Method for selecting loads to be subjected to power curtailment and control system of a power grid implementing such method

Abstract

A computer-implemented method (10) for selecting loads (8) to be subjected to power curtailment, including: storing (100), for each load (8), the number of times (t0,i) the load (8) was selected to be subjected to power curtailment and the total duration (d0,i) of the periods during which the load (8) was subjected to power curtailment; storing (100) a state vector (x) including, for each load (8), a corresponding state (xi) alternatively indicating the selection of the load (8) for power curtailment or non-selection of the load (8) for power curtailment; identifying (105), based on the state vector (x), a candidate set, each candidate being formed by a corresponding load (8) whose state (xi) indicates the non-selection for power curtailment; determining, by minimising a cost function (f(x',t'0,d'0)), a primary variable vector (x'), wherein each primary variable (x'j) is associated with a corresponding candidate and is equal to a first value, which is indicative of the non-selection of the candidate for power curtailment, or a second value, which is indicative of the selection of the candidate for power curtailment; and updating the state vector (x) based on the primary variable vector (x').

Description

[0001] " METHOD FOR SELECTING LOADS TO BE SUBJECTED TO POWER CURTAILMENT AND CONTROL SYSTEM OF A POWER GRID IMPLEMENTING SUCH METHOD"

[0002] Cross-Reference to Related Applications

[0003] This Patent Application claims priority from Italian Patent Application No. 102024000026463 filed on November 25, 2024, the entire disclosure of which is incorporated herein by reference.

[0004] Technical field

[0005] The present invention refers to a method for selecting loads to be subj ected to power curtailment and to a control system of a power grid implementing such method.

[0006] Background

[0007] As is known, in the electric energy distribution / transmission sector, the need is felt to manage possible overload episodes. For such purpose, numerous methods have been proposed over time which allow determining how to reduce the electric power delivered to the single loads, with the aim to satisfy corresponding criteria.

[0008] For example, algorithms are known which, in the presence of an overload, allow determining how to reduce the electric power provided to the loads so as to minimise the costs that burden the grid manager, alternatively understood as the number of loads (and, thus, customers) subj ected to power curtailment or as the total power curtailment. Such algorithms are used in the current management systems for managing the electric energy distribution / transmission and allow selecting, from the loads of the grid, a subset of loads to be subj ected to power curtailment.

[0009] However, the Applicant has observed that the algorithms implemented in the current management systems for managing the electric energy distribution / transmission are such that the power curtailments determined by said systems are not optimal with regard to the equity of power curtailments from the point of view of the loads, namely from the point of view of the single users.

[0010] US 2014 / 316598 Al describes a method for managing resources in a power distribution grid.

[0011] CN 117 833 351 A describes a method for evaluating the operation risk in a power grid.

[0012] JP 2004 129404 A describes a method for forming an optimal distribution system.

[0013] CN 118 646 016 B describes a method for controlling load emergencies.

[0014] Summary

[0015] The obj ect of the present invention is thus to provide a method for selecting the loads to be subj ected to power curtailment capable of overcoming at least in part the drawbacks of the prior art.

[0016] According to the present invention, a method for selecting loads and a control system are provided as defined in the appended claims.

[0017] Brief description of the figures

[0018] In order to better understand the present invention, embodiments thereof are now described, by mere non-limiting example, with reference to the accompanying drawings, wherein:

[0019] - Figure 1 shows a block diagram of a portion of a power grid; and

[0020] - Figures 2 and 3 show flow diagrams according to the present method.

[0021] Description of embodiments Figure 1 shows an electric energy distribution / transmission grid 1, in short referred to in the following as the distribution / transmission grid 1.

[0022] The distribution / transmission grid 1 comprises at least one input line 2, a substation 4, which is a distribution or transmission substation, and a plurality of output lines 6.

[0023] By mere example, the input line 2 may be a high-voltage line or a medium- voltage line; although not shown, the input line 2 is coupled to an electric energy generation system (not shown), which provides electric power to the input line 2. Furthermore, the input line 2 couples the electric energy generation system (not shown) to the substation 4, which has detectors (not shown) which allow measuring the active power (indicated in the following by Pmeas) and the reactive power (indicated in the following by Qmeas) transferred along the input line 2; based on the active power Pmeas and the reactive power Qmeas, the substation 4 is capable of also calculating the complex power Smeas flowing in the input line 2, which in the following is also referred to as the power flow Smeas.

[0024] The output lines 6 exit the substation 4 and are each directed to a respective load 8. In practice, each output line 6 electrically couples the substation 4 to a corresponding load 8; more in particular, the substation 4 provides each load 8, through the corresponding output line 6, with a corresponding share of the power flow Smeas. By way of example, the output lines 6 may be medium- voltage or low-voltage lines.

[0025] In Figure 1 a control system 10 is also visible, which, without any loss of generality, is shown as external with respect to the substation 4, to which it is coupled through a respective communication channel 12; furthermore, the control system 10 is coupled to each load 8 through a corresponding communication channel, indicated by 14 (only one is shown in Figure 1 ). The communication channels 14 may be active also only temporarily.

[0026] In the following, the operations carried out by the control system 10 are described. For simplicity, it is assumed that the loads 8 are in a number equal to n; furthermore, an integer index i= 1, 2,..., n is assumed to index the loads 8.

[0027] Without any loss of generality, it is further assumed that each load 8 is capable of detecting and communicating to the control system 10, through the respective communication channel 14, the active power Pc,i and the reactive power Qc,i which are absorbed by the load 8, so that the control system 10 is further capable of determining the complex power Sc,i absorbed by the load 8.

[0028] It is further assumed that the loads 8 are each absorbing a respective apparent power | Sc,i I and that they are associated with corresponding power thresholds Sthr,i, which are established for example by contract or based on technical reasons and are known to the control system 10.

[0029] That having been said, the control system 10 is configured to execute the operations shown in Figure 2, for example in a periodic manner with a period equal to Tc.

[0030] In particular, at every iteration, the control system 10 updates (block 100) information relative to the number of times (occurrences) each of the loads 8 was selected to be subj ected to power curtailment and to the total duration of the time intervals during which each load 8 was subj ected to power curtailment.

[0031] In particular, as explained in detail in the following, the control system 10 updates:

[0032] - the values of a vector to formed by a number of elements equal to n, wherein each element indicates the number of times the corresponding load 8 was selected to be subj ected to power curtailment;

[0033] - the values of a vector do formed by a number of elements equal to n, wherein each element indicates the sum of the durations of the time intervals during which the corresponding load 8 was subj ected to power curtailment; and

[0034] - the values of a vector x formed by a number of elements equal to n, wherein each element is associated with a corresponding load 8 and is alternatively equal to one, if the corresponding load 8 is selected to be subj ected to power curtailment, or to zero, if the corresponding load 8 is not selected to be subj ected to power curtailment.

[0035] At the first iteration of the operations mentioned in block 100, the vectors to, do, x are null, whereas in the subsequent iterations the relative updates are executed, as explained in the following, based on a vector x', also described in the following.

[0036] Subsequently, the control system 10 identifies (block 105) the loads 8 that, during the current iteration of the operations mentioned in block 105, and in particular in a corresponding reference time instant, i) are reachable, namely have the respective communication channels 14 active, and ii) are not selected to be subj ected to power curtailment; in particular, in the following, reference is made to the candidates to indicate the loads 8 that are reachable and are not currently selected to be subj ected to power curtailment, namely are associated with elements of the vector x equal to zero. Furthermore, in the following it is assumed, for simplicity, that the communication channels 14 are always active, therefore it is assumed that the loads 8 are always reachable; consequently, the operations mentioned in block 105 end up identifying as candidates the loads 8 associated with elements of the vector x equal to zero.

[0037] In general, the candidates are in a number equal to n', with n' at most equal to n; furthermore, each candidate is associated with a corresponding element of the above-mentioned vector x', which thus has a dimension equal to n'. At the first iteration of the operations mentioned in block 105, n' =n occurs.

[0038] Then, the control system 10 acquires (block 110) information relative to the input line 2. In particular, the control system 10 acquires, through the communication channel 12, the measurement of the complex power Smeas,' furthermore, the control system 10 acquires the so-called net transfer capacity NTC of the input line 2. For example, the piece of information relative to the net transfer capacity NTC may be set by a user or may be communicated by the substation 4 to the control system 10.

[0039] Without any loss of generality, the net transfer capacity NTC may be equal to the difference between the so-called total transfer capacity TTC of the input line 2 and a transmission reliability margin TRM and may be expressed as TTC - ( l_e), wherein e represents a safety margin. Different definitions of the net transfer capacity NTC are anyway possible.

[0040] Subsequently, the control system 10 acquires (block 120) from each candidate, through the corresponding communication channel 14, the measurements of the active power and the reactive power absorbed by the candidate and the corresponding power threshold, the latter being able to be acquired by the control system 10 also in another way ( for example, it may be preset). In such manner, as previously mentioned, the control system 10 is capable of determining the complex power Sc,i absorbed by each candidate, and thus also the apparent power | Sc,i l, and the relative phase angle.

[0041] In other words, adopting for greater clarity an integer index j = 1,..., n' to index the candidates, and generically referring to the j -th candidate, it communicates to the control system 10 the active power and the reactive power absorbed by it, so that the control system 10 calculates the complex power (and thus also the apparent power) absorbed by the j -th candidate; alternatively, it is anyway possible also for the complex power absorbed by the j -th candidate to be communicated to the control system 10 by the candidate. In such regard, for clarity, in the following, the active power, the reactive power, the complex power and the apparent power absorbed by the j -th candidate are indicated by P'c,j, Q'c,j, S'c,j and | S'c,j I, respectively; the relationships P'c,j = Pc,i, Q'c,j = Qc,i, S'c,j = Sc,i and S' thr,j = Sthr,i are thus valid, if the j -th candidate is formed by the i-th load 8.

[0042] Subsequently, the control system 10 executes (block 130) an overload management algorithm, which is described subsequently and is such that, at the end of the execution, the following occurs: referring to the j-th element x' j of the vector x', the element x' j is alternatively equal to zero, if the execution of the overload management algorithm determined that the j -th candidate was not selected to be subj ected to power curtailment, or to one, if the execution of the overload management algorithm determined that the j -th candidate was selected to be subj ected to power curtailment.

[0043] Then, the control system 10 sends (block 140) to each candidate, through the respective communication channel 14, an indication to curtail the absorbed power, if the corresponding element of the vector x' is equal to one, or an indication relative to the lack of need to curtail the absorbed power, if the corresponding element of the vector x' is equal to zero; in this second case, variants are possible wherein no indication is sent. In other words, the indication to curtail the absorbed power is sent to the sole candidates that were selected during the operations mentioned in block 130. Furthermore, without any loss of generality, it is for example possible for the loads 8 to be directly controllable by the control system 10, so that each selected candidate curtails the absorbed apparent power up to making it equal to or lower than the respective power threshold S' thr,j, after receiving, through the respective communication channel 14, the indication to curtail the absorbed power. It is also possible for the loads 8 not to be directly controlled by the control system 10, but to be anyway configured to curtail the absorbed apparent power, up to making it equal to or lower than the respective power threshold S' thr,j, after receiving the indication to curtail the absorbed power; in such case, the control system 10 may anyway implement a safeguard mechanism that forces the power curtailment of a load 8, if the latter, despite having been selected, does not autonomously curtail the absorbed power within a time limit.

[0044] At the subsequent iteration of the operations mentioned in block 100, the control system 10 executes the following operations:

[0045] - updates the vector to so that, referring to the i-th load 8, the i-th element to,i is increased by one unit, if the i-th load 8 was previously selected, during the operations mentioned in block 130, to be subj ected to power curtailment, and namely if the corresponding element of the vector x' is equal to one; on the contrary, the i-th element to,i is not modified, if the i-th load 8 was not selected, during the operations mentioned in block 130, to be subj ected to power curtailment, and namely if the corresponding element of the vector x' is equal to zero;

[0046] - updates the vector do so that, referring to the i-th load 8, the i-th element do,i is increased by a time equal to the period Tc, if the corresponding element of the vector x is equal to one, otherwise the i-th element do,i is not modified, if the corresponding element of the vector x is equal to zero; and subsequently

[0047] - updates the vector x, as is described in the following. In detail, as mentioned in the foregoing, the update of the vector x occurs subsequently the update of the vectors to and do and occurs based on the vector x' calculated during the previous execution of the operations mentioned in block 130. In greater detail, considering the i-th element x± of the vector x, it is updated in the following manner:

[0048] - if x± is equal to zero, it is set equal to one, if the corresponding element of the vector x', and namely the element of the vector x' relative to the same load 8 to which the i-th element x± of the vector x refers, is equal to one, otherwise x± is left equal to zero, if the corresponding element of the vector x' is equal to zero;

[0049] - if Xi is equal to one, it is set equal to zero if the corresponding load 8 has ceased curtailing its power, otherwise it is left equal to one; in particular, the cessation of the power curtailment may be detected by the control system 10 in different manners, such as for example counting the time elapsed between the instant when Xi was previously set equal to one and detecting when the time counting exceeds a threshold (in such case, the control system 10 detects the cessation of the power curtailment without any collaboration by the load 8 ) or detecting a reset command of the power curtailment carried out by an operator of the control system 10.

[0050] In light of the above, it results that, considering a generic execution of the overload management algorithm mentioned in block 130 and the vector x' thereby generated, the subsequent update of the vector to occurs based on the vector x', whereas the update of the vector do occurs based on the vector x as available before being updated based on the vector x'. In such manner, if the vector x' indicates that a generic candidate must be subj ected to power curtailment, the counting of the selection events for the purposes of power curtailment relative to such candidate is increased already during the immediately subsequent execution of the operations mentioned in block 100, whereas the total duration of the time intervals during which such candidate was subj ected to power curtailment is not increased in such immediately subsequent execution of the operations mentioned in block 100, since no further time has actually elapsed in which such candidate was subj ected to power curtailment; the increase in the total duration will thus occur at the subsequent iteration of the operations mentioned in block 100, because at that point the candidate will have actually spent a time equal to the period Tcin a state of power curtailment. Furthermore, the total duration of the time intervals during which such candidate was subj ected to power curtailment will continue to be increased by a time equal to the period Tcat each iteration of the operations mentioned in block 100, as long as the corresponding element of the vector x remains equal to one. Furthermore, with regard to the counting of the selection events for power curtailment relative to a generic load 8, it is increased by one unit when the corresponding element of the vector x' is equal to one; subsequently, such load 8 will no longer be part of the candidates, and thus it will no longer be possible to further increase the relative counting, until the load 8 has ceased curtailing its absorbed power, with consequent switching to zero of the corresponding element of the vector x and thus with consequent new possibility to be identified as a candidate.

[0051] In practice, the vector x is a state vector and indicates, for each load 8, whether it is currently in a selection state to be subj ected to power curtailment. Furthermore, given a generic load 8, the corresponding element of the vector x switches from zero to one after such switch was caused by the fact that the element of the vector x' referred to such load 8 assumed the value one; the switching to one of such corresponding element of the vector x initiates the subsequent update of the total duration of the time intervals during which such load 8 was subjected to power curtailment and temporarily (namely, during one or more of the subsequent iterations of the operations mentioned in block 105) makes such load 8 not identifiable as a candidate.

[0052] Referring now to the overload management algorithm that is executed by the control system 10, it is described with reference to Figure 3.

[0053] In detail, the control system 10 calculates (block 200) a quantity indicated as overload OVL, which is equal to:

[0054] O

[0055]

[0056] VL = \Smeas- ■ X;)| - NTC with

[0057] A

[0058]

[0059] SCit — (|SC,£| — Sthr i)

[0060] In other words, in the calculation of the overload OVL, each load 8 selected to be subj ected to power curtailment (therefore, such that x±=l ) generates a negative or null contribution, the magnitude of which depends on whether the load 8 actually curtailed the absorbed apparent power. In detail, in the case where the load 8 has not yet actually curtailed the absorbed apparent power, ASc,i>0 occurs, a corresponding contribution is thus generated equal to ASc,i which is subtracted from the complex power Smeas,' on the contrary, if the load 8 has already actually curtailed the absorbed apparent power, ASc,i<=0 occurs, therefore no corresponding contribution is generated to be subtracted from the complex power Smeas, which, however, already has in itself the piece of information relative to the corresponding power curtailment. In practice, in the determination of the overload OVL, both the power curtailments actually active at the moment of the calculation, as directly impacting on the measurement of the complex power Smeas, and the power curtailments not yet active, for example due to execution delays by the loads 8, but already planned, are considered.

[0061] Subsequently, the control system 10 verifies (block 210) whether the overload OVL is less than zero.

[0062] If the overload OVL is less than zero (output YES in block 210), it means that no overload is occurring or that anyway the current selection of the loads for power curtailment is sufficient to eliminate the overload when the selected loads will actually curtail the absorbed power, therefore the control system 10 may not signal anything to the loads 8; consequently, all the elements of the vector x' are set equal to zero (block 215) and the execution of the overload management algorithm is ended.

[0063] If the overload OVL is greater than or equal to zero (output NO in block 210), it means that the current selection of the loads for power curtailment is insufficient to eliminate the overload, even when the selected loads will actually curtail the absorbed power, therefore it is necessary to select further loads for power curtailment. Consequently, the control system 10 calculates (block 220) the total available limitation power ALP, which is equal to the vector sum of the available limitation capability of the candidates, wherein the available limitation capability of the j -th candidate is equal to the difference between the complex power absorbed by the j -th candidate and its own power threshold, if the candidate absorbs an apparent power higher than its own power threshold, otherwise it is null.

[0064] Then, the control system 10 verifies (block 230) whether the modulus of the total available limitation power ALP is greater than the overload OVL.

[0065] If the modulus of the total available limitation power ALP is lower than or equal to the overload OVL (output NO in block 230), the control system 10 selects (block 240) all the candidates, namely sets at one all the elements of the vector x', and ends the execution of the overload management algorithm, so that the operations mentioned in block 140 are then executed. In such manner, all the candidates are sent an indication to curtail the absorbed power.

[0066] If the modulus of the total available limitation power ALP is greater than the overload OVL (output YES in block 230), the control system 10 executes (block 250) an optimal selection algorithm, so as to select, from the candidates, a subset of candidates such that, by curtailing only the power absorbed by the candidates of the selected subset, the overload is eliminated, minimising the number of candidates subj ected to limitation and the total amount of limited power (these two parameters being indicative of the cost for the operator of the system) and optimising, at the same time, the equity of the power curtailments; in particular, as clarified in the following, the equity is understood both as capability to distribute in a fair manner the requests for power curtailment among the candidates, and as capability to equalise the total time in which the candidates are subj ected to power curtailments.

[0067] In greater detail, the optimal selection algorithm is a multi-obj ective optimisation algorithm of the mixed integer quadratic programming (MIQP) type.

[0068] Still in greater detail, the optimal selection algorithm can be formulated as:

[0069] mlnf x', t'o, d'o)

[0070] X!

[0071] subj ected to

[0072] h(x', t'Q, d'o) = 0

[0073] g(x',t'o, d'o) < 0

[0074] wherein: the vector t' o represents a vector formed by the elements of the vector to relative to the candidates, such vector having a dimension equal to n'; the vector d' o represents a vector formed by the elements of the vector do relative to the candidates, such vector having a dimension equal to n'; f (x', t ' o, d' o) represents a multi-obj ective function to be minimised, which depends on the elements of the vector x', which form corresponding primary variables, and on the elements of the vectors d' o and t' o, which in turn represent secondary variables that depend on the primary variables; h (x', t ' o, d' o) represents a set of equality constraints which must be respected; and g (x', t ' o, d' o) represents a set of inequality constraints which must be respected.

[0075] In particular, the equality constraints h (x', t ' o, d' o) include the following equations (wherein j = l,..., n' ):

[0076]

[0077] d'j = d'o+ At • x'j

[0078] wherein t' o,j indicates the number of times the j -th candidate was selected to be subj ected to power curtailment prior to the execution of the optimal selection algorithm, whereas d' o,j indicates the sum of the durations of the time intervals during which the j -th candidate was subj ected to power curtailment prior to the execution of the optimal selection algorithm. In such regard, it is reminded that the j -th candidate is the load 8 that corresponds to the j -th element of the vector x' during the execution of the optimal selection algorithm. Furthermore, At represents the expected duration of each event of power curtailment, namely the duration of the single time interval during which a load 8 is subj ected to power curtailment. For simplicity, it is assumed that the time At is fixed. More in particular, without any loss of generality, it is assumed that the time At may be set by a user or predetermined and is independent of the selected load 8. Furthermore, the relationship Tc< At can be valid. The equality constraints h (x', t' o, d' o) further comprise setting x' j=0 for each candidate that absorbs an apparent power I S'c,j I lower than the respective power threshold S' thr,j. Such constraint is anyway optional, but can allow quickening the execution of the optimal selection algorithm.

[0079] Additionally, referring to a generic j -th candidate, the equality constraints h (x', t ’ o, d' o) also comprise the following equation:

[0080]

[0081] = x’j ■ (|S'cJ| - S'thrj)

[0082] wherein ASc,j indicates the curtailment of the apparent power absorbed by the j -th candidate.

[0083] Consequently, the contribution of the j -th candidate in the total power curtailment can be expressed as:

[0084] ^

[0085]

[0086] Pcj & SCj • COS 4^c,j

[0087] Qcj & SCj • sin^>cj

[0088] wherein is the phase-displacement angle of the j -th candidate (namely the phase angle of the j -th candidate) and is equal to:

[0089]

[0090] Furthermore, the equality constraints h (x', t ' o, d' o) also comprise: n>

[0091] APtot=APcj

[0092] j=i

[0093] n>

[0094] AQtot=AQcj

[0095] j=l

[0096] AStot + AQ?

[0097]

[0098] ot

[0099] whereas the inequality constraints g (x', t ' o, d' o) comprise:

[0100] AStot> OVL

[0101] wherein APtot and AQtot indicate the total active power and reactive power curtailments, respectively, whereas AStot indicates the total apparent power curtailment. In greater detail, AStot is also equal to the modulus of the vector sum of the phasors that are relative to the candidates selected to be subj ected to power curtailment and have moduli each respectively equal to the difference ASc,j between the apparent power | S'c,j | absorbed by the corresponding candidate and the respective power threshold S' thr,j, such phasors further having phases respectively equal to the phase angles

[0102]

[0103] of the corresponding candidates.

[0104] Whereas, in that concerns the function f (x', t ’ o, d' o), it can be expressed as:

[0105] fA(x') fB(x',t'o) fc(x,d0) fD(x ) f(x',t'o,d'o) = A - + D - -; - +c• dd- - + D •

[0106]

[0107] kA kc kD

[0108] wherein:

[0109] - fA is a function that increases as the number of the candidates selected to be subj ected to power curtailment increases and is for example equal to: IV

[0110] fA(x') = x'j

[0111]

[0112] j=l

[0113] - fa is a function which increases as the dispersion of the numbers of selection occurrences increases, for the purposes of power curtailment, relative to the candidates and is for example equal to:

[0114] ru yn' f.

[0115] fB(x',t'o) = ^(t'j - tavg)2

[0116] Lavg” n'

[0117]

[0118] j=l

[0119] wherein tsvgindicates the average of the numbers of selection occurrences to which candidates would be subj ected;

[0120] - fc is a function which increases as the dispersion of the total durations of the periods of time during which the candidates are subj ected to power curtailment increases and is for example equal to:

[0121] V”1X”' rife (x', d'o) = 2 / d'j - davg)2davg=1

[0122]

[0123] j=i

[0124] wherein davgindicates the average of the total durations of the periods of time during which the candidates would be subj ected to power curtailment; and

[0125] - fn is a function which increases as the total apparent power curtailment increases and is for example equal to:

[0126] fD(x) = AStot

[0127] In practice, in the present example, the function f (x', t ' o, d' o) contains a term that linearly increases as the number of the candidates that are selected increases, a term that linearly increases as the total apparent power curtailment AStot increases, as well as a pair of additional terms which are directly proportional to the variance of the selection occurrences, for the purposes of power curtailment, of the candidates and to the variance of the total durations of the periods of time during which the candidates are subj ected to power curtailment, respectively.

[0128] Furthermore, the terms of the function f (x', t ’ o, d' o) comprise normalisation coefficients indicated respectively by kA, ke, kc, ko, which make the terms comparable with one another. In particular, the normalisation coefficients are respectively equal to the maximum values possible of the functions fA, fa, fc, fB, so that each of the ratios fA / kA, fB / kB, fc / kc, fB / kBis dimensionless and comprised between zero and one.

[0129] Still more in particular, kA is for example equal to the number n' of candidates.

[0130] With regard to kB, it is obtained by solving the following maximisation problem, as the control variable still represented by the vector x' varies, and with the same equality constraints h (x', t ’ o, d' o) (except the constraint relative to d' j ) and inequality constraints g (x', t ' o, d' o):

[0131] n'

[0132] max functl(x', t'o) = ^(t'j — tavg)2

[0133]

[0134] j=i

[0135] wherein the following is still valid: _ 2 y^Jn^'1 f L J.

[0136]

[0137] Lavg” n'

[0138] With regard to kc, it is obtained by solving the following maximisation problem, as the control variable still represented by the vector x' varies, and with the same equality constraints h (x', t ' o, d' o) (except the constraint relative to t' j ) and inequality constraints g (x', t ' o, d' o):

[0139] n'

[0140] max funct2 (x', d0) = ^(d'j — davg)2

[0141]

[0142] j=i

[0143] wherein the following is still valid:

[0144] 2 y^p='1 d a' j.

[0145] uavgn,

[0146]

[0147] Finally, with regard to kn, it is for example equal to the maximum total curtailment capacity available; for example, the relationship kD=ALP may be valid.

[0148] Still with reference to the terms of the function f (x', t ’ o, d' o), they also comprise the factors A, B, C, D, which may be set so as to assign each time different priorities, namely weights, to the terms of the function, so that the minimisation problem privileges respectively a minimisation criterion of the number of selected candidates, a minimisation criterion of the dispersion of the numbers of selection occurrences for power curtailment, a minimisation criterion of the dispersion of the total durations of the periods of time during which the candidates are subj ected to power curtailment and a minimisation criterion of the total apparent power curtailment. By way of mere example, it is anyway possible to assume A=D=1 and B=C=0.5.

[0149] Furthermore, in order to increase the calculation efficiency, and in particular to reduce the computational costs, it is possible for the optimal selection algorithm executed during the operations mentioned in block 250 to make use of a different function f (x', t ’ o, d' o), if corresponding initial conditions are respected. In particular, in the case where the vectors t' o and d' o both have all the elements equal, and thus in the case where the candidates were previously selected for power curtailment a same number of times and were further subj ected to power curtailment for total periods having a same duration, it is possible to adopt the following simplified function:

[0150] ,,. fA(x') fD(x')

[0151] / (x') = A - — - + D • — —

[0152]

[0153] KAKD

[0154] Whereas, in the case where only the vector d' o has all the elements equal, and thus only the total durations of the periods of power curtailment of the candidates are balanced, it is possible to adopt the following function:

[0155] fA(X'), „ fB(X'-t'o) fD(X')

[0156] f(x', t'o) =

[0157]

[0158] ’ “Kk -A+ B- kK-B+ D’ “Kk -D

[0159] Whereas, in the case where only the vector t' o has all the elements equal, and thus only the numbers of selection occurrences for power curtailment are balanced, it is possible to adopt the following function:

[0160] f(, X.fA(x'),rfc(x',d'o) fD(x') f(x,d0) = A -— - + C - - - + D -— — —

[0161]

[0162] KAKCKD The advantages that the present method allows obtaining clearly emerge from the previous description. In particular, thanks to the minimisation of the dispersion of the numbers of selection occurrences for power curtailment and of the total durations, the selection of the candidates to be subj ected to power curtailment results to be fair from the point of view of the candidates, besides optimised with regard to the operating cost.

[0163] Finally it is clear that modifications and variations can be made to the previously described method, without departing from the scope of protection of the present invention, as defined in the appended claims.

[0164] For example, the function f (x', t ’ o, d' o) may differ from what described. For example, referring to the function fB, it may be directly proportional, instead of to the variance of the selection occurrences for the purposes of power curtailment, to a different statistical dispersion index of the selection occurrences, such as for example the standard deviation; more in general, the dependence of the function fBon such statistical dispersion index may be non-linear. Similarly, referring to the function fc, it may be directly proportional, instead of to the variance of the total durations of the periods of power curtailment, to a different statistical dispersion index of the total durations of the periods of power curtailment, such as for example the standard deviation; more in general, the dependence of the function fc on such statistical dispersion index may be non-linear.

[0165] More in general, embodiments are possible wherein the function f (x, t' o, d' o) comprises only one of the term including the function fA and the term including the function fn and only one of the term including the function fe and the term including the function fc.

[0166] With regard to the function fn, embodiments are possible wherein it increases as APtot increases, instead of as AStot increases.

[0167] The arrangement of the control system 10 may differ from what shown. For example, the control system 10 may be integrated in the substation 4.

[0168] The distribution / transmission grid 1 and the communication channels 12, 14 may differ from what shown. For example, several input lines may be present which are connected to the substation 4 and the overload of one of them can be due, for example, to a problem manifested on another input line. It is further possible for other types of loads to be present, which are coupled to the substation 4 and are for example loads not controllable by the control system 10, but can anyway contribute to causing the overload; such types of loads are not considered during the execution of the present method, since they may not be subj ected to power curtailment.

Claims

CLAIMS1. A computer-implemented method ( 10 ) for selecting loads ( 8 ) to be subj ected to power curtailment, said loads being electrically coupled to an input line ( 2 ), said method comprising:- storing ( 100 ), for each load ( 8 ), the number of times ( to,i ) the load ( 8 ) was selected to be subj ected to power curtailment and the total duration ( do,i ) of the time intervals during which the load ( 8 ) was subj ected to power curtailment;- storing ( 100 ) a state vector (x ) comprising, for each load ( 8 ), a corresponding state (x± ) alternatively indicating the selection of the load ( 8 ) for power curtailment or nonselection of the load ( 8 ) for power curtailment;- identi fying ( 105 ), based on the state vector (x ), a candidate set, each candidate being formed by a corresponding load ( 8 ) whose state (x± ) indicates the non- selection for power curtailment;- acquiring ( 120 ), for each candidate, measurements of the active power ( P'c, j ) and of the reactive power ( Q'c, j ) absorbed by the candidate and determining the apparent power ( | S 'c, j I ) absorbed by the candidate and the phase angle of the candidate;- determining, by minimising a cost function ( f (x', t ’ o, d' o ) ), the values of a primary variable vector (x' ), wherein each primary variable (x ' j ) is associated with a corresponding candidate and is alternatively equal to a first value, which is indicative of the non-selection of the candidate for power curtailment, or a second value, which is indicative of the selection of the candidate for power curtailment; and- updating the state vector (x ) based on the values of the primary variable vector (x ' );and wherein the cost function ( f (x, t ' o, d' o ) ) comprises: - at least one operating cost term ( fA, fD) chosen from a first term ( fA), which increases as the number of primary variables (x' j ) equal to the second value increases, and a fourth term ( fD), which increases as a power quantity ( AStot; APtot) increases, which is equal to the modulus ( AStot) of a sum of phasors, each phasor having a modulus that is a function of the di f ference between the apparent power ( | S 'c, j I ) absorbed by a corresponding candidate associated with a primary variable (x ' j ) equal to the second value and a corresponding power threshold ( S ' thr, j ), each phasor further having a phase which depends on the phase angle of said corresponding candidate, or is equal to a sum (APtot) of contributions equal, each, to the product of the di fference between the apparent power ( | S 'c,j I ) absorbed by a corresponding candidate associated with a primary variable (x' j ) equal to the second value and the corresponding power threshold ( S ' thr, j ) and the cosine of the corresponding phase angle; and- at least one equity term ( fB, fc) chosen from a second term ( fB), which increases as a dispersion index of first auxiliary variables ( t ' j ) increases, and a third term ( fc), which increases as a dispersion index of second auxiliary variables ( d' j ) increases, each first auxiliary variable ( t ' j ) being a function of the primary variable (x' j ) associated with a corresponding candidate and of the stored number of times ( t ' o, j ) said corresponding candidate was selected to be subj ected to power curtailment, each second auxiliary variable ( d' j ) being a function of the primary variable (x' j ) associated with a corresponding candidate and of the stored total duration ( d' o, j ) of the time intervals during which said corresponding candidate was subj ected to power curtailment.

2. The method according to claim 1, further comprising: - acquiring a measurement of the complex power (Smeas) transiting on the input line ( 2 ); and- calculating a line quantity ( OVL ) that depends on the di f ference between the complex power ( Smeas ) transiting on the input line ( 2 ) and a sum of contributions comprising, for each load ( 8 ) whose state (x± ) indicates the selection for power curtailment, a null contribution, i f the apparent power ( | Sc,i l ) absorbed by the load ( 8 ) i s equal to or lower than the corresponding power threshold ( Sthr, i ), or a contribution ( I Sc,i I - Sthr, i ) equal to the di f ference between the apparent power ( | Sc,i l ) absorbed by the load ( 8 ) and the corresponding power threshold ( Sthr, i ), i f the apparent power ( | Sc,i I ) absorbed by the load ( 8 ) is higher than the corresponding power threshold ( Sthr, i );- detecting, based on the line quantity ( OVL ), whether the selected loads ( 8 ) are suf ficient to avoid an overload on the input line ( 2 ) or to eliminate the overload on the input line ( 2 );- i f it is detected that the loads ( 8 ) selected for power curtailment are not suf ficient to avoid or eliminate the overload on the input line ( 2 ), performing said steps of determining the values of the primary variable vector (x' ) and updating the state vector (x ) based on the values of the primary variable vector (x' ).

3. The method according to claim 2, wherein said minimisation of the cost function ( f (x ', t ’ o, d' o ) ) comprises determining the values of the primary variable vector (x' ) so that said modulus ( AStot) of said sum of phasors is at least equal to said line quantity ( OVL ).

4. The method according to any one of the preceding claims, comprising iterating the steps of: identi fying ( 105 )a candidate set; for each candidate, acquiring ( 120) measurements of active power (P'c,j ) and reactive power (Q'c,j ) and determining the absorbed apparent power ( | S'c,j I ) and the phase angle; and determining the values of the primary variable vector (x' ) and updating the state vector (x); and wherein storing ( 100) the number of times (to,i) each load ( 8 ) was selected to be subj ected to power curtailment comprises updating at each iteration, for each candidate associated with a primary variable (x' j ) equal to the second value, the corresponding number of times stored; and wherein storing ( 100) the total duration (do,i) of the time intervals during which each load ( 8 ) was subj ected to power curtailment comprises increasing the stored total duration (do,i) of each load ( 8 ) whose state (x±) indicates the selection for power curtailment, before updating the state vector (x) based on the values of the primary variable vector (x' ).

5. The method according to any one of the preceding claims, further comprising updating the state vector (x) so that, following the cessations of power curtailments of the loads ( 8 ), the corresponding states (x±) indicate the nonselection for power curtailment.

6. The method according to any one of the preceding claims, wherein each second auxiliary variable (d' j ) also depends on an expected duration (At) of the power curtailment.

7. The method according to any one of the preceding claims, wherein the cost function ( f (x', t ’ o, d' o) ) comprises the first, second, third and fourth terms ( fA, fB, fC, fD) and said power quantity (AStot) is equal to said modulus (AStot) of said sum of phasors.

8. The method according to claim 7, wherein, if the stored numbers of times (t' o,j ) the candidates were selected to be subj ected to power curtailment are equal, the cost function( f (x, t ' o, d' o ) ) is devoid of the second term ( fa); and wherein, i f the stored total durations ( d' o, j ) of the time intervals during which the candidates were subj ected to power curtailment are equal, the cost function ( f (x, t ' o, d' o ) ) is devoid of the third term ( fc).

9. The method according to any one of the preceding claims, wherein determining, by minimising a cost function ( f (x', t ’ 0, d' 0 ) ), the values of the primary variable vector (x' ) comprises setting as equal to the first value the primary variables (x' j ) associated with candidates absorbing apparent powers ( | S ' c, j I ) lower than or equal to their respective power thresholds ( S ' thr, j ).

10. A control system comprising media ( 10 ) configured to execute the method according to any one of the preceding claims.

11. An electrical system comprising the control system ( 10 ) according to claim 10 and the loads ( 8 ), the control system ( 10 ) being further configured to control the loads ( 8 ) so that each candidate associated with a primary variable (x' j ) equal to the second value curtails the absorbed apparent power ( | S ' c, j l ) so that the absorbed apparent power ( | S 'c, j I ) is lower than or equal to the corresponding power threshold ( S ' thr, j ).

12. A computer program comprising instructions which, when the program is executed by a computer, cause the method according to any one of claims 1 to 9 to be executed by the computer.

13. A computer-readable medium, on which the computer program according to claim 12 is stored.2 «

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