Control of operation of protection relay

FIELD

0001The present invention relates to control of a protection relay and more particularly to control of a protection relay operating in an electric network.

BACKGROUND

0002Relays are used in protection of electric networks and devices, for instance. Relay protection functions may be implemented as constant-time functions, where the operation time is independent of the value of the characteristic measure, such as current, voltage or frequency. Alternatively, relay protection functions may be inverse-time dependent, when the operation time is inversely dependent on the magnitude of the measured signal.

0003The inverse-time based algorithm analysis is typically based on the assumption that the current or overcurrent exceeding a set current threshold value or undercurrent undershooting a set current threshold value is constant during the measurement time. This results in a simple analogy between theoretical calculations and implementation. However, in practice fluctuation and variation in the characteristic measure magnitude level result in a realized operation time of the device.

0004<patcit id="pcit0001" dnum="US4672501A"><text>US 4,672,501</text></patcit> discloses a protective relay for continuously monitoring the electrical status of a protected power distribution system. The ROM and RAM storage elements within the processor are continuously tested and the circuit breaker contacts are opened upon indication that the ROM or RAM element is non-functional.

0005<patcit id="pcit0002" dnum="US5987393A"><text>US 5,987,393</text></patcit> discloses a system for generating a time overcurrent curve from a set of time and current inputs. The overcurrent curve is generated by simultaneously finding four coefficients of a standard overcurrent equation.

0006<patcit id="pcit0003" dnum="US6330141B"><text>US 6,330,141</text></patcit> discloses an electronic protective relay emulating an electromechanical protective relay so that operation of the two types of relays can be coordinated in providing protection in an electric power distribution network.

0007<patcit id="pcit0004" dnum="US20060291120A"><text>US 2006/0291120</text></patcit> discloses a dynamically configurable relay element configured to protect an electrical system.

SUMMARY

0008An object of the present invention is thus to provide a method and an apparatus for implementing the method so as to alleviate the above disadvantages.

0009The present invention is further defined in the appended claims.

DRAWINGS

0010In the following the invention will be described in greater detail by means of preferred embodiments with reference to the attached drawings, in which <ul id="ul0001" list-style="none" compact="compact"><li><figref idref="f0001">Figure 1</figref> shows a state diagram of an electronic device;</li><li><figref idref="f0002">Figure 2</figref> shows another state diagram of an electronic device;</li><li><figref idref="f0003">Figure 3</figref> shows an example of dependence of the signal magnitude on time;</li><li><figref idref="f0001">Figure 4</figref> shows an embodiment of a method; and</li><li><figref idref="f0004">Figure 5</figref> shows an embodiment of an apparatus.</li></ul>

DESCRIPTION OF EMBODIMENTS

0011<figref idref="f0001">Figure 1</figref> shows an embodiment of a state diagram of a protection relay. The protection relay inputs a characteristic quantity, upon which operation decisions and different functionalities may be carried out in the protection relay. In the following figures and description, the characteristic quantity is current, but may as well be some other measure, such as voltage, frequency, or temperature, for instance. In the following, the invention is explained in respect of an overcurrent relay that is the overfunction is overcurrent. The invention may as well be applied to an underfunction relay such as an undercurrent relay, in which case the operation is reverse to what is explained in the following.

0012In the simplified state diagram of <figref idref="f0001">Figure 1</figref>, four states have been depicted. In INITIAL state, the device is not yet in use. When the device is taken into use, that is coupled to the system to be used, a state transition "1" to state ACTING is carried out. In state ACTING, the device is measuring the characteristic quantity, on which the operation of the device is dependent. If the relay is responsive to an over function measure, such as overcurrent, the device will react on a current exceeding a threshold value of the current. An example of a relay responsive to an under function measure is an undercurrent relay, which will react on current undershooting a threshold value.

0013A state transition "2" from state ACTING to PICKUP depicts the situation where the current level exceeds a startup threshold value. In state transitions "3" and "4", the device is kept in PICKUP state. In "3", the nominator of equation 15 is increased but the nominator value does not yet exceed the denominator value. During this state transition, the value of the input variable is higher than the start-up threshold value.

0014A hysteresis region may be introduced around the startup threshold value, preventing unnecessary state transitions due to a current that oscillates around the startup threshold value. For overfunction, the hysteresis widens the signal range downwards, while for under function upwards. The state transition "4" describes a situation where the current is in the hysteresis region, which may be e.g. 2% under the startup threshold value, for instance, if 2% hysteresis has been set. Alternatively, the hysteresis region may extend to both sides of the startup threshold, which in the above example would give a +/- 2% region.

0015The hysteresis setting may be a factory setting value, which may be determined based upon the transformer measurement inaccuracy etc. In an ideal case, from a pure algorithm point of view, hysteresis may even be set to zero but in practice it may be set to a value above zero. During this time, the equation 15 ratio is freezed, that is it is neither increased nor decreased.

0016When the equation 15 nominator value finally exceeds the same equation denominator value, a state transition "5" PICKUP->OPERATE is executed. State OPERATE is kept as shown by arrow "6", while the signal stays above the startup threshold minus the hysteresis value.

0017If the input signal value drops below the startup threshold value minus the hysteresis value, the state is changed to ACTING as indicated by arrow "7". Alternatively, a different hysteresis value than that used in PICKUP state may be used in OPERATE state to reset the operation back to ACTING. In another embodiment, a reset type equation may be used to this. In this case, state RESET_OPERATE is first reached with a state transition "12" and then the reset equation is followed, which gradually decreases the equation 15 nominator to zero, causing the state change RESET_OPERATE->ACTING shown by arrow "13".

0018DROPOFF state may be reached from PICKUP state when the current falls under the threshold minus the hysteresis value as indicated by arrow "8".

0019In DROPOFF state, two internal state transitions 9 and 10 and the third transition 14 are introduced. The first transition "9" describes the situation where the input signal lies in the hysteresis region with the result that the calculation of the nominator/denominator of equation 15 is freezed, while the opposite state transition "14" follows if the signal magnitude exceeds the startup threshold value again. The state transition "10" describes the situation, where the input value is below the startup threshold value and outside the hysteresis region with the result that the equation 15 ratio value is being decreased while in this state.

0020If the equation 15 nominator value reaches 0, the device is reset with the result that the device returns to state ACTING.

0021In the following, the operation is explained mathematically. We may define two separate equations for current relays: the operation equation (1) and the reset equation (5), also introduced by standards. They are dependent on the signal, that is the characteristic measure quantity, so that the operate equation is only valid for signal magnitude ratios (I versus I>) above the startup threshold value, while the reset equation is only valid for signal magnitude ratios below the startup threshold value. The upper limit of the operate equation depends on the transformer dynamic measurement accuracy without saturation while the lower limit of the reset equation is zero. Because the hysteresis region creates a natural 'gray region' between the operating regions, only one of the equations is valid at a time. We are starting with the incrementation aspects of the final equation 15, i.e. explaining how the operate equation is constructed.

0022The operation equation of an overcurrent relay has the basic form of (1): <maths id="math0001" num=""><math display="block"><mi>t</mi><mfenced><mi>I</mi></mfenced><mo>≥</mo><mfenced separators=""><mfrac><mi>a</mi><mrow><msup><mfenced><mfrac><mi>I</mi><mrow><mi>I</mi><mo>></mo></mrow></mfrac></mfenced><mi>p</mi></msup><mo>−</mo><mi>c</mi></mrow></mfrac><mo>+</mo><mi>b</mi></mfenced><mo>∗</mo><mi>k</mi><mo>,</mo></math><img file="EP2232659B1_D0001.tif" /></maths> where <ul id="ul0002" list-style="none" compact="compact"><li><i>t</i>(<i>I</i>) gives the operate time in seconds</li><li><i>k</i> is a settable time multiplier of the function</li><li><i>a,b,p,c</i> are curve parameters</li><li><i>I</i> is the measured current input to the equation</li><li><i>I</i> > is the startup threshold value of the current settable by a user.</li></ul>

0023Equation (1) may be written in form (2) <maths id="math0002" num=""><math display="block"><mi>t</mi><mfenced><mi>I</mi></mfenced><mo>></mo><mo>=</mo><mfrac><mrow><mi>k</mi><mo>∗</mo><mi>a</mi></mrow><mrow><msup><mfenced><mfrac><mi>I</mi><mrow><mi>I</mi><mo>></mo></mrow></mfrac></mfenced><mi>p</mi></msup><mo>−</mo><mi>c</mi></mrow></mfrac><mo>+</mo><mi>k</mi><mo>∗</mo><mi>b</mi><mo>.</mo></math><img file="EP2232659B1_D0002.tif" /></maths>

0024Here we can see that the operation time, that is the time in which to reach OPERATE state with the assumption of a constant input signal magnitude, is inversely dependent on current I. Thus, the greater the current is, the shorter the time t to the operation of the relay is. Curves may be drawn having different parameters in this equation. Such curves may be drawn as a function of constant signal magnitude ratio. However, in practice, the current may fluctuate in time, resulting to a curve implementation with successive integrations.

0025Equation (2) may be written in form (3): <maths id="math0003" num=""><math display="block"><mfenced separators=""><mi mathvariant="italic">OT</mi><mo>+</mo><mi mathvariant="italic">delayC</mi><mo>−</mo><mi>k</mi><mo>∗</mo><mi>b</mi></mfenced><mo>∗</mo><msup><mfenced><mfrac><mi>I</mi><mrow><mi>I</mi><mo>></mo></mrow></mfrac></mfenced><mi>p</mi></msup><mo>−</mo><mi>c</mi><mo>></mo><mo>=</mo><mi>k</mi><mo>∗</mo><mi>a</mi><mo>,</mo></math><img file="EP2232659B1_D0003.tif" /></maths>where <dl id="dl0001" compact="compact"><dt><i>OT</i></dt><dd>is the operation time, and</dd><dt><i>delayC</i></dt><dd>is delay compensation.</dd></dl>

0026Operation time denotes the time that has elapsed since the current exceeded the startup threshold value and the device thus performed a state transition to PICKUP state. Delay compensation denotes a system delay, which is a fully implementational delay when the operation of the device actually starts as calculated from an order to do so. In that case it compensates the measurement delay. Another delay that might be included in this same variable is an output relay delay that might also be compensated by shortening the calculating operate time. An aspect regarding the delay compensation is that this parameter remains constant during execution.

0027When taking into account that the calculation contains several successive integrations, equation (3) may be written as (4) <maths id="math0004" num=""><math display="block"><mfenced separators=""><mi mathvariant="italic">OT</mi><mo>+</mo><mi mathvariant="italic">delayC</mi><mo>−</mo><mi>k</mi><mo>∗</mo><mi>b</mi></mfenced><mo>∗</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mn>0</mn><mi>n</mi></munderover><mfenced separators=""><msup><mfenced><mfrac><mi>I</mi><mrow><mi>I</mi><mo>></mo></mrow></mfrac></mfenced><mi>p</mi></msup><mo>−</mo><mi>c</mi></mfenced></mstyle><mo>></mo><mo>=</mo><mi>n</mi><mo>∗</mo><mi>k</mi><mo>∗</mo><mi>a</mi><mo>,</mo></math><img file="EP2232659B1_D0004.tif" /></maths><dl id="dl0002" compact="compact"><dt><i>n</i></dt><dd>is the number of successive execution intervals.</dd></dl>

0028In equation (4), the relation between <i>I</i> and <i>I</i>> (that is "current ratio") is integrated over time. The integration may be carried out in <i>n</i> successive execution intervals. Thereby the fluctuation of the current may be taken into account effectively.

0029Equation (4) now shows the incrementation aspect of the cumulative counter corresponding to the state transition 3 in <figref idref="f0001">Figure 1</figref>. The incrementative counter is in operation when the current is above the startup threshold.

0030However, during periods when the current is below the starting threshold setting minus hysteresis, the equation 15 nominator decreases as shown by the internal state transition 10 in <figref idref="f0001">Figure 1</figref>. This type of decreasing function, reset function, may be written in form <maths id="math0005" num=""><math display="block"><mi>t</mi><mfenced><mi>I</mi></mfenced><mo>></mo><mo>=</mo><mfenced><mfrac><mi mathvariant="italic">tr</mi><mrow><msup><mfenced><mfrac><mi>I</mi><mrow><mi>I</mi><mo>></mo></mrow></mfrac></mfenced><mi mathvariant="italic">pr</mi></msup><mo>−</mo><mi mathvariant="italic">cr</mi></mrow></mfrac></mfenced><mo>∗</mo><mi>k</mi><mo>,</mo></math><img file="EP2232659B1_D0005.tif" /></maths> where <ul id="ul0003" list-style="none" compact="compact"><li><i>t</i>(<i>I</i>) gives the reset time in seconds</li><li><i>k</i> is a settable time multiplier of the function (the same that is used for operate time calculation)</li><li><i>tr, pr, cr</i> are curve parameters</li><li><i>I</i> is the measured current inputted to the equation</li><li><i>I</i> > is a settable startup threshold value of the current.</li></ul>

0031The operate condition of an overcurrent protection function may be defined by a term called "start duration", which is a variable that indicates how far from operating the device is at a specific time instant. For example, if the curve operate time calculated from equation (1) has been found to be 1 second for a constant input signal, then starting with this particular input signal magnitude level, after half a second the "start duration" has a value of 50% and after 0.75 seconds its value will be 75%. Consequently, "start duration" runs from 0% to 100%, whereby at 0% the device is reset, and at 100% the device is configured to operate. The variable "start duration" thus aims to indicate how close to operating the device is if the same constant signal level remains. However, due to signal fluctuation this estimate cannot necessarily be realized. Also, drop-off periods during the operation lengthen the operate time, so that actually the definition of "start duration" may be extended to also include drop-off periods. Then the start duration may be defined as: Start duration = (integrated operate time - integrated reset time) / total operate time. Thus, the state transition DROPOFF->ACTING may take place when the "integrated operate time" minus "integrated reset time" => 0 and PICKUP->OPERATE takes place when (integrated operate time - integrated reset time) = total operate time. On the basis of this condition it may be found out that, while the total operate time in this context is a linear function, the nominator (integrated operate time - integrated reset time) as a derivative of the operate and reset equations has exponentially increasing characteristics, which can be seen in the following.

0032The integrated operate time of equations (1) to (4) and the integrated reset time of equation (5) may be combined to a single counter as follows.

0033When the current ratio (I/I>) is abbreviated as <i>M,</i> equation (1) can be written as <maths id="math0006" num=""><math display="block"><mi>t</mi><mfenced><mi>I</mi></mfenced><mo>≥</mo><mfrac><mrow><mi>k</mi><mo>∗</mo><mi>a</mi></mrow><mrow><msup><mi>M</mi><mi>p</mi></msup><mo>−</mo><mi>c</mi></mrow></mfrac><mo>+</mo><mi>k</mi><mo>∗</mo><mi>b</mi><mo>.</mo></math><img file="EP2232659B1_D0006.tif" /></maths>

0034Equation (6) may be written, by writing <i>n => operCounter</i> and including a <i>taskTime</i> (this is a synonym of the previously mentioned execution time/cycle) concept into the equation we will get operation inequality (7) <maths id="math0007" num=""><math display="block"><mfenced separators=""><mi mathvariant="italic">operCounter</mi><mo>+</mo><mi mathvariant="italic">delayC</mi></mfenced><mo>∗</mo><mi mathvariant="normal">Σ</mi><mfenced separators=""><msup><mi>M</mi><mi>p</mi></msup><mo>−</mo><mi>c</mi></mfenced><mo>≥</mo><mi mathvariant="normal">Σ</mi><mfenced separators=""><msup><mi>M</mi><mi>p</mi></msup><mo>−</mo><mi>c</mi></mfenced><mo>∗</mo><mi>k</mi><mo>∗</mo><mi>b</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi mathvariant="italic">taskTime</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi>k</mi><mo>∗</mo><mi>a</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi mathvariant="italic">taskTime</mi></math><img file="EP2232659B1_D0007.tif" /></maths>

0035By defining <i>timeShift => delayC</i> * <i>1000</i>/<i>taskTime, k*b*1</i>/<i>taskTime => curveDelay</i> and <i>k*a*1</i>/<i>taskTime => curveMult,</i> we get (8): <maths id="math0008" num=""><math display="block"><mfenced separators=""><mi mathvariant="italic">operCounter</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi></mfenced><mo>∗</mo><mi mathvariant="normal">Σ</mi><mfenced separators=""><msup><mi>M</mi><mi>p</mi></msup><mo>−</mo><mi>c</mi></mfenced><mo>≥</mo><mi mathvariant="normal">Σ</mi><mfenced separators=""><msup><mi>M</mi><mi>p</mi></msup><mo>−</mo><mi>c</mi></mfenced><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></math><img file="EP2232659B1_D0008.tif" /></maths>

0036Furthermore, the integral cumulative sum Σ(<i>M^p-c</i>) may be defined as <i>sumOfS.</i> These values may be either precalculated with predefined current ratio precision to an operate look-up-table so that it is a function of <i>M</i> or they may be calculated with a more precise current ratio value during the execution if sufficient computer power is available. Finally we obtain (9): <maths id="math0009" num=""><math display="block"><mfenced separators=""><mi mathvariant="italic">operCounter</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi></mfenced><mo>∗</mo><mi mathvariant="italic">sunOfS</mi><mo>≥</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></math><img file="EP2232659B1_D0009.tif" /></maths>

0037This is a so-called operate counter equation, where the left-hand side parameter is defined as <i>integTime1</i> and the right-hand side parameter as <i>integTime2</i> (these terms refer to the manner they have been calculated, i.e. by integrating the successive terms) so that <maths id="math0010" num=""><math display="block"><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>1</mn><mo>=</mo><mfenced separators=""><mi mathvariant="italic">operCounter</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi></mfenced><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>,</mo></math><img file="EP2232659B1_D0010.tif" /></maths>

0038and <maths id="math0011" num=""><math display="block"><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>2</mn><mo>=</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi><mo>.</mo></math><img file="EP2232659B1_D0011.tif" /></maths>

0039With regard to the reset equation, by beginning from (5) and defining similarly with <i>sumOfS</i> another look-up-table item (reset LUT) or calculating directly during the execution a cumulative sum called <i>decOfS</i> ≡ Σ(<i>M^pr-cr</i>) and <i>k*tr*1</i>/<i>taskTime => resetMult,</i> this leads to reset inequality (12): <maths id="math0012" num=""><math display="block"><mi mathvariant="normal">Σ</mi><mfenced separators=""><msup><mi>M</mi><mi mathvariant="italic">PR</mi></msup><mo>−</mo><mi mathvariant="italic">cr</mi></mfenced><mo>=</mo><mi mathvariant="italic">decOfS</mi><mo>≥</mo><mi>k</mi><mo>∗</mo><mi mathvariant="italic">tr</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi mathvariant="italic">taskTime</mi><mo>=</mo><mi mathvariant="italic">resetMult</mi><mo>.</mo></math><img file="EP2232659B1_D0012.tif" /></maths>

0040There can also be a so-called <i>resetCounter</i> parameter (equivalent to an <i>operCounter</i> parameter in the operate equation) so that actually, the equation will be (13), where <i>resetCounter</i> may be eliminated. <maths id="math0013" num=""><math display="block"><mi mathvariant="italic">resetCounter</mi><mo>∗</mo><mfrac><mrow><mi mathvariant="normal">Σ</mi><mfenced separators=""><msup><mi>M</mi><mi mathvariant="italic">PR</mi></msup><mo>−</mo><mi mathvariant="italic">cr</mi></mfenced></mrow><mi mathvariant="italic">resetCounter</mi></mfrac><mo>≥</mo><mi>k</mi><mo>∗</mo><mi mathvariant="italic">tr</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi mathvariant="italic">taskTime</mi><mo>.</mo></math><img file="EP2232659B1_D0013.tif" /></maths>

0041Now both factors of the "start duration" definition have been calculated in order to show the operate condition. As a result, a combined counter equation is obtained by combining both operate and reset counter equations as the same equation. Eventually, the start duration value in two counter systems can be calculated as <maths id="math0014" num=""><math display="block"><mi mathvariant="italic">startDuration</mi><mo>=</mo><mfenced separators=""><mfrac><mrow><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>1</mn></mrow><mrow><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mi mathvariant="italic">decOfS</mi><mi mathvariant="italic">resetMult</mi></mfrac></mfenced><mo>∗</mo><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>.</mo></math><img file="EP2232659B1_D0014.tif" /></maths>

0042This expands to be <maths id="math0015" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo><mfenced separators=""><mfrac><mrow><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>1</mn><mo>∗</mo><mi mathvariant="italic">resetMult</mi></mrow><mrow><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>2</mn><mo>∗</mo><mi mathvariant="italic">resetMult</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>2</mn></mrow><mrow><mi mathvariant="italic">resetMult</mi><mo>∗</mo><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>2</mn></mrow></mfrac></mfenced><mo>∗</mo><mn>100</mn><mo>⁢</mo><mi>%</mi></mtd></mtr><mtr><mtd><mo>=</mo><mrow><mo>(</mo><mrow><mfrac><mrow><mfenced separators=""><mi mathvariant="italic">operCounter</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi></mfenced><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">resetMult</mi></mrow><mrow><mfenced separators=""><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mfenced><mo>∗</mo><mi mathvariant="italic">resetMult</mi></mrow></mfrac><mo>−</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mfenced separators=""><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mfenced></mrow><mrow><mi mathvariant="italic">resetMult</mi><mo>∗</mo><mfenced separators=""><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mfenced></mrow></mfrac><mo>)</mo></mrow><mo>∗</mo><mn>100</mn><mo>⁢</mo><mi>%</mi></mtd></mtr><mtr><mtd><mo>=</mo><mrow><mo>(</mo><mfrac><mrow><mfenced separators=""><mi mathvariant="italic">operCounter</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi></mfenced><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">resetMult</mi><mo>−</mo></mrow><mfenced separators=""><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mfenced></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mfenced separators=""><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mfenced></mrow><mrow><mo>∗</mo><mi mathvariant="italic">resetMult</mi></mrow></mfrac><mo>)</mo></mrow><mo>∗</mo><mn>100</mn><mo>⁢</mo><mi>%</mi></mtd></mtr></mtable></math><img file="EP2232659B1_D0015.tif" /></maths>

0043Here, it can now be seen that the operate counter and the reset counter have been combined to a single counter, a "start duration" counter. This "start duration" counter is in a form having a term in parentheses multiplied by 100%. As a result, the tripping condition for a state transition to the OPERATE state is at 100% and is reached when the term in the parentheses equals 1. However, as already explained previously, the division in equation (15) is not calculated but the tripping (operating) condition occurs when the nominator value exceeds the denominator value in equation 15. Respectively, a state transition DROPOFF->ACTING state takes place when the nominator decreases to the value zero.

0044This same equation may also be used for curves, for which some other type of reset equation than an equation-based reset has been chosen. This simplifies the calculation, when many equation terms can be replaced by constants. For example, <i>decOfS</i> has the value zero, causing the second term of the nominator to be zero. Note also that in that particular case, the term re<i>setMult</i> both in the nominator and the denominator may be eliminated.

0045Another aspect that may be taken into account here is the delay compensation regarding the drop-off timer. If Eq. 7 and Eq. 13 are compared, it may be seen that the delay compensation does not affect the reset operation and thus <i>resetCounter</i> could be eliminated from the equation. In fact, the delay compensation may also affect the reset counter operation by shortening the reset time so that the actual start output may be deactivated at a correct time. However, this would mean that we should end the reset period calculation before the function itself has seen that the drop-off period has delayed for a set reset time, and this is not allowed. Thus, in an embodiment, the delay compensation may be omitted in the reset condition calculation.

0046In the following, the variables used in the equations are summarized: <ul id="ul0004" list-style="bullet" compact="compact"><li><i>operCounter</i> is a cumulative tick counter for pick-up function</li><li><i>timeShift</i> is <i>delayC</i> * <i>1000</i>/<i>taskTime</i> (where delayC may be given in seconds). This represents a fixed value during the pick-up operation.</li><li><i>curveMult</i> is <i>k*a*1</i>/<i>taskTime.</i> This represents a fixed value during the pick-up operation.</li><li><i>curveDelay</i> is <i>k*b*1</i>/<i>taskTime.</i> This represents a fixed value during the pick-up operation.</li><li><i>resetMult</i> is <i>k*tr*1</i>/<i>taskTime.</i> This represents a fixed value during the pick-up operation.</li><li><i>sumOfS</i> is Σ(<i>M^p-c</i>)<i>.</i> These values may have been stored in a look-up table (LUT) beforehand. This LUT is called operate-LUT in the following.</li><li><i>decOfS</i> is Σ(<i>M^pr-cr</i>)<i>.</i> These values may have been stored in a look-up table beforehand. This LUT is called reset-LUT in the following.</li></ul>

0047Equation 15 may be written out to give <maths id="math0016" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">resetMult</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">resetMult</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">resetMult</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDalay</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi><mo>∗</mo><mi mathvariant="italic">resetMult</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0016.tif" /></maths>

0048In the following, the overflow management of Equation 16 is explained. In a first embodiment, the denominator is made smaller. One way to do this is to divide both equation sides by <i>resetMult</i> or some other corresponding divisor. After dividing both sides by <i>resetMult,</i> Eq. 16 may be written: <maths id="math0017" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mfenced separators=""><mi mathvariant="italic">curveDelay</mi><mo>/</mo><mi mathvariant="italic">resetMult</mi></mfenced><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mfenced separators=""><mi mathvariant="italic">curveMult</mi><mo>/</mo><mi mathvariant="italic">resetMult</mi></mfenced></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0017.tif" /></maths>

0049If the variable <i>curveDelay</i>/<i>resetMult</i> is replaced by <i>BperTR</i> and <i>curveMult</i>/<i>resetMult</i> is replaced by <i>AperTR,</i> the equation may be written as <maths id="math0018" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">BperTR</mi><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">AperTR</mi></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0018.tif" /></maths>

0050A special case, where <i>tr has</i> the value zero, cannot be used to avoid division by zero. The parameter <i>tr</i> value zero actually means an immediate reset equation and consequently, the latter part of eq. 14 will be zero, and as a result, eq. 14 can be given in a more simple form <maths id="math0019" num=""><math display="block"><mi mathvariant="italic">startDuration</mi><mo>=</mo><mfrac><mrow><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>1</mn></mrow><mrow><mi>int</mi><mspace width="1ex" /><mi mathvariant="italic">egTime</mi><mn>2</mn></mrow></mfrac><mo>∗</mo><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>.</mo></math><img file="EP2232659B1_D0019.tif" /></maths>

0051Equation expansion gives then <maths id="math0020" num=""><math display="block"><mi mathvariant="italic">starDuration</mi><mo>=</mo><mfenced><mfrac><mrow><mfenced separators=""><mi mathvariant="italic">operCounter</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi></mfenced><mo>∗</mo><mi mathvariant="italic">sumOfS</mi></mrow><mfenced separators=""><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMullt</mi></mfenced></mfrac></mfenced><mo>∗</mo><mn>100</mn><mo>⁢</mo><mi>%</mi></math><img file="EP2232659B1_D0020.tif" /></maths>

0052When comparing this equation to Eq. 15, it may be seen that instead of setting <i>resetMult</i> to zero (implying tr to be zero), <i>resetMult</i> has been set to unity. Another question is, if <i>AperTR</i> and <i>BperTr</i> can have too high values when <i>resetMult</i> has been set to a very low value. Actually, highest <i>AperTR</i> and <i>BperTr</i> results when <i>resetMult</i> has its minimum. For very small <i>tr</i> values in Eq. 18, either <i>a</i> and <i>b</i> may be restricted, or alternatively the lowest value of <i>tr</i> or all these three parameters may be restricted. Typically parameter value range is specified already in productization phase and, thus, it is possible to certify already before hand that these execution phase fixed values are restricted However, it is possible to use a similar approach like told below with <i>sumOfS</i> and <i>decOfS</i> restriction, if needed, to restrict also <i>AperTR</i> and <i>BperTr.</i>

0053In Eq. 18, the overflow of the cumulative sums, i.e. <i>sumOfS</i> and <i>decOfS</i> may be investigated. Another non-fixed parameter during execution in the equation (Eq. 18) is <i>operCounter,</i> because the parameters <i>timeShift, curveDelay</i> and <i>curveMult</i> may be fixed during execution.

0054In the following, an embodiment of a process for determining a limit value to the cumulative operate sum is described. The process itself is the same for the cumulative reset sum, too. At first, the LUT item content is investigated in order to find the maximum item value to be inserted to the cumulative sum <i>sumOfS.</i> Operate LUT-equation (and item content) is <i>M^p-c,</i> and its fixed point representation depends on the selected integer and fragment bit lengths, where selected bit length is a sum between the integer and fragment bit lengths. An operate overflow limit may then be calculated by solving inequality log₂(cumulative sum + maximum item value) ≤ selected bit length for cumulative sum. Now we may select an overflow limit to be smaller than log₂(cumulative sum) and the maximum allowed LUT-insertion value is then difference between 2^{selectedBitLength} and the overflow limit. Similarly, for user programmable curves, parameters <i>p</i> and <i>c</i> maximum value may be selected so that the maximum LUT-value is also restricted. For calculation accuracy point of view it may be feasible to use more fragment bit to LUT-item that is later used in cumulative sum.

0055In Eq. 18 there is the multiplication <i>sumOfS*decOfS*BperTR.</i> If cumulative sum bit length is assumed to be 28, a 64-bit representation for the multiplication result may be used, if 36 bits are also sufficient for the multiplication value <i>decOfS*BperTR.</i> Of course, these selections depends highly on selected processor characteristics. In an embodiment, for example 22 bits may be reserved for <i>decOfS</i> and 12 bits for <i>BperTR</i> so that in the worst case 28+18+12 = 58 bits are used here. If now all these three variables have their maximum value, there is still some marginal for overflow. If the signed integer is used for registering, a total number of 63 bits might be used and so 5 additional bits may be used to increase the operate overflow limit and the reset overflow limit.

0056Thus, the highest possible LUT item and the cumulative sum limit for both operate and reset equation parts may be defined. If, in the operate equation part, the <i>sumOfS</i> is increases over the overflow limit, the <i>sumOfS</i> may be divided by a divisor <i>N</i>. The divisor <i>N</i> may be any number but preferably a multiple of 2, such as 2, 4, 8, etc. resulting simple bit-shift in implementation. Then, in the equation the previous <i>sumOfS</i> may be replaced by <i>sumOfS</i> / <i>N.</i> To preserve the value of the equation, all the multiplications in the inequality equation may be divided by <i>N,</i> thus giving: <maths id="math0021" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>/</mo><mi>N</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>/</mo><mi>N</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">sumOfS</mi><mo>/</mo><mi>N</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>/</mo><mi>N</mi><mo>∗</mo><mi mathvariant="italic">BperTR</mi><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">AperTR</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>N</mi></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>N</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0021.tif" /></maths> which may be written as: <maths id="math0022" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">BperTR</mi><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">AperTR</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>N</mi></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>N</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0022.tif" /></maths>

0057As the original <i>sumOfS</i> has been divided by <i>N,</i> subsequently LUT-item / <i>N</i> should be used instead of a pure LUT-item to keep the equation in shape. If the overflow limit is later exceeded again, the new <i>sumOfS</i> may be <i>sumOfS</i> / (<i>N</i>+<i>N</i>) when compared to the original equation value. Then, the inserted LUT value will be LUT item / (<i>N</i>+<i>N</i>), accordingly. By this way, overflow may be avoided.

0058To prevent overflow of <i>decOfS,</i> similar operations as above for <i>sumOfS</i> may be made but now <i>decOfS</i> may be replaced by <i>decOfS</i> / <i>L,</i> where a good choice for <i>L</i> is also 2, and the next good alternatives are 4, 8 etc. <i>L</i> may also equal <i>N</i>. In this case, Eq. 18 gives <maths id="math0023" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>/</mo><mi>L</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">BperTR</mi><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>/</mo><mi>L</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">AperTR</mi></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0023.tif" /></maths>

0059When replacing <i>decOfS</i> / <i>L</i> => <i>decOfS,</i> it may be continued from the equation: <maths id="math0024" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">BperTR</mi><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">AperTR</mi></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0024.tif" /></maths>

0060Also here it may be continued with successive divisions (actually bit shifts) by <i>L</i> as in the case of the operate sum. Correspondingly, the inserted LUT values may also be divided by <i>L, L</i>+<i>L</i> etc.

0061The combined equation may be written as: <maths id="math0025" num=""><math display="block"><mtable columnalign="left"><mtr><mtd><mi mathvariant="italic">startDuration</mi><mo>=</mo></mtd></mtr><mtr><mtd><mn>100</mn><mo>⁢</mo><mi>%</mi><mo>∗</mo><mrow><mo>(</mo><mfrac><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>+</mo><mi mathvariant="italic">timeShift</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>−</mo></mrow><mrow><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">curveDelay</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>L</mi><mo>+</mo></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">sumOfS</mi><mo>∗</mo><mi mathvariant="italic">BperTR</mi><mo>−</mo><mi mathvariant="italic">decOfS</mi><mo>∗</mo><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">AperTR</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mi>N</mi></mrow><mrow><mi mathvariant="italic">operCounter</mi><mo>∗</mo><mi mathvariant="italic">curveMult</mi><mo>∗</mo><mn>1</mn><mo>/</mo><mfenced separators=""><mi>N</mi><mo>∗</mo><mi>L</mi></mfenced></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable></math><img file="EP2232659B1_D0025.tif" /></maths>

0062<figref idref="f0002">Figures 2</figref> and <figref idref="f0003">3</figref> show the current ratio I/I> varying in time T (<figref idref="f0002">Figure 2</figref>) and the respective cumulation of the start duration value (<figref idref="f0003">Figure 3</figref>) in accordance with the fluctuation of the current in <figref idref="f0002">Figure 2</figref>. It has to be noted that the example situation depicted in <figref idref="f0002">Figure 2</figref> corresponds to an ideal situation where the current levels change abruptly.

0063In <figref idref="f0002">Figure 2</figref>, the current ratio level "1" depicts a startup threshold level, that is a level where a state transition ACTING->PICKUP occurs in accordance with <figref idref="f0001">Figure 1</figref>. Values greater than 1 depict the operate situation, where the equation 15 ratio value increases. Before 4000 ms, operate periods thus occur in time intervals 0..610, 870..1550, 1770..2250 and change in the signal level at the moment 3670 ms. Values lower than 1 depict the reset situation where the startup counter value decreases. Before 4000 ms, reset periods thus occur in time periods 610..870, 1550..1770, 2250..2800. Referring to the state diagram of <figref idref="f0001">Figure 1</figref>, at the moment 0 ms the apparatus performs a state transition to PICKUP state and stays in the PICKUP state until 610 ms has elapsed, whereafter a state transition to DROPOFF state is performed.

0064<figref idref="f0003">Figure 3</figref> shows the value of the startup duration counter as a function of time in the situation of <figref idref="f0002">Figure 2</figref>. It may be seen that the value of the startup duration increases during the operate periods, such as 0..610 ms, and decreases during the reset periods, such as 610..870 ms. The figure also shows that a trip condition occurs at a moment 3900 ms, when the startup counter value reaches 100% and the state machine goes to OPERATE state. When the current falls below the threshold value "1-hysteresis" (which has been 2% in this simulation) after reaching OPERATE, the device goes to ACTING state.

0065In <figref idref="f0003">Figure 3</figref>, the OPERATE condition occurs, referring to equation (15), when the clause in parentheses reaches "1", that is the nominator becomes as great as or greater than the denominator. When the state transition OPERATE->ACTING occurs, equation (15) parameters are reset to zero. When the simulation continues, a new start takes place in 6200 but after the state transition ACTING>DROPOFF occurs, and the nominator in equation (15) falls gradually to zero. After reaching the value zero, the state transition DROPOFF->ACTING takes place in 8100.

0066<figref idref="f0001">Figure 4</figref> shows an embodiment of a method. The method may be implemented in an overcurrent relay applying an IDMT (Inverse Definite Minimum Timer) principle.

0067In 400, the relay monitors the input current, and in 402, the input current is compared to a startup threshold of the relay protection function. If the outcome of the comparison indicates that the input current is greater than the threshold, the method proceeds to 406 where <i>sumOfS</i> and <i>operCounter</i> counters are incremented. Correspondingly, if the comparison 404 indicates that the input current is lower than the startup threshold minus the hysteresis value, the <i>decOfS</i> counter is incremented in 408. At the incrementation 406, it is checked in 410 whether the equation 15 nominator exceeds the denominator value. If this is the case, the device starts to operate in 414. At the incrementation 408, a check 412 is carried out whether the equation 15 nominator has gone down to 0. If yes, then the device goes to ACTING state. After reaching OPERATE, when the input current undershoots the startup threshold minus the hysteresis next time, a state transition to ACTING state takes place. Alternatively, if reset is after OPERATE based on a reset equation, the method proceeds to ACTING when equation 15 nominator has gone down to 0.

0068The counters processed in the method are arranged into a form, in which the checking of the operate condition may be carried out by a simple comparison of two measures. In equation (15) these two measures have been placed in the nominator and denominator. However, in equation (15), the denominator may be multiplied to the right-hand side of the equation, whereby again the tripping condition may be performed by means of a comparison of the two sides of the equation. By this way, no divisions, which take a lot of processing capacity of the computer of the relay, need to be carried out.

0069<figref idref="f0004">Figure 5</figref> shows a protection relay 500 showing only portions relevant to the disclosure. The relay includes an input port 502 for inputting a characteristic measure, such as current, voltage or frequency. The relay also includes a control unit 504 configured to control the operation of the device. The control unit may be implemented as a processor, and the functionalities may be implemented onto the processor by means of software, for instance.

0070<figref idref="f0004">Figure 5</figref> also shows a calculating 506 unit, which may update a calculation equation upon the input characteristic measure. The relay may also include a module 508 responsible for overflow management of the calculation equation. A memory 510 may also be provided for storing LUT table items for use by the calculation equation. Instead of having a separate memory for lookup tables, the values may also be calculated during execution. All these functionalities 506 to 510 may, instead of separate units, be implemented on the control unit, such as a processor. The device may also include an output unit 512 for providing an output signal. The output signal is dependent on the outcome of the result of the calculation equation. If, for instance, the calculation equation shows that a tripping or reset condition has been reached, the output unit provides the respective output signal.

0071By way of the embodiments disclosed, the reset functionality may be embedded in the implementation such that the accuracy of the calculation is kept good. The shown embodiments provide an accurate way to implement an inverse definite time operation to calculate the operation time from the equations themselves. The embodiments also provide a way to reduce computational complexity by avoiding divisions when making real time computations. The only calculation operations needed are multiplications, additions and subtractions.

0072It will be obvious to a person skilled in the art that, as the technology advances, the inventive concept can be implemented in various ways. The invention and its embodiments are not limited to the examples described above but may vary within the scope of the claims.