GB2476553A

GB2476553A - Steam turbine starting method

Info

Publication number: GB2476553A
Application number: GB1020966A
Authority: GB
Inventors: Dileep Sathyanarayana; Steven Dipalma
Original assignee: General Electric Co
Current assignee: General Electric Co
Priority date: 2009-12-23
Filing date: 2010-12-10
Publication date: 2011-06-29
Also published as: JP2011132951A; GB201020966D0; RU2010152280A; DE102010061449A1; US20110146276A1

Abstract

A method of starting a high pressure steam turbine 120 of a power plant comprises increasing the pressure of steam 130 upstream of an admission valve 115 to a pressure matching range, the admission valve being located upstream of the turbine. The step of increasing the steam pressure has the effect to reducing the temperature of the steam 135 prior to admission into the turbine. The admission valve may be opened to allow steam to enter the turbine. Start-up of the turbine may be initiated if a start-up permissive is satisfied. The permissive may involve determining whether a turbine rotor stress is within an acceptable range. The steam turbine may also comprise a bypass system having a bypass valve 110 therein.

Description

METHOD OF STARTING A STEAM TURBINE

BACKGROUND OF THE INVENTION

The present invention relates generally to the operation of a turbomachine, and more particularly, to a method of reducing the start-up time of a steam turbine.

The start-up and loading process of some known steam turbines, typically involves a plurality phases occurring at different load ranges. One reason for this method of starting and loading the steam turbine is rotor stress control. A rotor of the steam turbine can experience an overstress event during the start-up and the initial loading phases. Overstressing can degrade the material properties of the rotor. A rotor stress control may stage the loading of the steam turbine with the goal of maintaining the rotor stress within an allowable range.

Known methods of reducing the likelihood of an overstress event involve maintaining the temperature of the steam exiting a boiler, such as, but not limiting of, a Heat Recovery Steam Generator (HIRSG) at a relative low temperature. For example, but not limiting of, on a combined cycle powerplant the gas turbine is held at a low load spinning reserve, or the like, to ensure that the temperature of the steam generated within the HRSG is acceptable to the steam turbine. For a cold start, this temperature may around 700 degrees Fahrenheit. A cold start may be considered the start-up of the steam turbine after a period on in operation.

On combined cycle applications, the steam pressure is typically related to gas turbine load. On a cold start, the gas turbine may limited to operate at a load equivalent to approximately 40% of rated pressure prior to steam turbine start. Due to the relatively low initial upstream pressure, when steam is admitted to the steam turbine, the upstream steam enthalpy is also relatively high. In addition, when steam is admitted to the steam turbine, the pressure ratio across the upstream and downstream admission valves is relatively high. These operational factors may result in steam temperature inside a section of the steam turbine, at the turbine bowl, to be roughly 40-50 degrees Fahrenheit lower than the upstream temperature of the steam. During a cold start of the steam turbine, this reduction in steam temperature may be insufficient to prevent an overstressing event on the turbine rotor.

Therefore, there is a desire for an improved method of starting a steam turbine. The method should reduce the start-up time. This method should also eliminate or reduce or the level of overstressing experienced by the rotor.

BRIEF DESCRIPTION OF THE INVENTION

In an embodiment of the present invention, a method of starting a powerplant machine, the method comprising: providing a steam turbine configured for converting steam to a mechanical torque; wherein the steam turbine comprises an HP section; and increasing a pressure of steam upstream of an admission valve to a pressure matching range, wherein the admission valve is located upstream of the HP section; wherein the step of increasing the pressure of the steam decreases a temperature of the steam prior to admission into the HP section.

In an alternate embodiment of the present invention, a method of starting a powerplant comprising a steam turbine, the method comprising: providing a steam turbine configured for converting steam to a mechanical torque; wherein the steam turbine comprises an HP section and a bypass system; determining whether a cold start of the steam turbine is requested; increasing a pressure the steam upstream of an admission valve to a pressure matching range, wherein the admission valve is located upstream of the HP section; determining whether the steam upstream of the admission valve is within the pressure matching range; initiating a start-up of the steam turbine if a start-up permissive is satisfied; and modulating the admission valve such that allow the steam flows into the HP section; wherein the step of increasing the pressure of the steam decreases a temperature of the steam before steams flows into the HP section.

BRIEF DESCRIPTION OF THE DRAWINGS

There follows a detailed description of embodiments of the invention by way of example only with reference to the accompanying drawings, in which: FIG. 1 is a schematic illustrating a HP section of a steam turbine representing an environment within which an embodiment of the present invention may operate.

FIG. 2 is a chart illustrating operating curves in accordance with a known method of starting a steam turbine.

FiG. 3 is a block diagram illustrating a method used to start-up a turbomachine, in accordance with an embodiment of the present invention.

FIG. 4 is a block diagram illustrating a method used to start-up a turbomachine, in accordance with an alternate embodiment of the present invention.

FIG. 5 is a chart illustrating operating curves in accordance with a method of starting a steam turbine in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention has the technical effect of reducing the start-up time associated with starting a steam turbine. Embodiments of the present invention provide a new methodology for reducing the steam-to-metal temperature mismatch present during the start-up of a steam turbine. Essentially, embodiments of the invention may raise the pressure of the steam upstream of an admission valve associated with a High Pressure (HP) section of a steam turbine. The initial high pressure of the steam may reduce the enthalpy of steam, thus reducing temperature of the steam admitted to the HP section.

Detailed example embodiments are disclosed herein. However, specific structural and functional details disclosed herein are merely representative for purposes of describing example embodiments. Example embodiments may, however, be embodied in many alternate forms, and should not be construed as limited to only the embodiments set forth herein.

Accordingly, while example embodiments are capable of various modifications and alternative forms, embodiments thereof are illustrated by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit example embodiments to the particular forms disclosed, but to the contrary, example embodiments are to cover all modifications, equivalents, and alternatives falling within the scope of example embodiments.

It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of example embodiments.

As used herein, the term "and/or" includes any, and all, combinations of one or more of the associated listed items.

The terminology used herein is for describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms "a", "an" and the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises", "comprising", "includes" and/or "including", when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

It should also be noted that in some alternative implementations, the functions/acts noted might occur out of the order noted in the FIGS. Two successive FIGS., for example, may be executed substantially concurrently or may sometimes be executed in the reverse order, depending upon the functionality/operations involved.

Referring now to the FIGS., where the various numbers represent like parts throughout the several views. FIG. 1 is a schematic illustrating a HP section 120 of a steam turbine 100 representing an environment within which an embodiment of the present invention may operate. Typically, a steam turbine 100 typically comprises multiple sections, such as, but not limiting of, a High-Pressure (HP), an Intermediate-Pressure (IP), and a Low-Pressure (LP). Embodiments of the present invention may control the steam flow into the HP section 120. Therefore, FIG. 1 and the following discussion focus on the HP section 120 which is integrated with a condensor 140. For simplicity, the IP drum and IP section, the LP drum and LP section, and reheat components are not illustrated in FIG. 1. However, embodiments of the present invention may apply to a steam turbine 100 comprising some or all of those sections and components, or the like.

A control system 190 applying known methods of starting up the steam turbine 100 may perform the following steps. Steam from an IP drum may be admitted to the IP section of the steam turbine 100. Next, the steam turbine 100 may accelerate to full-speed-no-load (FSNL). Next, the steam turbine 100 may synchronize with a grid system, or the like. Next, turbine transfer of the steam from the IF section to full flow to the 1-IP section 120 may occur. Here, an admission valve 115 may begin to open, allowing steam to from the HP drum 105 to the HP section 120. Concurrently, the control system 190 monitors the rotor stress. If the rotor stresses exceed an allowable range then the control system 190 may hold or reduce the steam flow into the HP section 120, for a predetermined waiting period. After, the rotor stresses decrease to an allowable range, the control system 190 may continue to admit steam into the HP section 120 via the admission valve 115 until full steam flow is achieved or the steam turbine load meets a load set point.

FIG. 2 is a chart 200 illustrating operating curves in accordance with a known method of starting a steam turbine 100, as described in FIG. 1. A first vertical axis represents Temperature (in deg. F.) and Pressure (in psia). A second vertical axis represents stress (in percentage). The first and second vertical axes are versus the start-up time (in minutes) on the horizontal axis. Data series 205 represents the actual HP rotor stress and data series 210 represents the allowable stress limit. Data series 215 and 220 represent HP upstream pressure and temperature respectively. The upstream area is illustrated as the upstream location 130 in FIG. 1. Data series 225 may represent the HP bowl temperature, illustrated as HP bowl 125 in FIG. 1.

The upstream area 130 may be considered a region upstream and adjacent to the admission valve 115. The downstream area 135 may be considered a region downstream and adjacent to the admission valve 115.

FIG. 2 illustrated that from approximately 8 minutes to approximately 24 minutes, the HP rotor stress 205 exceeded the allowable stress limit 210. To correct this situation the control system 190 may modulate the admission valve 115 towards a closed position for a predetermined waiting period. As illustrated in FIG. 2, at approximately 25 minutes, the rotor stresses decreases to an allowable range. Here, the control system 190 may modulate the admission valve 115 towards an open position to continue to admit steam into the HP section 120, as described. The period that the HP rotor stress 205 exceeded the allowable stress 210, approximately 16 minutes, prevented the steam turbine 100 from completing the start-up process.

As will be appreciated, the present invention may be embodied as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects all generally referred to herein as a "circuit", "module," or system". Furthermore, the present invention may take the form of a computer program product on a computer-usable storage medium having computer-usable program code embodied in the medium. As used herein, the terms "software" and "firmware" are interchangeable, and include any computer program stored in memory for execution by a processor, including RAM memory, ROM memory, EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are exemplary only, and are thus not limiting as to the types of memory usable for storage of a computer program.

Any suitable computer readable medium may be utilized. The computer-usable or computer-readable medium may be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. More specific examples (a non exhaustive list) of the computer-readable medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a transmission media such as those supporting the Internet or an intranet, or a magnetic storage device. Note that the computer-usable or computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory. In the context of this document, a computer-usable or computer-readable medium may be any medium that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.

The term processor, as used herein, refers to central processing units, microprocessors, microcontrollers, reduced instruction set circuits (RISC), application specific integrated circuits (ASIC), logic circuits, and any other circuit or processor capable of executing the functions described herein.

Computer program code for carrying out operations of the present invention may be written in an object oriented programming language such as Java7, Smailtalk or C++, or the like. However, the computer program code for carrying out operations of the present invention may also be written in conventional procedural programming languages, such as the "C" programming language, or a similar language. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer. In the latter scenario, the remote computer may be connected to the user's computer through a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

The present invention is described below with reference to flowchart illustrations and/or block diagrams of methods, apparatuses (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a public purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart andlor block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory. These instructions can direct a computer or other programmable data processing apparatus to function in a particular manner. The such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function/act specified in the flowchart and/or block diagram block or blocks. The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus. These instructions may cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process. Here, the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions/acts specified in the flowchart and/or block diagram blocks.

Embodiments of the present invention provide a new start-up methodology. As described below, embodiments of this methodology may increase the pressure of the steam upstream of the HP section 120. This may reduce the temperature of the steam prior to admission into the HP section 120; which may reduce the rotor stresses.

Then, during initial steam turbine loading, the methodology may reduce the upstream steam pressure. This may increase the temperature of the steam flowing into the HP section 120 to a normal operating range at the HP bowl 125.

Referring again to the Figures, FIG. 3 is a block diagram illustrating a method 300 used to start-up a steam turbine 100, in accordance with an embodiment of the present invention. The method 300 may be operated by the control system 190, as illustrated in FIG. 1. The control system 190 may provide a graphical user interface (GUI), or the like, that allows an operator to interact with the method 300.

In step 305, the method 300 may determine the initial steam turbine metal temperatures. Here, the control system 190 may receive data on the metal temperatures from a temperature sensing devices integrated with the rotor of the steam turbine 100.

In step 310, the method 300 may determine if a cold start of the steam turbine 100 is required. A cold start may be considered a start-up of a steam turbine 100 that has been idle for a certain period. Components of the steam turbine 100 typically require longer warming periods when operating under a cold start. The control system 190 may comprise an operating timer, or the like, which determines when a cold start is required. if a cold start is required, then the method 300 may proceed to step 315; otherwise the method 300 may proceed to step 325.

In step 315, the method 300 may increase the pressure of the 1-IP steam at the upstream location 130 to a matching pressure range. Referring again to FIG. 1, embodiments of the present invention may modulate the bypass valve 110 to a position allowing for the matching pressure range. In an embodiment of the present invention, the pressure range may be from approximately 1200 deg. F to approximately 1500 deg. F. In step 320, the method 300 may determine whether the pressure of the steam at the upstream location 130 is within the matching pressure range. If the pressure of the steam is within the matching pressure range, then the method 300 may proceed to step 325; otherwise the method 300 may revert to step 315.

In step 325, the method 300 may determine whether a start-up permissive is satisfied.

Here, the control system 190 may include start-up permissives that serve to ensure that various systems of the steam turbine 100 are ready and/or enable for the start-up process. If the start-up permissive is satisfied, then the method 300 may proceed to step 330; otherwise the method 300 may revert to step 325 until the start-up permissive is satisfied.

In step 330, the method 300 may initiate the start-up process of the steam turbine 100.

Here, steam from an IF drum may be admitted to the IP section of the steam turbine 100. Next, the steam turbine 100 may accelerate to full-speed-no-load (FSNL).

In step 335, the method 300 may synchronize the steam turbine 100. Here, the steam turbine 100 may be electrically connected with a grid system, or the like.

In step 340, the method 300 may begin to modulate the admission valve 115. This may allow steam from the HP drum 105 to fill and warm the piping adjacent the HP section 120.

In step 345, the method 300 may transfer to full flow of the steam from the IP section to the I-IF section 120. Here, the admission valve 115 may further open, allowing steam to enter the HP section 120.

In step 350, the method 300 may determine if the rotor stress level is allowable. Here, the control system 190 may monitor the rotor stress in real-time and compare the actual rotor stress to the allowable stress limit, if the rotor stresses are not in the allowable range, then the method 300 may proceed to step 355; otherwise the method 300 may proceed to step 360.

In step 355, the method 300 may maintain or reduce the steam flow into the HP section 120, for a predetermined waiting period. After, the rotor stresses decrease to the allowable range; the control system 190 may continue to admit steam into the HP section 120 via the admission valve 115.

In step 360, the method 300 may increase the temperature of the steam at the upstream location 130 to approximately a rated temperature. Here, the control system may modulate the bypass valve 110 to a position allowing for decreasing the pressure of the steam, allowing for an increasing the steam temperature, as described.

In step 365, the method 300 may increase the temperature of the steam in the HP bowl 125. Here, the control system 190 may modulate the bypass valve 110 to a position allowing for decreasing the pressure of the steam, allowing for an increasing the steam temperature, as described.

In step 370, the method 300 may increase the load to a base load, or other load setpoint. Here, the control system 190 may continue to admit steam into the HP section 120 via the admission valve 115 until the desired load is reached.

In step 375, the method 300 may maintain the load setpoint. Here, the method 300 may modulate the admission valve 115 as needed to maintain the load.

FIG. 4 is a block diagram illustrating a method 400 used to start-up a turbomachine, in accordance with an alternate embodiment of the present invention. The majority of the steps described in FIG. 3 may be repeated. Therefore, the discussion of FIG. 4 will focus on the differences between the methods 300 and 400. Steps 360 and 365 of the method 300 are swapped in the method 400. Here, the method 400 prioritizes the step of increasing the temperature of the steam in the HP bowl 125, in step 460, over the step of increasing the temperature of the steam at the upstream location 130. This approach in the method 400 is opposite to the approach used in the method 300; and may be used to further mitigate the rotor stress level.

Embodiments of the present invention reduce the enthalpy of the steam upstream of the admission valve 115. hi addition, the pressure ratio across the admission valve may be reduced. Together, these actions may collectively reduce the temperature inside the HP bowl 125. In an embodiment of the present invention, the temperature reduction across the admission valve 115 may range from approximately 125 deg. F. to approximately 150 deg. F. In comparison, the method described in conjunction with FIG. 2, may merely provide a temperate reduction of up to approximately 50 deg. F. The increased temperature reduction that may be provided by an embodiment of the present invention may reduce the steam-metal temperature mismatch and, thus mitigate rotor stress.

FIG. 5 is a chart 500 illustrating operating curves in accordance with method 300 of FIG. 3 and 400 of FIG. 4 in accordance with embodiments of the present invention. A first vertical axis represents Temperature (in deg. F.) and Pressure (in psia). A second vertical axis represents stress (in percentage). The first and second vertical axes are versus the start-up time (in minutes) on the horizontal axis. Data series 505 represents the actual HP rotor stress and data series 510 represents the allowable stress limit.

Data series 515 and 520 represent HP upstream pressure and temperature respectively.

The upstream area may be adjacent the upstream location 130 (illustrated in FIG. 1).

Data series 525 may represent the HP bowl temperature, illustrated as HP bowl 125 in FIG. 1.

FIG. 5 illustrates that throughout the start-up of the steam turbine 100, the HP rotor stress 505 did not exceed the allowable stress limit 510. Here, the bypass valve 110 was modulated to increase the pressure at the upstream location 130 to approximately 1400 psig. In FIG. 5 the HP bowl temperature 525 is approximately 575 deg. F. In contrast, the HP bowl temperature of FIG. 2 is approximately 725 deg. F. FIG. 5 also illustrates increases in the HP upstream pressure arid temperature, 520, 525 respectively as the upstream pressure 515 is decreased, as described.

As one of ordinary skill in the art will appreciate, the many varying features and configurations described above in relation to the several exemplary embodiments may be further selectively applied to form the other possible embodiments of the present invention. Those in the art will further understand that all possible iterations of the present invention are not provided or discussed in detail, even though all combinations and possible embodiments embraced by the several claims below or otherwise are intended to be part of the instant application. In addition, from the above description of several exemplary embodiments of the invention, those skilled in the art will perceive improvements, changes, and modifications. Such improvements, changes, and modifications within the skill of the art are also intended to be covered by the appended claims. Further, it should be apparent that the foregoing relates only to the described embodiments of the present application and that numerous changes and modifications may be made herein without departing from the spirit and scope of the application as defmed by the following claims and the equivalents thereof.

Claims

CLAIMS1. A method of starting a powerplant machine, the method comprising: providing a steam turbine configured for converting steam to a mechanical torque; wherein the steam turbine comprises an HP section; and increasing a pressure of steam upstream of an admission valve to a pressure matching range, wherein the admission valve is located upstream of the FIP section; wherein the step of increasing the pressure of the steam decreases a temperature of the steam prior to admission into the HP section.
2. The method of claim 1, further comprising the step of initiating a start-up of the steam turbine if a start-up permissive is satisfied.
3. The method of claim 2, further comprising the step of opening the admission valve to allow the steam to enter the HP section.
4. The method of claim 2, further comprising the step of determining whether a rotor stress is within an acceptable range.
5. The method of claim 4, further comprising the step of maintaining a current load on the steam turbine until the rotor stress is within the acceptable range.
6. The method of claim 5, further comprising the step of decreasing the pressure of the steam upstream of the admission valve.
7. The method of claim 6, further comprising the step of increasing a temperature of the steam in an HP bowl region of the HP section.
8. The method of claim 5, further comprising the step of increasing a temperature of the steam in an HP bowl region of the HP section.
9. The method of claim 8, further comprising the step of decreasing the pressure of the steam upstream of the admission valve.
10. A method of starting a powerplant comprising a steam turbine, the method comprising: providing a steam turbine configured for converting steam to a mechanical torque; wherein the steam turbine comprises an FIP section and a bypass system; determining whether a cold start of the steam turbine is requested; increasing a pressure the steam upstream of an admission valve to a pressure matching range, wherein the admission valve is located upstream of the HP section; determining whether the steam upstream of the admission valve is within the pressure matching range; initiating a start-up of the steam turbine if a start-up permissive is satisfied; and modulating the admission valve such that allow the steam flows into the HP section; wherein the step of increasing the pressure of the steam decreases a temperature of the steam before steams flows into the HP section.
11. The method of claim 10, wherein the step of increasing the pressure of the steam upstream of the admission valve to a pressure matching range, further comprises the step of modulating a bypass valve of the bypass system.
12. The method of claim 11, further comprising the step of determining whether a rotor stress is within an acceptable range.
13. The method of claim 12, further comprising the step of adjusting a loading rate of the steam turbine until the rotor stress is within the acceptable range.
14. The method of claim 13, further comprising the step of modulating the bypass valve to decrease the pressure of the steam upstream of the admission valve.
15. The method of claim 14, further comprising the step of increasing a temperature of the steam in an HP bowl region of the HP section.
16. The method of claim 13, further comprising the step of increasing a temperature of the steam in an HP bowl region of the HP section.
17. The method of claim 16, further comprising the step of modulating the bypass valve to decrease the pressure of the steam upstream of the admission valve.
18 A system configured for starting a steam turbine, the system comprising: a steam turbine configured for converting steam to a mechanical torque; wherein the steam turbine comprises an 1-IP section; and a control system configured for starting the steam turbine, wherein the control system performs the steps of: determining whether a cold start of the steam turbine is requested; increasing a pressure the steam upstream of an admission valve to a pressure matching range, before the steam flows into the FJP section, wherein an admission valve is located upstream of the 1-1P section; determining whether the steam upstream of the admission valve is within the pressure matching range; initiating a start-up of the steam turbine if a start-up permissive is satisfied; and opening the admission valve to allow the steam to flow into the FIP section; wherein the step of increasing the pressure of the steam decreases a temperature of the steam prior to admission into the 1-IP section.
19. The system of claim 18, wherein the control system performs the step of modulating a bypass valve of the bypass system to increase the pressure of the steam upstream of the admission valve.
20. The system of claim 19, wherein the control system further performs the steps of: modulating the bypass valve to decrease the pressure of the steam upstream of the admission valve in order to increase a temperature of the steam in an HP bowl region of the HP section.
21. A method of starting a powerplant substantially as herein described with reference to the accompanying drawings.
22. A system substantially as herein described with reference to the accompanying drawings.