Analysing the effects of different types of FACTS devices on the steady-state performance of the Hydro-Québec network

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1 Published in IET Generation, Transmission & Distribution Received on 7th May 2013 Revised on 4th July 2013 Accepted on 20th August 2013 Analysing the effects of different types of FACTS devices on the steady-state performance of the Hydro-Québec network Esmaeil Ghahremani 1, Innocent Kamwa 2 1 R&D Team, OPAL-RT Technologies Inc., Montreal, QC, Canada 2 Research Institute of Hydro-Québec/IREQ, Power System and Mathematics, Varennes, QC, Canada esmaeil.ghahremani.1@ulaval.ca ISSN Abstract: Hydro-Québec s electrical transmission system is an extensive, international grid located in Québec, Canada with extensions into the northeastern United States of America. For large power systems such as this, one of the major issues is to maintain the steady-state performance of the network. From this point of view, flexible AC transmission system (FACTS) devices could be effective tools to improve power system security by reducing the power flow on overloaded lines, which in turn would result in an increased loadability of the power system, reduced transmission line losses, improved stability and security and, ultimately, a more energy-efficient transmission system. Therefore in this study, the authors will present the effects of different types of FACTS devices on the performance of Hydro-Québec s power system. The optimal locations and rating of these FACTS controllers will be determined with a view to improving network security using an optimisation algorithm based on a genetic algorithm. The effects of six different FACTS devices including static VAR compensator (SVC), thyristor-controlled series capacitor (TCSC), thyristor-controlled voltage regulator (TCVR), thyristor-controlled phaseshifting transformer (TCPST), unified power flow controller (UPFC) and static synchronous compensator (STATCOM) with energy storage are compared. Using the presented results, the effects of different types of FACTS devices on the Hydro- Québec network will be analysed and compared with those of a STATCOM equipped with energy storage from the viewpoints of static loadability and losses. 1 Introduction The Hydro-Québec network, comprising of over km of power transmission lines, is managed by Hydro-Québec TransÉnergie, a division of the crown corporation Hydro-Québec. The system is unlike any other, with electrical transmission lines that stretch more than 1000 km from the northern hydroelectric dams and power stations of the James Bay project and Churchill Falls to the population centres of Montréal and Québec cities. For this purpose, Hydro-Québec uses a voltage of AC 735 kv or 315 kv to transmit and distribute the electrical power it produces [1]. Generation is 98% from northern hydro resources with almost all the load of this winter-peaking grid ( MW) on 24 January 2013) concentrated in the southern part of the province. Much of the electricity generated by Hydro-Québec s production facilities comes from 60 hydroelectric plants, most of them located in the north, far from load centres such as Montréal. Major expansion of the network began with the commissioning of an alternating-current (AC) 735-kV power line in November 1965 to meet the need to transmit electricity over vast distances from the hydroelectric power stations in northwestern Québec and Labrador to southern Québec [1, 2]. The 735-kV power lines form the backbone of the entire transmission system, and thus much of Québec s population is supplied by a handful of 735-kV power lines. However, long lines require extensive control to maximise the transfer capability and maintain system integrity. Hydro-Québec has therefore started to use power grid control components such as large synchronous condensers (in the early 1970s) and FACTS devices such as static compensators (in the early 1980s) and series compensation (in early 1990s) [2]. FACTS devices improve power network efficiency by re-dispatching the power flow on the transmission lines in such a way that the thermal limits are not exceeded, while fulfilling contractual requirements between grid stakeholders and increasing system loadability [3]. From the steady-state point of view, FACTS devices operate by supplying or absorbing reactive power, increasing or reducing voltage and controlling the series impedance of transmission lines or phase angle [4]. However, the benefits of FACTS devices are dependent on their type, size, number and location in the transmission system [5]. There are several approaches, heuristic or analytical methods, to find the optimal locations for the given FACTS devices in the power system such as genetic algorithm (GA) [6 10], Tabu search (TS) [11, 12], simulated annealing (SA) [12], particle swarm optimisation (PSO) [13 15] and evolutionary algorithm (EA) [16 19]. 1

2 In this paper, the optimal allocation of FACTS devices will be developed using an optimisation process based on the GA to find the optimal locations and values of a given number of FACTS devices in the Hydro-Québec network in order to maximise the power system loadability [20, 21]. Using the optimisation process presented in this paper, we will analyse and compare the effect of six different FACTS devices on the steady-state performance of the Hydro-Québec network. We will then assess the steady-state effect (if any) of including storage in the FACTS devices, namely the static synchronous compensator (STATCOM). A key contribution is the study of the potential effects of a FACTS device with storage on a network s steady-state performance. The paper is organised as follows. A general description of FACTS devices and the optimisation process is given in Sections 2 and 3, respectively. The optimal allocation of one and two static VAR compensators (SVCs) in the Hydro-Québec network is presented in Sections 4 and 5. The effects of different numbers of SVCs are analysed in Section 6. Section 7 discusses the effects of energy storage devices on network performance. Section 8 presents the results of the allocation process for other types of FACTS devices such as unified power flow controller (UPFC), thyristor-controlled voltage regulator (TCVR), thyristor-controlled phase-shifting transformer (TCPST) and thyristor-controlled series capacitor (TCSC). Section 9 discusses the results, whereas Section 10, finally, concludes the paper. 2 FACTS devices The allocation process will be conducted for six different FACTS devices as presented in Fig. 1. Since our allocation process is developed in steady-state conditions, the modelling of the STATCOM and SVCs will be the same [20, 21]. Each of the above six FACTS devices has its own properties and could be used for a specific goal [22]. The simplified models of SVC, TCVR, TCPST, TCSC and UPFC, presented in [20], will be used for our power flow calculations in Matpower [23]. The modelling of the STATCOM associated with energy storage superconducting magnetic energy storage (SMES) (Fig. 1f ) is described briefly as follows. The symbol and the model of STATCOM with SMES are also presented in Figs. 2a and b, respectively. The model of STATCOM with SMES consists of two parts: a variable inductance for absorbing or producing reactive power Fig. 2 a Symbol b Simplified model STATCOM with SMES device Fig. 1 FACTS devices a SVC b TCVR c TCSC d TCPST e UPFC f STATCOM with energy storage 2

3 ( r SMES ) for modelling the active-power production and positive resistance ( + r SMES ) for modelling the active-power consumption. The STATCOM with SMES is a device that could be installed in the network buses in addition to the branches. If the allocation process inserts the device in the buses, in this case the device is modelled only as reactive and active power injected at the bus as presented in Fig. 3. The reactive power injected or absorbed by the STATCOM part at a voltage of 1 pu (rated system voltage) could change between the following values Fig. 3 Equivalent injected active and reactive power for modelling the STATCOM with SMES device (STATCOM part) and a variable resistance for absorbing or producing the active power (SMES part). The SMES resistance has two operating modes: negative resistance 300 Q SVC 300 MVar (1) Also, the range of SMES part for injected (produced) or absorbed active power are 300 P SMES +300 MW (2) Inserting the STATCOM with SMES in the branches changes Fig. 4 Effects of P SMES and Q STATCOM on branch parameters ay kk = y ii and b c br ik, x ik 3

4 the parameters of the classic equivalent π-model. The influence of P SMES and Q STATCOM with the abovementioned ranges on the modified parameters of a branch such as line resistance, x ik line inductance, y kk = y ii line admittance and b c susceptance can be seen in Fig. 4. For example, it may be observed that, by increasing the value of Q STATCOM in capacitive mode in Fig. 4a, the value of b c increases. Taking another example, in Fig. 4b, it is shown that in the absorption mode of SMES ( + P SMES ) in the network the value of r ik decreases whereas in production mode ( P SMES ) the value of r ik increases. 3 Optimisation process 3.1 Genetic algorithm The GA is a kind of stochastic method for solving both constrained and unconstrained optimisation problems based on the mechanism of natural selection. The GA repeatedly modifies a population of individual solutions. At each step, some individuals are randomly selected from the current population to be parents for the next generation. Over successive generations, the population evolves towards an optimal solution [24, 25]. The GA begins by creating a random initial population. To take an example, assume the two individuals in Fig. 5a as an initial population. The algorithm then creates a sequence of new populations. This is done by ranking the members of the current population according to their fitness values. Some of the individuals in the current population that have the best fitness value are chosen as elite children. These elite individuals are passed on to the next population. In addition to elite children, there are two other methods for generating a new child population: mutation and crossover. Mutation children are generated by randomly changing the genes of a single individual parent (see Fig. 5b) and the crossover children created by combining pairs of parents in the current population as the third type of children (see Fig. 5c). Finally, the current population will be replaced with selected children to form the next generation. The algorithm stops when one of the stopping criteria such as the number of generations, time limit and fitness limit, is met [24, 25]. 3.2 Objective function of the optimisation process The goal of our optimisation process is to maximise system loadability (transmitted power) on the network without any bus voltage violation or branch loading. To achieve this objective, the load factor (λ) of the network will be increased in an iterative optimisation process as follows. At initial condition λ is equal to 1 (λ 0 = 1). First of all, the generating powers in generation buses (PG buses) are modified as in the following equation P Gi = l P G0i (3) where P G0i is the initial power generation at bus i and P Gi is the modified power generation. Then, for the load buses (PQ buses) the active and reactive demands (P L and Q L ) are modified as the following equations P Li = lp L0i Q Li = lq L0i (4) where P L0i and Q L0i are the initial active and reactive load power at bus i and P Li and Q Li are the modified values. At each iteration, according to (3) and (4), the load factor is increased and the optimisation constraints, which are bus voltage violation and branch loading, are verified. When it is no longer possible to satisfy the constraints, it is concluded that the maximum loadability has been reached. This is, in fact, a multi-stage greedy algorithm that follows the solving heuristic of making the locally optimal choice at each stage in the hope of finding a global optimum. On some problems, a greedy sequential strategy need not produce an optimal solution, but nonetheless, a greedy heuristic may yield locally optimal solutions that approximate a global optimal solution. The corresponding objective function which maximises the power system loadability (λ) could be formalised as follows J = Max{l} (5) Subject to the following security constraints S l S lmax : for all branches of the network (6) 0.05: for all buses of the network (7) DV bi P min gi P gi P max gi : for all generation buses (8) Fig. 5 GA begins by creating a random initial population a Original individuals b Mutation on each single individual c Crossover between two original individuals where S lmax is the maximum value for apparent power of the line l, S l is the current apparent power of the line l and ΔV bi is the difference between the nominal voltage at bus i and the current voltage, P gi is the generation at bus i, P min gi and P max gi are the minimum and maximum bounds on P gi, respectively. To simplify enforcement of the process constraints while placing FACTS at random locations, let us define a fitness function (Fit) to include two terms targeting separately, branch overloading (OVL) and second term is related to bus voltage violations (VLB) Fit = 2 ( OVL Line + ) VLB Bus Line Bus (9) 4

5 with 1; if S l S ( l max OVL l = exp m 1 1 S ) l S ; if S l. S l max i max { 1; if DV bi 0.05 VBL i = exp ( m DV ) ; if bi DVbi 0.05 (10) where S lmax, S l and ΔV bi were defined in (6) (8) and the parameters μ 1 and μ 2 are constant coefficients. This means that, if the constraints are fulfilled, each term of the fitness function in (10) (OVL and VBL) will be equal to 1 and the value of the Fit in (9) will be equal to zero. On the other hand, if the constraints are not met, the above-defined fitness function penalises the overloaded branches and overor under-voltage buses. 3.3 Optimisation approach The optimisation process implemented to find the maximum loading factor λ max (maximum system loadability) could be presented as follows [20]: Step 1: Initialise λ 0 = 1. Select the number and types of FACTS devices and build the GA individual structure. Then, based on the individual structure, create the initial population of the GA. The GA individual is built based on FACTS types, FACTS locations and FACTS values as presented in Fig. 6. As shown in Table 1, for each type of FACTS devices there are a number of variables and a specific code, namely: 1 for SVC, 2 for TCSC, 3 for TCVR, 4 for TCPST, 5 for UPFC and 6 for STATCOM with SMES. The possible number of Table 1 FACTS device properties: specific code, number of variables, variable names and possible location Code FACTS device Number of variable Variables Installation on 1 SVC 1 Q SVC bus/line (STATCOM) 2 TCSC (SSSC) 1 X TCSC line 3 TCVR 1 k TCVR line 4 TCPST 1 δ TCPST line 5 UPFC 3 V SE, I SE and Φ SE bus with adjoining line 6 STATCOM with SMES 2 Q STATCOM, P SMES bus/line locations for each FACTS device is related firstly to the bus/line installation and secondly to the selected test network. Three typical individuals for GA optimisation process are presented in Fig. 6. As is apparent from Fig. 6, the first part of each individual s string is related to the FACTS type. In the examples of Fig. 6, since we have five FACTS devices (n FACTS = 5), the FACTS types slot shown in the individual s string has five columns. The number of total columns of each individual s (n individual ) string could be calculated by n individual =3n FACTS +2n UPFC + n SMES. The second slot of each individual s string corresponds to the locations associated with the first slot in the string. Each specific FACTS device has its own location. Repeated locations are not allowed in the optimisation process and each line or bus should appear only once in the string. In GA implementation, the upper and lower limit of locations should be determined. This is related to test network and FACTS type. For example, in IEEE 14-bus test system with 14 bus and 20 lines; there are 14 possible locations for a TCSC for installation and 34 ( ) possible locations for SVC. The third and last part of the individual s string includes the rating values of the FACTS devices, which are normalised between 0 and 1 with 0 corresponding to the minimum Fig. 6 Typical example of an individual of multi-type FACTS device allocation a Without UPFC and STATCOM with SMES b Including just UPFC c Including both UPFC and STATCOM with SMES 5

6 value of the device and 1 to the maximum. To use these normalised values in the power flow calculations, we need to convert them to physical real values of the device as follows [5] ( ) v real = v min + v max v min vnormalised (11) where v min and v max are the minimum and maximum values for each specific device. For example, STATCOM with SMES device these values were presented in (1) and (2). Step 2: Increase λ = λ + 0.1, create an initial population of GA and then verify the constraint satisfaction for each individual by means of the Fit presented in (9). The optimisation algorithm (GA) randomly selects the locations and values for all given FACTS devices after setting them into the power system at each generation. The Fit is then calculated for each individual. If the constraints are met, the value of the Fit in (9) will be equal to 0; otherwise it will be greater than 0. Based on the Fit value, the GA performs the GA operations such as elite generation, mutation and crossover for creating the next generation. Step 3: If there is any individual with Fit = 0, it means that at current load factor (λ) we have a configuration that satisfies the security constraints and as a result we should increase the load factor. This loop continues until we reach a load factor for which there is no individual with a Fit equal to zero. This means that at this load factor, there is no configuration of FACTS device which can bring the network voltage level and loading constraints into acceptable ranges. At this point, we should report the previous load factor corresponding to maximum load factor (λ max ) and previous individual with zero value of (Fit) which includes optimal locations and values of selected FACTS device. In summary, global optimisation (5) is a complex, possibly untrackable problem which is converted into several simpler sequential optimisation problems. In fact, global problem solving requires a continuation optimal power flow (OPF) to find the objective function whereas greedy problem solving only relies on ordinary power flows to enforce security constraints (6) (8) at each stress level. The pitfall is that there is no guaranty of global optimum, only the certainty to obtain one solution, at a given stress level. 4 One SVC allocation in the Hydro-Québec network The Hydro-Québec network has 884 buses and 650 branches. The MatPower format of this network, which was used for the power flow calculations, was obtained from the PSS/E version of the network dated 29 January The total Fig. 7 Overall plan of Hydro-Québec network 6

7 load of this network is MW and the total power production is MW. An overall view of the Hydro-Québec network is schematised in Fig. 7. Using the optimisation process described in the previous section, the allocation process for one SVC in the Hydro-Québec network is developed and the following results, presented in Table 2, are obtained. As can be seen from this table, for the Hydro-Québec network, with one SVC of MVar allocated in bus number 10 (BCV315), which is located in Boucherville (see Fig. 7) on the South Shore of Montréal, the maximum load factor was determined as λ max = This means that, with one SVC having the above-mentioned capacity, we would have 2.4% improvement in system loadability, which is equal to ( = ) MW. For each network, there is a load threshold factor (λ LRI ) (LRI: loss reduction improvement) above which we observe a reduction in transmission line losses. For one SVC Table 2 Allocation and effects of one SVC on the Hydro-Québec network Network test system FACTS devices Values and locations λ max Location Name Value, MVar Loadability λ Reduction Region improvement, % λ LRI Loss reduction Hydro-Québec SVC Bus 10 BCV MW (0.047%) LSERiveSud MW (0.071%) Fig. 8 Comparison of voltage magnitudes of all buses in the Hydro-Québec network at maximum load factor λ max = Fig. 9 Comparison of voltage magnitudes of all buses in the Hydro-Québec network at another selected load factor λ =

8 allocated in the network, the value of λ LRI is determined as equal to 0.90 (λ LRI = 0.90). From Table 2, it can be seen that for the initial condition with λ = 1.00 we have 16 MW (0.047%) loss reduction in the network whereas at maximum load factor (λ max = 1.02) there is 26.5 MW (0.071%) loss reduction in the network. The bus voltages for the networks with and without FACTS devices for two load factors λ max = and λ = 1.08 are presented in Figs. 8 and 9, respectively. As is clear from these plots, under the same loadability conditions, the network without FACTS devices has a greater voltage drop on the buses, confirming the significant influence of FACTS devices on keeping the bus voltage in the acceptable ranges. It is an effective demonstration of the significant influence of FACTS devices (here SVC) on keeping the steady-state voltage of buses in the acceptable ranges. The nominal bus voltages curve in Figs. 8 and 9 corresponds to the voltage profile without FACTS device at λ =1. To show how far the result of the allocation for one SVC is acceptable, let us compare the effects of the allocated SVC with the two most recent SVC locations determined by Hydro-Québec experts. These locations are near the Montréal area at Chénier (bus 23:CHE315) and Bout-de-l Ile (bus 51:BDL315) with ratings of 600 MVar for each. The number 315 refers to the nominal voltage of the local buses. Generally, the previous SVCs in Montréal are installed to solve long term voltage stability problems to increase the load of the network without risk of voltage collapse after a line outage around Montréal. However, we have compared those already installed SVCs with our allocated SVC in terms of loadability improvement which means that, the location of the SVC is fixed on a specific location (here the location of previously installed SVCs) and the size is set to 592 MVar. Then, the comparison is done in terms of loadability improvement between the SVC installed physically in the network and an SVC allocated by the GA as given in Table 3. As can be seen from this table, the influence of the current SVCs at buses 23 and 51 physically installed at Chénier or planned at Bout-de-l Ile in the Hydro-Québec network is very much the same and similar to the results of the SVC at bus 10. Although the maximum loadability for real SVCs is λ max = and Table 3 Comparison between real installed SVCs on the Hydro-Québec network with SVCs allocated by the optimisation method No. Network test system FACTS device Values and locations λ max Voltage deviations Loss reduction Location Name Value, MVar Region Loadability Improvment, % λ LRI λ Abs. value λ Reduction 1 Hydro-Québec SVC Bus 10 (paper result) 2 Hydro-Québec SVC Bus 51 (physically installed) 3 Hydro-Québec SVC Bus 23 (physically installed) BCV MW (0.047%) LSERiveSud MW (0.071%) BDL MW (0.041%) LSEMontreal MW (0.072%) CHE MW (0.047%) LSELaval MW (0.1%) Fig. 10 Comparison of the stress level for voltage collapse in the network with and without FACTS at λ = 1.09 the voltage collapse occurs just for the network without FACTS devices (SVC) 8

9 Fig. 11 Comparison of the stress level for voltage collapse in the network with and without FACTS at λ = 1.11 the voltage collapse occurs for both conditions: the network with and without SVC device λ max = 1.023, for the selected SVC at bus 10, this value is λ max = We have similar results also on λ LRI values and loss-reduction improvements. The results presented in Table 3 show that the location and value obtained by the presented optimisation process are near to the case set in reality to find a suitable location for an SVC of approximately 600 MVar near a big load such as Montréal where we already had the same size of SVC physically installed. We repeated this optimisation (one SVC device) several times from various initial conditions and in all of them the optimal location was determined in the area around Montréal. As mentioned before, the objective function of the optimisation process is to maximise the power system loadability. Considering a V P graph of a load bus (PQ-bus) in CPF analysis, an increase in the load of a PQ-bus would reduce the voltage of that bus until the critical point is reached, which shows the bus voltage collapse. Using the same methodology, we made a similar study of the Hydro-Québec network in which, instead of increasing the load of one specific bus, we increased the load of all buses while monitoring the voltage level of the entire network. Using this method, we were able to determine the loading level at which the network with and without FACTS devices would collapse. The results are illustrated in Figs. 10 and 11. It is clear in Fig. 10 that λ = 1.09 is the critical load factor for the network without a FACTS device (here one SVC). This means that, when the loading of the network is equal to λ = 1.09, we have voltage collapse in the network without FACTS and the network with FACTS devices (one SVC) remains stable. However, the scenario for a load factor equal to λ = 1.11 is quite different. As may be observed in Fig. 11, at this stress level (λ = 1.11) the network will collapse in both conditions: with and without an SVC device. We can therefore conclude that the network with one SVC, allocated near the Montréal area, would have better steady-state stability against an increase in the loading level of the network. According to the allocation results, we would have 2.4% loadability improvement in the network with one SVC. In the results of the graphs presented in Figs. 10 and 11, the loadability improvement is equal to 2% (Δλ = = 0.02), which, as expected, is close to the allocation result (2.4%). 5 Two SVCs allocated in the Hydro-Québec network We repeated the allocation process for two SVCs on the Hydro-Québec network. The optimal locations, regions and values and also the effects of two SVCs on loadability and loss reduction are presented in Table 4. As can be seen from this table, for the Hydro-Québec network, with two SVCs with the size of 581 and 538 MVar allocated to bus number 11 (DUV315) in the area of Laval (a suburb of Montréal) and DSOUR1 in the Montréal Table 4 Allocation and effects of Two SVCs on the Hydro-Québec network Network test system FACTS devices Values and locations λ max Loss reduction Location Name Value, MVar Loadability,% λ LRI λ Reduction Region Hydro-Québec SVC Bus 11 DUV MW LSELaval (0.077%) SVC Bus 552 DSOUR MW LSEMontreal 1110 MW (0.15%) 9

10 Fig. 12 Comparison of voltage magnitudes of all buses in the Hydro-Québec network at maximum load factor λ max = region, the maximum load factor was determined as λ max = This means that, with two SVCs having the above-mentioned capacity, we have 3.3% improvement in the system loadability, which is equal to ( = ) 1110 MW. The bus voltages for the network with and without SVC devices at the maximum load factor λ max = are presented in Figs. 12 and 13. Similar to the previous section, we again compare the results obtained for two SVCs with the effects of two SVC locations determined by Hydro-Québec experts. The results are presented in Table 5 where it can be seen that the influence of the actual SVCs on buses 23 and 51 physically installed at Chénier and Bout-de-l Ile in the Hydro- Québec network is similar to the results of the allocated SVCs at buses 11 and 552. Although the maximum loadability for a real group of SVCs is λ max = 1.032, for the allocated SVCs this value is λ max = 1.033, that is, nearly the same. The influence of a two-svcs group on the total loss reduction is shown in Table 5 as well. The value of λ LRI is determined as 0.88 (λ LRI = 0.88). Under initial conditions with λ = 1.00, we would have a 26 MW (0.077%) loss reduction in the network whereas at maximum load factor (λ max = 1.033) we have 49 MW (0.15%) loss reduction. If a loss reduction of 26 MW can be sustained throughout the year (average value), it will have the same price as the transfer capacity, which has a price of about $80 /kw a year in the Hydro-Québec system. This means about $2.08 M of additional revenue a year could possibly be saved by properly locating the SVC, which is also serving other network functions. A 300 MVA SVC in Montréal area typically increases the voltage stability limit by 400 MW on the south interface which is voltage stability limited. Fig. 13 Comparison of voltage magnitudes of all buses in the Hydro-Québec network at another selected load factor λ =

11 Table 5 Comparison between allocation and effects of two SVCs on the Hydro-Québec network Type FACTS devices Values and locations λ max Voltage deviations Loss reduction Location Name Value, Region MVar Loadability Improvment, % λ lri λ Abs. value λ Reduction Paper result SVC Bus 552 DSOUR1 (LSEMontreal) SVC Bus 11 DUV315 (LSELaval) Actual SVC Bus 51 BDL315 (LSEMontreal) SVC Bus 23 CHE315 (LSELaval) MW (0.077%) MW (0.15%) MW (0.047%) MW (0.14%) 6 Comparing the effects of different number of SVCs on the Hydro-Québec network In this section, by repeating similar simulations as those in previous sections, the effects of different number of SVCs on the Hydro-Québec network are analysed and compared. The comparison between different number of SVCs for power system loadability is presented in Fig. 14a where it can be seen that by inserting three, four or five compared with two SVCs, there is no significant improvement in system loadability. Therefore two is the optimum number of SVCs for the Hydro-Québec network. Fig. 14 Comparing the influence of different numbers of SVCs on a Maximising power system loadability λ max b Reduction of total voltage deviation (TVD) 11

12 Fig. 15 Comparing the influence of different numbers of SVCs on a Loss reduction of transmission lines at initial load factor λ = 1.00 b Loss reduction of transmission lines at maximum load factor λ max The improvement in the reduction of voltage deviation at maximum loadability condition is also presented in Fig. 14b, from which it is clear that, by increasing the number of SVCs, there would be more reductions in the voltage deviation of buses. Also, Figs. 15a and b present the effect of different number of SVCs on the loss reduction of transmission lines. Specifically, Fig. 15b shows the loss reduction for an initial load factor λ = 1.00, whereas Fig. 15b shows the same variable at maximum load factor. As observed for system loadability, considering also the loss reduction of transmission lines, the optimum number of SVCs in the Hydro-Québec network is two. 7 Analysing the effects of STATCOM with energy storage in the Hydro-Québec network To understand the effect of a SMES in a better manner (associated with STATCOM), we compare this device with a STATCOM without storage. Since our entire optimisation process is conducted with the power system in steady-state condition, the modelling of the STATCOM is the same as that of an SVC. The analyses for a single STATCOM without storage and one STATCOM with SMES were performed for the Hydro-Québec network and for other IEEE test systems. The results, presented in Table 6, show quite clearly that, in the Hydro-Québec network when the STATCOM is associated with energy storage devices (SMES), there is not more improvement in loss reduction whereas the values for the maximum load factor are the same for both devices. For other IEEE test systems, the results are a little different. For example, in the 57-bus test system, with just one STATCOM we have 11% improvement in system loadability however, with one STATCOM associated with SMES this rate is 14%. For the 300-bus test system, though we have λ max = 1.05 with one STATCOM alone, for one STATCOM associated 12

13 Table 6 Comparison between the STATCOM with SMES device and a STATCOM alone in different power networks Network test system Location Value, MVar λ max Loadabilily Improvment, % One STATCOM One STATCOM with SMES λlri Voltage deviations λ Abs. value Loss reduction Location Value λ max Voltage deviations λ Reduction Loadability Improvment, % λlri λ Abs. value Loss reduction λ Reduction 9Bus Bus Bus Bus Bus Bus Bus Bus Bus Bus Hydro-Quebec Bus MW MW Bus MVar MW MW MW Branch MVar MW MW MW Bus MVar MW MW MW Bus MVar MW MW MW Bus MVar MW MW MW (0.047%) MW (0.071%) Bus MVar MW MW MW MW MW MW MW MW MW MW MW MW MW (0.038%) MW (0.068%) 13

14 with SMES this value is λ max = Using the results of this table we could conclude that, generally speaking, using energy storage devices (SMES) with STATCOM could result in greater loss reduction and greater loadability improvement. 8 Analysing the effects of different type of FACTS devices on the Hydro-Québec network This section describes the effects of different types of FACTS devices, comparing one and two devices for each of them, on the Hydro-Québec network. These simulations were performed to analyse the effects of different FACTS devices on system loadability and loss reduction. For example, comparisons of the effects of different FACTS devices on maximising the power system loadability are presented in Fig. 16a. As is clear from this figure, allocating one UPFC results in a maximum load factor of l UPFC max = 1.028, whereas for the SVC, it results in l SVC max = The TCPST has less effect on maximising the system loadability compared with other FACTS devices. Comparisons of the influences of different type of FACTS devices on the voltage deviation reduction at maximum load factor λ max, are also presented in Fig. 16b where it can be seen that one UPFC and one TCVR are the most effective devices for reducing the voltage deviation of buses. The effects of different types of FACTS devices on the loss reduction of transmission lines are presented in Figs. 17a and b. Fig. 17a shows the loss reduction at initial load factor λ = 1.00, whereas Fig. 17b shows the same objective at maximum load factor λ max. As is clear from this figure, considering the loss reduction, a UPFC is the most effective device, which must be related to the fact that the UPFC device actually consists of both shunt and series FACTS devices. Using the same results presented in Figs. 16 and 17, we can present as well the comparison between two devices of different types of FACTS (i.e. 2 SVCs against 2 UPFCs). We will then be in a position to compare the effects of Fig. 16 Comparing the influence of different type of FACTS devices on a Maximising power system loadability λ max b Reduction of TVD 14

15 Fig. 17 Comparing the influence of different type of FACTS devices on a Loss reduction of transmission lines at initial load factor λ =1 b Loss reduction of transmission lines at maximum load factor λ max different FACTS devices (with two units) on the steady-state performance of the Hydro-Québec network. As is clear from Fig. 16a, the maximum load factor with two UPFCs allocated is l 2 max UPFC = 1.036, whereas for the two SVCs it is l 2 max SVC = It is interesting that by increasing the number of TCPSTs from one to two, there is no improvement in the power system loadability. The graph related to the reduction of voltage deviation at maximum load factor is presented in Fig. 16b. We could also mention that by increasing the number of UPFCs from one to two, there is no improvement in the reduction of losses in transmission lines. Finally, as observed in Figs. 17a and b, the TCVR offers the greatest improvement in loss reduction by increasing the number of devices from one to two. Considering the loss reduction, there is no difference between one or two devices for TCPST as shown in Figs. 17a and b. Using the optimisation process presented here, these analyses could be repeated for three, four or five units of each device, as was done for the SVC in the paper. 9 Discussion We have identified several research papers aiming at quantifying the benefits, in terms of monetary values, of FACTS devices when used in deregulated electricity market for congestion management [26 28]. For example, in [28], using an OPF and GA-based optimisation procedure, different types of FACTS devices are optimally placed in a multi-machine power system to reduce the overall costs of power generation. The placement methodology considers simultaneously the cost of generating active and reactive powers and acquisition cost of selected FACTS devices for a range of operating conditions. The net present value (NPV) method is used to assess the economic value of the proposed methodology. The NPV is an engineering economy method to analyse between long-term benefits of a project (here FACTS installation on the network) againsttheinitialcostofthatproject[28]. In this paper, our goal was not to perform an investment-based planning study but rather to establish some basic locations for FACTS to maximise loadability 15

16 while hopefully minimising losses and comparing the effects of different FACTS on this goal. Once a good location is found, a systematic planning study with monetary inputs can be conducted to compare a FACTS solution with alternatives (lines, power plant and other equipment upgrades) and further investigate the economic savings resulting from the use of FACTS devices. For example, the price of an SVC installed in the Hydro-Québec network is typically from 50 to 80 M$ CAD. As we mentioned before, with a brief calculation based on our results in this paper, if a loss reduction of 26 MW can be sustained throughout the year (average value), it will have the same price as the transfer capacity, which has a price of about $80/kW a year in the Hydro-Québec system. This means about $2.08 M of additional revenue a year could possibly be saved by properly locating the SVC, which is also serving other network functions. As a result, similar to the methods used in [26 28] other investigation could be conducted to find out the long-term benefit of installing a FACTS device (e.g. SVC) by maximising loadability and/or minimising losses against the payment for the initial cost of that device. Regarding the reason of choosing GA as an optimisation algorithm in our FACTS placement study, let us recall that in Section 1 of this paper, there are two main approaches for optimal allocation of FACTS devices in power networks: heuristic methods and analytical methods. However, since the objective function of our optimisation process is complex, multi-layer and un-trackable with no direct algebraic function for the optimal problem, it is not practical to solve it using classic analytical methods which often rely on derivatives of the objective function such as line flow index (LFI) [29 31], the extended voltage phasors approach (EVPA) [32], mixed integer linear programming (MILP) [33 35]. In fact, to solve such a hard optimisation problem, heuristic derivative-free methods are more efficient. Among them, we have chosen GA. In [12], three different heuristic algorithms (GA, TS and SA) have been used for optimal allocation of FACTS devices and it was shown that the GA converged faster than TS and SA. Other attempts have been made to compare GA and PSO. For example, in [36], it is shown that in terms of computational effort, the GA approach is faster, although it should be noted that both algorithms took what was then considered an unacceptably long time to determine their results. Also, the GA seems to arrive at its final parameter values in fewer generations than the PSO [36]. In addition, the GA is flexible and easy to implement, in terms of building different types of individual and different number of populations. Finally, we should also mention that since the analysis reported in this paper has been conducted in steady-state condition, the modelling of SSSC and TCSC are similar to each other. For load-flow purposes in Matpower package [23], these two FACTS devices are represented by a variable-reactance inserted in the allocated branch line. In a similar way, the modelling of the STATCOM is similar to the SVC and both devices are represented by injected reactive power in the allocated bus. Therefore for load-flow analysis and modelling purposes SSSC and STATCOM have identical modelling features with TCSC and SVC, respectively. 10 Conclusion This paper presented analyses and a discussion of the effects of different types of FACTS devices on the steady-state performance of the Hydro-Québec network. Using a GA-based optimisation method, the optimal locations and values of different types of FACTS devices were determined and the performance of the network was analysed before and after inserting the FACTS devices. The effects of five different FACTS devices including SVC, TCSC, TCVR, TCPST, UPFC and STATCOM with SMES were presented. Based on the results, the UPFC was the most effective FACTS device if we want to increase the loadability while reducing the losses at the same time, even when the main objective function is maximising power system loadability. Another contribution of this paper is the study of the potential effects of FACTS with storage on steady-state network performance. 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