Index Terms—Full state feedback, secondary **voltage** **control**, Linear Quadratic Integral, **reactive** **power**, pilot points.
I. I NTRODUCTION
In **power** systems, **voltage** regulation plays an important role **and** its synthesis is a great challenge to ensure the safety of the whole electrical network [1], [2]. In fact, besides the com- mitment to the customers, Transmission Systems Operators (TSO) have to maintain grid **voltage** in specified limits which guarantee the operating safety **and** optimality. The **voltage** **control** is usually ensured by a hierarchical system with three levels: primary, secondary **and** tertiary **voltage** **control** (see, e.g., [3], [4], [5]). The primary **voltage** **control** is performed by local regulators, Automatic **Voltage** Regulators (AVR) **and** aims to fast regulate the terminal **voltage** of the generator. The grid is next shared into zones **and**, for each zone, a regional level called Secondary **Voltage** **Control** (SVC) adjusts **and** maintain the voltages at well-chosen buses inside the zone, called pilot-points [6], to desired values. This action is performed by computing the adjustment of AVR’s set-points of each generator which participates to the SVC, its dynamics is slower than the one of AVRs (arround 2 − 3 minutes). The tertiary **voltage** **control** performed at the dispatching center for the whole system is usually an optimal **power**-flow which determines an optimal **voltage** profile of the network according to safety **and** economic criteria. This strategy is now being extended to microgrids **and** to renewable energies **power** sources (see, e.g., [7], [8]). In most of the existing implementations, the SVC computes for each zone of the grid a signal representing the required **reactive** **power** level (e.g., [4]). This signal is used to adjust the AVR’s set-points of each generator by a local unit **reactive** **power** **control** that regulates the **reactive** **power** generation. These two **control** loops are time decoupled in order to avoid interactions. How- ever, this hierarchization suffers from a structural problem.

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Traditionally, many **power** utilities relied or still rely on this controls. However, this type of controls are costly since applied in normal system state **and** impact economic operation of the system while postulated disturbances could never occur.
Design of these controls is based on the use of **voltage** security assessment (VSA) tools. These tools use different **power** system models **and** algorithmic solutions: repetitive **power** flows, continuation **power** flows [5,25], security-constrained optimal **power** flows [35], quasi static simulation [2,36], **and** full time domain simulations. The results of VSA are preventive controls such as generation rescheduling, keeping some generation units in operation for **voltage** support, setting of ULTC transformers tap positions, **reactive** **power** compensation devices switching, network switching (topology changes) **and** as a last resort load shedding.

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4.5 Conclusion **and** Future Works
In this paper, a new CSVC strategy is proposed which coordinates discrete **and** continuous type compensators in transmission system to improve **voltage** proﬁle at pilot buses of the network when facing large disturbances. The controller consists of two parts: The identiﬁed nonlinear sensitivity model of the network **and** an optimizer. The nonlinear sensitivity model is identiﬁed using Neural Networks based on Input-Output data generated from random disturbances on the network. The optimizer utilizes SA algorithm **and** is combined with NN model to ﬁnd the opti- mal switching of the capacitor/inductor banks after sensing any disturbance. The effectiveness of the proposed algorithm is tested by applying the controller on IEEE 118-bus **power** system while perturbing the network by different levels of disturbance. The simulation results show that the proposed controller is able to bring **voltage** back into the desired limits for different disturbance cases. Beside **voltage** **control** the algorithm also minimizes the **reactive** **power** in- jected to the network. Comparing the simulation results of the proposed method with linear CSVC method **and** also the traditional approach showed that taking into account the nonlinear model of the system leads to a faster convergence of the method. However both linear based CSVC **and** the proposed methods had the same steady state **voltage** error. Moreover it was observed that the traditional method is not able to track the reference **voltage** change while the other two can compensate the tracking error.

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1.3 Optimization techniques
Several optimization techniques are used by researchers for an optimal integration of DGs in distribution network. (Abu-Mouti et El-Hawary, 2011) presents an optimization approach that employs an artificial bee colony algorithm to determine the optimal DG size, **power** factor **and** location in order to minimize the real **power** loss. The appropriate selection **and** the optimal DG location are determined using the fuzzy logic **and** the Bellman-Zadeh algorithm in (Barin et al., 2008). (Ahmidi et al., 2012) use a multilevel **control** system, **and** a probabilistic method is used to predict the available **reactive** **power** reserve. A repeated load flow is used to find an appropriate size **and** location of DG to reduce significantly the total **power** loss in distribution network (Anwar et Pota, 2011). A novel algorithm combining the MO particle swarm optimization (MOPSO) with support vector machine is proposed to find the optimal allocation of DG in distribution network (Fu et al., 2015). (Kiprakis et Wallace, 2004) analyze the implications of the DGs in distribution networks, they use a deterministic system **and** fuzzy logic to adjust the **power** factor in response to the terminal **voltage**. (Li et al., 2013; Zhang. et al., 2015) work with Game Theory **and** MO optimization problems that allow minimizing total system **power** losses **and** maximizing **voltage** improvement. DGs can reduce distribution losses if they are placed appropriately in distribution network with the implementation method of tabu search as demonstrated in (Nara et al., 2001). In (Ochoa et Harrison, 2011) a multi-period AC optimal **power** flow (OPF) is used to determine the optimal accommodation of DGs in a way that minimizes the system energy losses.

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system operators (TSOs) have implemented emergency **control** strategies to steer away the system from in- stability [3]. In addition, preventive **voltage** **control** schemes have been developed to maximize stability margins **and** minimize the operation costs. Many of the implemented **voltage** **control** schemes are hierarchical, i.e., they involve different **control** actions, objectives, **and** time/space delineations [4]. More specifically, fast **control** of **reactive** **power** injections from generators **and** flexible compensation devices is designed to un- dertake sudden changes in the system, resulting from the natural uncertainty among generation, demand, **and** transmission [5]. As those local actions rely on local measurements of **voltage** magnitudes **and** **reactive** **power** injections, the overall effectiveness of short- term **voltage** **control** depends on the distribution of **reactive** **power** reserves. In practice, those reserves are scheduled by each TSO using a particular type of optimal **power** flow based on a steady-state forecast of operational conditions in its **control** area. As TSOs only have local knowledge **and** **control** of the system, coordination issues should be carefully addressed to avoid stressed conditions, especially close to intercon- nections [6], [7]. Consequently, two main trends in development of coordination strategies have emerged. On one hand, centralized operation has been pro- posed to coordinate **reactive** **power** dispatch [8]. It usu- ally consists of a centralized **control** center gathering information from different utilities, making decisions for the entire system, **and** advising system operators. Such a center was recently created to coordinate con- trol actions between France **and** Belgium [9]. The main challenge for centralized coordination is the design of the decision-making process, which should have prop- erties of fairness to be accepted by every party [10]. In addition, the necessary exchange of information might affect the robustness of the coordination scheme with respect to opportunistic behavior of the TSOs or the loss of communication channels, for example.

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Correction of voltages after a 0.05 pu **voltage** drop taking place in the external grid, at t = 10 s.
Under the effect of local **control**, DGUs with terminal volt- age outside the dead-band inject **reactive** **power** right af- ter the disturbance. The voltages are rapidly but partly corrected, leading to fewer buses in low **voltage** situation.

consequently, the active **power** consumption of **voltage**-dependent loads including TCLs is changed which further supports the frequency regulation.
Some works in the literature have employed resistive TCLs for **voltage** **control**. This is exclusively possible in case of distribution networks where the R/X ratio is high entailing a coupling between active **power** **and** **voltage** [73]. For example, the work presented in [74] concluded that the coordination between demand response **and** distributed generators (DGs) in distribution networks could reduce the cost of **voltage** **control**. To this end, the problem has been cast in the form of a centralized optimization to minimize **voltage** **control** costs related to tap changers, DGs **and** demand response, **and** is subject to various constraints among which is maintaining **voltage** profile within acceptable ranges. In [71], TCLs are considered as a ‘**voltage** controlled reserve’ for participating in a short-term **voltage** **control** scheme. Two **control** logics have been considered for controlling TCLs; TCLs can either be switched ON/OFF based on local **voltage** measurements, or their set-point temperature is modified linearly with the **voltage** variation. The majority of works that considered **reactive** **power** consumption fall under the category of load curtailment. In [75], loads have been curtailed as part of an emergency DR program in order to participate in a real-time **voltage** **control** scheme in coordination with tap changers. Considering the impact of both active **and** **reactive** powers on **voltage** profile in distribution networks, load sensitivity matrices have been used to study the effect of the load variation on the **voltage** [75]. Optimization problems are usually formulated as in [76] **and** [22] to determine the optimal active **and** **reactive** powers to be adjusted by load manipulation. However, the demand response model used in these works is usually very general as no specific model for TCLs is developed, but rather it assumes that specific amounts of loads are curtailable at certain times. In general, the **reactive** **power** consumption of TCLs is usually ignored, **and** only a few studies (e.g. [16]) have considered this feature.

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In this simple example **and** under the assumption α, β > 1 there is always an intersec-
tion point between the short-term load characteristic **and** the post-disturbance network characteristic. However, in a more complex system, there may be a last point of intersec- tion between the two characteristics as intentionally depicted by the point G in Fig. 2.4. Beyond this point, a further decrease of the ratio r will lead to a loss of short-term equilib- rium. The short-term dynamics thus become unstable **and** the system collapses. Note that the final outcome of an LT1 instability may also be a pseudo-stabilization at low **voltage** due to LTC limitation. We mention that such a state should not be mistaken by declared it stable because other load recovery mechanisms, such as distribution regulating trans- former, thermostatic loads, etc. may become active driving the **voltage** decline further towards a collapse. Thus it is more reasonable to consider the final operating condition as unstable, since any attempt to restore load will drive the system to further degradation. We finally mention that, in a real-life system, the maximum **power** that can be delivered to loads, **and** hence the critical point, is strongly influenced by the **reactive** **power** limitation of generators (**and** compensators). The switching of generators from AVR **control** to field current limit by OELs causes the network P V characteristic seen by the loads to further shrink, in addition to the disturbance effect. This is shown graphically in Fig. 2.5. Since the limitation takes place after some delay, the operating point moves as indicated by the dotted arrows. The maximal **power** delivered to the load with the generator under OEL **control**, which corresponds to the point C (see Fig. 2.5), is significantly less than with the generator under AVR **control**.

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In grid-connected mode, the grid provides a robust fre- quency reference (because of the presence of large rotating masses) **and** it supplies the mismatch between DG generation **and** demand in the microgrid. An excess of generation can be stored or supplied to the grid **and** DGs can provide **voltage** support services to the grid [2]. In autonomous or stand- alone mode, load must be shared among generators, while frequency **and** **voltage** (active **and** **reactive** powers) must be controlled locally [4], [5]. While in grid-connected mode, DGs can behave like constant **power** sources, in autonomous mode, they must share load while keeping frequency **and** **voltage** within established security limits. The frequency response of large **power** systems is based on rotating masses, which are essential for the stability of the system [2]. However, in stand- alone mode there is a lack of rotating masses **and** the microgrid is highly dominated by DGs interfaced with **power** electronics converters. Another interesting fact is that a generator cannot be assumed to be connected to an infinite bus, **and** the system cannot be studied with conventional **power** flow techniques because none of the generators can be considered as a slack node [5]. The system dynamics are imposed by VSCs, **power** regulation controllers **and** the network variable parameters [6]. Although there are some important difficulties in the operation of grid-connected mode, autonomous mode has challenging problems to be analyzed as it can be stated.

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Additionally, distributed agent-based solutions that solely rely on local measurements have been investigated. The general appli- cability of MAS for real-time **control** problems in electric **power** systems has been shown in [13]. A MAS-based solution that only relies on information measured locally or obtained from the neigh- bouring buses has been proposed by [14]. However, as the focus of the aforementioned optimal **reactive** **power** **control** approach is the minimization of real **power** losses **and** the improvement of **voltage** profiles, it is not suitable as an emergency **control** scheme. Another agent-based solution relying on distributed **control** **and** communica- tion between neighbouring agents to counteract **voltage** instability is presented in [15]. However, agents need information about volt- age angles that, under normal circumstances, cannot be provided without a comprehensive installation of PMUs. The authors in [16] propose an agent-based solution that performs calculation of the dis- tance of the current operating point to the maximum loadability. Yet, the approach also requires information from PMUs **and** is based on steady-state load flow calculations. In [17], a MAS for emergency **control** against **voltage** collapse is proposed where agents coordinate different devices in post-fault situations. Yet, details on the algorithm for the identification of **voltage** instability are not presented. Another agent-based approach for **power** system restoration after a distur- bance has been presented in [18]. In [19], an agent-based distributed **reactive** **power** management scheme has been presented whose pur- pose is to improve **voltage** stability of distribution systems based on inter-agent communication but is not applicable as an emergency **control** concept at transmission level. One main issue of distributed agent-based solution is the consensus problem which is defined as agents’ need to agree on a common consent [20]. For agent-based **control** of emergency situations, it is therefore critical that the sta- bilization of the system is not prevented by the agents themselves. For this purpose, the MAS developed in this paper is not based on a negotiation between the agents which requires a positive outcome. Instead, agents follow their own goals **and** therewith enable reaching the main objective of stabilizing the **power** system.

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As an alternative with more information exchange, an agent- based scheme was proposed in [6] in which, by using locally collected measurements, the distributed controllers mitigate the **voltage** violations **and**, when needed, initiate an additional **reactive** **power** support request from the neighbouring con- trollers. Using an Optimal **Power** Flow (OPF), Ref. [7] dis- cussed the impact of centralized **and** distributed **voltage** **control** schemes on potential penetration of dispersed generation. A distributed architecture, comprising several cooperative smart agents, was proposed in [8] to solve the **voltage** regulation problem. After obtaining the operating values, each agent optimizes its own design. In Ref. [9] an agent-based system was proposed to **control** the DGUs in a low-**voltage** grid in a distributed manner. That work also considered different local **reactive** **power** characteristics **and** compared the corresponding system behaviours.

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selected load buses, **and** switching all **reactive** sources under constant **power**. The value of a generator **reactive** reserve is computed by a weighted sum combining the value of the reserve in various contingencies. The proper location of the synchronous condensers is a key step in order to obtain meaningful results. Ref. [11] monitors **reactive** **power** margins on pre-defined **voltage** **control** areas in order to assess the **voltage** profile quality. The margin is computed as the differ- ence between the individual reserves of generators within an area **and** the additional **reactive** generation needed to maintain acceptable **voltage** levels after any given contingency. Ref. [12] relies on the notion of “**reactive** reserve basin” of an area which is defined as the sum of the **reactive** reserves exhausted at the minimum of the VQ curve [2], [3] relative to any bus of the area. The percentage of basin **reactive** reserve remaining after a disturbance is used as a measure of proximity to **voltage** instability. Ref. [13] proposes two methods for determining the “effective” **reactive** reserve of an area. The former method computes the reserve as the sum of individual reserves of the generators under limit at the minimum of the VQ curve relative to a bus or an area. The latter approach computes an effective **power** reserve as the weighted sum of individual reserves; the weights are based on sensitivities of generator **reactive** outputs to **reactive** loads. Ref. [14] monitors the effective **reactive** reserve defined as the difference between the maximum **reactive** **power** provided by generators in the marginally stable scenario relative to a contingency **and** their current **reactive** **power** output. The system operator is alerted as soon as, for a contingency, the effective reserve approaches the minimum **reactive** reserve, defined as the generators response to the contingency in the marginally stable scenario. Ref. [15] proposes a **reactive** reserve management scheme based on multi-objective optimal **power** flow in order to meet **reactive** **power** demands during **voltage** emergencies. The management scheme uses participation factors for each generator which are determined based on the VQ curves. Ref. [16] derives, at the nose of PV curves, constraints on **reactive** **power** reserve requirements, **and** include them in a SCOPF which aims to enhance **voltage** stability margins. Ref. [17] examines by a regression model the nonlinear relation between the **reactive** **power** reserves **and** both **voltage** stability margins **and** **voltage** limits. Ref [18] discusses several issues related to the **reactive** reserves as seen from both load **and** generation side.

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The increasing use of electronically powered **and** controllable systems in the industrial sector, mo- tivated by improved performance, has led to a proliferation of static converters. Today, the number of these devices connected to electricity grids is constantly increasing. The switching operation of the semiconductor components constituting these converters is the reason why their behavior with respect to the **power** source is non-linear. Indeed, they take non-sinusoidal currents **and** for the most part consume **reactive** **power**, which poses serious problems for electrical networks. Static converters have become the most important sources of harmonics on the network. The uncontrolled diode **and** controlled thyristor rectifier is the most polluting **and** widespread static converter in both industry **and** domestic appliances. Under certain operating conditions, it can introduce a harmonic distortion rate (THDi) of current greater than 30%. For this reason, some recent adapted international standards, such as IEEE Standard 519, IEC 61000 **and** EN 50160, impose limits on the THD of currents **and** voltages within the supply network (5% for currents **and** 3% for voltages). In view of this state of affairs, **and** in order to limit the harmonic disturbance caused by the **power** electronics systems connected to the network, it is necessary to develop curative devices such as active filtering on one side **and** the other to design preventive actions such as non-polluting converters, equipped with a **control** device making the current drawn on the network as sinusoidal as possible.

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Keywords: **Power** systems, **voltage** instability, emergency **control**, distributed **control**, wide-area monitoring, adaptive systems,
load shedding, load tap changer.
1. Introduction
**Voltage** instability of **power** systems is linked to the inabil- ity of the combined generation-transmission system to provide the **power** requested by loads [1]. In a typical **voltage** insta- bility scenario, the maximum **power** deliverable to loads drops under the e ﬀects of a large disturbance **and** the limitations on **reactive** **power** generation; concurrently, the loads connected to the transmission system tend to restore their powers near the value before the disturbance. Those antagonistic e ﬀects pre- vent the system from regaining a state of operating equilibrium with network voltages in acceptable ranges of values [2]. De- pending on the involved component dynamics **and** the severity of the disturbance, **voltage** instability can evolve in time frames of several seconds (short-term instability) or tens of seconds up to several minutes (long-term instability). In this paper, the emphasis is on long-term **voltage** instability, in which network voltages undergo a generally monotonic decrease after the ini- tiating disturbance.

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as a correction function for scope raw data. It allows the extraction of V(t) **and** I(t) characteristics for pulse voltages up to 1000 V **and** pulse widths from 1.25 to 100 ns. The time resolution is 60 ps **and** the **voltage** error less than 4 V. Even though the purpose of the t- TLP tool development was to characterize the overshoot of the ESD protections, it can also be used as a precise “quasi-static” TLP/vf-TLP tester, by averaging V(t) **and** I(t) waveforms in the last nanoseconds. Then a set of I-V points is obtained for every TLP pulse **voltage**, as in the conventional TLP setup.

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Here, the considered paradigm is the one developed in chapter 2 which associates to a continuous-time flow whose model is of a differential equation type, a discrete- time behavior capturing the switched characteristic imposed by the **control** law. Two subsets included in an extended space, built from the state **and** the **control** spaces, determine the regions where the continuous **and** discrete dynamics are active. The main tool for proving stability of a compact attractor defined in this extended space, proceeds by an appropriate extension of Lyapunov stability theory developed in the context of hybrid dynamic systems in [26] **and** [34]. Due to the affine structure of the modes, a quadratic Lyapunov function can be selected from a positive definite symmetric matrix satisfying a set of Lyapunov inequalities. A hybrid **control** law with its two associated flow **and** jump is deduced from this matrix **and** an upper bound of a LQ performance index for the controlled system can be computed. It is possible to deduce an optimal guaranteed cost **control** law leading to the tight upper bound, by solving a LMI optimization problem.

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2.2.6 Bulk Biasing
In a r ectifier s tructure supplied b y a n i nductive l ink, M OS t ransistors s hare t he s ame substrate. Their sources are connected to the secondary coil. The terminals of this coil are subject to large variations in the source-bulk **voltage**. They go above the output **voltage**, **and** below the ground. T herefore, t he transistors t hat e xperience s uch l arge f luctuations m ay be s ubject t o significant substrate leakage currents leading to latch-up. This phenomenon could constrain the **power** efficiency of the circuit **and** compromise its reliability. It is crucial then to reduce this risk by preventing the vertical parasitic transistors from turning on. T herefore, the body potential of main pa ss M OS t ransistors s hould be pr ecisely controlled. U se of f ixed [ 54,119] or d ynamic [2,8,16-20,28-29,47-48,52,56,89,114,127,154,169] bi asing s chemes ha ve be en i ntroduced f or such pur pose. Authors have a lso m ade a dditional e fforts t o r educe t he r isk of l atch-up b y following s trict la yout guidelines. S ome o f th ese g uidelines in clude a ttention to large c urrent handling capability, obs erving a m inimum di stance be tween l arge d evices, a nd i nsertions of guard rings around potential injectors. Separating the wells of large transistors from the rest of circuit is also suggested in processes where deep n-wells are available [47,52,76].

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2. Assuming that (some of) these machines belong to a **power** plant equipped with a generation tripping scheme, select the number of units to trip in the emergency mode.
3. Run SIME, starting with the initial scenario up to reaching the assumed delay of generation tripping; at this time, shed the machines selected in step 2, **and** pursue the simulation until reaching instability or stability conditions (see equations (1) **and** (3)). If stability is met, stop; otherwise, determine the new stability margin **and** corresponding critical machines (they might have changed from the previous simulation).

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G. Gambarelli **and** G. Owen G., Indirect **control** of corporations, International Journal of Game Theory 23 (1994) 287–302.
X. Hu X **and** L.S. Shapley, On authority distributions in organizations: Equilibrium, Games **and** Economic Behavior 45 (2003) 132–152.

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