamic power components Notice the dramatic change in the N u ( ) and Q u ( ) components, which captures the effect of load imbalance during the onset of the fault. Also notice that our dynamic power components assume their classical (steady-state) values away from the fault. The 16

17 use of dynamic phasors makes it possible to enforce P(t) = S(t) (with negligible line impedance) even during transients, by employing the adaptive compensator of [34], which we describe below. The role of compensation in controlling power flow in cyber-physical energy systems is to reduce the power consumption of the Thevenin equivalent source (or "line") impedance, so that most of the generated power is delivered to the load. This impedance represents the combined effect of all power sources, loads and transmission/distribution lines in a power network. With the dispersion of energy sources to lower-voltage networks, the line impedances are bound to increase. They will also vary much more, as the topology changes are much more frequent is such networks. In addition, many renewable sources are inherently single phase (e.g., small rooftop photovoltaics), and their intermittency will lead to increased unbalances in polyphase networks. Together with increased injection of harmonics by new loads and sources, this will result in modes of operation that are qualitatively very different from the ones assumed traditionally for network compensators such as active and passive filters and shunt capacitors. Traditional compensation methods, such as Fryze compensation, lose their effectiveness when the equivalent line impedance is no longer negligible in comparison with the load impedance. Moreover, constantly changing network conditions require continuous readjustment of the compensator current in order to ensure continuing efficient operation of the power system. Recently, we have introduced an adaptive nearoptimal compensation scheme that relies only on measurements of the load voltage and current or, equivalently, on the phasor description of these waveforms [34]. Our compensator tracks variations in both network and load conditions, continuously adjusting the polyphase compensator current so as to reduce the power dissipated in the source impedance, for both linear and nonlinear loads. We show in Figure 10 an example of the performance of our adaptive near-optimal compensation method: P line are the line losses, P cload is the power supplied to the compensated load, and P comp is the (real) power supplied by the compensator (which is zero on the upper parabolic cross-section curve). The nonlinear (electrical) load to be compensated is an induction machine rated at 25 kw, connected to a mechanical load with a quadratic torque-speed characteristic, and supplied over a long, unbalanced line [34]. The solid line in the figure connects the points obtained by our iterative algorithm. We use the cross-section curve, which indicates the theoretical optimum (dash-dot line in Figure 10) achievable with exact knowledge of network and load characteristics, as a benchmark for comparison. Due to the near-optimal characteristic of our compensator it is observed that the steady-state points (white circle markers in Fig. 10) lie very nearly on the optimum cross section curve. 17

18 Figure 10: Convergence trajectory of the adaptive compensator. Future research is needed to validate our approach with a wide variety of nonlinear loads, to establish the boundaries of stable operation, both in steady-state and in the presence of network transients, and to develop safeguards against loss of stability even under the most compromising conditions. Our ultimate goal is to develop a methodology of collaborative adaptive networked power flow control that can use network status information, extracted from the information layer of a cyber-physical energy system, to improve overall energy delivery efficiency beyond what can be achieved with standalone (i.e., network-blind) adaptive compensators. In particular, network information can be used to speed up the convergence of our adaptive compensation scheme, as well as expand the region of its stable operation. The sensing, communication, and processing resources available in each hub can also be used to detect and locate faults in power lines, using the technique proposed by [35] and [36]. In this work, arrival time differences of signals from the fault point to the synchronized monitoring instruments are used for accurate fault location. When a fault occurs, electromagnetic waves which originated at the fault point travel along neighboring transmission lines. Since these traveling waves follow different paths, they arrive at distant recorder locations with distinct time delays. Referring to these wavearrival delays of a certain fault transient at various locations in the network, the fault location can be determined. The previously proposed methods assumed either a single recorder at one end of the faulted line, or a pair of synchronized recorders at both ends of the faulted line. In this work we take advantage of sparsely distributed available synchronized recorders throughout the network. The captured waveforms are processed together in order to identify the exact location of the fault under study. 18

19 2.2 Intelligent device interfaces Under the concept of flat control, a key property for development of an inclusive power grid infrastructure is effective local control. In general, the objective is to seek control approaches at each level of hierarchy that acts in accordance with limited information, but in such a way that the overall system performance in enhanced. This implies requirements for communications and device interfaces. An implication of the local control approach is that many types of electrical loads will participate as active entities at the lowest level of grid control. This task will identify, analyze, and implement examples of useful communication and device interfaces to establish the concepts. We have developed an information infrastructure for vehicle to grid generation that provides benefits to the owners and regulation services for the utility. We also investigate how the PV interface can be used to enhance power quality providing dual functionality for the PV system. We have developed new wind turbine models and power electronic interface for improved control. Finally, a control system that allows plug-and-play capability for a STATCOM is described. Vehicle-to-grid informational infrastructure Initial work has focused on the informational aspects associated with the integration of electric vehicles in the grid. In particular, vehicle-to-grid emphasizes bidirectional power flow as a means of providing V2G benefits to the utility, but the work suggests that bidirectional flow may not be necessary to gain nearly all of the benefits. These benefits include ancillary services such as reactive power support, active power regulation, and storage support as well as revenue generation or discounted rates for vehicle owners. The goal of this work is to establish the principles of a unidirectional charge scheduling algorithm that can provide cost benefits to EV owners and regulation services to the power system while guaranteeing the desired charge energy. Basic principles have been established that suggest the use of low-rate communications and a unidirectional charger for V2G control. Figure 11 shows an example of this charging. These results are reported in detail in [37, 38]. 19

20 Figure 11: Unidirectional EV Charger Performing Regulation Services. PV to grid integration for improved power quality In grid-connected systems, the panels needed to reach the required power levels are usually arranged in strings. The cascaded H-bridge multilevel inverter requires a separate DC source for each H-bridge; thus, the high power and/or high voltage from the combination of the multiple modules would favor this topology in grid-connected PV applications [39, 40]. shown in Fig. 12, the cascaded multilevel inverter topology consists of n H-bridge converters connected in series, and each DC link is fed by a short string of PV panels. By different combinations of the four switches in each H-bridge, three output voltage levels can be generated, v c, 0, or +v c. A cascaded multilevel inverter with n input sources will provide 2n+1 levels to synthesize the AC output waveform. This (2n+1)-level voltage waveform enables the reduction of harmonics in the generated current, reducing the output filters. In addition, the multilevel inverter also presents the advantages of reducing the device voltage stress and being high efficiency [41]. The grid-connected PV systems should provide both the active power and reactive power, especially in a grid system with high renewable penetration. In Figure 12, the photovoltaic cascaded H-bridge multilevel inverter is connected to the grid through an inductor L. A generalized nonactive power theory is applied to generate the nonactive current reference [42]. In addition to providing the active power, the multilevel inverter could also provide the reactive power required by the local load to maintain good power quality in the grid. Simulation is carried out in Matlab/Simulink to validate the proposed ideas. An 11-level cascaded H-bridge inverter is considered. Each H-bridge has its own 195 W PV panel connected as an independent source. The system parameters are shown in Table 1. The PV panel is modeled according to the specification of the commercial 20

21 PV panel from Sanyo, HIP-195BA19. The I-V characteristic of the panel obtained by simulation is shown in Figure 13. Figure 12: Topology for grid connection. Table 1. System parameters Parameters Value DC-link capacitor 2200 µf Connection inductor L Load inductor Load resistor Grid inductor Grid resistor Grid rated RMS voltage 6 mh 20 mh 20 ohm 5 mh 0.2 ohm 120 V 21

22 The power generated by the solar panel depends on the solar irradiation on the panel, the operating temperature and the operating voltage of the panel. To use all of the available output power, PV systems should be operated at their maximum output power levels for any solar irradiation and any temperature. Thus, tracking the maximum power point of PV panels is an essential part of PV systems. The incremental conductance method is applied, and simulation results are shown in Figure 14-Figure 15. When temperature T=25 C and irradiation S=1000 W/m 2, the maximum power point voltage V mpp of PV panel HIP-195BA19 is 55.3 V. It can be seen that the voltage reference would achieve 55.3 V by maximum power point tracking (MPPT) control no matter what the start voltage reference is, and the output power would be 195 W. The voltage and current waveforms of the grid and load are shown in Figure 16. It can be seen that the load voltage is tracking the grid voltage. The load current is lagging the voltage, however, even if the grid is sending power to the local load or receiving power from the PV system, the grid current has the same phase as the voltage, which means the grid has unity power factor. Figure 17 shows the THD of the load voltage and grid current when PV operated under irradiance S=1000 W/m 2. Due to the cascaded H- bridge multilevel inverter, the THD is low even without any filter. The high order harmonics could be easily eliminated by adding a small capacitor, and the THD can be further reduced. In a grid system with high renewable penetration, the grid-connected PV systems should provide both the active power and reactive power to improve grid power quality. The cascaded H-bridge multilevel inverter is suitable for grid-connected PV applications, and presents the advantages of reducing the device voltage stress and output filters. Future plans include experimental tests to validate the proposed ideas and compare with the simulation results. Besides reactive power compensation, other auxiliary functions, like harmonics compensation, will be also considered in grid-connected PV systems. In addition, three-phase grid-connected PV systems will be studied in the future. Figure 13: I-V characteristic under different irradiance. 22

23 Figure 14: Voltage reference and output power when start voltage reference is 59V (T=25 C, S=1000 W/m 2 ). Figure 15: Voltage reference and output power when start voltage reference is 53V (T=25 C, S=1000 W/m 2 ). 23

24 (a) S=1000 W/m 2, grid receives power from PV (b) S=400 W/m 2, local load receives power from grid Figure 16: Voltage and current waveforms of grid and load (T=25 C). 24

25 (a) THD of the load voltage (b) THD of the grid current Figure 17: THD of the load voltage and grid current (S=1000 W/m 2, T=25 C). Wind turbine modeling and controls for grid integration The first year effort has focused on offshore wind turbine modeling and control for grid integration. A baseline 1,000 MW offshore wind farm with high-voltage direct current (HVDC) transmission connection to onshore ac power grid has been defined and modeled in a circuit simulation program (Saber). The modeled wind farm consists of 400 turbines each rated at 2.5 MW and using a permanent-magnet generator and two back-toback voltage source converters (VSC). The turbines are connected to a 33 kv local power collection bus, which is stepped up to 211 kv at a central location for interfacing with an offshore HVDC rectifier station. Both line commutated converter (LCC) and VSC-based HVDC technologies have been considered, and an LCC HVDC system was designed. A 300 MVA static synchronous compensator (STATCOM) is used in parallel with the HVDC rectifier to support the stability of the 33 kv ac bus. To reduce the complexity and simulation time, the 400 wind turbines are lumped into 5 equivalent turbines each rated for 200 MW. Startup and steady-state operation of the system has been simulated to verify the circuit and control design. Currently, smallsignal impedance models of the wind turbine system, the STATCOM, and the HVDC rectifier are being developed using harmonic linearization methods. These impedance 25

26 models will be used to analyze the voltage stability of the 33 kv local collection bus, and to determine control requirements for the turbine, the STATCOM, and the HVDC rectifier to ensure system voltage stability. The models will also provide a foundation for optimal system control development to minimize the required capacity of the STATCOM, thereby minimizing overall system cost. The overall objective of this task is to development analytical methods and tools for local control design to ensure system stability and power quality of future power grid. A fundamental challenge for the analysis and control of an ac power system is the timevarying (sinusoidal) operation trajectory, which prevents direct linearization of any nonlinear device models. Existing power system analysis methods overcome this difficulty by using phasor-based models, in which voltages and currents are represented by their amplitudes and phase angles. These phasor quantities become constant once the system reaches a steady-state, thereby permitting the application of traditional smallsignal linearization techniques [43]. However, phasor-based models are only meaningful below the grid fundamental frequency and cannot capture the fast dynamics of power electronic circuits and control that are becoming increasingly pervasive due to the proliferation of renewable generation, energy storage, as well as load management and energy-efficiency technologies (such as solid-state lighting and variable-speed drives) that rely on power electronics. New analytical methods and tools are needed for the modeling and control design of such power electronics-enabled sources and loads, as well as for the analysis of power systems incorporating such devices. One way to overcome the frequency limitations of traditional phasor-based models is to use dynamic phasor models [44]. In this approach, a periodic dynamic variable is represented by its fundamental component as well as a selected number of harmonics, and each such frequency component is represented by its amplitude and phase angle (or real and imaginary parts of the Fourier representation.) Task 1.4 in this project will tackle modeling and control at different time-scales using dynamic phasors. A different method based on harmonic linearization will be used in this task to develop small-signal models particularly suitable for fast dynamic stability and power quality analysis, as well as for local control design that enables autonomous operation of distributed resources, energy storage devices, and actively controlled loads with minimal requirement for communication. The harmonic linearization method develops a small-signal input and/or output impedance model directly in the frequency-domain. The method works by first injecting a voltage or current perturbation at a particular harmonic frequency, and then using harmonic balance principle to determine the response of the device at the perturbation frequency. Input or output impedance of the device at the perturbation frequency is obtained by the ratio between the input or output voltage to the input or output current. This method has been successfully applied to multi-pulse rectifiers [45] as well as phasecontrolled rectifiers [46] used in motor drive systems. One objective of this task is to extend the harmonic linearization method to other power electronic circuits, and to develop system analysis and control design techniques based on the resulting impedance models. 26

27 A particular type of system that we want to investigate is offshore wind farm with HVDC connection to onshore power grid. Such a system involves different types of switching power converters, such as PWM rectifiers and inverters, STATCOM, and HVDC converters. Stability is a critical issue at multiple interconnecting points in such a system, including the dc bus within each wind turbine, the local ac collection bus, the HVDC link, and the onshore power grid. The impedance models developed by using the harmonic linearization method can be used in conjunction with impedance-based system stability criterion to determine the stability of these buses [47]. The impedance models also provide a basis for control design of individual converters to ensure system stability and power quality, and to minimize converter size and system cost. One form of instability in ac power systems involving power electronics is harmonic resonance formed between a converter and the network, or between different converters connected to the system. For example, an inverter interfacing a wind turbine with the grid usually exhibits capacitive output impedance above the grid fundamental frequency. Such capacitive output can form an un-damped or very lightly damped resonance with the typically inductive impedance of the grid, producing high harmonic currents that represent a major power quality problem and can lead to tripping of inverter disconnect switches and other protection devices. The impedance models developed using harmonic linearization techniques were found to be very effective in predicting such system harmonic resonance [48]. The impedance models also provide a basis for converter and system design to mitigate such resonance by means of passive and active damping, as well as inverter control design to purposely reshape its output impedance. Wind turbines using full-power conversion architecture are typically controlled to act as current sources. The grid must have low enough impedance in order to provide a stable interface for such turbines. In the case of an offshore wind farm with HVDC transmission connection, the grid seen by these turbines is formed by the HVDC rectifier. Existing design approaches measure the strength of the grid by its MVA rating, which makes no sense when the turbines are connected to a HVDC rectifier, as the MVA rating at the fundamental frequency has very little correlation to its impedance at other frequencies, particularly above the line fundamental frequency where harmonic resonance is a major concern. Input impedance of the rectifier, as pursued in this project, provides a much more suitable performance measurement of HVDC rectifiers for offshore wind applications. A STATCOM is required to stabilize the local collection bus when a LCC HVDC rectifier is used [49]. Sizing of the STATCOM is important for system optimization, as it significantly affects overall system cost. The existing design method based on steadystate power ratings of the turbines doesn t address the high-frequency impedance compatibility issue mentioned above, and often leads to either an overly sized design that drives up system cost, or an inappropriate design that is unable to stabilize the ac bus despite its high MVA rating at the fundamental frequency. A specific objective of this research is to develop system impedance models that can be used to guide the design of the STATCOM and individual turbine control that results in minimal converter size and system cost. 27

28 A 1,000 MW offshore wind farm with high-voltage direct current (HVDC) transmission connection to onshore ac power grid has been defined and modeled in Saber. The wind farm consists of 400 turbines each rated at 2.5 MW and using a permanent-magnet generator and two back-to-back voltage source converters (VSC). Each turbine is equipped with a step-up transformer for interfacing with a 33 kv power collection bus, and includes several control loops that affect its behavior at the grid interface, including dc bus voltage control, grid current control, remote bus voltage control, and a phase-locked loop for grid synchronization. To reduce the model complexity, the 400 turbines are lumped into 5 equivalent turbines each rated at 200 MW. These turbines are connected to a 33 kv local collection bus, which is stepped up to 211 kv at a central location for interfacing with an offshore HVDC rectifier station. Both line commutated converter (LCC) and VSC-based HVDC technologies have been considered, and an LCC HVDC system has been designed. To stabilize the 33 kv local collection bus, a 300 MVA static synchronous compensator (STATCOM) is placed in parallel with the LCC HVDC rectifier. A 7 km medium voltage submarine cable is assumed between each lumped wind turbine model and the HVDC rectifier station. The nominal voltage of the HVDC link is set at 500 kv. Filters are placed at both the input of the HVDC rectifier and the output of the onshore HVDC inverter to attenuate the large 11 th and 13 th harmonic. The onshore power network is assumed to be a weak grid with high impedance. The grid voltage can also be modulated by a control signal to simulate various operation conditions. Figure 18 shows the overall schematic of the system including all components and major connections. Figure 19 gives additional details for the five lumped turbine models, where each model consists of a permanent-magnet generator, a PWM rectifier and a PWM inverter connected back to back, a step-up transformer that converters the 690 V ac output of the inverter to 33 kv, and an impedance circuit represents a 7 km submarine cable. Figure 18: Overall schematic of the simulated offshore wind system as implemented in Saber. 28

29 Figure 19: Details of a lumped wind turbine model with a step-up transformer and 7 km cable. While the control of the system is still being revised, preliminary simulation results have been obtained for the system during startup and steady-state operation. Figure 20 shows the simulated startup transient response of the HVDC link current settling at 2 ka rated current, as well as the STATCOM dc bus voltage, which has a steady-state value of 37 kv. Overshoot of the dc bus voltage is critical for the design of the STATCOM and is limited by incorporating a feedforward signal into the HVDC rectifier current control loop to minimize the transient power imbalance between the wind turbines and the HVDC rectifier that otherwise has to be absorbed by the STATCOM dc bus capacitor. Responses of the system to gust wind conditions have also been simulated. Figure 20: Startup transient responses of HVDC link current (left) and STATCOM dc bus voltage (right). Small-signal modeling of the wind inverter, the STATCOM, and the HVDC converters has been pursed in parallel with numerical simulation of the system. The inverter output impedance is modeled by the harmonic linearization method. A particular issue studied is the coupling between positive-sequence and negative-sequence output impedance of the inverter. Through analytical modeling and numerical simulation, it was concluded that, although the phase-locked look creates cross coupling between the two sequence component subsystems, the coupling term can be ignored for small-signal analysis, thereby permitting the stability of each sequence subsystem to be studied independently. Figure 21 illustrates the calculated (solid lines) and simulated (dots) inverter output admittance in the positive and negative-sequence domain. 29

30 1 Hz 10 Hz 10 2 Hz 10 3 Hz 1 Hz 10 Hz 10 2 Hz 10 3 Hz Figure 21: Positive- and negative-sequence output admittance (in db) of one wind turbine inverter. Preliminary modeling results have also been obtained for the LCC HVDC rectifier input impedance. The following equations give the input impedance of an N-phase rectifier in the positive and negative sequence domain (Z p and Z n ) as a function of the dc link impedance, Z dc, as measured between the dc output terminals of the rectifier, where α 0 is the phase control angle of the rectifier at the given steady-state operation point, H c (s) is the transfer function of the HVDC rectifier dc link current controller, V 1 is the amplitude of grid phase voltage, and f 1 is the grid fundamental frequency (60 Hz). The infinite summation over m can be truncated to include only the first few terms without significantly affecting the accuracy of the model. In addition to dc link cable impedance, Z dc is also affected by the onshore grid impedance and control of the onshore HVDC inverter, and can be determined using similar impedance mapping functions. Application of these basic impedance models to develop a complete input impedance model for the 12-pulse HVDC rectifier will be pursued in the 2 nd year of the project along with system small-signal analysis. 30

31 The impedance-based system stability analysis method has also been applied to determine harmonic resonance between a wind inverter and a traditional ac grid in a related project. An experimental setup (distributed generation test-bed) at RPI allows the grid impedance as seen by the wind inverter to be varied to simulate different grid conditions. Figure 22 shows the measured grid voltage and wind inverter output current under two different grid conditions. Harmonic resonance was found to occur in the second case when the grid impedance is high. To find the origin of such harmonic resonance, the grid impedance and the inverter output impedance were measured and their responses are plotted in Figure 23. In the case of high grid impedance, the inverter output impedance intersects with the grid impedance at about 400 Hz where the phase difference between the two impedance approaches 180 o, indicating a highly underdamped resonance between the inverter and the grid at about 400 Hz. Spectrum analysis of the grid current, shown in Figure 24, indicates that the dominant components are the 5 th and 7 th harmonics, which correlate closely with the predicted system resonant frequency. 31

32 Figure 22: A wind inverter output voltage (upper traces) and current (lower traces) under different grid conditions: Left: Strong grid with low grid impedance; right: weak grid with high grid impedance. Figure 23: Inverter output impedance (blue) vs. grid impedance under two different grid conditions. a) Low grid impedance (dashed lines); b) high grid impedance (solid lines). Figure 24: Measured grid current harmonics. 32