A wind turbine generator unit primary frequency modulation relaxation control method and system

Abstract

The present invention discloses a method and system for primary frequency modulation relaxation control of a wind turbine generator set, comprising: 1) detecting an externally input frequency modulation flag; if entry is required, calculating the active power change, and sequentially executing steps 2) and 3); if entry is not required, the active power change is directly given by the external input, and step 4) is executed; 2) switching the variable speed and pitch control in conventional mode to variable speed and pitch control in frequency modulation mode; 3) determining whether frequency modulation is completed or whether the request flag has exited; if so, executing step 4); otherwise, continuing to execute variable speed and pitch control in frequency modulation mode; and 4) executing variable speed and pitch control in conventional mode. The present invention can effectively suppress power drop and blade stall problems in primary frequency modulation of wind farms.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wind power generation, in particular to a wind turbine generator unit primary frequency modulation relaxation control method, system, storage medium and computing device. BACKGROUND

[0002] In recent years, wind power generation has become the main force in the renewable energy industry. With large-scale wind power grid connection, the stage of adapting primary frequency modulation technology to wind turbine generator units has arrived. According to the Wind Turbine Generator Unit Grid Adaptability Test Regulations (GB / T 36994-2018), wind turbine generator units must have inertia response and primary frequency modulation capability, need to respond quickly to grid frequency change rate and frequency deviation, participate in system frequency modulation, and support system frequency recovery. Due to the instability and volatility of wind energy and the large inertia of the unit itself, in the process of frequency modulation, the power needs to be quickly, accurately and stably reached to the target value, which is a great test for single machine control. Moreover, the existing control technology cannot effectively solve the problems of power drop and blade stall in the primary frequency modulation process. Therefore, an improved power control method is needed to meet the above and other requirements. SUMMARY

[0003] The first object of the present application is to overcome the shortcomings and deficiencies of the prior art, and to provide a wind turbine generator unit primary frequency modulation relaxation control method. According to the operating state (pitch angle, power, etc.) of the unit itself, self-judgment is performed. If the upper limit of the capability is reached, no longer fast response, flexible transition to normal operating state, thereby effectively inhibiting the power drop and blade stall problems of wind farm primary frequency modulation.

[0004] The second object of the present application is to provide a wind turbine generator unit primary frequency modulation relaxation control system.

[0005] The third object of the present application is to provide a storage medium.

[0006] The fourth object of the present application is to provide a computing device.

[0007] The first object of the present application is achieved by the following technical solution: a wind turbine generator unit primary frequency modulation relaxation control method, comprising the following steps:

[0008] 1) Detect the frequency modulation flag bit input from outside. If it needs to enter, calculate the active power change amount, and then execute steps 2) and 3) in turn. If it does not need to enter, the active power change amount is directly given by external input, and step 4) is executed;

[0009] 2) Switch the variable speed variable pitch control of the conventional mode to the variable speed variable pitch control of the frequency modulation mode;

[0010] 3) judge whether the frequency modulation is completed or the request flag is exited, if yes, execute step 4), otherwise, still execute the variable speed variable pitch control in the frequency modulation mode;

[0011] 4) execute the variable speed variable pitch control in the normal mode.

[0012] Further, in step 1), the active power variation is calculated according to the following formula:

[0013]

[0014] In the formula, ΔP t is the active power variation of the wind farm; K f is the active frequency modulation coefficient; Δf is the frequency deviation of the power system; f N is the rated frequency of the power system; P t is the active power of the wind farm.

[0015] Further, in step 2), compared with the variable speed variable pitch control in the normal mode, the variable speed variable pitch control in the frequency modulation mode is different in the calculation of the speed set value and the output lower limit. The variable speed variable pitch control in the frequency modulation mode includes torque control and variable pitch control, and the details are as follows:

[0016] a. The torque control process in the frequency modulation is as follows: the filtered generator speed is compared with the set speed, the deviation obtained by comparison is PI controlled with the torque bias, and the output is obtained after amplitude limiting; when the unit changes from the normal mode to the frequency modulation mode, the calculation method of the speed set value and the torque lower limit is adjusted, and the details are as follows:

[0017] ①Switching of the speed set value:

[0018] The switching of the speed set value is realized by adjusting the gain value KoptFre of the unit operation, and the calculation formula is as follows:

[0019] KoptFre=Kopt×MovAv(FCKoptRatio,Step)

[0020] In the formula, Kopt represents the theoretical optimal gain value, MovAv represents the moving average filter, FCKoptRatio represents the scaling coefficient, and Step represents the step length;

[0021] When the frequency modulation is needed, the gain value KoptFre of the unit operation is scaled on the basis of the theoretical optimal gain value Kopt, and the scaling coefficient FCKoptRatio is processed by the average moving filter; compared with the normal mode, the speed set value in the low power segment (0-2500 kW) in the frequency modulation mode is higher, which aims to ensure that the unit stores sufficient rotational inertia;

[0022] ②Switching of the calculation method of the torque lower limit:

[0023] The calculation process of the torque lower limit output during frequency modulation is as follows: when the rated flag is true, the torque lower limit TorqueMin is calculated according to the deviation of the current pitch angle and the minimum limit of the pitch angle PitchDiff, the set margin value PitchMargin and the required increment of torque TorqueDemand, and the calculation formula is as follows:

[0024]

[0025] In the formula, TorqueMinLast is the torque lower limit output of the last period, and the required increment of torque TorqueDemand is essentially the difference between the power set value and the actual speed ratio of the previous two periods; when the rated flag is false, the torque lower limit is transitioned to the optimal torque TorqueOpt within the set time length from the current lower limit value; the rated flag is whether the current power reaches 90% of the set power, true if yes, and false otherwise.

[0026] The calculation formula of the optimal torque TorqueOpt is as follows:

[0027] TorqueOpt = Kopt x GenSpeed 2

[0028] In the formula, GenSpeed is the generator speed.

[0029] b. The pitch control process during frequency modulation is as follows: the generator measured speed is compared with the set speed after filtering, the deviation obtained by comparison is PID controlled with the pitch bias, and the given blade angle set output is obtained after limiting; when the unit changes from the normal mode to the frequency modulation mode, the calculation method of the speed set value and the pitch lower limit is adjusted, and the details are as follows:

[0030] ①Switching of the speed set value:

[0031] The mapping relationship between the set speed and the power is consistent with the above torque control;

[0032] ②Switching of the calculation method of the pitch lower limit:

[0033] The speed limit of reducing the pitch angle is adjusted to one half of the original value, so that the unit can quickly absorb wind energy.

[0034] Further, for whether the frequency modulation in step 3) is completed, that is, whether the rotating speed of the unit enters the set rotating speed deviation band, P1, P2 and P3 represent power equivalent curves, that is, the power values on the same curve are equal, and there is a relationship P1 < P2 < P3, A1, B1, A2 and B2 represent the rotating speed and torque values of the unit in operation, when the active power change amount is positive, the unit is set to operate at point A1, that is, the P1 power value, now the power grid frequency is disturbed downward, the power needs to reach the P2 power value, through the switching of the torque control, the unit is quickly operated from point A1 to point B1, then the unit is operated on the P2 power equivalent curve, if the rotating speed enters the set rotating speed deviation band through the pitch PID (proportional-integral-derivative) control, the torque PI (proportional-integral) control can be taken over, and through the size of the set deviation band, the fluctuation amplitude of the rotating speed and torque of the unit when the torque PI (proportional-integral) control is taken over can be adjusted; when the active power change amount is negative, the unit is set to operate at point A2, that is, the P3 power value, now the power grid frequency is disturbed upward, the power needs to reach the P2 power value, through the switching of the torque control, the unit is quickly operated from point A2 to point B2, then the unit is operated on the P2 power equivalent curve, if the rotating speed enters the set rotating speed deviation band through the pitch PID (proportional-integral-derivative) control, the torque PI (proportional-integral) control can be taken over.

[0035] Further, in step 4), when it is detected that the externally input frequency modulation flag bit is FALSE or the frequency modulation is executed, the variable speed variable pitch control is adjusted to the normal mode.

[0036] The second object of the application is achieved by the following technical scheme: a wind turbine unit primary frequency modulation relaxation control system for realizing the wind turbine unit primary frequency modulation relaxation control method, comprising:

[0037] A first judgment module is configured to detect an externally input frequency modulation flag bit, if the unit needs to enter, calculate an active power change amount, and execute a frequency modulation control module and a second judgment module in turn; otherwise, the active power change amount is directly given by the outside, and a normal execution module is executed;

[0038] A frequency modulation control module is configured to switch the variable speed variable pitch control in the normal mode to the variable speed variable pitch control in the frequency modulation mode;

[0039] A second judgment module is configured to judge whether the frequency modulation is completed or the request flag bit is exited, if yes, a normal execution module is executed, otherwise, the variable speed variable pitch control in the frequency modulation mode is still executed;

[0040] A normal execution module is configured to execute the variable speed variable pitch control in the normal mode.

[0041] The third object of the present invention is achieved through the following technical solution: a storage medium stores a program, and when the program is executed by a processor, the above-mentioned wind turbine primary frequency modulation relaxation control method is implemented.

[0042] The fourth object of the present invention is achieved through the following technical solution: a computing device, comprising a processor and a memory for storing a program executable by the processor, wherein when the processor executes the program stored in the memory, the above-mentioned primary frequency modulation relaxation control method of the wind turbine generator set is implemented.

[0043] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0044] 1. In the unit performance curve, the operating point during frequency modulation is biased to the right of the optimal operating point. On the one hand, it can ensure that it stores sufficient kinetic energy. On the other hand, if the wind speed drops, the operating point can be closer to the optimal operating point instead of gradually deviating from it, thus avoiding the occurrence of unit stall.

[0045] 2. Compared with the conventional mode, the variable speed and variable pitch control in the frequency modulation mode adjusts the speed setting value, pitch angle, and the calculation method of the torque output lower limit, so that the unit can make a transient response of frequency modulation according to the target output requirement and its own situation.

[0046] 3. Adaptive control is performed based on the unit's own operating status, such as pitch angle, power and other information. For example, under the current wind conditions, the output limit has been reached and the unit will no longer forcibly respond to the frequency regulation requirements. Instead, it will flexibly transition to normal operating status to avoid a significant drop in power due to overdraft.

[0047] 4. The present invention can effectively suppress the power drop and blade stall problems of the primary frequency modulation of the wind farm. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Flowchart of the method of the present invention.

[0049] Figure 2 This is the torque control logic flow chart.

[0050] Figure 3 This is the logic flow chart of pitch control.

[0051] Figure 4 This is the calculation flow chart of the minimum torque limit during primary frequency modulation.

[0052] Figure 5 This is a mapping diagram of power-speed setting values ​​during frequency modulation.

[0053] Figure 6 This is the speed-torque curve of the unit during frequency modulation.

[0054] Figure 7This is an architecture diagram of the system of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0056] Example 1

[0057] like Figure 1 As shown, this embodiment discloses a method for controlling the primary frequency modulation relaxation of a wind turbine generator set, the details of which are as follows:

[0058] 1) Detect the frequency modulation flag of the external input. If entry is required, calculate the active power change and execute steps 2) and 3) in sequence. If entry is not required, the active power change is directly given by the external input and execute step 4). The active power change is calculated as follows:

[0059]

[0060] Where: ΔP t is the change in active power of the wind farm, in MW; K f is the active frequency modulation coefficient; Δf is the power system frequency deviation, in Hz; f N is the rated frequency of the power system, in Hz; P t is the active power of the wind farm, in MW.

[0061] 2) Switching from the variable speed and pitch control in the conventional mode to the variable speed and pitch control in the frequency modulation mode;

[0062] Compared with the variable speed and pitch control in conventional mode, the variable speed and pitch control in frequency modulation mode differs in the calculation method of the speed set value and the output lower limit. The variable speed and pitch control in frequency modulation includes torque control and pitch control, as follows:

[0063] a. Figure 2 As shown in the figure, the torque control process during frequency modulation is as follows: the measured generator speed is filtered and compared with the set speed, the deviation obtained from the comparison is used in PI control with the torque offset, and the output is obtained after limiting. When the unit changes from normal mode to frequency modulation mode, the calculation method of the speed set value and the torque lower limit is adjusted as follows:

[0064] ①Switch of speed setting value:

[0065] The speed setting value is switched by adjusting the gain value KoptFre of the unit operation, which is calculated as follows:

[0066] KoptFre=Kopt×MovAv(FCKoptRatio,Step)

[0067] Where Kopt represents the theoretical optimal gain value, MovAv represents the sliding average filter, FCKoptRatio represents the scaling factor, and Step represents the step size, which is generally 0.01.

[0068] When frequency modulation is required, the unit's operating gain value KoptFre is scaled based on the theoretical optimal gain value Kopt, and the scaling factor FCKoptRatio is processed by moving average filtering; Figure 5 As shown in the figure, compared with the normal mode, the speed setting value of the low power range (0-2500kW) in the frequency modulation mode is higher, in order to ensure that the unit stores sufficient rotational inertia;

[0069] ② Switch the calculation method of the torque lower limit:

[0070] like Figure 4 As shown in the figure, the calculation process of the torque lower limit output during frequency modulation is as follows: when the rated flag is true, the torque lower limit TorqueMin is calculated based on the deviation PitchDiff between the current pitch angle and the minimum pitch angle limit, the set margin value PitchMargin and the torque demand increment TorqueDemand. The calculation formula is as follows:

[0071]

[0072] Where TorqueMinLast is the torque lower limit output of the previous cycle, and the torque demand increment TorqueDemand is actually the difference between the power setting and the actual speed ratio of the two cycles. When the rated flag is false, the torque lower limit transitions to the optimal torque TorqueOpt within the set time at the current lower limit value. The rated flag indicates whether the current power reaches 90% of the set power. If it reaches 90%, it is true, otherwise it is false.

[0073] The optimal torque TorqueOpt is calculated as follows:

[0074] TorqueOpt=Kopt×GenSpeed 2

[0075] Where, GenSpeed ​​is the generator speed;

[0076] b. Figure 3 As shown in the figure, the pitch control process during frequency modulation is as follows: the measured generator speed is filtered and compared with the set speed, the deviation obtained by comparison is PID controlled with the pitch offset, and the given blade angle setting output is obtained after limiting. When the unit changes from normal mode to frequency modulation mode, the calculation method of adjusting the speed set value and the pitch lower limit is as follows:

[0077] ①Switch of speed setting value:

[0078] The mapping relationship between the set speed and power is consistent with the above torque control. Figure 5 Way;

[0079] ② Switch the calculation method of the lower limit of pitch control:

[0080] Reduce the rate limit of the pitch angle and adjust the value to half of the original value to allow the unit to absorb wind energy as quickly as possible.

[0081] 3) Determine whether the frequency modulation is completed or the request flag is exited. If so, execute step 4); otherwise, still execute the variable speed and pitch control in the frequency modulation mode;

[0082] Whether the frequency modulation in step 3) is completed, that is, whether the unit speed enters the set speed deviation band, Figure 6 For the speed-torque curve of the frequency modulation unit, let P1, P2, P3, P4, and P5 represent the power equivalent curves, that is, the power values ​​on the same curve are equal, and there is a relationship P1 <P2<P3<P4<P5,设A1、B1、C1、A2、B2、C2表示机组运行的转速和转矩值,当有功功率变化量为正值时,设机组限功率运行在点A1,即P1功率值,现电网频率向下扰动,功率需达到P2功率值,通过转矩控制的切换,使机组快速从点A1向点B1运行,随后,机组运行在等功率曲线P2上,若通过变桨PID(比例-积分-微分)控制使转速进入设定的转速偏差带,如图C1点,可使转矩PI(比例-积分)控制接管,通过设定偏差带的大小能调整接管时机组转速、转矩的波动幅度;当有功功率变化量为负值时,设机组限功率运行在点A2,即P3功率值,现电网频率向上扰动,功率需达到P2功率值,通过转矩控制的切换,使机组快速从点A2向点B2运行,随后,机组运行在等功率曲线P2上,若通过变桨PID(比例-积分-微分)控制使转速进入设定的转速偏差带,如图C2点,可使转矩PI(比例-积分)控制接管。

[0083] 4) Execute variable speed and pitch control in normal mode;

[0084] When it is detected that the frequency modulation flag of the external input is FALSE or the frequency modulation is completed, the variable speed and pitch control is adjusted to the normal mode.

[0085] Example 2

[0086] This embodiment discloses a wind turbine primary frequency modulation relaxation control system, which is used to implement the wind turbine primary frequency modulation relaxation control method described in Example 1. Figure 7 Shown, including:

[0087] The first judging module is configured to detect a frequency modulation flag bit inputted from outside, and if the frequency modulation is needed, calculate a change amount of active power, and execute the frequency modulation control module and the second judging module in sequence; otherwise, the change amount of active power is directly given from outside, and the normal execution module is executed;

[0088] The frequency modulation control module is configured to switch the variable speed and variable pitch control in the normal mode to the variable speed and variable pitch control in the frequency modulation mode.

[0089] The second judging module is configured to judge whether the frequency modulation is completed or the request flag bit is exited, and if yes, execute the normal execution module, otherwise, still execute the variable speed and variable pitch control in the frequency modulation mode.

[0090] The normal execution module is configured to execute the variable speed and variable pitch control in the normal mode.

[0091] Embodiment 3

[0092] The embodiment discloses a storage medium, which stores a program, and when the program is executed by a processor, the wind turbine unit primary frequency modulation relaxation control method in the embodiment 1 is realized.

[0093] The storage medium in the embodiment can be a disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), a U disk, a mobile hard disk, and the like.

[0094] Embodiment 4

[0095] The embodiment discloses a computing device, which comprises a processor and a memory for storing a program executable by the processor, and when the processor executes the program stored in the memory, the wind turbine unit primary frequency modulation relaxation control method in the embodiment 1 is realized.

[0096] The computing device in the embodiment can be a desktop computer, a notebook computer, a smart phone, a PDA handheld terminal, a tablet computer, a programmable logic controller (PLC), or other terminal devices with a processor function.

[0097] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application should be equivalent replacement modes, and all are included in the protection scope of the present application.

Claims

1. A method for controlling primary frequency modulation relaxation of a wind turbine generator set, characterized in that: It includes the following steps: 1) Detect the frequency modulation flag bit of the external input. If it needs to enter, calculate the change in active power, and then execute steps 2) and 3) in sequence; if it doesn't need to enter, the change in active power is directly given by the external input, and execute step 4); 2) Switch the variable-speed variable-pitch control in the normal mode to the variable-speed variable-pitch control in the frequency modulation mode; Compared with the variable-speed variable-pitch control in the normal mode, the difference in the variable-speed variable-pitch control in the frequency modulation mode is reflected in the calculation methods of the speed set value and the output lower limit. The variable-speed variable-pitch control during frequency modulation includes torque control and pitch control, which are specifically as follows: a. The torque control process during frequency modulation is as follows: The measured speed of the generator is filtered and compared with the set speed. The deviation obtained from the comparison is subjected to PI control with the torque offset, and after limiting, the output is obtained; when the unit changes from the normal mode to the frequency modulation mode, adjust the calculation methods of the speed set value and the torque lower limit, which are specifically as follows: Switching of speed setting value: The speed setting value is switched by adjusting the gain value of the unit operation , the calculation formula is as follows: ； Where, represents the theoretical optimal gain value, represents the moving average filter, represents the scaling factor, represents the step length; When frequency modulation is required, the gain value of the unit operation Theoretically optimal gain value Scaling is performed based on the scaling factor After moving average filtering, the speed setting value in the low power range (0-2500kW) in frequency modulation mode is higher than that in conventional mode, in order to ensure that the unit has sufficient rotational inertia. Switch the calculation method of the torque lower limit: The calculation process of the torque lower limit output during frequency modulation is as follows: when the rated flag is true, the deviation between the current pitch angle and the minimum limit of the pitch angle is calculated. , set margin value and torque demand increment Calculate the lower torque limit , the calculation formula is as follows: ； Where, The torque lower limit output of the previous cycle, the torque demand increment In essence, it is the difference between the power setting and the actual speed ratio in the two cycles before and after; When the rated flag is false, the torque lower limit transitions to the optimal torque within the set time at the current lower limit value. ; Rated flag bit means whether the current power reaches 90% of the set power, if it reaches, it is true, otherwise it is false; Optimal torque The calculation formula is as follows: ； Where, is the generator speed; b. The pitch control process during frequency modulation is as follows: The measured speed of the generator is filtered and compared with the set speed. The deviation obtained from the comparison is subjected to PID control with the pitch offset, and after limiting, the set output of the blade angle is given; when the unit changes from the normal mode to the frequency modulation mode, adjust the calculation methods of the speed set value and the pitch lower limit, which are specifically as follows: Switching of speed setting value: The mapping relationship between the set speed and the power is the same as that of the above torque control; Switch the calculation method of the pitch lower limit: Reduce the rate limit of the pitch angle, and adjust the value to half of the original value to enable the unit to absorb wind energy as soon as possible; 3) Judge whether the frequency modulation is completed or whether the request flag bit exits. If so, execute step 4); otherwise, still execute the variable-speed variable-pitch control in the frequency modulation mode; 4) Execute the variable-speed variable-pitch control in the normal mode.

2. A wind turbine generator primary frequency modulation relaxation control method according to claim 1, characterized in that: In step 1), the change in active power is calculated according to the following formula: ； Where: is the change in active power of the wind farm; is the active frequency modulation coefficient; is the power system frequency deviation; is the rated frequency of the power system; is the active power of the wind farm.

3. A wind turbine generator primary frequency modulation relaxation control method according to claim 1, characterized in that: Regarding whether the frequency modulation in step 3) is completed, that is, whether the unit speed enters the set speed deviation band. Let P1, P2, and P3 represent the power equivalent curves, that is, the power values on the same curve are equal, and there is a relationship P1 < P2 < P3. Let A1, B1, A2, and B2 represent the speed and torque values of the unit operation. When the change in active power is positive, assume that the unit operates with power limit at point A1, that is, the P1 power value. Now the grid frequency is disturbed downward, and the power needs to reach the P2 power value. Through the switching of torque control, the unit quickly runs from point A1 to point B1. Subsequently, the unit operates on the equal-power curve P2. If the speed enters the set speed deviation band through pitch PID (proportional-integral-derivative control), the torque PI (proportional-integral control) can take over. By setting the size of the deviation band, the fluctuation amplitude of the unit speed and torque at the takeover time can be adjusted; when the change in active power is negative, assume that the unit operates with power limit at point A2, that is, the P3 power value. Now the grid frequency is disturbed upward, and the power needs to reach the P2 power value. Through the switching of torque control, the unit quickly runs from point A2 to point B2. Subsequently, the unit operates on the equal-power curve P2. If the speed enters the set speed deviation band through pitch PID (proportional-integral-derivative control), the torque PI (proportional-integral control) can take over.

4. A wind turbine generator primary frequency modulation relaxation control method according to claim 1, characterized in that: In step 4), when it is detected that the frequency modulation flag of the external input is FALSE or the frequency modulation is completed, the variable speed and variable pitch control is adjusted to the normal mode.

5. A wind turbine primary frequency modulation relaxation control system, characterized in that: A method for realizing a primary frequency modulation relaxation control method of a wind turbine generator set according to any one of claims 1 to 4, comprising: The first judgment module is used to detect the frequency modulation flag bit of the external input. If it is required, the active power change is calculated and the frequency modulation control module and the second judgment module are executed in sequence; otherwise, the active power change is directly given by the external and the conventional execution module is executed; A frequency modulation control module is used to switch the variable speed and pitch control in the conventional mode to the variable speed and pitch control in the frequency modulation mode; The second judgment module judges whether the frequency modulation is completed or the request flag is exited. If so, the conventional execution module is executed; otherwise, the variable speed and pitch control in the frequency modulation mode is still executed; The conventional execution module is used to execute the variable speed and pitch control of the conventional mode.

6. A storage medium storing a program, characterized in that: When the program is executed by a processor, the primary frequency modulation relaxation control method of a wind turbine generator set according to any one of claims 1 to 4 is implemented.

7. A computing device comprising a processor and a memory for storing a program executable by the processor, characterized in that When the processor executes the program stored in the memory, the primary frequency modulation relaxation control method of the wind turbine generator set according to any one of claims 1 to 4 is implemented.

Images