<PAGE>   1

                             SECOND AMENDMENT TO THE
              AMENDED AND RESTATED LIMITED PARTNERSHIP AGREEMENT OF
                       LSP-WHITEWATER LIMITED PARTNERSHIP


         THIS SECOND AMENDMENT TO THE AMENDED AND RESTATED LIMITED PARTNERSHIP
AGREEMENT OF LSP-WHITEWATER LIMITED PARTNERSHIP (this "SECOND AMENDMENT") is
made as of the 11th day of December, 1998, by and among LSP-WHITEWATER I, INC.,
a Delaware corporation (the "COMPANY"), TPC WHITEWATER, INC., a Delaware
corporation ("TPC") and COGENTRIX WHITEWATER, LLC, a Delaware limited liability
company ("COGENTRIX").

                              STATEMENT OF PURPOSE

         WHEREAS, the Company, Cogentrix and TPC are parties to that certain
Amended and Restated Limited Partnership Agreement, of LSP-Whitewater Limited
Partnership (the "LIMITED PARTNERSHIP") dated June 30, 1995 (as amended by the
First Amendment thereto, dated March 20, 1998, the "AGREEMENT").

         WHEREAS, the Parties wish to provide for the posting from time to time
of Debt Service Letters of Credit (defined below) by the Partners pursuant to
Section 3.10(d) of the Deposit and Disbursement Agreement, and the related
distribution of funds from the Debt Service Reserve Fund (defined below) to the
Partner or Partners posting any such Debt Service Letters of Credit.

                                    AGREEMENT

         NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties agree as follows:

         1. CERTAIN TERMS. All capitalized terms used herein without definition
shall have the meanings assigned thereto in the Agreement.

         2. AMENDMENTS TO AGREEMENT.

         (a) The following definitions in Section 1.2 of the Agreement are
hereby amended and restated as follows:

                  "Available Funds" means an amount of cash, other than cash in
                  an amount required to be distributed to the Partners pursuant
                  to the second full paragraph of Section 6.22 of the
                  Partnership Trust Indenture and Section 3.15 of the Deposit &
                  Disbursement Agreement to cover the Partner's Income Tax
                  Deficiency, on hand at the end of each fiscal quarter equal to
                  the excess of: (x) the amount of cash (including proceeds of
                  borrowings) available at such time; over (y) the sum of (i)
                  the amount of cash which the General Partner reasonably
                  believes will be required during the upcoming fiscal quarter
                  (after taking into account reasonably expected 


<PAGE>   2

                  revenues during such period) to meet all reasonably expected
                  costs and expenses of the Partnership (including capital
                  expenditures, payments under the Management Services Agreement
                  and payments of principal and interest on any debts and other
                  obligations of the Partnership), plus (ii) the amount of any
                  reasonable reserve the General Partner may establish from time
                  to time. Available Funds shall not include any funds held by
                  the Depositary Agent and available to be distributed to any
                  Partner in connection with the posting by such Partner of a
                  Debt Service Letter of Credit pursuant to Section 3.10(d) of
                  the Deposit and Disbursement Agreement.

                  "Book Value" means, with respect to any asset of the
                  Partnership, the adjusted basis of such asset as of the
                  relevant date for federal income tax purposes, except as
                  follows:

                           (i) the initial Book Value of any asset contributed
                  by a Partner to the Partnership shall be the fair market value
                  of such asset;

                           (ii) the Book Values of all Partnership assets
                  (including intangible assets such as goodwill) shall be
                  adjusted to equal their respective fair market values as of
                  the following times:

                                    (A) the acquisition of an additional
                  interest in the Partnership by any new or existing Partner in
                  exchange for more than a de minimis Capital Contribution;

                                    (B) the distribution by the Partnership to a
                  Partner of more than a de minimis amount of money or
                  Partnership property as consideration for an interest in the
                  Partnership; and

                                    (C) the liquidation of the Partnership
                  within the meaning of Regulations section
                  1.704-1(b)(2)(iv)(f)(5)(ii); and

                           (iii) if the Book Value of an asset has been
                  determined or adjusted pursuant to subsection (i) or (ii)
                  above, such Book Value shall thereafter be adjusted by the
                  Depreciation taken into account with respect to such asset for
                  purposes of computing Profits and Losses and other items
                  allocated pursuant to Section 3.2.

                           The foregoing definition of Book Value is intended to
                  comply with the provisions of Regulations section
                  1.704(b)(2)(iv) and shall be interpreted and applied
                  consistently therewith. Notwithstanding the foregoing, no
                  Contribution to Capital pursuant to Section 2.2 will require
                  an adjustment of the Book Value of the Partnership assets, and
                  no distribution pursuant to Section 6.2 will require an
                  adjustment to the Book Value of the Partnership's assets.


                                     - 2 -
<PAGE>   3

                  "Partner Loans" has the meaning specified in Section 2.3(a).

         (b) The following definitions shall be added to Section 1.2 of the
Agreement:

                  "Debt Service Reserve Fund" shall have the meaning ascribed
                  thereto in the Partnership Trust Indenture.

                  "Debt Service Letter of Credit" shall have the meaning
                  ascribed thereto in the Partnership Trust Indenture.

                  "Depositary Agent" shall have the meaning ascribed thereto in
                  the Partnership Trust Indenture.

         (c) Section 2.1(c)(iv) shall be added to Section 2.1:

                  2.1(c)(iv) Effect of Section 2.2 and 6.2 on Rate of Return
                  Computation. Contributions to Capital pursuant to Section 2.2
                  and distributions pursuant to Section 6.2 shall not be
                  considered in making rate of return computations for purposes
                  of this Section 2.1(c).

         (d) Section 2.2 of the Agreement shall be redesignated 2.3, and Section
2.2 shall be replaced and amended as follows:

                  Section 2.2 Capital Contributions to Reflect Debt Service
                  Letters of Credit. If any Partner shall provide a Debt Service
                  Letter of Credit pursuant to Section 3.10(d) of the Deposit
                  and Disbursement Agreement, such Partner shall, at such time,
                  contribute to the Partnership a promissory note in an amount
                  equal to the stated amount of such Debt Service Letter of
                  Credit, substantially in the form of Exhibit A attached
                  hereto. The aggregate principal amount of each such note shall
                  be treated as a Capital Contribution by the Partner
                  contributing such note.

         (e) The following Section 4.9 shall be added to the Agreement:

                  Section 4.9 Debt Service Letters of Credit. Any Partner may,
                  from time to time, deliver to the Depositary Agent a Debt
                  Service Letter of Credit in a stated amount equal to all or
                  any portion of the amount of cash then on deposit in the Debt
                  Service Reserve Fund pursuant to Section 3.10(d) of the
                  Deposit and Disbursement Agreement. Amounts released from the
                  Debt Service Reserve Fund by the Depositary Agent to any
                  Partner shall be characterized as contemplated in Section 6.2
                  below.

         (f) Section 6.2 shall be redesignated 6.3, and 6.2 shall be replaced
and amended as follows:

                  Section 6.2 Funds Remitted from the Debt Service Reserve Fund.
                  Funds remitted from the Depositary Agent to any Partner
                  pursuant to Section 3.10(d) of the Deposit and Disbursement
                  Agreement shall be treated as reductions in the 



                                     - 3 -
<PAGE>   4

                  Capital Account of the recipient Partner pursuant to Section
                  5.1 of this Agreement.

         3. NO OTHER AMENDMENTS. Except as specifically amended pursuant to this
Second Amendment, the Agreement and the First Amendment thereto remain in full
force and effect in accordance with their terms.

         4. GOVERNING LAW. All questions concerning the construction, validity
and interpretation of this Second Amendment will be governed by and construed in
accordance with the internal law (and not the law of conflicts) of Delaware.

         5. COUNTERPARTS. This Second Amendment may be executed in any number of
counterparts, each of which shall constitute an original but all of which when
taken together shall constitute but one agreement.

         6. AMENDMENT OR WAIVER. The parties agree that this Second Amendment is
entered into in accordance with Sections 10.4 and 10.5 of the Agreement.

                  [Remainder of page intentionally left blank.]



                                     - 4 -
<PAGE>   5

         IN WITNESS WHEREOF, the parties hereto have caused this Second
Amendment to be duly executed by their duly authorized officers, all as of the
date first above written.


                                           COMPANY:

                                               LSP-WHITEWATER I, INC.


                                               By: /s/ Thomas F. Schwartz
                                                  ------------------------------
                                                   Name: Thomas F. Schwartz
                                                   Title: Assistant Treasurer


                                           TPC:

                                               TPC WHITEWATER, INC.


                                               By: /s/ Keiichi Matsuzuka
                                                  ------------------------------
                                               Name: Keiichi Matsuzuka
                                               Title: C.F.O.


                                           COGENTRIX:

                                               COGENTRIX WHITEWATER, LLC


                                               By: /s/ Thomas F. Schwartz
                                                  ------------------------------
                                               Name: Thomas F. Schwartz
                                               Title: Senior Vice President-
                                                      Finance and Treasurer


                                     - 5 -
<PAGE>   6

                                    EXHIBIT A


                                  FORM OF NOTE




                                     - 6 -
<PAGE>   7

                                 PROMISSORY NOTE


                                                               December 11, 1998
                                                       Charlotte, North Carolina


Initial Principal Amount:    $6,900,000.00

Interest Rate:     (5.47%) per annum (as adjusted pursuant to Paragraph 2 below)
-------------

         FOR VALUE RECEIVED, COGENTRIX ENERGY, INC., located at 9405 Arrowpoint
Boulevard, Charlotte, NC 28273 (hereinafter called "Payor"), promises to pay to
the order of LSP-WHITEWATER LIMITED PARTNERSHIP or its assigns (hereinafter
called "Payee"), the principal amount of SIX MILLION, NINE HUNDRED THOUSAND
DOLLARS ($6,900,000.00) (as such amount may be decreased from time to time in
accordance herewith, the "Principal Amount") on December 15, 2016 (the "Maturity
Date"). Payor promises to pay interest on the Principal Amount at the Interest
Rate stated above from the date this Note is issued until the Maturity Date,
payable monthly in arrears, with the first of such payments being prorated
according to the date hereof. Interest on this Note will accrue from the most
recent date to which interest has been paid or, if no interest has been paid,
from the date hereof.

         AND IT IS EXPRESSLY AGREED AS FOLLOWS:

         1. The Principal Amount of this Note equals the stated amount ("Stated
Amount") of a letter of credit (the "Debt Service Letter of Credit") issued on
the date hereof and provided as security for debt service obligations of the
Payee under a trust indenture, dated as of May 1, 1995, between the Payee and
IBJ Schroder Bank & Trust Company, as trustee (the "Indenture"). The Principal
Amount of this Note shall decrease, from time to time and on a dollar for dollar
basis, with any decrease in the Stated Amount of the Debt Service Letter of
Credit resulting from any draw thereunder or any replacement thereof with cash
deposits by the Payor into the relevant debt service fund under the Indenture.
Any such reduction in the Principal Amount shall be deemed a prepayment of such
Principal Amount for all purposes hereunder. All such prepayments shall be noted
on Schedule I hereto by an authorized officer of the Payee.

         2. The Interest Rate set forth above shall be adjusted every ninety
(90) days from the date of issuance hereof (each, an "Adjustment Date") to equal
the sum of the 3-month LIBOR Rate in effect on each such Adjustment Date, as
such rate appears on Page 3750 of the Dow Jones Market Service (commonly known
as the Telerate Screen) as of 11:00 a.m. on the relevant Adjustment Date plus
0.25%.

         3. This Note is subject to the express condition that at no time shall
Payor be obligated or required to pay interest on the principal balance at a
rate which could subject Payee to either civil or criminal liability as a result
of being in excess of the maximum rate which Payor is permitted by law to
contract or agree to pay. If by the terms of this Note Payor is at any time
required or obligated to pay interest on the principal balance at a rate in
excess of such maximum rate, the rate of interest under this Note shall be
deemed to be immediately reduced



<PAGE>   8

to such maximum rate and interest payable hereunder shall be computed at such
maximum rate and the portion of all prior interest payments in excess of such
maximum rate shall be applied and shall be deemed to have been payments in
reduction of the principal balance.

         4. Payor hereby waives presentment and demand for payment, notice of
dishonor, protest and notice of protest of this Note and agrees to pay all costs
of collection when incurred, including reasonable attorneys' fees (which costs
may be added to the amount due under this Note and be receivable therewith) and
to perform and comply with each of the terms, covenants and provisions contained
in this Note on the part of Payor to be observed or performed. No release of any
security for the principal sum due under this Note or extension of time for
payment of this Note, or any installment hereof, and no alteration, amendment or
waiver of any provision of this Note made by agreement between Payee and any
other person or party shall release, discharge, modify, change or affect the
liability of Payor under this Note.

         5. This Note may not be changed orally, but only by an agreement in
writing, signed by the party against whom enforcement of any waiver, change,
modification or discharge is sought.

         6. The provisions of this Note are severable, and if any one or more of
the provisions contained in this Note shall for any reason be held invalid,
illegal or unenforceable in whole or in part in any jurisdiction, then such
invalidity, illegality or unenforceability shall not in any manner affect such
provision or provisions in any other jurisdiction or any other provisions of
this Note in any jurisdiction.

         7. This Note is and shall be deemed to have been made and delivered in
the State of North Carolina and shall be construed and enforced in accordance
with the laws of the State of North Carolina.

         8. Payor represents that it has full power, authority and legal right
to execute and deliver this Note and that the debt hereunder constitutes a valid
and binding obligation of Payor.

         9. Payor may, upon not less than ten (10) days' prior written notice,
at any time and from time to time prepay this Note in whole or in part. If
notice of prepayment is given, the principal amount of the Note specified in
such notice shall become due and payable on the prepayment date set forth in
such notice. All prepayments shall include payment of accrued interest on the
principal amount so prepaid and shall be applied to payment of interest before
application to principal.

         10. Any capitalized terms used herein that are not otherwise defined,
shall have the same meanings ascribed to them in the Amended and Restated
Agreement of Limited Partnership of LSP-Whitewater Limited Partnership, as
amended (the "Partnership Agreement").

         11. If any one or more of the following events ("Events of Default")
shall occur and be continuing the entire unpaid balance of the principal of and
accrued but unpaid interest outstanding on this Note and all other obligations
and indebtedness of Payor to Payee arising hereunder shall immediately become
due and payable upon written notice to that effect given to Payor by Payee
(except that in the case of the occurrence of any Event of Default described in



                                     - 2 -
<PAGE>   9

subparagraph (b) of this paragraph 10, no such notice shall be required and such
termination and acceleration shall be automatic), without presentment or demand
for payment, notice of nonpayment, protest or further notice or demand of any
kind, all of which are expressly waived by Payor:

                  (a) Failure to make any payment of principal when due or
failure to pay any interest upon any Note within five days after the date due;
or

                  (b) Any action by Payor to file a petition in bankruptcy, make
an assignment for the benefit of creditors, be adjudicated insolvent, petition
or apply to any tribunal for the appointment of a receiver, custodian, or any
trustee for it or a substantial part of it, or any action to commence any
proceeding or case under any bankruptcy, reorganization, arrangement,
readjustment of debt, dissolution or liquidation law or statute of any
jurisdiction, whether now or hereafter in effect, or to take any action to
authorize any of the foregoing actions; or to permit any such petition or
application to be filed, or any such proceeding or case to be commenced against
Payor, which remains undismissed for a period of thirty (30) days or more; or
permit any order or relief to be entered in any proceeding; or any act or
omission that indicates Payor's consent to, approval of or acquiescence in any
such petition, application or proceeding or the appointment of a custodian,
receiver or any trustee for it or any substantial part of any of its assets, or
to suffer or permit any custodianship, receivership or trusteeship to continue
undischarged for a period of thirty (30) days or more.

         12. Whenever used, the singular number shall include the plural, the
plural the singular, and the words "Payee" and "Payor" shall include their
respective heirs, legal representatives, successors and assigns.



                                     - 3 -
<PAGE>   10

IN WITNESS WHEREOF, Payor has duly executed this Note the day and year first
above written.




                                               COGENTRIX ENERGY, INC.



                                               By:_________________________
                                               Name:
                                               Title:



                                     - 4 -
<PAGE>   11

                                                               Schedule I to the
                                                               Promissory Note


                              PAYMENTS OF PRINCIPAL




                     Amount of
                     Principal              Unpaid
                     Paid or                Principal                Notation
Date                 Prepaid                Balance                  Made By





                                     - 5 -