<PAGE>
 
                                                            HECO Exhibit 10.5(b)
                                                            --------------------



                AMENDMENT TO PURCHASE POWER CONTRACT, AS AMENDED
                ------------------------------------------------


     THIS AMENDMENT, made this ______ day of October, 1993, by HAWAII ELECTRIC
LIGHT COMPANY, INC., a Hawaii corporation ("Company"), and PUNA Geothermal
VENTURE, a Hawaii general partnership ("Seller");

                           R  E  C  I  T  A  L  S  :
                           -  -  -  -  -  -  -  -   

          A.   The Company and Thermal Power Company, as seller therein, had
previously entered into that certain Purchase Power Contract For Unscheduled
Energy made Available From A Qualifying Facility, dated March 24, 1986
("Purchase Power Contract"), which was subsequently approved by the Public
Utilities Commission ("PUC") in its Decision and Order ("D &  O") No. 8692,
filed in PUC Docket No. 5525 on March 25, 1986.

          B.   The Seller subsequently succeeded to the interest of Thermal
Power Company under the Purchase Power Contract.

          C.   The Company and the Seller entered into that certain Firm
Capacity Amendment To Purchase Power Contract Dated March 24, 1986, dated July
28, 1989 ("Firm Capacity Amendment"), which was subsequently approved by the PUC
in its D & O No. 10519, filed in PUC Docket No. 6498 on February 14, 1990.

          D.   The Seller's geothermal power project located in Kapoho, Hawaii
("Facility") was from its inception a "qualifying facility" ("QF"), under
Subchapter 2 of the "Standards for Small Power Production and Cogeneration,"
Hawaii Administrative Rules, Title 6, Chapter 74 ("PUC Standards").

          E.   As a result of a restructuring of the ownership of the Seller and
the Facility in connection with financing for the Facility, the Facility may,
following such restructuring, no longer qualify as a QF under the PUC Standards,
but such restructuring will not otherwise affect or modify the Seller's
capability of performing its obligations under the Purchase Power Contract, as
amended, and/or the rights of the Company thereunder.

          F.   The Company and the Seller firmly believe that the rates for
purchase set forth in the Purchase Power Contract, as amended, are fully
consistent with the provisions of H.R.S. (S)269-27.2 and continue to be in
furtherance of the State's policy to encourage the development of the State's

<PAGE>
 
renewable alternate energy resources, including the geothermal resources.

          G.   The company and the Seller further believe that it is in the best
interests of the parties to amend the Purchase Power Contract, as amended, to
(i) provide that the Facility shall be either (i) a QF or (ii) a producer of
electricity generated from nonfossil fuel sources and thus falling within the
meaning of Section 269-27.2, Hawaii Revised Statutes ("nonfossil fuel
producer"), and to advise the PUC of such amendment.

          NOW, THEREFORE, in consideration of the premises, the parties hereby
agree to amend the Purchase Power Contract and the Firm Capacity Amendment as
follows:

          1.   Amendments to the Purchase Power Contract.
               ----------------------------------------- 

          a.   The second WHEREAS clause on page 1 of the Purchase Power
Contract is amended by (i) deleting the following portion of that clause:

          "of a cogeneration facility or small power production facility which
          is a qualifying facility under Subchapter 2 of the PUC's Standards for
          Small Power Production and Cogeneration in the State of Hawaii,
          Chapter 74 of Title 6; and"

and (ii) substituting in lieu thereof the following new portion:

          "of a cogeneration facility or small power production facility which
          is (i) a qualifying facility under Subchapter 2 of the PUC's Standards
          for Small Power Production and Cogeneration in the State of Hawaii,
          Chapter 74 of Title 6, or (ii) a producer of electricity generated
          from nonfossil fuel sources and thus falling within the meaning of
          Section 269-27.2, Hawaii Revised Statutes ("nonfossil fuel producer");
          and"

          b.   APPENDIX E on page 19 of the Purchase Power Contract is amended
by deleting subparagraph 1.(a)(ii) in its entirety and substituting in lieu
thereof the following new subparagraphs l.(a)(ii):

          "(ii)     failure of the Seller's facility, upon its completion and
                    operation, to be (i) a qualifying facility under Subchapter
                    2 of the PUC's Standards for Small Power

                                       2
<PAGE>
 
                    Production and Cogeneration in the State of Hawaii, Chapter
                    74 of Title 6 in effect as of the date of this Contract, or
                    (ii) a nonfossil fuel producer falling within the meaning of
                    Section 269-27.2, Hawaii Revised Statutes; or"

          c.   All other references or requirements in the Purchase Power
Contract to the Facility being a "QF" or "qualifying facility" are similarly
amended by adding to each such reference or requirement the phrase "or nonfossil
fuel producer falling within the meaning of Section 269-27.2, Hawaii Revised
Statutes."

          2.   Amendments to the Firm Capacity Amendment.
               ----------------------------------------- 

          a.   The sixth (6th) WHEREAS clause on page 1 of the Firm Capacity
Amendment is amended by deleting that WHEREAS cause in its entirety and
substituting in lieu thereof the following new WHEREAS clause;

          "WHEREAS, the Seller's facility will be (i) a qualifying facility
          under Subchapter 2 of the PUC's Standards for Small Power Production
          and Cogeneration in the State of Hawaii, Chapter 74 of Title 6, or
          (ii) a facility which generates electricity from nonfossil fuel
          sources and thus falling within the meaning of Section 269-27.2,
          Hawaii Revised Statutes;"

          b.   All other references or requirements in the Firm Capacity
Amendment to the Facility being a "QF" or "qualifying facility" are similarly
amended by adding to each such reference or requirement the phrase "or nonfossil
fuel producer falling within the meaning of Section 269-27.2, Hawaii Revised
Statutes".

          3.   Continuing Effect.  Except as amended by this instrument, the
               -----------------                                            
Power Purchase Contract, as amended by the Firm Capacity Amendment, remains in
otherwise unmodified and in full force and effect.

          4.   Further Action.  The Company and the Seller shall take such
               --------------                                             
further action as may be necessary or desirable to implement the provisions, and
advise the PUC, of this Amendment to Purchase Power Contract, as amended, as
expeditiously as possible.

          5.   Counterparts.  This instrument may be executed in any number of
               ------------                                                   
counterparts, each of which shall be deemed an

                                       3
<PAGE>
 
original, and all of which together shall constitute one and the same
instrument.

          6.   Effective Date.  This Amendment to Purchase Power Contract, as
               --------------                                                
amended, shall become effective when signed by the Seller and the Company.

          IN WITNESS WHEREOF, the Company and the Seller have executed this
Amendment to Purchase Power Contract, as amended, as of the day and year first
above written.


                              HAWAII ELECTRIC LIGHT COMPANY, INC


                              By /s/ Warren H. W. Lee
                                 ------------------------
                                 Warren H. W. Lee
                                 Its President
                                 Date:  October 14, 1993

                              By /s/ Edward Y. Hirata
                                 ------------------------
                                 Edward Y. Hirata
                                 Its Vice President
                                 Date:  October 14, 1993



                              PUNA GEOTHERMAL VENTURE

                              By CE PUNA LIMITED PARTNERSHIP,
                                 a Maryland Limited partnership


                              By CE PUNA I, INC.,
                                 a Maryland corporation
                                 Its General Partners


                                 By /s/ Bruce M. Ambler
                                    -------------------
                                    Bruce M. Ambler
                                    Its President

                                       4
<PAGE>
 
STATE OF HAWAII               )
                              )     SS.
CITY AND COUNTY OF HONOLULU   )


          On this 14th day of October, 1993, before me personally appeared
WARREN H. W. LEE and EDWARD Y. HIRATA, to me personally known, who, being by me
duly sworn, did say that they are the President and Vice President,
respectively, of HAWAII ELECTRIC LIGHT COMPANY, INC., a Hawaii corporation, and
that the seal affixed to the foregoing instrument is the corporate seal of said
corporation and that said instrument was signed and sealed on behalf of said
corporation by authority of its Board of Directors, and the said officers
acknowledged said instrument to be the free act and deed of said corporation.



                              /s/ Wendy E. Oda
                              Notary Public, State of Hawaii

                              My Commission Expires:  8/25/95

<PAGE>
 
STATE OF MARYLAND      )
                       )    SS.
COUNTY OF BALTIMORE    )



          On this 19th day of October, l993, before me appeared Bruce M. Ambler,
to me personally known, who, being by me duly sworn, did say that he is the
President of CE PUNA I, INC, a Maryland corporation; that said corporation is a
general partner of CE Puna Limited Partnership, a Maryland limited partnership
named in the foregoing instrument; that said instrument was executed by said
corporation as the duly authorized general partner of and on behalf of CE Puna
Limited Partnership, and acknowledged that the seal affixed to the foregoing
instrument is the corporate seal of said corporation, and that said instrument
was signed and sealed on behalf of said corporation by authority of its Board of
Directors and in the name of and on behalf of said limited partnership, and said
officer acknowledged said instrument to be the free act and deed of said
corporation and as said general partner of said limited partnership.


                              /s/ Melissa A. Hill
                              Notary Public, State of Maryland
                              My Commission Expires:  September 24, 1996