【正文】 next sampling time [(n+l)T] as a function of disturbances and inputs at the next sampling time [(n + 1)Tl。 and (iii) subtracting these two equilibria relations. Applying this process to model after taking , The resulting model takes on the form Quasistationary models of this type were used in [22] to model hierarchically deposed demand balancing in largescale electric power grids, and have led to some of the stateofart voltage control implementations in the French electric power grid. Here we will use these models as the starting models for system monitoring over broad ranges of operating conditions. The corresponding output variables (measurements) of interest are expressed as2 Mult ilayered system constraints The dynamics described in the previous section are a result of the unconstrained system response to a variety of disturbances and local controllers3. The basic objective of monitoring and controlling system dynamics is to ensure that the system is stabilizable within constraints imposed on both the control and output/state variables. Defining control constraints is fairly straightforward. However, defining meaningful constraints on the output/state variables is conceptually a challenging task. A meaningful set of constraints is the one which ensures prespecified performance with respect to both system reliability and efficiency. A basic lack of understanding of observability for candidate output variables in electric power systems has a direct practical implication of not 2~hroughoutth is chapter notations for outputs y and m are used interchangeably。 initially the only output variable referred to was line flow y. However, the concepts extend to all relevant outputs/measurements m. 3We recognize that not every node is equipped with fast controllers. One of the important questions is how to aggregate a large work in order to get away with fewer measurements/ outputs when designing stabilizing control. Very little is known on this subject. As an aggressive campaign is set in place for online monitoring and wide area measurements, , more research must be done to decide on the most critical measurements in order to ensure systemwide stabilization. 120 APPLIED MATHEMATICS FOR POWER SYSTEMS knowing what is critical to measure for what purpose. This, further, raises the question of the basic rationale for defining constraints on the output/state variables. At least in principle, these constraints are threefold, namely: They are caused by the need to ensure that the individual equipment ponents are operated within the manufacturer specifications (turbine blades are not spun faster than specified。 currents do not exceed design limits, etc). = The quality of service (QoS) in terms of frequency and voltage deviations and the rate of interruptions is met. Finally, the system as a whole is robust with respect to both small disturbances as well as with respect to major equipment failures. Robustness has traditionally been measured in the electric power works in terms of steadystate, smallsignal, and transient stability [7]. Depending on the system design and the range of operating conditions over which it is operated, the most critical constraints could be one of the above. If the limiting constraints are determined by the limitation of the system as a whole, it is very difficult to pute these constraints once and for all. Current industry practices have been to repute the output limits for what is believed to be the worst conditions in terms of demand and equipment status. Moreover, the basic approach has been preventive, so that enough control capacity is kept in a standby mode in case one of the worstcase events takes place so that the customers are not interrupted. It is important to notice that these putations do not rely on realtime corrective actions and feedback. Unfortunately, as the system is beginning to be operated in ranges previously not experienced nor studied, it bees impossible to understand the worst case scenario and to actually preplan for guaranteed performance. Moreover, the preventive planning approach is also one of the major causes of inefficiencies. Our proposed approach introduces basic logic for updating the output constraints. In what follows it is assumed that the state/output constraints are updated in a quasistationary way, . ymin [K~y]m, ax[ Kh],y min [K], and ym ax[K],a re updated online in order 6 ensure reliable conamp。ol without any of the systemwide constraints being violated. 4. Structural Spatial Aggregation: Managing Large Network Complexity by Means of Systematic Estimation and Control In addition to managing temporal plexity, a significant part of the ultimate quest for automation design lies in managing the spatial plexity of the electric power grid. In the regulated industry boundaries between various different entities such as utility panies and power pools, are preset and the spatial plexity is managed assuming that the interactions between these entities are relatively weak. The vast interconnected power grid has worked well without systemwide online coordination of these entities. Instead, each control area (utility, power pool) has implemented ingenuous means of balancing supply and demand in an entirely decentralized way on a minutebyminute basis in response to demand fluctuations ,by means of AGC. Similarly, the individual pieces of equipment are protected for safety using relays, and/or have primary local controllers intended to stabilize fast dynamics of each control area during normal operation in response to the very fast deviations d(t). Only very recently, as the use of the grid has extended beyond the objectives of each control area relying solely on its own resources to balance hardtopredict demand deviations 2, the real need for online coordination across multicontrol areas is in